Week 1 Predicting Loan Values My Money Mantra
Sahil Garg
5/14/2018
Understanding the dataset
We have been provided with 2 sets of data - training data with 17 columns from V1 to V17 which are independent and a dependent variable DV of 2053 records, as well as test data with 16 columns and the dependent variable DV, it contains columns V1,V3..V17 and so, V2 is missing in the test data set. First step is to read the data into R. The dataset is related to loan approved and we must predict the loan value for the next customer.
##setwd("/Volumes/Untitled/My Money Mantra/week 1")
library(readxl)train <- read_excel('Training DataSet.xlsx')
test <- read_excel('Test DataSet.xlsx')Summarise the data
Summarize the dataset Create summary statistics (e.g. mean, standard deviation, median, mode) for the important variables in the dataset using summary() and describe().
summary(train)## Unique Id DV V1 V2
## Min. : 1 Min. :147000 Min. :720 Min. :0.0000
## 1st Qu.: 514 1st Qu.:359000 1st Qu.:826 1st Qu.:0.0000
## Median :1027 Median :429000 Median :846 Median :0.0000
## Mean :1027 Mean :469718 Mean :841 Mean :0.3229
## 3rd Qu.:1540 3rd Qu.:631000 3rd Qu.:865 3rd Qu.:1.0000
## Max. :2053 Max. :750000 Max. :900 Max. :1.0000
## V3 V4 V5 V6
## Min. :25.00 Min. :0.0000 Min. : 0 Min. :0.0000
## 1st Qu.:34.00 1st Qu.:0.0000 1st Qu.: 0 1st Qu.:0.0000
## Median :38.00 Median :0.0000 Median : 0 Median :0.0000
## Mean :39.57 Mean :0.4632 Mean : 1451935 Mean :0.2284
## 3rd Qu.:45.00 3rd Qu.:1.0000 3rd Qu.: 2095000 3rd Qu.:0.0000
## Max. :55.00 Max. :7.0000 Max. :65903173 Max. :5.0000
## V7 V8 V9 V10
## Min. : 0 Min. :0.0000 Min. : 0 Min. :0.0000
## 1st Qu.: 0 1st Qu.:0.0000 1st Qu.: 0 1st Qu.:0.0000
## Median : 0 Median :0.0000 Median : 0 Median :0.0000
## Mean : 589706 Mean :0.1851 Mean : 73091 Mean :0.2333
## 3rd Qu.: 0 3rd Qu.:0.0000 3rd Qu.: 0 3rd Qu.:0.0000
## Max. :65903173 Max. :4.0000 Max. :3280000 Max. :3.0000
## V11 V12 V13
## Min. : 0 Min. :0.000000 Min. : 0
## 1st Qu.: 0 1st Qu.:0.000000 1st Qu.: 0
## Median : 0 Median :0.000000 Median : 0
## Mean : 156946 Mean :0.004871 Mean : 109939
## 3rd Qu.: 0 3rd Qu.:0.000000 3rd Qu.: 0
## Max. :9837000 Max. :4.000000 Max. :212300000
## V14 V15 V16 V17
## Min. :0.000000 Min. : 0 Min. :0.000 Min. : 0
## 1st Qu.:0.000000 1st Qu.: 0 1st Qu.:1.000 1st Qu.: 0
## Median :0.000000 Median : 0 Median :1.000 Median : 0
## Mean :0.001948 Mean : 1578 Mean :1.462 Mean : 71375
## 3rd Qu.:0.000000 3rd Qu.: 0 3rd Qu.:2.000 3rd Qu.: 100000
## Max. :2.000000 Max. :2000000 Max. :8.000 Max. :1000000library(psych)
describe(train)## vars n mean sd median trimmed mad
## Unique Id 1 2053 1027.00 592.79 1027 1027.00 760.57
## DV 2 2053 469717.97 182934.74 429000 471056.00 167533.80
## V1 3 2053 840.95 31.98 846 844.83 28.17
## V2 4 2053 0.32 0.47 0 0.28 0.00
## V3 5 2053 39.57 7.24 38 39.12 7.41
## V4 6 2053 0.46 0.70 0 0.34 0.00
## V5 7 2053 1451935.30 3496999.73 0 767185.53 0.00
## V6 8 2053 0.23 0.57 0 0.09 0.00
## V7 9 2053 589705.59 2548663.35 0 112362.36 0.00
## V8 10 2053 0.19 0.46 0 0.07 0.00
## V9 11 2053 73091.07 257067.17 0 6960.86 0.00
## V10 12 2053 0.23 0.52 0 0.12 0.00
## V11 13 2053 156946.12 494897.47 0 45234.46 0.00
## V12 14 2053 0.00 0.11 0 0.00 0.00
## V13 15 2053 109939.11 4688422.41 0 0.00 0.00
## V14 16 2053 0.00 0.05 0 0.00 0.00
## V15 17 2053 1578.18 49620.82 0 0.00 0.00
## V16 18 2053 1.46 0.73 1 1.45 1.48
## V17 19 2053 71374.77 122206.63 0 44145.67 0.00
## min max range skew kurtosis se
## Unique Id 1 2053 2052 0.00 -1.20 13.08
## DV 147000 750000 603000 0.24 -0.92 4037.40
## V1 720 900 180 -1.19 1.52 0.71
## V2 0 1 1 0.76 -1.43 0.01
## V3 25 55 30 0.47 -0.78 0.16
## V4 0 7 7 1.99 7.53 0.02
## V5 0 65903173 65903173 7.76 98.52 77179.35
## V6 0 5 5 3.26 14.02 0.01
## V7 0 65903173 65903173 13.62 275.56 56249.41
## V8 0 4 4 2.76 8.95 0.01
## V9 0 3280000 3280000 5.80 45.18 5673.51
## V10 0 3 3 2.42 6.23 0.01
## V11 0 9837000 9837000 7.97 107.09 10922.47
## V12 0 4 4 29.22 978.49 0.00
## V13 0 212300000 212300000 45.16 2040.64 103474.24
## V14 0 2 2 30.76 1020.73 0.00
## V15 0 2000000 2000000 35.84 1358.56 1095.14
## V16 0 8 8 1.11 5.87 0.02
## V17 0 1000000 1000000 3.03 12.82 2697.12summary(test)## Unique Id DV (Predict) V1 V3
## Min. : 1.0 Mode:logical Min. :721.0 Min. :25.00
## 1st Qu.: 513.8 NA's:2052 1st Qu.:826.8 1st Qu.:34.00
## Median :1026.5 Median :846.0 Median :38.00
## Mean :1026.5 Mean :841.0 Mean :39.54
## 3rd Qu.:1539.2 3rd Qu.:865.0 3rd Qu.:45.00
## Max. :2052.0 Max. :900.0 Max. :55.00
## V4 V5 V6 V7
## Min. :0.0000 Min. : 0 Min. :0.0000 Min. : 0
## 1st Qu.:0.0000 1st Qu.: 0 1st Qu.:0.0000 1st Qu.: 0
## Median :0.0000 Median : 0 Median :0.0000 Median : 0
## Mean :0.4751 Mean : 1370357 Mean :0.2256 Mean : 439524
## 3rd Qu.:1.0000 3rd Qu.: 2109800 3rd Qu.:0.0000 3rd Qu.: 0
## Max. :4.0000 Max. :41000000 Max. :5.0000 Max. :24000000
## V8 V9 V10 V11
## Min. :0.0000 Min. : 0 Min. :0.0000 Min. : 0
## 1st Qu.:0.0000 1st Qu.: 0 1st Qu.:0.0000 1st Qu.: 0
## Median :0.0000 Median : 0 Median :0.0000 Median : 0
## Mean :0.1769 Mean : 66448 Mean :0.2524 Mean : 179033
## 3rd Qu.:0.0000 3rd Qu.: 0 3rd Qu.:0.0000 3rd Qu.: 0
## Max. :4.0000 Max. :3530000 Max. :3.0000 Max. :37000000
## V12 V13 V14 V15
## Min. :0.000000 Min. : 0 Min. :0.000000 Min. : 0
## 1st Qu.:0.000000 1st Qu.: 0 1st Qu.:0.000000 1st Qu.: 0
## Median :0.000000 Median : 0 Median :0.000000 Median : 0
## Mean :0.004386 Mean : 2747 Mean :0.003899 Mean : 2203
## 3rd Qu.:0.000000 3rd Qu.: 0 3rd Qu.:0.000000 3rd Qu.: 0
## Max. :2.000000 Max. :2320000 Max. :3.000000 Max. :1400000
## V16 V17
## Min. : 0.000 Min. : 0
## 1st Qu.: 1.000 1st Qu.: 0
## Median : 1.000 Median : 0
## Mean : 1.418 Mean : 67231
## 3rd Qu.: 2.000 3rd Qu.: 100000
## Max. :15.000 Max. :1133261describe(test)## vars n mean sd median trimmed mad min
## Unique Id 1 2052 1026.50 592.51 1026.5 1026.50 760.57 1
## DV (Predict)* 2 0 NaN NA NA NaN NA Inf
## V1 3 2052 840.97 31.92 846.0 844.83 28.17 721
## V3 4 2052 39.54 7.15 38.0 39.13 7.41 25
## V4 5 2052 0.48 0.68 0.0 0.35 0.00 0
## V5 6 2052 1370356.69 2715181.86 0.0 793330.17 0.00 0
## V6 7 2052 0.23 0.56 0.0 0.09 0.00 0
## V7 8 2052 439523.53 1445951.46 0.0 87952.07 0.00 0
## V8 9 2052 0.18 0.45 0.0 0.06 0.00 0
## V9 10 2052 66448.48 248880.86 0.0 4608.65 0.00 0
## V10 11 2052 0.25 0.53 0.0 0.14 0.00 0
## V11 12 2052 179032.66 930623.12 0.0 54210.06 0.00 0
## V12 13 2052 0.00 0.07 0.0 0.00 0.00 0
## V13 14 2052 2746.78 63933.34 0.0 0.00 0.00 0
## V14 15 2052 0.00 0.10 0.0 0.00 0.00 0
## V15 16 2052 2202.73 50373.76 0.0 0.00 0.00 0
## V16 17 2052 1.42 0.79 1.0 1.41 0.00 0
## V17 18 2052 67231.36 118514.41 0.0 40824.56 0.00 0
## max range skew kurtosis se
## Unique Id 2052 2051 0.00 -1.20 13.08
## DV (Predict)* -Inf -Inf NA NA NA
## V1 900 179 -1.18 1.51 0.70
## V3 55 30 0.42 -0.83 0.16
## V4 4 4 1.45 2.21 0.02
## V5 41000000 41000000 4.70 39.20 59939.10
## V6 5 5 3.19 13.70 0.01
## V7 24000000 24000000 7.01 78.28 31920.16
## V8 4 4 2.91 10.06 0.01
## V9 3530000 3530000 6.50 59.67 5494.18
## V10 3 3 2.21 4.97 0.01
## V11 37000000 37000000 30.83 1194.32 20544.01
## V12 2 2 18.53 385.01 0.00
## V13 2320000 2320000 30.15 990.17 1411.36
## V14 3 3 28.29 835.65 0.00
## V15 1400000 1400000 23.31 554.12 1112.03
## V16 15 15 3.63 51.30 0.02
## V17 1133261 1133261 3.14 14.30 2616.27Looking at the dependent variable
We can now study the dependent variable in the training dataset and try to understand some of its properties, so that we can figure out what the data is trying to hint at.
summary(train$DV)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 147000 359000 429000 469718 631000 750000Generating some plots
The next step into data analysis is to generate some plots and find out relations between the fields. Since we are concerned with the dependent variable and we do know that the rest of the variables are independent, we can compare DV with V1-V17.
hist(train$DV, breaks=10,col="yellow",xlab="DV", main="DV")
plot(train$DV,main="DV")
boxplot(train$DV, horizontal =TRUE, main="Boxplot of DV" ,col="lightblue")
We can now generate some scatterplots to understand how the variables are co-related pair wise.
library(car)##
## Attaching package: 'car'## The following object is masked from 'package:psych':
##
## logitscatterplot(train$DV ~ train$V1,
spread=FALSE, smoother.args=list(lty=2),
main="Scatter plot of DV vs V1",
xlab="DV",
ylab="V1")
scatterplot(train$DV ~ train$V3,
spread=FALSE, smoother.args=list(lty=2),
main="Scatter plot of DV vs V3",
xlab="DV",
ylab="V3")
scatterplot(train$DV ~ train$V4,
spread=FALSE, smoother.args=list(lty=2),
main="Scatter plot of DV vs V4",
xlab="DV",
ylab="V4")
scatterplot(train$DV ~ train$V8,
spread=FALSE, smoother.args=list(lty=2),
main="Scatter plot of DV vs V8",
xlab="DV",
ylab="V8")
scatterplot(train$DV ~ train$V12,
spread=FALSE, smoother.args=list(lty=2),
main="Scatter plot of DV vs V12",
xlab="DV",
ylab="V12")
Each graph varies and there does not seem to be a common correlation between the DV and the other independent variables.
We now generate a scatterplot matrix to see the relations with all the fields.
scatterplotMatrix(train, spread=FALSE, smoother.args=list(lty=2), main="Scatter Plot Matrix")
CORRGRAM
The next step is to draw a corrgram and create a variance-covariance matrix for the fields.
library(corrgram)
corr.test(train)## Call:corr.test(x = train)
## Correlation matrix
## Unique Id DV V1 V2 V3 V4 V5 V6 V7 V8
## Unique Id 1.00 0.06 0.93 -0.02 0.03 0.06 0.01 0.01 0.00 -0.17
## DV 0.06 1.00 0.04 0.86 0.07 0.40 0.40 0.32 0.25 -0.01
## V1 0.93 0.04 1.00 -0.03 0.01 0.05 -0.01 0.01 0.00 -0.16
## V2 -0.02 0.86 -0.03 1.00 0.10 0.44 0.40 0.35 0.24 0.08
## V3 0.03 0.07 0.01 0.10 1.00 0.01 0.05 0.09 0.08 -0.10
## V4 0.06 0.40 0.05 0.44 0.01 1.00 0.58 0.24 0.12 -0.02
## V5 0.01 0.40 -0.01 0.40 0.05 0.58 1.00 0.31 0.59 -0.04
## V6 0.01 0.32 0.01 0.35 0.09 0.24 0.31 1.00 0.54 -0.03
## V7 0.00 0.25 0.00 0.24 0.08 0.12 0.59 0.54 1.00 -0.03
## V8 -0.17 -0.01 -0.16 0.08 -0.10 -0.02 -0.04 -0.03 -0.03 1.00
## V9 -0.13 0.10 -0.13 0.14 -0.05 -0.05 0.00 -0.02 0.00 0.70
## V10 -0.28 0.11 -0.25 0.19 0.14 -0.02 0.03 0.00 0.03 -0.02
## V11 -0.19 0.17 -0.17 0.21 0.10 -0.03 0.07 0.02 0.12 -0.05
## V12 -0.06 -0.02 -0.08 -0.03 0.05 0.05 0.12 0.05 0.06 -0.01
## V13 0.02 -0.01 0.02 -0.02 0.04 -0.01 0.00 -0.01 0.00 -0.01
## V14 -0.05 -0.02 -0.07 -0.02 0.04 0.01 0.04 0.02 0.00 0.01
## V15 -0.05 -0.01 -0.07 -0.02 0.04 0.01 0.04 0.02 0.00 -0.01
## V16 -0.17 -0.02 -0.18 -0.02 -0.06 -0.05 0.06 0.04 0.05 0.17
## V17 -0.08 0.06 -0.09 0.08 0.08 -0.01 0.09 0.08 0.09 0.02
## V9 V10 V11 V12 V13 V14 V15 V16 V17
## Unique Id -0.13 -0.28 -0.19 -0.06 0.02 -0.05 -0.05 -0.17 -0.08
## DV 0.10 0.11 0.17 -0.02 -0.01 -0.02 -0.01 -0.02 0.06
## V1 -0.13 -0.25 -0.17 -0.08 0.02 -0.07 -0.07 -0.18 -0.09
## V2 0.14 0.19 0.21 -0.03 -0.02 -0.02 -0.02 -0.02 0.08
## V3 -0.05 0.14 0.10 0.05 0.04 0.04 0.04 -0.06 0.08
## V4 -0.05 -0.02 -0.03 0.05 -0.01 0.01 0.01 -0.05 -0.01
## V5 0.00 0.03 0.07 0.12 0.00 0.04 0.04 0.06 0.09
## V6 -0.02 0.00 0.02 0.05 -0.01 0.02 0.02 0.04 0.08
## V7 0.00 0.03 0.12 0.06 0.00 0.00 0.00 0.05 0.09
## V8 0.70 -0.02 -0.05 -0.01 -0.01 0.01 -0.01 0.17 0.02
## V9 1.00 -0.02 -0.04 0.01 0.00 0.02 0.00 0.13 0.02
## V10 -0.02 1.00 0.74 0.00 -0.01 0.02 0.01 -0.03 -0.02
## V11 -0.04 0.74 1.00 0.01 -0.01 0.03 0.03 -0.01 0.01
## V12 0.01 0.00 0.01 1.00 0.23 0.75 0.82 0.01 0.00
## V13 0.00 -0.01 -0.01 0.23 1.00 0.02 0.02 -0.01 -0.01
## V14 0.02 0.02 0.03 0.75 0.02 1.00 0.95 0.05 0.01
## V15 0.00 0.01 0.03 0.82 0.02 0.95 1.00 0.01 0.01
## V16 0.13 -0.03 -0.01 0.01 -0.01 0.05 0.01 1.00 0.32
## V17 0.02 -0.02 0.01 0.00 -0.01 0.01 0.01 0.32 1.00
## Sample Size
## [1] 2053
## Probability values (Entries above the diagonal are adjusted for multiple tests.)
## Unique Id DV V1 V2 V3 V4 V5 V6 V7 V8 V9 V10
## Unique Id 0.00 0.73 0.00 1.00 1.00 0.45 1.00 1.00 1.00 0.00 0.00 0.00
## DV 0.01 0.00 1.00 0.00 0.18 0.00 0.00 0.00 0.00 1.00 0.00 0.00
## V1 0.00 0.11 0.00 1.00 1.00 1.00 1.00 1.00 1.00 0.00 0.00 0.00
## V2 0.35 0.00 0.21 0.00 0.00 0.00 0.00 0.00 0.00 0.03 0.00 0.00
## V3 0.26 0.00 0.73 0.00 0.00 1.00 1.00 0.01 0.07 0.00 1.00 0.00
## V4 0.00 0.00 0.03 0.00 0.53 0.00 0.00 0.00 0.00 1.00 1.00 1.00
## V5 0.55 0.00 0.60 0.00 0.03 0.00 0.00 0.00 0.00 1.00 1.00 1.00
## V6 0.65 0.00 0.69 0.00 0.00 0.00 0.00 0.00 0.00 1.00 1.00 1.00
## V7 0.95 0.00 0.86 0.00 0.00 0.00 0.00 0.00 0.00 1.00 1.00 1.00
## V8 0.00 0.72 0.00 0.00 0.00 0.27 0.11 0.15 0.15 0.00 0.00 1.00
## V9 0.00 0.00 0.00 0.00 0.02 0.04 0.85 0.38 0.94 0.00 0.00 1.00
## V10 0.00 0.00 0.00 0.00 0.00 0.43 0.14 0.91 0.11 0.32 0.33 0.00
## V11 0.00 0.00 0.00 0.00 0.00 0.23 0.00 0.31 0.00 0.02 0.11 0.00
## V12 0.01 0.35 0.00 0.16 0.01 0.03 0.00 0.04 0.01 0.70 0.55 0.90
## V13 0.29 0.81 0.45 0.46 0.05 0.57 0.99 0.78 0.96 0.71 0.87 0.64
## V14 0.01 0.33 0.00 0.26 0.05 0.50 0.04 0.43 0.89 0.82 0.26 0.40
## V15 0.03 0.63 0.00 0.32 0.09 0.64 0.04 0.32 0.94 0.73 1.00 0.68
## V16 0.00 0.27 0.00 0.32 0.01 0.02 0.01 0.06 0.04 0.00 0.00 0.15
## V17 0.00 0.01 0.00 0.00 0.00 0.81 0.00 0.00 0.00 0.29 0.47 0.30
## V11 V12 V13 V14 V15 V16 V17
## Unique Id 0.00 1.00 1.00 1.00 1.00 0 0.02
## DV 0.00 1.00 1.00 1.00 1.00 1 0.62
## V1 0.00 0.02 1.00 0.08 0.22 0 0.01
## V2 0.00 1.00 1.00 1.00 1.00 1 0.05
## V3 0.00 1.00 1.00 1.00 1.00 1 0.02
## V4 1.00 1.00 1.00 1.00 1.00 1 1.00
## V5 0.10 0.00 1.00 1.00 1.00 1 0.00
## V6 1.00 1.00 1.00 1.00 1.00 1 0.05
## V7 0.00 1.00 1.00 1.00 1.00 1 0.01
## V8 1.00 1.00 1.00 1.00 1.00 0 1.00
## V9 1.00 1.00 1.00 1.00 1.00 0 1.00
## V10 0.00 1.00 1.00 1.00 1.00 1 1.00
## V11 0.00 1.00 1.00 1.00 1.00 1 1.00
## V12 0.61 0.00 0.00 0.00 0.00 1 1.00
## V13 0.75 0.00 0.00 1.00 1.00 1 1.00
## V14 0.13 0.00 0.33 0.00 0.00 1 1.00
## V15 0.20 0.00 0.29 0.00 0.00 1 1.00
## V16 0.64 0.70 0.61 0.02 0.67 0 0.00
## V17 0.63 0.83 0.57 0.63 0.66 0 0.00
##
## To see confidence intervals of the correlations, print with the short=FALSE optionWe can also understand the correlations in the test dataset as -
library(corrgram)
corr.test(test)## Call:corr.test(x = test)
## Correlation matrix
## Unique Id DV (Predict) V1 V3 V4 V5 V6 V7
## Unique Id 1.00 NA 0.93 0.05 0.05 0.06 -0.03 0.00
## DV (Predict) NA NA NA NA NA NA NA NA
## V1 0.93 NA 1.00 0.04 0.04 0.03 -0.02 0.00
## V3 0.05 NA 0.04 1.00 0.00 0.06 0.10 0.11
## V4 0.05 NA 0.04 0.00 1.00 0.67 0.15 0.12
## V5 0.06 NA 0.03 0.06 0.67 1.00 0.18 0.33
## V6 -0.03 NA -0.02 0.10 0.15 0.18 1.00 0.67
## V7 0.00 NA 0.00 0.11 0.12 0.33 0.67 1.00
## V8 -0.20 NA -0.19 -0.10 -0.02 -0.07 -0.02 -0.04
## V9 -0.16 NA -0.15 -0.05 -0.06 -0.06 -0.02 -0.03
## V10 -0.27 NA -0.24 0.17 -0.01 0.02 0.02 0.03
## V11 -0.13 NA -0.13 0.12 -0.01 0.03 0.01 0.04
## V12 -0.08 NA -0.10 0.06 0.05 0.03 0.02 0.02
## V13 -0.06 NA -0.09 0.05 0.05 0.04 0.05 0.03
## V14 -0.06 NA -0.08 0.05 0.02 0.06 0.06 0.06
## V15 -0.05 NA -0.07 0.06 0.02 0.07 0.04 0.03
## V16 -0.17 NA -0.17 -0.06 -0.06 -0.03 0.04 0.04
## V17 -0.09 NA -0.09 0.07 0.03 0.04 0.12 0.12
## V8 V9 V10 V11 V12 V13 V14 V15 V16 V17
## Unique Id -0.20 -0.16 -0.27 -0.13 -0.08 -0.06 -0.06 -0.05 -0.17 -0.09
## DV (Predict) NA NA NA NA NA NA NA NA NA NA
## V1 -0.19 -0.15 -0.24 -0.13 -0.10 -0.09 -0.08 -0.07 -0.17 -0.09
## V3 -0.10 -0.05 0.17 0.12 0.06 0.05 0.05 0.06 -0.06 0.07
## V4 -0.02 -0.06 -0.01 -0.01 0.05 0.05 0.02 0.02 -0.06 0.03
## V5 -0.07 -0.06 0.02 0.03 0.03 0.04 0.06 0.07 -0.03 0.04
## V6 -0.02 -0.02 0.02 0.01 0.02 0.05 0.06 0.04 0.04 0.12
## V7 -0.04 -0.03 0.03 0.04 0.02 0.03 0.06 0.03 0.04 0.12
## V8 1.00 0.73 -0.02 -0.03 0.02 0.02 0.03 0.04 0.13 0.00
## V9 0.73 1.00 -0.01 -0.02 0.04 0.06 0.06 0.05 0.13 0.03
## V10 -0.02 -0.01 1.00 0.43 0.01 0.01 0.02 0.02 -0.02 0.02
## V11 -0.03 -0.02 0.43 1.00 0.03 0.05 0.05 0.05 0.01 0.03
## V12 0.02 0.04 0.01 0.03 1.00 0.83 0.40 0.29 0.21 0.07
## V13 0.02 0.06 0.01 0.05 0.83 1.00 0.54 0.39 0.29 0.10
## V14 0.03 0.06 0.02 0.05 0.40 0.54 1.00 0.86 0.25 0.08
## V15 0.04 0.05 0.02 0.05 0.29 0.39 0.86 1.00 0.20 0.05
## V16 0.13 0.13 -0.02 0.01 0.21 0.29 0.25 0.20 1.00 0.29
## V17 0.00 0.03 0.02 0.03 0.07 0.10 0.08 0.05 0.29 1.00
## Sample Size
## Unique Id DV (Predict) V1 V3 V4 V5 V6 V7 V8
## Unique Id 2052 0 2052 2052 2052 2052 2052 2052 2052
## DV (Predict) 0 0 0 0 0 0 0 0 0
## V1 2052 0 2052 2052 2052 2052 2052 2052 2052
## V3 2052 0 2052 2052 2052 2052 2052 2052 2052
## V4 2052 0 2052 2052 2052 2052 2052 2052 2052
## V5 2052 0 2052 2052 2052 2052 2052 2052 2052
## V6 2052 0 2052 2052 2052 2052 2052 2052 2052
## V7 2052 0 2052 2052 2052 2052 2052 2052 2052
## V8 2052 0 2052 2052 2052 2052 2052 2052 2052
## V9 2052 0 2052 2052 2052 2052 2052 2052 2052
## V10 2052 0 2052 2052 2052 2052 2052 2052 2052
## V11 2052 0 2052 2052 2052 2052 2052 2052 2052
## V12 2052 0 2052 2052 2052 2052 2052 2052 2052
## V13 2052 0 2052 2052 2052 2052 2052 2052 2052
## V14 2052 0 2052 2052 2052 2052 2052 2052 2052
## V15 2052 0 2052 2052 2052 2052 2052 2052 2052
## V16 2052 0 2052 2052 2052 2052 2052 2052 2052
## V17 2052 0 2052 2052 2052 2052 2052 2052 2052
## V9 V10 V11 V12 V13 V14 V15 V16 V17
## Unique Id 2052 2052 2052 2052 2052 2052 2052 2052 2052
## DV (Predict) 0 0 0 0 0 0 0 0 0
## V1 2052 2052 2052 2052 2052 2052 2052 2052 2052
## V3 2052 2052 2052 2052 2052 2052 2052 2052 2052
## V4 2052 2052 2052 2052 2052 2052 2052 2052 2052
## V5 2052 2052 2052 2052 2052 2052 2052 2052 2052
## V6 2052 2052 2052 2052 2052 2052 2052 2052 2052
## V7 2052 2052 2052 2052 2052 2052 2052 2052 2052
## V8 2052 2052 2052 2052 2052 2052 2052 2052 2052
## V9 2052 2052 2052 2052 2052 2052 2052 2052 2052
## V10 2052 2052 2052 2052 2052 2052 2052 2052 2052
## V11 2052 2052 2052 2052 2052 2052 2052 2052 2052
## V12 2052 2052 2052 2052 2052 2052 2052 2052 2052
## V13 2052 2052 2052 2052 2052 2052 2052 2052 2052
## V14 2052 2052 2052 2052 2052 2052 2052 2052 2052
## V15 2052 2052 2052 2052 2052 2052 2052 2052 2052
## V16 2052 2052 2052 2052 2052 2052 2052 2052 2052
## V17 2052 2052 2052 2052 2052 2052 2052 2052 2052
## Probability values (Entries above the diagonal are adjusted for multiple tests.)
## Unique Id DV (Predict) V1 V3 V4 V5 V6 V7 V8
## Unique Id 0.00 NA 0.00 1.00 1.00 0.71 1.00 1.00 0.00
## DV (Predict) NA NA NA NA NA NA NA NA NA
## V1 0.00 NA 0.00 1.00 1.00 1.00 1.00 1.00 0.00
## V3 0.03 NA 0.08 0.00 1.00 0.46 0.00 0.00 0.00
## V4 0.02 NA 0.11 0.85 0.00 0.00 0.00 0.00 1.00
## V5 0.01 NA 0.19 0.01 0.00 0.00 0.00 0.00 0.19
## V6 0.13 NA 0.30 0.00 0.00 0.00 0.00 0.00 1.00
## V7 0.87 NA 0.84 0.00 0.00 0.00 0.00 0.00 1.00
## V8 0.00 NA 0.00 0.00 0.41 0.00 0.49 0.07 0.00
## V9 0.00 NA 0.00 0.02 0.00 0.01 0.40 0.17 0.00
## V10 0.00 NA 0.00 0.00 0.62 0.40 0.26 0.20 0.48
## V11 0.00 NA 0.00 0.00 0.71 0.12 0.64 0.04 0.20
## V12 0.00 NA 0.00 0.01 0.04 0.12 0.29 0.42 0.35
## V13 0.00 NA 0.00 0.02 0.03 0.04 0.04 0.12 0.28
## V14 0.01 NA 0.00 0.03 0.30 0.01 0.00 0.01 0.20
## V15 0.03 NA 0.00 0.01 0.48 0.00 0.08 0.12 0.10
## V16 0.00 NA 0.00 0.01 0.00 0.20 0.04 0.04 0.00
## V17 0.00 NA 0.00 0.00 0.25 0.09 0.00 0.00 0.99
## V9 V10 V11 V12 V13 V14 V15 V16 V17
## Unique Id 0.00 0.00 0.00 0.02 0.33 0.88 1.00 0.00 0.00
## DV (Predict) NA NA NA NA NA NA NA NA NA
## V1 0.00 0.00 0.00 0.00 0.00 0.02 0.12 0.00 0.00
## V3 1.00 0.00 0.00 0.88 1.00 1.00 0.46 0.82 0.16
## V4 0.36 1.00 1.00 1.00 1.00 1.00 1.00 0.38 1.00
## V5 0.60 1.00 1.00 1.00 1.00 0.63 0.07 1.00 1.00
## V6 1.00 1.00 1.00 1.00 1.00 0.32 1.00 1.00 0.00
## V7 1.00 1.00 1.00 1.00 1.00 0.78 1.00 1.00 0.00
## V8 0.00 1.00 1.00 1.00 1.00 1.00 1.00 0.00 1.00
## V9 0.00 1.00 1.00 1.00 0.49 0.82 1.00 0.00 1.00
## V10 0.58 0.00 0.00 1.00 1.00 1.00 1.00 1.00 1.00
## V11 0.46 0.00 0.00 1.00 1.00 1.00 1.00 1.00 1.00
## V12 0.05 0.68 0.14 0.00 0.00 0.00 0.00 0.00 0.12
## V13 0.01 0.52 0.04 0.00 0.00 0.00 0.00 0.00 0.00
## V14 0.01 0.40 0.02 0.00 0.00 0.00 0.00 0.00 0.02
## V15 0.02 0.42 0.02 0.00 0.00 0.00 0.00 0.00 1.00
## V16 0.00 0.42 0.60 0.00 0.00 0.00 0.00 0.00 0.00
## V17 0.18 0.30 0.25 0.00 0.00 0.00 0.01 0.00 0.00
##
## To see confidence intervals of the correlations, print with the short=FALSE optionThese tables enable us to understand relations between the independent variables. We learn that the DV is most related to V2,V4 and V5 since their correlation values are closer to 1.
We get covariance and correlation matrices as -
cov(train)## Unique Id DV V1 V2
## Unique Id 3.514052e+05 6.472275e+06 1.763963e+04 -5.681287e+00
## DV 6.472275e+06 3.346512e+10 2.088964e+05 7.371832e+04
## V1 1.763963e+04 2.088964e+05 1.022854e+03 -4.124521e-01
## V2 -5.681287e+00 7.371832e+04 -4.124521e-01 2.187570e-01
## V3 1.076584e+02 9.201232e+04 1.794134e+00 3.216840e-01
## V4 2.605702e+01 5.045819e+04 1.077191e+00 1.441921e-01
## V5 2.757361e+07 2.585957e+11 -1.292177e+06 6.618975e+05
## V6 3.337232e+00 3.319311e+04 1.585710e-01 9.236851e-02
## V7 2.222797e+06 1.151925e+11 -3.205386e+05 2.894204e+05
## V8 -4.515400e+01 -6.714571e+02 -2.268938e+00 1.719397e-02
## V9 -2.026710e+07 4.857575e+09 -1.034748e+06 1.714262e+04
## V10 -8.510526e+01 1.066135e+04 -4.205231e+00 4.693507e-02
## V11 -5.458995e+07 1.563356e+10 -2.625821e+06 4.923242e+04
## V12 -3.662768e+00 -4.065203e+02 -2.916777e-01 -1.573792e-03
## V13 6.534539e+07 -4.647083e+09 2.516990e+06 -3.552126e+04
## V14 -1.753899e+00 -2.143625e+02 -1.290492e-01 -6.295166e-04
## V15 -1.423158e+06 -9.668920e+07 -1.083262e+05 -5.099085e+02
## V16 -7.560478e+01 -3.260895e+03 -4.317105e+00 -7.539957e-03
## V17 -6.049021e+06 1.363014e+09 -3.448846e+05 4.428722e+03
## V3 V4 V5 V6
## Unique Id 1.076584e+02 2.605702e+01 2.757361e+07 3.337232e+00
## DV 9.201232e+04 5.045819e+04 2.585957e+11 3.319311e+04
## V1 1.794134e+00 1.077191e+00 -1.292177e+06 1.585710e-01
## V2 3.216840e-01 1.441921e-01 6.618975e+05 9.236851e-02
## V3 5.235675e+01 7.008120e-02 1.190633e+06 3.660276e-01
## V4 7.008120e-02 4.836615e-01 1.412743e+06 9.636827e-02
## V5 1.190633e+06 1.412743e+06 1.222901e+13 6.235679e+05
## V6 3.660276e-01 9.636827e-02 6.235679e+05 3.225432e-01
## V7 1.398882e+06 2.191456e+05 5.274069e+12 7.847619e+05
## V8 -3.398882e-01 -7.809614e-03 -5.642916e+04 -8.191787e-03
## V9 -9.356942e+04 -8.078660e+03 -3.701840e+09 -2.824685e+03
## V10 5.089761e-01 -6.279025e-03 5.926935e+04 -6.947946e-04
## V11 3.648463e+05 -9.073104e+03 1.271841e+11 6.275012e+03
## V12 4.207127e-02 3.590524e-03 4.446460e+04 2.785350e-03
## V13 1.447895e+06 -4.088552e+04 -5.240323e+09 -1.666737e+04
## V14 1.692597e-02 5.590165e-04 8.490380e+03 5.293447e-04
## V15 1.343226e+04 3.602108e+02 7.757763e+09 6.139544e+02
## V16 -3.002239e-01 -2.612091e-02 1.435316e+05 1.715623e-02
## V17 7.301795e+04 -4.573465e+02 3.889300e+10 5.425693e+03
## V7 V8 V9 V10
## Unique Id 2.222797e+06 -4.515400e+01 -2.026710e+07 -8.510526e+01
## DV 1.151925e+11 -6.714571e+02 4.857575e+09 1.066135e+04
## V1 -3.205386e+05 -2.268938e+00 -1.034748e+06 -4.205231e+00
## V2 2.894204e+05 1.719397e-02 1.714262e+04 4.693507e-02
## V3 1.398882e+06 -3.398882e-01 -9.356942e+04 5.089761e-01
## V4 2.191456e+05 -7.809614e-03 -8.078660e+03 -6.279025e-03
## V5 5.274069e+12 -5.642916e+04 -3.701840e+09 5.926935e+04
## V6 7.847619e+05 -8.191787e-03 -2.824685e+03 -6.947946e-04
## V7 6.495685e+12 -3.670033e+04 1.013347e+09 4.621684e+04
## V8 -3.670033e+04 2.093879e-01 8.276904e+04 -5.195174e-03
## V9 1.013347e+09 8.276904e+04 6.608353e+10 -2.881800e+03
## V10 4.621684e+04 -5.195174e-03 -2.881800e+03 2.686360e-01
## V11 1.468057e+11 -1.138294e+04 -4.483072e+09 1.890370e+05
## V12 1.574218e+04 -4.146929e-04 3.699266e+02 -1.623640e-04
## V13 1.294859e+10 -1.792245e+04 -4.408879e+09 -2.500528e+04
## V14 -4.185294e+02 1.265205e-04 3.448517e+02 5.198497e-04
## V15 -2.001199e+08 -1.752962e+02 1.552109e+06 2.358931e+02
## V16 8.642927e+04 5.621095e-02 2.473710e+04 -1.189957e-02
## V17 2.701557e+10 1.296750e+03 5.027954e+08 -1.451386e+03
## V11 V12 V13 V14
## Unique Id -5.458995e+07 -3.662768e+00 6.534539e+07 -1.753899e+00
## DV 1.563356e+10 -4.065203e+02 -4.647083e+09 -2.143625e+02
## V1 -2.625821e+06 -2.916777e-01 2.516990e+06 -1.290492e-01
## V2 4.923242e+04 -1.573792e-03 -3.552126e+04 -6.295166e-04
## V3 3.648463e+05 4.207127e-02 1.447895e+06 1.692597e-02
## V4 -9.073104e+03 3.590524e-03 -4.088552e+04 5.590165e-04
## V5 1.271841e+11 4.446460e+04 -5.240323e+09 8.490380e+03
## V6 6.275012e+03 2.785350e-03 -1.666737e+04 5.293447e-04
## V7 1.468057e+11 1.574218e+04 1.294859e+10 -4.185294e+02
## V8 -1.138294e+04 -4.146929e-04 -1.792245e+04 1.265205e-04
## V9 -4.483072e+09 3.699266e+02 -4.408879e+09 3.448517e+02
## V10 1.890370e+05 -1.623640e-04 -2.500528e+04 5.198497e-04
## V11 2.449235e+11 5.986787e+02 -1.642084e+10 8.902278e+02
## V12 5.986787e+02 1.167217e-02 1.183141e+05 4.376470e-03
## V13 -1.642084e+10 1.183141e+05 2.198130e+13 5.424095e+03
## V14 8.902278e+02 4.376470e-03 5.424095e+03 2.920179e-03
## V15 6.896405e+08 4.378274e+03 5.464813e+09 2.550530e+03
## V16 -3.771619e+03 6.712945e-04 -3.844163e+04 2.022904e-03
## V17 6.365358e+08 -6.274256e+01 -7.219161e+09 7.041954e+01
## V15 V16 V17
## Unique Id -1.423158e+06 -7.560478e+01 -6.049021e+06
## DV -9.668920e+07 -3.260895e+03 1.363014e+09
## V1 -1.083262e+05 -4.317105e+00 -3.448846e+05
## V2 -5.099085e+02 -7.539957e-03 4.428722e+03
## V3 1.343226e+04 -3.002239e-01 7.301795e+04
## V4 3.602108e+02 -2.612091e-02 -4.573465e+02
## V5 7.757763e+09 1.435316e+05 3.889300e+10
## V6 6.139544e+02 1.715623e-02 5.425693e+03
## V7 -2.001199e+08 8.642927e+04 2.701557e+10
## V8 -1.752962e+02 5.621095e-02 1.296750e+03
## V9 1.552109e+06 2.473710e+04 5.027954e+08
## V10 2.358931e+02 -1.189957e-02 -1.451386e+03
## V11 6.896405e+08 -3.771619e+03 6.365358e+08
## V12 4.378274e+03 6.712945e-04 -6.274256e+01
## V13 5.464813e+09 -3.844163e+04 -7.219161e+09
## V14 2.550530e+03 2.022904e-03 7.041954e+01
## V15 2.462225e+09 3.422558e+02 5.981761e+07
## V16 3.422558e+02 5.342712e-01 2.825275e+04
## V17 5.981761e+07 2.825275e+04 1.493446e+10cor(train)## Unique Id DV V1 V2 V3
## Unique Id 1.000000000 0.059683834 0.930418713 -0.02049093 0.025099060
## DV 0.059683834 1.000000000 0.035704897 0.86158513 0.069512588
## V1 0.930418713 0.035704897 1.000000000 -0.02757310 0.007752856
## V2 -0.020490927 0.861585127 -0.027573099 1.00000000 0.095052176
## V3 0.025099060 0.069512588 0.007752856 0.09505218 1.000000000
## V4 0.063204771 0.396610953 0.048430064 0.44329169 0.013926579
## V5 0.013301295 0.404230925 -0.011553659 0.40468222 0.047053939
## V6 0.009912617 0.319490409 0.008730174 0.34773544 0.089070430
## V7 0.001471239 0.247067521 -0.003932429 0.24279272 0.075854675
## V8 -0.166462480 -0.008021329 -0.155038638 0.08033770 -0.102653555
## V9 -0.132996695 0.103294376 -0.125858038 0.14257704 -0.050303827
## V10 -0.276993914 0.112443379 -0.253688548 0.19361292 0.135715335
## V11 -0.186077299 0.172681742 -0.165898714 0.21269384 0.101884557
## V12 -0.057191246 -0.020568864 -0.084415176 -0.03114515 0.053817501
## V13 0.023511708 -0.005418231 0.016786026 -0.01619872 0.042679966
## V14 -0.054751461 -0.021684427 -0.074669605 -0.02490700 0.043287515
## V15 -0.048382143 -0.010651674 -0.068259426 -0.02197087 0.037410965
## V16 -0.174487490 -0.024387079 -0.184673607 -0.02205500 -0.056764664
## V17 -0.083499958 0.060969039 -0.088241339 0.07748232 0.082575001
## V4 V5 V6 V7
## Unique Id 0.063204771 0.0133012953 0.009912617 0.001471239
## DV 0.396610953 0.4042309247 0.319490409 0.247067521
## V1 0.048430064 -0.0115536593 0.008730174 -0.003932429
## V2 0.443291688 0.4046822188 0.347735441 0.242792723
## V3 0.013926579 0.0470539387 0.089070430 0.075854675
## V4 1.000000000 0.5808940252 0.243988471 0.123637302
## V5 0.580894025 1.0000000000 0.313974363 0.591749219
## V6 0.243988471 0.3139743628 1.000000000 0.542164999
## V7 0.123637302 0.5917492190 0.542164999 1.000000000
## V8 -0.024540481 -0.0352640514 -0.031521648 -0.031468910
## V9 -0.045187880 -0.0041178966 -0.019347707 0.001546675
## V10 -0.017419646 0.0327003532 -0.002360371 0.034986917
## V11 -0.026361485 0.0734889668 0.022325712 0.116389837
## V12 0.047787162 0.1176909344 0.045395209 0.057171093
## V13 -0.012539265 -0.0003196213 -0.006259597 0.001083635
## V14 0.014874731 0.0449290046 0.017248045 -0.003038847
## V15 0.010438113 0.0447071511 0.021786036 -0.001582392
## V16 -0.051385027 0.0561527425 0.041328244 0.046394606
## V17 -0.005381209 0.0910083179 0.078174754 0.086737501
## V8 V9 V10 V11 V12
## Unique Id -0.166462480 -0.1329966954 -0.276993914 -0.18607730 -0.057191246
## DV -0.008021329 0.1032943760 0.112443379 0.17268174 -0.020568864
## V1 -0.155038638 -0.1258580382 -0.253688548 -0.16589871 -0.084415176
## V2 0.080337700 0.1425770351 0.193612923 0.21269384 -0.031145150
## V3 -0.102653555 -0.0503038267 0.135715335 0.10188456 0.053817501
## V4 -0.024540481 -0.0451878802 -0.017419646 -0.02636149 0.047787162
## V5 -0.035264051 -0.0041178966 0.032700353 0.07348897 0.117690934
## V6 -0.031521648 -0.0193477073 -0.002360371 0.02232571 0.045395209
## V7 -0.031468910 0.0015466749 0.034986917 0.11638984 0.057171093
## V8 1.000000000 0.7036319198 -0.021904947 -0.05026474 -0.008388321
## V9 0.703631920 1.0000000000 -0.021628936 -0.03523821 0.013319659
## V10 -0.021904947 -0.0216289360 1.000000000 0.73696949 -0.002899559
## V11 -0.050264738 -0.0352382148 0.736969492 1.00000000 0.011197029
## V12 -0.008388321 0.0133196591 -0.002899559 0.01119703 1.000000000
## V13 -0.008354007 -0.0036580940 -0.010290178 -0.00707707 0.233579176
## V14 0.005116588 0.0248245318 0.018560556 0.03328750 0.749623957
## V15 -0.007720275 0.0001216779 0.009172108 0.02808301 0.816701288
## V16 0.168059967 0.1316501535 -0.031410035 -0.01042634 0.008500735
## V17 0.023189198 0.0160047878 -0.022914269 0.01052477 -0.004752167
## V13 V14 V15 V16
## Unique Id 0.0235117081 -0.054751461 -0.0483821433 -0.174487490
## DV -0.0054182313 -0.021684427 -0.0106516736 -0.024387079
## V1 0.0167860257 -0.074669605 -0.0682594260 -0.184673607
## V2 -0.0161987185 -0.024907004 -0.0219708728 -0.022054997
## V3 0.0426799659 0.043287515 0.0374109645 -0.056764664
## V4 -0.0125392647 0.014874731 0.0104381128 -0.051385027
## V5 -0.0003196213 0.044929005 0.0447071511 0.056152743
## V6 -0.0062595971 0.017248045 0.0217860359 0.041328244
## V7 0.0010836354 -0.003038847 -0.0015823916 0.046394606
## V8 -0.0083540070 0.005116588 -0.0077202749 0.168059967
## V9 -0.0036580940 0.024824532 0.0001216779 0.131650153
## V10 -0.0102901777 0.018560556 0.0091721083 -0.031410035
## V11 -0.0070770698 0.033287503 0.0280830057 -0.010426336
## V12 0.2335791763 0.749623957 0.8167012881 0.008500735
## V13 1.0000000000 0.021408975 0.0234900910 -0.011217451
## V14 0.0214089747 1.000000000 0.9511779932 0.051214113
## V15 0.0234900910 0.951177993 1.0000000000 0.009436392
## V16 -0.0112174506 0.051214113 0.0094363924 1.000000000
## V17 -0.0125998460 0.010663352 0.0098643932 0.316289773
## V17
## Unique Id -0.083499958
## DV 0.060969039
## V1 -0.088241339
## V2 0.077482320
## V3 0.082575001
## V4 -0.005381209
## V5 0.091008318
## V6 0.078174754
## V7 0.086737501
## V8 0.023189198
## V9 0.016004788
## V10 -0.022914269
## V11 0.010524775
## V12 -0.004752167
## V13 -0.012599846
## V14 0.010663352
## V15 0.009864393
## V16 0.316289773
## V17 1.000000000library(corrplot)## corrplot 0.84 loadedcorrplot(cor(train),method = 'color')
corrgram(train, order=TRUE, lower.panel=panel.shade,
upper.panel=panel.pie, text.panel=panel.txt,
main="Loan Data")
Running some simple tests - chisquare etc
We can test the accuracy of our understanding of the correlations between the DV and other fields using the chisquare and t-tests etc.
chisq.test(xtabs(~DV + V1, data = train))##
## Pearson's Chi-squared test
##
## data: xtabs(~DV + V1, data = train)
## X-squared = 80419, df = 74800, p-value < 2.2e-16chisq.test(xtabs(~DV + V2, data = train))##
## Pearson's Chi-squared test
##
## data: xtabs(~DV + V2, data = train)
## X-squared = 2053, df = 440, p-value < 2.2e-16chisq.test(xtabs(~DV + V3, data = train))##
## Pearson's Chi-squared test
##
## data: xtabs(~DV + V3, data = train)
## X-squared = 12833, df = 13200, p-value = 0.9886chisq.test(xtabs(~DV + V4, data = train))##
## Pearson's Chi-squared test
##
## data: xtabs(~DV + V4, data = train)
## X-squared = 3309.6, df = 2640, p-value < 2.2e-16chisq.test(xtabs(~DV + V5, data = train))##
## Pearson's Chi-squared test
##
## data: xtabs(~DV + V5, data = train)
## X-squared = 301820, df = 231000, p-value < 2.2e-16chisq.test(xtabs(~DV + V6, data = train))##
## Pearson's Chi-squared test
##
## data: xtabs(~DV + V6, data = train)
## X-squared = 1364.9, df = 2200, p-value = 1chisq.test(xtabs(~DV + V7, data = train))##
## Pearson's Chi-squared test
##
## data: xtabs(~DV + V7, data = train)
## X-squared = 122040, df = 113080, p-value < 2.2e-16chisq.test(xtabs(~DV + V8, data = train))##
## Pearson's Chi-squared test
##
## data: xtabs(~DV + V8, data = train)
## X-squared = 2232.3, df = 1760, p-value = 9.667e-14chisq.test(xtabs(~DV + V9, data = train))##
## Pearson's Chi-squared test
##
## data: xtabs(~DV + V9, data = train)
## X-squared = 93726, df = 59400, p-value < 2.2e-16chisq.test(xtabs(~DV + V10, data = train))##
## Pearson's Chi-squared test
##
## data: xtabs(~DV + V10, data = train)
## X-squared = 2105.5, df = 1320, p-value < 2.2e-16chisq.test(xtabs(~DV + V11, data = train))##
## Pearson's Chi-squared test
##
## data: xtabs(~DV + V11, data = train)
## X-squared = 169050, df = 106920, p-value < 2.2e-16chisq.test(xtabs(~DV + V12, data = train))##
## Pearson's Chi-squared test
##
## data: xtabs(~DV + V12, data = train)
## X-squared = 1288.7, df = 1320, p-value = 0.726chisq.test(xtabs(~DV + V13, data = train))##
## Pearson's Chi-squared test
##
## data: xtabs(~DV + V13, data = train)
## X-squared = 2061, df = 2640, p-value = 1chisq.test(xtabs(~DV + V14, data = train))##
## Pearson's Chi-squared test
##
## data: xtabs(~DV + V14, data = train)
## X-squared = 344.38, df = 880, p-value = 1chisq.test(xtabs(~DV + V15, data = train))##
## Pearson's Chi-squared test
##
## data: xtabs(~DV + V15, data = train)
## X-squared = 688.18, df = 1320, p-value = 1chisq.test(xtabs(~DV + V16, data = train))##
## Pearson's Chi-squared test
##
## data: xtabs(~DV + V16, data = train)
## X-squared = 2714.6, df = 3080, p-value = 1We next run t-tests -
attach(train)
t.test(DV,V1, data = train)##
## Welch Two Sample t-test
##
## data: DV and V1
## t = 116.13, df = 2052, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 460959.2 476794.8
## sample estimates:
## mean of x mean of y
## 469717.9737 840.9523t.test(DV,V2, data = train)##
## Welch Two Sample t-test
##
## data: DV and V2
## t = 116.34, df = 2052, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 461799.8 477635.5
## sample estimates:
## mean of x mean of y
## 4.69718e+05 3.22942e-01t.test(DV,V3, data = train)##
## Welch Two Sample t-test
##
## data: DV and V3
## t = 116.33, df = 2052, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 461760.6 477596.2
## sample estimates:
## mean of x mean of y
## 469717.97370 39.56698t.test(DV,V4, data = train)##
## Welch Two Sample t-test
##
## data: DV and V4
## t = 116.34, df = 2052, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 461799.7 477635.3
## sample estimates:
## mean of x mean of y
## 4.697180e+05 4.632245e-01t.test(DV,V5, data = train)##
## Welch Two Sample t-test
##
## data: DV and V5
## t = -12.709, df = 2063.2, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -1133781.8 -830652.8
## sample estimates:
## mean of x mean of y
## 469718 1451935t.test(DV,V6, data = train)##
## Welch Two Sample t-test
##
## data: DV and V6
## t = 116.34, df = 2052, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 461799.9 477635.6
## sample estimates:
## mean of x mean of y
## 4.697180e+05 2.284462e-01t.test(DV,V7, data = train)##
## Welch Two Sample t-test
##
## data: DV and V7
## t = -2.1277, df = 2073.1, p-value = 0.03348
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -230582.633 -9392.596
## sample estimates:
## mean of x mean of y
## 469718.0 589705.6t.test(DV,V8, data = train)##
## Welch Two Sample t-test
##
## data: DV and V8
## t = 116.34, df = 2052, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 461800.0 477635.6
## sample estimates:
## mean of x mean of y
## 4.69718e+05 1.85095e-01t.test(DV,V9, data = train)##
## Welch Two Sample t-test
##
## data: DV and V9
## t = 56.959, df = 3706.1, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 382974.4 410279.4
## sample estimates:
## mean of x mean of y
## 469717.97 73091.07t.test(DV,V10, data = train)##
## Welch Two Sample t-test
##
## data: DV and V10
## t = 116.34, df = 2052, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 461799.9 477635.6
## sample estimates:
## mean of x mean of y
## 4.697180e+05 2.333171e-01t.test(DV,V11, data = train)##
## Welch Two Sample t-test
##
## data: DV and V11
## t = 26.859, df = 2602.5, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 289937.9 335605.8
## sample estimates:
## mean of x mean of y
## 469718.0 156946.1t.test(DV,V12, data = train)##
## Welch Two Sample t-test
##
## data: DV and V12
## t = 116.34, df = 2052, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 461800.1 477635.8
## sample estimates:
## mean of x mean of y
## 4.697180e+05 4.870921e-03t.test(DV,V13, data = train)##
## Welch Two Sample t-test
##
## data: DV and V13
## t = 3.4743, df = 2058.2, p-value = 0.0005227
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 156699.3 562858.4
## sample estimates:
## mean of x mean of y
## 469718.0 109939.1t.test(DV,V14, data = train)##
## Welch Two Sample t-test
##
## data: DV and V14
## t = 116.34, df = 2052, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 461800.1 477635.8
## sample estimates:
## mean of x mean of y
## 4.697180e+05 1.948368e-03t.test(DV,V15, data = train)##
## Welch Two Sample t-test
##
## data: DV and V15
## t = 111.91, df = 2352.3, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 459936.5 476343.1
## sample estimates:
## mean of x mean of y
## 469717.974 1578.178t.test(DV,V16, data = train)##
## Welch Two Sample t-test
##
## data: DV and V16
## t = 116.34, df = 2052, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 461798.7 477634.3
## sample estimates:
## mean of x mean of y
## 4.69718e+05 1.46225e+00t.test(DV,V17, data = train)##
## Welch Two Sample t-test
##
## data: DV and V17
## t = 82.041, df = 3579.3, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 388823.5 407862.9
## sample estimates:
## mean of x mean of y
## 469717.97 71374.77From the t-tests and chi-square tests, using the p-value < 0.05, we can reject the null hypothesis and say that the DV is affected by the factors - V1 to V17 directly.
Running the Regression model
After understanding relations in the data, we can now move on to creating our model to predict values of DV from V1-V17.
Since we know that these are numerical values, and with our analysis are able to get some understanding of the relations between the data, we will first run a model that depends on all the variables.
fit1 <- lm(DV ~ ., data=train)
summary(fit1)##
## Call:
## lm(formula = DV ~ ., data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -236432 -60184 40563 62004 201166
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.576e+05 1.354e+05 5.597 2.48e-08 ***
## `Unique Id` 4.253e+01 9.216e+00 4.615 4.18e-06 ***
## V1 -4.973e+02 1.697e+02 -2.930 0.00343 **
## V2 3.306e+05 5.301e+03 62.375 < 2e-16 ***
## V3 -4.636e+02 2.812e+02 -1.649 0.09931 .
## V4 -6.332e+03 4.053e+03 -1.562 0.11841
## V5 3.882e-03 9.465e-04 4.102 4.27e-05 ***
## V6 3.772e+03 4.463e+03 0.845 0.39812
## V7 -6.835e-04 1.207e-03 -0.566 0.57141
## V8 -4.671e+04 6.178e+03 -7.561 6.00e-14 ***
## V9 5.172e-02 1.103e-02 4.689 2.93e-06 ***
## V10 -2.605e+04 5.852e+03 -4.451 9.00e-06 ***
## V11 1.930e-02 6.020e-03 3.206 0.00137 **
## V12 -6.216e+04 3.536e+04 -1.758 0.07892 .
## V13 5.332e-04 4.557e-04 1.170 0.24210
## V14 -3.241e+05 1.220e+05 -2.656 0.00797 **
## V15 4.610e-01 1.554e-01 2.967 0.00304 **
## V16 2.914e+03 2.978e+03 0.978 0.32801
## V17 -1.609e-02 1.729e-02 -0.930 0.35235
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 89320 on 2034 degrees of freedom
## Multiple R-squared: 0.7637, Adjusted R-squared: 0.7616
## F-statistic: 365.2 on 18 and 2034 DF, p-value: < 2.2e-16fitted(fit1)## 1 2 3 4 5 6 7 8
## 685802.7 358782.3 375729.7 380011.6 678108.4 700177.8 460724.1 704025.9
## 9 10 11 12 13 14 15 16
## 385487.5 681313.6 381829.8 304291.6 723401.1 385667.8 385773.6 685896.8
## 17 18 19 20 21 22 23 24
## 706433.1 364824.2 376905.0 375556.6 377730.1 356328.8 281559.1 341273.6
## 25 26 27 28 29 30 31 32
## 375933.0 374555.7 378132.7 519673.7 666864.5 379583.8 703084.4 699361.5
## 33 34 35 36 37 38 39 40
## 375692.3 703809.6 706779.8 362415.4 678652.6 356333.0 675217.0 765335.9
## 41 42 43 44 45 46 47 48
## 693308.9 324949.5 665351.4 707452.8 642105.0 321334.7 371201.8 688911.8
## 49 50 51 52 53 54 55 56
## 711540.1 350939.0 357529.9 350212.9 356425.4 705543.9 374373.7 312868.1
## 57 58 59 60 61 62 63 64
## 737299.8 371623.7 339779.0 368354.3 336681.9 707220.4 671790.6 360701.7
## 65 66 67 68 69 70 71 72
## 372316.5 699559.3 364596.3 367024.9 305191.5 665953.7 850005.1 726672.3
## 73 74 75 76 77 78 79 80
## 348707.4 366715.7 737451.1 368707.9 369442.2 671493.1 356350.4 350188.5
## 81 82 83 84 85 86 87 88
## 419964.6 698253.4 356450.1 716569.1 310511.1 354899.0 367459.2 660954.4
## 89 90 91 92 93 94 95 96
## 351073.6 345947.1 339868.9 342142.2 688879.8 327928.4 314879.4 366703.2
## 97 98 99 100 101 102 103 104
## 355291.4 314183.8 364704.2 367528.5 362606.7 695831.0 363511.1 366772.7
## 105 106 107 108 109 110 111 112
## 671160.9 667896.0 343385.5 324018.1 355248.7 296889.2 697334.1 359364.2
## 113 114 115 116 117 118 119 120
## 650657.5 347178.3 355015.0 362719.4 362558.1 690583.9 327544.8 338235.7
## 121 122 123 124 125 126 127 128
## 230711.8 363822.7 360085.0 684973.2 344957.5 354352.2 310516.7 364342.9
## 129 130 131 132 133 134 135 136
## 643908.1 360014.0 348944.9 674525.4 672802.3 152000.0 367223.2 362664.3
## 137 138 139 140 141 142 143 144
## 362398.2 351997.4 359881.5 685246.0 338192.0 356588.4 667560.1 342120.7
## 145 146 147 148 149 150 151 152
## 321590.6 314781.6 691944.2 697847.8 328768.4 253826.1 296305.8 665337.3
## 153 154 155 156 157 158 159 160
## 342081.4 357209.7 355643.5 672344.6 732707.1 320975.3 347945.0 693217.7
## 161 162 163 164 165 166 167 168
## 680722.0 335075.8 659897.4 697644.3 351748.9 361444.5 358950.5 359311.5
## 169 170 171 172 173 174 175 176
## 324647.4 578371.5 674043.5 283212.6 353988.4 351591.3 349404.8 674585.0
## 177 178 179 180 181 182 183 184
## 313209.6 342013.4 335343.2 344801.4 672328.8 671641.6 323514.0 413137.9
## 185 186 187 188 189 190 191 192
## 359798.7 684059.8 687831.6 340610.6 357403.2 650004.0 663898.1 669565.3
## 193 194 195 196 197 198 199 200
## 349219.6 313233.0 358683.9 354351.6 691593.8 729582.0 352661.1 355761.1
## 201 202 203 204 205 206 207 208
## 669148.6 694467.4 327849.2 284716.0 356929.8 667969.7 723030.6 336474.6
## 209 210 211 212 213 214 215 216
## 328091.9 354120.8 357975.9 356392.0 356434.5 633563.1 300869.5 357408.2
## 217 218 219 220 221 222 223 224
## 350089.3 320074.9 312810.9 349516.3 357241.7 355856.3 359602.0 666645.4
## 225 226 227 228 229 230 231 232
## 358729.5 358546.8 339087.6 346341.5 355113.7 355235.6 352869.1 628222.2
## 233 234 235 236 237 238 239 240
## 691480.9 361281.5 331580.7 347454.3 359579.5 679201.9 665046.2 681607.2
## 241 242 243 244 245 246 247 248
## 685990.8 699607.0 339208.9 318023.7 343562.0 344889.0 672244.5 697035.6
## 249 250 251 252 253 254 255 256
## 669272.4 345232.9 341040.4 361473.6 312055.0 346613.8 364421.4 663424.2
## 257 258 259 260 261 262 263 264
## 677164.3 648168.6 668927.3 655963.7 319124.4 352394.5 355117.8 328899.9
## 265 266 267 268 269 270 271 272
## 354271.1 326967.4 329492.0 353603.4 355832.1 334761.5 678883.1 687996.2
## 273 274 275 276 277 278 279 280
## 688312.0 324245.5 337096.9 323389.9 331992.8 351171.9 350792.1 339394.9
## 281 282 283 284 285 286 287 288
## 697094.9 674816.3 662936.0 351496.5 323752.0 336626.6 352815.4 357339.2
## 289 290 291 292 293 294 295 296
## 357357.2 334444.8 698571.9 264493.9 356928.4 330337.3 689239.9 685284.7
## 297 298 299 300 301 302 303 304
## 691283.8 715839.2 676201.9 347619.2 344974.2 355750.9 356679.7 355331.3
## 305 306 307 308 309 310 311 312
## 355373.8 356012.0 347312.4 690739.8 670816.0 679361.9 691836.5 689912.7
## 313 314 315 316 317 318 319 320
## 339012.1 340145.5 348631.1 356558.1 314821.8 334550.1 358849.3 354587.1
## 321 322 323 324 325 326 327 328
## 354166.0 351426.8 351137.6 355684.5 355263.4 358522.5 333388.3 680141.3
## 329 330 331 332 333 334 335 336
## 601398.0 657784.9 336509.8 335881.7 350601.9 666639.7 643774.7 661350.7
## 337 338 339 340 341 342 343 344
## 645587.5 352503.5 315930.4 333949.3 346825.1 637780.5 698335.8 689188.2
## 345 346 347 348 349 350 351 352
## 638450.4 695884.3 655346.2 697611.9 329841.0 307427.8 335223.2 339168.0
## 353 354 355 356 357 358 359 360
## 359730.5 336883.0 673582.8 672683.0 681432.3 702585.9 354167.8 306405.1
## 361 362 363 364 365 366 367 368
## 356381.3 297906.0 326702.6 355987.3 353505.7 356735.2 335881.9 350002.8
## 369 370 371 372 373 374 375 376
## 342606.2 326713.3 316099.6 350172.9 662322.6 334755.0 316477.2 330620.3
## 377 378 379 380 381 382 383 384
## 330305.8 333297.8 355822.2 336213.6 342606.6 298537.8 684752.8 795799.2
## 385 386 387 388 389 390 391 392
## 664645.4 324764.1 338538.7 349798.3 339194.2 351289.2 296458.6 317307.4
## 393 394 395 396 397 398 399 400
## 702067.3 644704.8 324027.6 339669.1 336984.9 354629.4 351889.6 356826.2
## 401 402 403 404 405 406 407 408
## 358380.0 299929.3 682420.4 631928.8 692538.4 353338.6 323649.5 319975.5
## 409 410 411 412 413 414 415 416
## 327446.3 353640.7 351233.1 669611.5 689593.4 329936.6 337878.1 347224.8
## 417 418 419 420 421 422 423 424
## 308884.3 359291.0 358162.5 357562.2 295513.8 355508.2 326314.7 630866.5
## 425 426 427 428 429 430 431 432
## 771195.0 807646.3 329764.5 358047.9 343618.6 350549.8 346452.7 314332.3
## 433 434 435 436 437 438 439 440
## 351088.1 350752.9 354276.7 359315.4 354769.9 680546.1 715457.7 348878.6
## 441 442 443 444 445 446 447 448
## 355927.1 321203.9 291067.4 319866.7 334440.0 292511.9 355969.9 670266.9
## 449 450 451 452 453 454 455 456
## 672636.3 698219.1 673135.6 656377.8 334557.8 357136.7 328587.2 341109.5
## 457 458 459 460 461 462 463 464
## 314234.7 354779.7 357628.6 345433.2 358978.8 360559.0 352418.3 688549.7
## 465 466 467 468 469 470 471 472
## 678986.3 672020.0 681547.6 722246.1 684210.4 705318.0 669092.3 320023.8
## 473 474 475 476 477 478 479 480
## 337357.8 289912.6 314208.3 358638.2 660485.4 737980.9 686822.2 327162.5
## 481 482 483 484 485 486 487 488
## 356682.2 348905.0 297690.7 329040.1 332543.6 352767.2 347655.7 356025.9
## 489 490 491 492 493 494 495 496
## 335401.1 339481.2 324091.4 338688.8 701115.1 686555.0 689697.3 690123.9
## 497 498 499 500 501 502 503 504
## 665712.7 341595.6 356524.4 333326.7 297007.3 353245.3 355837.0 362147.4
## 505 506 507 508 509 510 511 512
## 326190.4 357848.7 362630.0 352340.6 353215.4 657992.4 678029.9 684927.9
## 513 514 515 516 517 518 519 520
## 698959.3 679967.0 330827.1 358122.0 342485.3 318453.7 335065.4 339528.9
## 521 522 523 524 525 526 527 528
## 357573.0 353810.9 354075.4 332087.3 333425.4 677472.4 660068.3 657151.1
## 529 530 531 532 533 534 535 536
## 692520.6 670975.8 337736.2 340628.8 320950.9 332346.0 354465.1 334890.3
## 537 538 539 540 541 542 543 544
## 341578.1 358352.5 356837.0 353302.4 357892.1 360341.9 644157.0 681072.6
## 545 546 547 548 549 550 551 552
## 663903.4 613086.1 678549.8 694853.2 701815.4 693358.8 315702.2 333373.5
## 553 554 555 556 557 558 559 560
## 354030.2 355422.7 353311.0 358759.5 354897.0 356795.6 670195.9 681271.3
## 561 562 563 564 565 566 567 568
## 683748.1 665069.1 685153.5 349932.0 354753.1 338596.7 334590.3 310416.4
## 569 570 571 572 573 574 575 576
## 353455.3 354374.3 352103.2 350291.2 351483.3 303826.9 353796.2 356952.2
## 577 578 579 580 581 582 583 584
## 361390.1 356021.7 352236.0 687304.2 677150.2 689991.4 652623.6 715403.2
## 585 586 587 588 589 590 591 592
## 660958.7 696202.2 352881.9 323421.8 334190.4 351023.0 351585.1 357704.3
## 593 594 595 596 597 598 599 600
## 352079.8 328218.8 359495.1 333354.8 302948.6 666981.3 669802.1 688915.1
## 601 602 603 604 605 606 607 608
## 671099.6 692633.8 685405.5 357201.3 348351.6 332138.0 353220.6 356391.1
## 609 610 611 612 613 614 615 616
## 355897.1 358462.7 316146.8 300806.4 358499.3 355683.1 354834.3 358679.8
## 617 618 619 620 621 622 623 624
## 361091.7 357828.5 359431.9 351801.5 356016.7 358841.0 356101.7 361839.8
## 625 626 627 628 629 630 631 632
## 335131.0 342784.3 688080.8 539942.0 690360.9 689554.5 677182.0 681254.3
## 633 634 635 636 637 638 639 640
## 687880.3 670449.3 696125.8 685002.0 689355.5 352076.5 346732.9 331218.4
## 641 642 643 644 645 646 647 648
## 339228.8 343566.4 348352.7 355988.4 348194.6 353853.7 330400.2 352958.5
## 649 650 651 652 653 654 655 656
## 330361.6 344257.9 355536.2 356472.5 353458.2 363081.9 356038.0 350980.5
## 657 658 659 660 661 662 663 664
## 365527.7 355667.5 691234.9 678873.3 665331.7 686045.1 689109.6 696857.4
## 665 666 667 668 669 670 671 672
## 648344.0 809271.1 770454.7 350945.6 343519.3 314055.8 355162.0 341479.6
## 673 674 675 676 677 678 679 680
## 357498.5 356910.7 363664.9 356176.7 358330.8 358373.3 355662.3 349185.7
## 681 682 683 684 685 686 687 688
## 344962.6 354370.7 359513.2 358628.5 361930.1 683051.1 692571.4 690291.6
## 689 690 691 692 693 694 695 696
## 686703.7 706302.9 701162.6 645205.3 337175.7 357743.2 356876.4 356455.3
## 697 698 699 700 701 702 703 704
## 337360.4 321811.8 363073.7 362641.0 357463.2 361367.0 353160.9 359577.3
## 705 706 707 708 709 710 711 712
## 362865.2 361848.5 357749.1 358265.9 360092.7 362544.1 312953.5 699759.6
## 713 714 715 716 717 718 719 720
## 635192.8 669641.5 689499.4 681469.8 746680.9 703859.6 674200.2 329407.0
## 721 722 723 724 725 726 727 728
## 318412.0 346628.6 333185.2 352380.4 310848.7 356694.1 348691.6 352287.9
## 729 730 731 732 733 734 735 736
## 345240.9 337818.5 360096.2 359675.1 339770.9 362078.3 351297.9 361699.7
## 737 738 739 740 741 742 743 744
## 359509.0 366089.5 337855.7 695718.6 652081.3 665096.4 664894.6 662228.8
## 745 746 747 748 749 750 751 752
## 665692.1 696452.1 704279.1 689222.4 703308.7 700875.0 648599.4 676366.5
## 753 754 755 756 757 758 759 760
## 682250.0 685384.3 354128.6 333627.2 338118.9 354505.3 337147.2 353150.5
## 761 762 763 764 765 766 767 768
## 352111.0 325391.6 304157.0 336026.5 361220.6 352864.8 350910.9 350448.4
## 769 770 771 772 773 774 775 776
## 349902.0 362430.4 361114.6 365647.1 364448.0 360714.4 306558.2 310517.1
## 777 778 779 780 781 782 783 784
## 696345.3 698808.0 724486.2 705323.8 691443.5 699092.5 305459.4 328637.5
## 785 786 787 788 789 790 791 792
## 359961.6 340052.7 354447.8 329191.9 363664.3 364060.8 365494.2 364145.8
## 793 794 795 796 797 798 799 800
## 358406.9 362244.4 360896.0 362793.0 362556.3 360475.6 317675.1 367018.0
## 801 802 803 804 805 806 807 808
## 662455.1 691266.2 685128.6 703216.4 718313.8 693413.7 669392.7 715640.6
## 809 810 811 812 813 814 815 816
## 698333.5 656749.5 357623.5 371227.3 343517.5 343106.7 353149.4 332059.9
## 817 818 819 820 821 822 823 824
## 322136.8 367072.3 363273.8 365302.9 366711.5 358301.4 361924.7 362186.3
## 825 826 827 828 829 830 831 832
## 364421.5 362644.2 362681.3 365047.5 353035.5 365728.1 360207.0 357571.7
## 833 834 835 836 837 838 839 840
## 363073.9 366693.9 364776.6 358896.8 364417.0 365132.3 362733.5 364630.5
## 841 842 843 844 845 846 847 848
## 362169.5 365642.8 362903.6 367242.0 363587.8 362633.3 684098.5 687193.9
## 849 850 851 852 853 854 855 856
## 680081.5 685642.2 691678.8 296601.9 351312.5 353251.4 362784.7 323824.1
## 857 858 859 860 861 862 863 864
## 295647.6 362495.6 362849.8 364520.1 354362.7 363214.2 356093.5 366676.7
## 865 866 867 868 869 870 871 872
## 356423.9 334447.9 318881.0 688531.4 661779.7 641372.0 670664.5 666882.4
## 873 874 875 876 877 878 879 880
## 701493.8 675439.8 675153.6 691081.4 706142.2 662818.8 698975.7 700699.1
## 881 882 883 884 885 886 887 888
## 363831.5 352904.2 364491.5 353363.0 367781.0 363737.6 365889.5 349736.5
## 889 890 891 892 893 894 895 896
## 673601.0 701205.3 754114.3 686682.0 690727.8 831140.8 791622.7 686430.3
## 897 898 899 900 901 902 903 904
## 671083.0 366838.9 355084.2 364339.1 321852.2 343250.8 364381.4 367296.9
## 905 906 907 908 909 910 911 912
## 321438.2 340217.4 294333.3 369729.3 344562.4 369029.2 372453.9 367524.1
## 913 914 915 916 917 918 919 920
## 357401.9 330539.3 676314.5 649662.9 678539.8 784608.8 343923.9 300678.0
## 921 922 923 924 925 926 927 928
## 347143.6 360564.8 360505.4 340671.4 325029.9 362864.5 318660.2 369311.0
## 929 930 931 932 933 934 935 936
## 367753.0 364150.4 366974.8 366090.0 364410.0 358425.3 365852.4 359769.3
## 937 938 939 940 941 942 943 944
## 366302.7 364954.3 366387.7 359348.6 370313.8 347385.9 336242.8 366049.6
## 945 946 947 948 949 950 951 952
## 630570.4 700180.1 683217.6 706592.8 701635.7 725038.7 728596.1 692310.1
## 953 954 955 956 957 958 959 960
## 673563.1 691259.2 653929.2 357931.6 366431.5 351975.7 361977.8 366915.4
## 961 962 963 964 965 966 967 968
## 337296.6 367403.5 363797.6 297236.9 366806.3 348935.9 339899.9 363878.2
## 969 970 971 972 973 974 975 976
## 360398.5 364890.5 368310.5 367448.8 367220.8 367170.0 364771.5 364218.4
## 977 978 979 980 981 982 983 984
## 357770.1 357349.0 368518.7 364852.2 360239.7 361646.6 361039.6 367316.0
## 985 986 987 988 989 990 991 992
## 359273.0 700721.6 683694.1 694447.0 688566.2 688167.9 722692.9 694742.7
## 993 994 995 996 997 998 999 1000
## 709033.2 344712.6 366383.6 344579.4 331989.3 368526.6 306749.8 345376.7
## 1001 1002 1003 1004 1005 1006 1007 1008
## 355153.8 369504.1 312502.4 362307.4 357256.9 367637.2 345525.6 371862.1
## 1009 1010 1011 1012 1013 1014 1015 1016
## 699672.9 684040.9 657827.5 701760.9 700129.1 655347.2 713126.9 699640.8
## 1017 1018 1019 1020 1021 1022 1023 1024
## 673822.0 365216.9 351319.2 361849.5 350880.6 355186.2 373767.3 359724.6
## 1025 1026 1027 1028 1029 1030 1031 1032
## 365585.4 364768.4 363736.1 374346.7 374157.9 366454.1 368808.2 363787.7
## 1033 1034 1035 1036 1037 1038 1039 1040
## 358549.2 700770.5 693586.7 692347.1 708380.1 681954.9 704088.9 706108.7
## 1041 1042 1043 1044 1045 1046 1047 1048
## 691144.6 725692.1 688470.9 706186.7 709832.5 744041.3 356332.5 364190.2
## 1049 1050 1051 1052 1053 1054 1055 1056
## 367808.3 367089.7 358497.8 366545.0 339532.0 356117.9 366591.5 358710.4
## 1057 1058 1059 1060 1061 1062 1063 1064
## 368232.2 365428.2 371488.1 373848.8 368908.0 686599.9 665139.8 705664.5
## 1065 1066 1067 1068 1069 1070 1071 1072
## 714581.9 696049.7 713612.2 702942.3 662531.9 369935.7 363155.7 358610.8
## 1073 1074 1075 1076 1077 1078 1079 1080
## 328160.0 364076.8 369281.1 374869.4 370904.1 284834.3 691801.9 696480.8
## 1081 1082 1083 1084 1085 1086 1087 1088
## 680881.4 741141.0 722471.9 686332.5 699519.4 703599.5 695407.6 362126.5
## 1089 1090 1091 1092 1093 1094 1095 1096
## 340170.1 289697.4 325815.3 347154.9 326161.4 369566.7 367984.5 363049.6
## 1097 1098 1099 1100 1101 1102 1103 1104
## 370270.0 368533.3 353062.7 351097.4 684909.7 684358.0 705025.6 661429.6
## 1105 1106 1107 1108 1109 1110 1111 1112
## 685591.0 648441.0 682247.9 697935.1 368745.1 368160.9 323521.6 370479.3
## 1113 1114 1115 1116 1117 1118 1119 1120
## 368219.1 326967.1 369707.7 376795.7 375217.5 364292.9 371952.1 376201.5
## 1121 1122 1123 1124 1125 1126 1127 1128
## 708625.5 709098.3 707628.9 703193.4 704590.9 658866.8 703377.8 695429.1
## 1129 1130 1131 1132 1133 1134 1135 1136
## 703692.2 695660.9 333535.1 357984.7 372903.1 346508.9 361339.6 344720.8
## 1137 1138 1139 1140 1141 1142 1143 1144
## 302831.7 370214.7 367337.3 363538.8 368935.8 372831.7 704973.0 685292.3
## 1145 1146 1147 1148 1149 1150 1151 1152
## 678008.2 703721.3 710172.7 663073.4 703619.8 696976.2 761263.2 691912.9
## 1153 1154 1155 1156 1157 1158 1159 1160
## 677974.0 711852.5 362752.1 338510.6 372007.9 349874.4 364761.4 330929.3
## 1161 1162 1163 1164 1165 1166 1167 1168
## 347457.4 374689.5 367174.1 347066.0 365608.5 369842.8 375247.1 700986.9
## 1169 1170 1171 1172 1173 1174 1175 1176
## 695947.9 654448.1 700964.1 707077.9 675371.0 757575.6 728316.2 708674.1
## 1177 1178 1179 1180 1181 1182 1183 1184
## 705941.3 329064.4 343917.2 373508.8 373829.6 367722.1 373427.1 320662.7
## 1185 1186 1187 1188 1189 1190 1191 1192
## 364178.6 372824.3 367240.3 368490.1 689127.9 671378.0 712200.0 729318.2
## 1193 1194 1195 1196 1197 1198 1199 1200
## 716008.4 650127.7 727281.8 297819.9 316169.4 360137.3 338281.8 371553.0
## 1201 1202 1203 1204 1205 1206 1207 1208
## 362786.4 321774.9 311023.3 367597.3 368922.9 319419.6 371010.1 366476.2
## 1209 1210 1211 1212 1213 1214 1215 1216
## 324223.3 376282.9 370298.2 366631.6 322040.2 373008.7 373415.4 374452.6
## 1217 1218 1219 1220 1221 1222 1223 1224
## 348454.9 708598.1 646351.1 676409.9 689372.3 671517.3 904639.4 701364.6
## 1225 1226 1227 1228 1229 1230 1231 1232
## 707225.6 309668.3 365699.4 360674.8 375979.3 362123.9 370410.1 377126.7
## 1233 1234 1235 1236 1237 1238 1239 1240
## 664428.0 690296.4 701449.6 699249.9 688070.0 680664.3 710989.9 664495.4
## 1241 1242 1243 1244 1245 1246 1247 1248
## 703243.3 706305.9 373793.6 353713.2 344629.0 356167.3 365822.8 368689.2
## 1249 1250 1251 1252 1253 1254 1255 1256
## 368570.9 337329.7 375640.9 370049.3 374052.3 368924.9 374646.9 363696.2
## 1257 1258 1259 1260 1261 1262 1263 1264
## 694709.0 695896.4 709782.6 714000.5 712082.0 696747.9 719100.6 704364.7
## 1265 1266 1267 1268 1269 1270 1271 1272
## 773136.6 674543.9 646710.3 749414.9 736763.8 704221.7 690242.4 368874.2
## 1273 1274 1275 1276 1277 1278 1279 1280
## 371996.4 372975.3 377551.4 369488.9 376021.8 337038.9 374479.8 351333.5
## 1281 1282 1283 1284 1285 1286 1287 1288
## 367100.0 370344.1 338317.0 694864.5 698880.3 713141.5 704377.7 689137.8
## 1289 1290 1291 1292 1293 1294 1295 1296
## 655665.2 805151.8 703293.6 709759.0 670137.5 698971.9 709976.9 367411.7
## 1297 1298 1299 1300 1301 1302 1303 1304
## 371370.6 369976.8 371339.7 375538.1 285446.1 373898.5 375021.4 371898.3
## 1305 1306 1307 1308 1309 1310 1311 1312
## 377813.0 377571.8 345996.0 704855.3 713705.9 712912.9 709476.9 711849.7
## 1313 1314 1315 1316 1317 1318 1319 1320
## 708294.7 700907.9 366722.1 352730.2 354410.3 374044.4 370857.4 367901.0
## 1321 1322 1323 1324 1325 1326 1327 1328
## 367219.9 331938.7 365419.6 365258.8 375435.1 354501.8 377540.5 374973.4
## 1329 1330 1331 1332 1333 1334 1335 1336
## 370379.6 379826.7 374637.3 368566.7 372536.2 370592.2 372548.1 372656.5
## 1337 1338 1339 1340 1341 1342 1343 1344
## 376747.0 363771.3 375441.2 371774.6 373208.0 373693.2 366892.3 709816.2
## 1345 1346 1347 1348 1349 1350 1351 1352
## 709486.7 713725.6 697660.0 708883.5 701156.2 715321.9 700331.6 726553.8
## 1353 1354 1355 1356 1357 1358 1359 1360
## 728455.5 787996.4 725117.6 367576.2 367563.7 327999.6 339146.0 380182.6
## 1361 1362 1363 1364 1365 1366 1367 1368
## 374453.6 378794.8 376541.1 375543.4 377094.9 371312.5 374794.2 370945.2
## 1369 1370 1371 1372 1373 1374 1375 1376
## 372737.3 368569.5 350730.2 630099.9 672621.1 745351.4 710880.9 724144.6
## 1377 1378 1379 1380 1381 1382 1383 1384
## 718328.8 759227.7 698140.7 376745.3 374086.3 251838.7 367331.2 371007.4
## 1385 1386 1387 1388 1389 1390 1391 1392
## 350412.8 379995.1 368606.0 370175.6 376876.1 383284.0 337771.1 381361.0
## 1393 1394 1395 1396 1397 1398 1399 1400
## 377875.6 352116.7 380669.0 379320.7 362851.0 367824.8 371102.8 371113.2
## 1401 1402 1403 1404 1405 1406 1407 1408
## 374301.4 373491.6 370809.3 376879.1 375398.7 374182.3 376067.4 376726.7
## 1409 1410 1411 1412 1413 1414 1415 1416
## 381022.2 372462.9 371975.8 705809.3 708008.1 699434.5 650623.5 719267.1
## 1417 1418 1419 1420 1421 1422 1423 1424
## 718476.3 734830.9 720151.2 754217.5 701354.5 709599.5 723352.6 718325.8
## 1425 1426 1427 1428 1429 1430 1431 1432
## 712524.5 366154.3 340224.9 355106.9 356654.2 371983.4 347862.8 371336.7
## 1433 1434 1435 1436 1437 1438 1439 1440
## 376791.6 373669.2 376266.9 372974.3 372798.4 370152.1 373565.5 376389.8
## 1441 1442 1443 1444 1445 1446 1447 1448
## 369098.9 362933.0 707864.8 672310.5 691544.2 666739.5 709442.6 733330.6
## 1449 1450 1451 1452 1453 1454 1455 1456
## 691671.7 706576.2 379045.9 374531.5 360043.7 353370.2 379114.3 377737.7
## 1457 1458 1459 1460 1461 1462 1463 1464
## 380486.1 380367.0 371136.9 373497.6 381033.2 382523.7 369452.5 375058.6
## 1465 1466 1467 1468 1469 1470 1471 1472
## 370148.2 371689.4 377040.7 379865.0 377873.2 380852.9 379197.3 379571.5
## 1473 1474 1475 1476 1477 1478 1479 1480
## 378016.4 380871.1 346795.5 705454.4 705007.9 707428.6 705496.6 708866.9
## 1481 1482 1483 1484 1485 1486 1487 1488
## 683243.2 683351.0 706975.8 732971.8 725564.9 670606.4 357229.7 355195.1
## 1489 1490 1491 1492 1493 1494 1495 1496
## 369144.0 377000.1 352932.3 359989.4 382922.0 382889.4 383155.1 377832.3
## 1497 1498 1499 1500 1501 1502 1503 1504
## 369103.8 380238.6 371070.1 688818.7 706061.6 714208.0 697605.8 713924.9
## 1505 1506 1507 1508 1509 1510 1511 1512
## 719453.8 711425.2 714120.5 713024.8 705670.1 306260.3 374689.8 314085.9
## 1513 1514 1515 1516 1517 1518 1519 1520
## 345519.1 368062.7 334473.3 383886.9 379278.2 383910.5 377793.8 377844.1
## 1521 1522 1523 1524 1525 1526 1527 1528
## 378806.1 381885.3 379818.5 377674.8 382135.8 380508.1 374093.3 372881.0
## 1529 1530 1531 1532 1533 1534 1535 1536
## 379647.0 374479.4 378767.8 373246.7 384548.4 380943.3 384169.8 378980.4
## 1537 1538 1539 1540 1541 1542 1543 1544
## 377754.9 379529.1 379614.4 378160.8 376973.7 377942.7 380669.0 383625.3
## 1545 1546 1547 1548 1549 1550 1551 1552
## 382144.9 384564.5 383289.2 386845.9 717014.7 698412.0 817998.9 719479.2
## 1553 1554 1555 1556 1557 1558 1559 1560
## 666896.5 714232.5 682594.4 376309.3 382827.9 376173.2 380209.1 349819.5
## 1561 1562 1563 1564 1565 1566 1567 1568
## 385756.7 376417.3 374819.9 378385.9 376693.2 380686.1 378410.5 366358.5
## 1569 1570 1571 1572 1573 1574 1575 1576
## 378229.1 379465.3 372089.7 373986.8 371834.0 378708.2 382591.7 371838.7
## 1577 1578 1579 1580 1581 1582 1583 1584
## 379422.3 378414.6 383093.5 385816.7 389238.8 383953.6 387381.5 362529.7
## 1585 1586 1587 1588 1589 1590 1591 1592
## 383232.6 386890.0 676173.0 718573.2 722339.0 716871.7 723874.3 719013.0
## 1593 1594 1595 1596 1597 1598 1599 1600
## 740333.5 728589.3 749468.7 624716.9 720448.2 714446.3 705599.6 719209.1
## 1601 1602 1603 1604 1605 1606 1607 1608
## 704799.1 725771.1 377125.9 333750.4 380393.0 372605.9 385938.7 381698.9
## 1609 1610 1611 1612 1613 1614 1615 1616
## 377527.4 378611.7 388664.3 718605.0 686287.5 736617.4 673646.5 329712.0
## 1617 1618 1619 1620 1621 1622 1623 1624
## 378019.4 380272.4 376605.2 378653.8 379388.0 379435.7 381110.6 377843.0
## 1625 1626 1627 1628 1629 1630 1631 1632
## 382364.9 379965.9 386717.7 374446.4 370184.2 384006.9 383420.3 386884.8
## 1633 1634 1635 1636 1637 1638 1639 1640
## 717547.1 668076.6 717900.2 714535.0 721213.4 673304.0 709991.5 721322.2
## 1641 1642 1643 1644 1645 1646 1647 1648
## 712122.9 666232.8 727582.3 732547.8 733999.2 718408.3 725641.3 718993.6
## 1649 1650 1651 1652 1653 1654 1655 1656
## 720300.6 720776.4 725548.4 718756.4 715405.0 380076.1 380398.0 383426.3
## 1657 1658 1659 1660 1661 1662 1663 1664
## 382136.8 383261.0 388915.1 384118.9 381041.8 383276.7 384782.2 385545.4
## 1665 1666 1667 1668 1669 1670 1671 1672
## 378407.2 385102.5 387710.7 382571.0 381719.8 384080.5 381061.9 373418.7
## 1673 1674 1675 1676 1677 1678 1679 1680
## 378416.4 383455.4 387252.3 378772.1 377707.5 370813.3 379424.7 376624.0
## 1681 1682 1683 1684 1685 1686 1687 1688
## 379694.1 385054.5 388010.8 381998.0 386744.1 387211.1 386194.4 375170.1
## 1689 1690 1691 1692 1693 1694 1695 1696
## 382570.4 385858.3 384037.8 383161.6 386449.5 386955.7 651822.7 688040.6
## 1697 1698 1699 1700 1701 1702 1703 1704
## 753678.9 733040.0 381078.5 360485.8 383330.8 338299.9 383000.2 377339.2
## 1705 1706 1707 1708 1709 1710 1711 1712
## 381947.1 384852.6 379961.8 377317.5 380549.0 389248.6 386144.7 384574.0
## 1713 1714 1715 1716 1717 1718 1719 1720
## 377643.1 383731.8 385175.1 381962.3 427353.2 381583.8 387653.5 382927.7
## 1721 1722 1723 1724 1725 1726 1727 1728
## 379204.2 380694.6 386713.8 379852.4 384067.6 382851.2 376240.8 386049.7
## 1729 1730 1731 1732 1733 1734 1735 1736
## 381587.9 387600.7 379222.8 385888.2 378380.6 379492.3 379988.5 385462.7
## 1737 1738 1739 1740 1741 1742 1743 1744
## 385167.7 384198.2 382977.0 384206.5 708439.1 710341.7 707637.2 712407.7
## 1745 1746 1747 1748 1749 1750 1751 1752
## 686643.9 711006.9 715822.2 721528.1 731778.4 729549.6 710255.3 727362.7
## 1753 1754 1755 1756 1757 1758 1759 1760
## 719565.8 380078.5 381881.9 384142.2 381356.9 381672.2 388400.6 389041.6
## 1761 1762 1763 1764 1765 1766 1767 1768
## 385135.0 380317.7 385261.3 385531.6 374378.3 384386.6 379310.2 384961.7
## 1769 1770 1771 1772 1773 1774 1775 1776
## 389888.0 384850.7 383065.4 385569.0 390682.6 387972.3 386528.9 384811.9
## 1777 1778 1779 1780 1781 1782 1783 1784
## 395030.2 389043.4 723993.4 725719.6 722526.2 725313.3 711178.8 714908.9
## 1785 1786 1787 1788 1789 1790 1791 1792
## 720893.7 706827.3 738051.6 680681.3 736213.3 387228.2 387770.5 386849.5
## 1793 1794 1795 1796 1797 1798 1799 1800
## 391611.1 390080.9 376449.7 383442.5 373622.7 379686.5 388074.5 674613.8
## 1801 1802 1803 1804 1805 1806 1807 1808
## 726358.6 722643.9 725263.8 378517.1 328906.1 386546.9 385088.8 388887.2
## 1809 1810 1811 1812 1813 1814 1815 1816
## 384293.4 387249.7 379742.1 387374.2 390102.0 388686.4 384886.9 721205.1
## 1817 1818 1819 1820 1821 1822 1823 1824
## 673488.6 659518.1 721183.1 714571.7 727407.8 346451.5 382839.5 385425.3
## 1825 1826 1827 1828 1829 1830 1831 1832
## 381917.8 381273.5 382025.5 382285.9 383807.7 387840.0 716605.9 724110.9
## 1833 1834 1835 1836 1837 1838 1839 1840
## 730979.0 774228.9 730455.5 386301.5 382880.7 377034.4 382317.8 391235.3
## 1841 1842 1843 1844 1845 1846 1847 1848
## 389418.8 391193.0 387956.5 390350.7 385756.9 389972.2 386409.5 385966.1
## 1849 1850 1851 1852 1853 1854 1855 1856
## 382491.6 382300.4 382766.7 385775.3 388093.6 389848.7 383507.7 386224.7
## 1857 1858 1859 1860 1861 1862 1863 1864
## 390903.6 390482.5 392047.9 389500.6 384582.8 392024.8 389304.2 388201.6
## 1865 1866 1867 1868 1869 1870 1871 1872
## 389852.9 714114.4 731127.7 725876.5 723317.0 685544.5 729529.8 380752.2
## 1873 1874 1875 1876 1877 1878 1879 1880
## 381452.0 389755.3 378476.2 383273.4 388011.4 386161.3 381650.9 390125.4
## 1881 1882 1883 1884 1885 1886 1887 1888
## 382901.6 381733.1 381969.1 382413.8 380595.3 388526.1 388436.6 716259.6
## 1889 1890 1891 1892 1893 1894 1895 1896
## 718690.9 708538.7 707035.7 390880.5 379973.4 724555.9 711050.6 681722.7
## 1897 1898 1899 1900 1901 1902 1903 1904
## 728191.0 704913.7 389432.4 362140.8 383866.6 388973.5 382827.0 390671.7
## 1905 1906 1907 1908 1909 1910 1911 1912
## 389101.1 388580.5 391040.6 389228.6 387906.6 387742.9 387127.4 379822.1
## 1913 1914 1915 1916 1917 1918 1919 1920
## 375943.3 391338.3 391512.8 384005.2 389279.7 389653.9 384974.2 390666.2
## 1921 1922 1923 1924 1925 1926 1927 1928
## 389913.4 389644.1 389866.5 388367.5 388206.7 387992.2 392845.1 385609.7
## 1929 1930 1931 1932 1933 1934 1935 1936
## 387803.5 388773.3 390892.7 392699.4 720149.0 674422.0 722005.0 731499.0
## 1937 1938 1939 1940 1941 1942 1943 1944
## 722960.2 388375.2 357260.9 388137.2 392591.9 385410.8 389202.9 384235.0
## 1945 1946 1947 1948 1949 1950 1951 1952
## 392754.9 389266.5 393909.1 390432.4 379224.4 389984.0 387472.5 386893.4
## 1953 1954 1955 1956 1957 1958 1959 1960
## 385397.7 383940.8 380974.7 383354.4 384324.2 385889.6 384409.3 391137.4
## 1961 1962 1963 1964 1965 1966 1967 1968
## 386017.2 383146.0 389319.6 388794.6 389764.4 383316.1 385738.2 386182.9
## 1969 1970 1971 1972 1973 1974 1975 1976
## 390398.1 389513.4 388165.0 381716.7 386215.7 382729.0 392507.8 404627.7
## 1977 1978 1979 1980 1981 1982 1983 1984
## 388401.2 393231.0 394664.4 391329.6 391749.8 391414.6 390292.3 383617.9
## 1985 1986 1987 1988 1989 1990 1991 1992
## 386417.4 716751.6 741618.8 721520.0 755354.2 692330.2 726780.3 392972.1
## 1993 1994 1995 1996 1997 1998 1999 2000
## 386723.0 388491.4 393593.5 396549.0 726975.5 731126.3 728666.2 768594.0
## 2001 2002 2003 2004 2005 2006 2007 2008
## 733131.6 397395.3 384663.2 385424.1 395095.4 378020.7 389470.7 391656.4
## 2009 2010 2011 2012 2013 2014 2015 2016
## 386432.4 388790.7 727464.1 724994.4 724212.4 726468.0 753984.2 726109.9
## 2017 2018 2019 2020 2021 2022 2023 2024
## 725915.1 731467.8 723045.5 733436.8 728045.2 745758.6 730826.0 725513.6
## 2025 2026 2027 2028 2029 2030 2031 2032
## 748326.9 380810.0 385442.0 347149.6 382449.5 720748.4 723119.9 722739.9
## 2033 2034 2035 2036 2037 2038 2039 2040
## 742549.1 384557.9 383260.8 394800.9 741341.4 376741.7 395428.5 339646.6
## 2041 2042 2043 2044 2045 2046 2047 2048
## 676037.3 688013.3 393587.1 385074.0 390491.4 721817.4 690050.9 691010.9
## 2049 2050 2051 2052 2053
## 385138.4 376153.0 376780.1 384445.2 715728.9residuals(fit1)## 1 2 3 4 5
## -7.080265e+04 -1.837823e+05 -6.872965e+04 4.898835e+04 -1.511084e+05
## 6 7 8 9 10
## -1.651778e+05 -3.172410e+04 4.597407e+04 4.351248e+04 6.868642e+04
## 11 12 13 14 15
## 4.717018e+04 8.870841e+04 2.659889e+04 -1.406678e+05 4.322639e+04
## 16 17 18 19 20
## 6.410324e+04 4.356690e+04 9.617581e+04 5.209503e+04 5.344340e+04
## 21 22 23 24 25
## 5.126994e+04 1.286712e+05 6.144089e+04 -8.527361e+04 5.306705e+04
## 26 27 28 29 30
## -2.115557e+05 5.086726e+04 -9.067367e+04 -1.018645e+05 4.941621e+04
## 31 32 33 34 35
## 4.691557e+04 5.063852e+04 -2.206923e+05 4.619044e+04 4.322025e+04
## 36 37 38 39 40
## -8.941545e+04 -1.406526e+05 1.076670e+05 7.478305e+04 -1.533592e+04
## 41 42 43 44 45
## 5.669106e+04 -9.094950e+04 6.564862e+04 4.254717e+04 -4.210503e+04
## 46 47 48 49 50
## -1.283347e+05 5.779817e+04 6.108818e+04 3.845990e+04 -1.869390e+05
## 51 52 53 54 55
## -1.485299e+05 -1.972129e+05 1.385746e+05 4.445612e+04 -1.337372e+04
## 56 57 58 59 60
## 9.613192e+04 1.270016e+04 -1.946237e+05 8.922104e+04 -1.003543e+05
## 61 62 63 64 65
## 9.231811e+04 4.277959e+04 7.820937e+04 -9.370171e+04 5.668352e+04
## 66 67 68 69 70
## 5.044066e+04 -1.035963e+05 5.197514e+04 1.388085e+05 8.404635e+04
## 71 72 73 74 75
## -1.000051e+05 2.332772e+04 -1.567074e+05 6.228427e+04 1.254889e+04
## 76 77 78 79 80
## -2.157079e+05 5.955777e+04 -2.549314e+04 -1.883504e+05 5.281153e+04
## 81 82 83 84 85
## 9.035368e+03 5.174659e+04 7.254986e+04 3.343088e+04 -3.951111e+04
## 86 87 88 89 90
## -7.989897e+04 5.408293e+02 4.804560e+04 -1.990736e+05 -6.094713e+04
## 91 92 93 94 95
## 1.713112e+04 -1.021422e+05 6.112017e+04 -1.529284e+05 -4.887937e+04
## 96 97 98 99 100
## 6.229681e+04 -1.922914e+05 -6.018381e+04 6.429584e+04 6.147152e+04
## 101 102 103 104 105
## 6.639327e+04 -1.008310e+05 -6.511121e+03 6.222727e+04 -1.671609e+05
## 106 107 108 109 110
## -3.789605e+04 -1.903855e+05 -1.520181e+05 -1.202487e+05 1.241108e+05
## 111 112 113 114 115
## 5.266590e+04 6.963578e+04 9.934250e+04 -1.751783e+05 7.398499e+04
## 116 117 118 119 120
## 6.628063e+04 1.324419e+05 5.941608e+04 -1.505448e+05 -1.152357e+05
## 121 122 123 124 125
## 7.128818e+04 2.217733e+04 -7.208498e+04 -8.497316e+04 -1.609575e+05
## 126 127 128 129 130
## 5.364779e+04 1.184833e+05 6.465706e+04 2.309195e+04 6.898600e+04
## 131 132 133 134 135
## 8.005514e+04 7.547461e+04 7.719772e+04 2.160050e-10 -8.322322e+04
## 136 137 138 139 140
## -5.266426e+04 1.760175e+04 7.700262e+04 6.911855e+04 6.475400e+04
## 141 142 143 144 145
## -9.219195e+04 7.241160e+04 1.643991e+04 -1.581207e+05 1.154094e+05
## 146 147 148 149 150
## 1.642184e+05 -1.519442e+05 5.215224e+04 -1.757684e+05 -4.082610e+04
## 151 152 153 154 155
## 1.286942e+05 8.466265e+04 -1.490814e+05 -8.320973e+04 7.335652e+04
## 156 157 158 159 160
## -7.934461e+04 1.729288e+04 -1.339753e+05 8.105498e+04 3.378228e+04
## 161 162 163 164 165
## 6.927800e+04 -7.907581e+04 9.010255e+04 5.235566e+04 -1.087489e+05
## 166 167 168 169 170
## -5.144450e+04 3.304954e+04 6.968854e+04 1.043526e+05 1.716285e+05
## 171 172 173 174 175
## 7.595648e+04 -4.221257e+04 -1.998843e+04 7.740875e+04 1.305952e+05
## 176 177 178 179 180
## 7.541497e+04 3.779041e+04 7.898659e+04 9.365676e+04 8.419862e+04
## 181 182 183 184 185
## -1.343288e+05 -1.764164e+04 -1.395140e+05 1.586205e+04 1.302013e+05
## 186 187 188 189 190
## 6.594016e+04 6.216836e+04 -1.106106e+05 7.159684e+04 -9.600402e+04
## 191 192 193 194 195
## -5.189807e+04 5.043472e+04 -1.092196e+05 2.676702e+04 7.031612e+04
## 196 197 198 199 200
## 7.764842e+04 -1.285938e+05 2.041798e+04 -6.566110e+04 7.323887e+04
## 201 202 203 204 205
## -1.531486e+05 5.553256e+04 -1.648492e+05 8.328399e+04 7.207016e+04
## 206 207 208 209 210
## -1.329697e+05 2.696936e+04 -7.947455e+04 5.590813e+04 6.287923e+04
## 211 212 213 214 215
## 7.102412e+04 7.260799e+04 7.256546e+04 1.004369e+05 -1.228695e+05
## 216 217 218 219 220
## -1.734082e+05 -1.350893e+05 -9.007493e+04 -2.281086e+04 7.948374e+04
## 221 222 223 224 225
## 7.175832e+04 7.314367e+04 7.839801e+04 8.335458e+04 -1.837295e+05
## 226 227 228 229 230
## -3.154678e+04 4.691237e+04 8.265849e+04 7.388626e+04 7.376441e+04
## 231 232 233 234 235
## 1.371309e+05 6.277779e+04 5.851906e+04 -1.762815e+05 6.841930e+04
## 236 237 238 239 240
## 8.154569e+04 1.364205e+05 -1.202019e+05 3.195381e+04 6.839279e+04
## 241 242 243 244 245
## 6.400921e+04 5.039299e+04 -1.302089e+05 1.397632e+04 7.343801e+04
## 246 247 248 249 250
## 8.411099e+04 -1.022445e+05 -3.803557e+04 8.072755e+04 -1.922329e+05
## 251 252 253 254 255
## -1.260404e+05 -1.004736e+05 1.694501e+04 8.238618e+04 1.255786e+05
## 256 257 258 259 260
## 3.757579e+04 7.283572e+04 1.018314e+05 8.107269e+04 9.403632e+04
## 261 262 263 264 265
## -1.551244e+05 -1.403945e+05 -1.251178e+05 7.610006e+04 7.472887e+04
## 266 267 268 269 270
## 1.020326e+05 9.950799e+04 7.539659e+04 7.316787e+04 1.522385e+05
## 271 272 273 274 275
## 7.111689e+04 6.200383e+04 6.168797e+04 -1.762455e+05 -1.280969e+05
## 276 277 278 279 280
## -6.938988e+04 -2.799285e+04 7.782808e+04 7.820791e+04 9.060508e+04
## 281 282 283 284 285
## -1.350949e+05 4.418366e+04 8.706399e+04 -1.354965e+05 -4.575199e+04
## 286 287 288 289 290
## 2.837338e+04 7.618465e+04 7.166084e+04 9.364278e+04 1.615552e+05
## 291 292 293 294 295
## 5.142814e+04 8.050609e+04 7.207164e+04 1.116627e+05 -1.172399e+05
## 296 297 298 299 300
## -3.128472e+04 5.871616e+04 3.416081e+04 7.379809e+04 -1.156192e+05
## 301 302 303 304 305
## -8.397417e+04 -2.875086e+04 7.232033e+04 7.366870e+04 7.362618e+04
## 306 307 308 309 310
## 7.298804e+04 8.168756e+04 -1.677398e+05 7.918403e+04 7.063812e+04
## 311 312 313 314 315
## 5.816350e+04 6.008730e+04 -1.910121e+05 -1.871455e+05 -1.886311e+05
## 316 317 318 319 320
## -1.065581e+05 -2.182177e+04 -2.155013e+04 7.015071e+04 7.441286e+04
## 321 322 323 324 325
## 7.483397e+04 7.757324e+04 7.786238e+04 7.331549e+04 7.373660e+04
## 326 327 328 329 330
## 7.047754e+04 1.206117e+05 6.985872e+04 1.486020e+05 9.221507e+04
## 331 332 333 334 335
## -1.465098e+05 -1.588172e+04 7.839806e+04 -1.046397e+05 4.522531e+04
## 336 337 338 339 340
## 8.864926e+04 1.044125e+05 -1.835035e+05 -5.493044e+04 4.050667e+03
## 341 342 343 344 345
## 8.217491e+04 -6.178054e+04 5.166416e+04 6.081176e+04 1.115496e+05
## 346 347 348 349 350
## 5.411574e+04 9.465376e+04 5.238812e+04 -8.284098e+04 -2.442777e+04
## 351 352 353 354 355
## 4.577682e+04 8.283205e+04 6.926949e+04 9.211704e+04 -2.558281e+04
## 356 357 358 359 360
## 5.331696e+04 6.856773e+04 4.741412e+04 -1.501678e+05 -5.740514e+04
## 361 362 363 364 365
## -7.638129e+04 3.109399e+04 1.029737e+04 5.201265e+04 7.549425e+04
## 366 367 368 369 370
## 7.226482e+04 9.311811e+04 7.899719e+04 8.639377e+04 1.092867e+05
## 371 372 373 374 375
## 1.259004e+05 1.388271e+05 8.767744e+04 -1.817550e+05 -1.614772e+05
## 376 377 378 379 380
## -1.646203e+05 -1.273058e+05 -1.092978e+05 -9.582216e+04 4.978636e+04
## 381 382 383 384 385
## 8.639336e+04 1.644622e+05 6.524717e+04 -4.579920e+04 8.535456e+04
## 386 387 388 389 390
## -1.687641e+05 -1.595387e+05 -4.679835e+04 -1.942393e+02 7.771078e+04
## 391 392 393 394 395
## 1.345414e+05 1.506926e+05 4.793272e+04 1.052952e+05 -1.600276e+05
## 396 397 398 399 400
## -1.576691e+05 1.015145e+03 4.370594e+03 7.711039e+04 7.217379e+04
## 401 402 403 404 405
## 7.062004e+04 1.740707e+05 -5.142042e+04 4.907116e+04 5.746163e+04
## 406 407 408 409 410
## -1.533386e+05 -8.464946e+04 -4.497555e+04 4.155370e+04 7.535930e+04
## 411 412 413 414 415
## 7.776691e+04 8.038852e+04 6.040664e+04 -1.659366e+05 -1.498781e+05
## 416 417 418 419 420
## -3.722478e+04 7.115740e+03 -3.029102e+04 -9.162459e+03 3.443782e+04
## 421 422 423 424 425
## 1.324862e+05 7.349176e+04 1.586853e+05 3.113347e+04 -2.119503e+04
## 426 427 428 429 430
## -5.764630e+04 -1.787645e+05 -1.940479e+05 -1.576186e+05 -7.454975e+04
## 431 432 433 434 435
## -4.645265e+04 3.266766e+04 5.091187e+04 7.824707e+04 7.472326e+04
## 436 437 438 439 440
## 6.968464e+04 1.352301e+05 6.945389e+04 3.454226e+04 -1.998786e+05
## 441 442 443 444 445
## -1.589271e+05 -9.520393e+04 3.193264e+04 3.113326e+04 8.656004e+04
## 446 447 448 449 450
## 1.364881e+05 7.303014e+04 -5.626693e+04 7.736367e+04 5.178091e+04
## 451 452 453 454 455
## 7.686436e+04 9.362217e+04 -1.625578e+05 -1.731367e+05 -1.305872e+05
## 456 457 458 459 460
## -1.341095e+05 -6.823470e+04 -7.677975e+04 -6.162862e+04 5.566766e+03
## 461 462 463 464 465
## 7.002122e+04 9.644095e+04 1.175817e+05 -1.785497e+05 -1.209863e+05
## 466 467 468 469 470
## 6.198003e+04 6.145236e+04 2.775389e+04 6.578955e+04 4.468202e+04
## 471 472 473 474 475
## 8.090773e+04 -1.420238e+05 -1.403578e+05 -2.891261e+04 -3.020829e+04
## 476 477 478 479 480
## 6.536182e+04 -1.284854e+05 1.201905e+04 6.317776e+04 -1.541625e+05
## 481 482 483 484 485
## -1.196822e+05 -1.039050e+05 -4.269066e+04 -7.404007e+04 -4.554361e+04
## 486 487 488 489 490
## -4.176718e+04 1.734428e+04 7.297411e+04 9.359888e+04 8.951884e+04
## 491 492 493 494 495
## 1.109086e+05 1.523112e+05 -2.411513e+04 5.544505e+04 6.030273e+04
## 496 497 498 499 500
## 5.987611e+04 8.428732e+04 -1.795956e+05 -1.925244e+05 -1.363267e+05
## 501 502 503 504 505
## -7.300732e+04 -1.082453e+05 -9.483701e+04 -4.147424e+03 7.580963e+04
## 506 507 508 509 510
## 7.115126e+04 6.637005e+04 7.665943e+04 7.578464e+04 -5.899235e+04
## 511 512 513 514 515
## 1.097014e+04 6.507211e+04 5.104070e+04 7.003297e+04 -1.668271e+05
## 516 517 518 519 520
## -1.781220e+05 -1.344853e+05 -8.845365e+04 -3.506538e+04 3.347109e+04
## 521 522 523 524 525
## 6.642705e+04 7.518912e+04 7.492463e+04 9.891274e+04 1.585746e+05
## 526 527 528 529 530
## -1.454724e+05 -8.806828e+04 5.484888e+04 5.747936e+04 7.902417e+04
## 531 532 533 534 535
## -1.777362e+05 -1.676288e+05 -1.119509e+05 -5.534599e+04 -4.446511e+04
## 536 537 538 539 540
## -3.890278e+03 4.042188e+04 4.664752e+04 7.216304e+04 7.569761e+04
## 541 542 543 544 545
## 7.110793e+04 6.865806e+04 -1.001570e+05 -9.807264e+04 -5.090339e+04
## 546 547 548 549 550
## 1.369139e+05 7.145019e+04 5.514682e+04 4.818458e+04 5.664118e+04
## 551 552 553 554 555
## -1.607022e+05 -4.537353e+04 -1.803015e+04 1.157733e+04 4.068901e+04
## 556 557 558 559 560
## 7.024048e+04 7.410299e+04 8.420444e+04 -1.581959e+05 -6.271310e+03
## 561 562 563 564 565
## 6.625192e+04 8.493092e+04 6.484648e+04 -1.659320e+05 -1.517531e+05
## 566 567 568 569 570
## -1.085967e+05 -5.859029e+04 2.258361e+04 2.054468e+04 5.362572e+04
## 571 572 573 574 575
## 7.689680e+04 7.870881e+04 7.751670e+04 1.251731e+05 7.520382e+04
## 576 577 578 579 580
## 7.204784e+04 6.760993e+04 1.209783e+05 1.357640e+05 -1.093042e+05
## 581 582 583 584 585
## -7.715020e+04 6.000864e+04 9.737641e+04 3.459685e+04 8.904127e+04
## 586 587 588 589 590
## 5.379783e+04 -1.998819e+05 -1.204218e+05 -1.191904e+05 -1.170230e+05
## 591 592 593 594 595
## -5.758514e+04 3.429571e+04 4.792022e+04 8.278118e+04 6.950489e+04
## 596 597 598 599 600
## 1.056452e+05 1.750514e+05 -1.579813e+05 -1.388021e+05 -7.591514e+04
## 601 602 603 604 605
## -1.099631e+03 5.736618e+04 6.459454e+04 -2.102013e+05 -1.953516e+05
## 606 607 608 609 610
## -1.571380e+05 -1.552206e+05 -1.493911e+05 -1.238971e+05 -8.046267e+04
## 611 612 613 614 615
## -2.414680e+04 9.193608e+03 -3.149926e+04 -3.683083e+03 6.116574e+04
## 616 617 618 619 620
## 7.032017e+04 6.790831e+04 7.117148e+04 6.956808e+04 7.719855e+04
## 621 622 623 624 625
## 7.298332e+04 7.015899e+04 7.289827e+04 6.716017e+04 9.386898e+04
## 626 627 628 629 630
## 1.032157e+05 -1.600808e+05 1.505803e+04 -3.536090e+04 2.044551e+04
## 631 632 633 634 635
## 4.381802e+04 6.874568e+04 6.211970e+04 7.955067e+04 5.387416e+04
## 636 637 638 639 640
## 6.499801e+04 6.064448e+04 -2.000765e+05 -1.937329e+05 -1.732184e+05
## 641 642 643 644 645
## -1.752288e+05 -1.485664e+05 -1.203527e+05 -1.109884e+05 -6.919459e+04
## 646 647 648 649 650
## -5.885372e+04 -2.240022e+04 -3.795851e+04 1.863842e+04 4.474214e+04
## 651 652 653 654 655
## 7.346377e+04 7.252754e+04 7.554184e+04 6.591806e+04 7.296201e+04
## 656 657 658 659 660
## 7.801945e+04 6.347232e+04 1.013325e+05 -1.902349e+05 -9.087333e+04
## 661 662 663 664 665
## -3.633169e+04 4.695488e+04 6.089040e+04 5.314260e+04 1.016560e+05
## 666 667 668 669 670
## -5.927110e+04 -2.045470e+04 -1.819456e+05 -1.315193e+05 -8.505575e+04
## 671 672 673 674 675
## -1.181620e+05 -7.847962e+04 -2.349853e+04 4.808928e+04 6.533510e+04
## 676 677 678 679 680
## 7.282332e+04 7.066921e+04 7.062669e+04 7.333772e+04 7.981431e+04
## 681 682 683 684 685
## 8.403745e+04 7.462929e+04 6.948679e+04 7.037153e+04 6.806995e+04
## 686 687 688 689 690
## -1.500511e+05 -1.305714e+05 -9.029157e+04 -7.370367e+04 4.369712e+04
## 691 692 693 694 695
## 4.883741e+04 1.047947e+05 -1.891757e+05 -1.647432e+05 -1.448764e+05
## 696 697 698 699 700
## -1.244553e+05 -4.336044e+04 1.618821e+04 6.592628e+04 6.635903e+04
## 701 702 703 704 705
## 7.153680e+04 6.763301e+04 7.583905e+04 6.942271e+04 6.613475e+04
## 706 707 708 709 710
## 6.715147e+04 7.125085e+04 7.073407e+04 6.890733e+04 6.645593e+04
## 711 712 713 714 715
## 1.560465e+05 -1.767596e+05 -4.219276e+04 6.358545e+03 6.050058e+04
## 716 717 718 719 720
## 6.853018e+04 3.319075e+03 4.614035e+04 7.579978e+04 -1.754070e+05
## 721 722 723 724 725
## -1.374120e+05 -1.386286e+05 -1.071852e+05 -1.153804e+05 -3.584873e+04
## 726 727 728 729 730
## -2.969411e+04 -1.691551e+03 2.271209e+04 5.075907e+04 6.718151e+04
## 731 732 733 734 735
## 6.890380e+04 6.932490e+04 8.922908e+04 6.692168e+04 7.770208e+04
## 736 737 738 739 740
## 6.730027e+04 6.949103e+04 6.291054e+04 1.201443e+05 -1.817186e+05
## 741 742 743 744 745
## -1.360813e+05 -8.609637e+04 -4.089463e+04 4.577119e+04 7.530786e+04
## 746 747 748 749 750
## 5.354787e+04 4.572086e+04 6.077757e+04 4.669128e+04 4.912500e+04
## 751 752 753 754 755
## 1.014006e+05 7.363350e+04 6.775004e+04 6.461572e+04 -1.941286e+05
## 756 757 758 759 760
## -1.526272e+05 -1.341189e+05 -8.550526e+04 -5.514724e+04 -3.615050e+04
## 761 762 763 764 765
## -2.811099e+04 3.660845e+04 6.884304e+04 6.797353e+04 6.777937e+04
## 766 767 768 769 770
## 7.613522e+04 7.808910e+04 7.855156e+04 7.909802e+04 6.656957e+04
## 771 772 773 774 775
## 6.788541e+04 6.335286e+04 6.455201e+04 9.328562e+04 1.774418e+05
## 776 777 778 779 780
## 1.884829e+05 -1.573453e+05 -4.480798e+04 2.551377e+04 4.467624e+04
## 781 782 783 784 785
## 5.855651e+04 5.090750e+04 -1.174594e+05 -1.176375e+05 -1.149616e+05
## 786 787 788 789 790
## -6.305274e+04 -1.444784e+04 7.180805e+04 6.533570e+04 6.493924e+04
## 791 792 793 794 795
## 6.350581e+04 6.485419e+04 7.059314e+04 6.675564e+04 6.810402e+04
## 796 797 798 799 800
## 6.620696e+04 6.644375e+04 6.852445e+04 1.563249e+05 1.229820e+05
## 801 802 803 804 805
## -1.274551e+05 -9.126625e+04 -6.212864e+04 4.678360e+04 3.168622e+04
## 806 807 808 809 810
## 5.658628e+04 8.060734e+04 3.435937e+04 5.166653e+04 9.325046e+04
## 811 812 813 814 815
## -1.586235e+05 -1.592273e+05 -9.751746e+04 -6.610669e+04 -2.614940e+04
## 816 817 818 819 820
## 6.694009e+04 7.886324e+04 6.192765e+04 6.572617e+04 6.369714e+04
## 821 822 823 824 825
## 6.228853e+04 7.069856e+04 6.707531e+04 6.681374e+04 6.457847e+04
## 826 827 828 829 830
## 6.635575e+04 6.631869e+04 6.395253e+04 7.596448e+04 6.327188e+04
## 831 832 833 834 835
## 6.879295e+04 7.142835e+04 6.592610e+04 6.230612e+04 6.422339e+04
## 836 837 838 839 840
## 7.010319e+04 6.458297e+04 6.386767e+04 6.626655e+04 6.436949e+04
## 841 842 843 844 845
## 6.683047e+04 6.335717e+04 6.609644e+04 6.175798e+04 9.341225e+04
## 846 847 848 849 850
## 1.273667e+05 -1.350985e+05 2.480615e+04 6.991847e+04 6.435775e+04
## 851 852 853 854 855
## 5.832123e+04 -1.416019e+05 -1.673125e+05 -1.382514e+05 -8.078469e+04
## 856 857 858 859 860
## -1.782414e+04 9.935243e+04 4.550443e+04 6.615022e+04 6.447991e+04
## 861 862 863 864 865
## 7.463732e+04 6.578576e+04 7.290652e+04 6.232330e+04 7.257607e+04
## 866 867 868 869 870
## 1.025521e+05 1.541190e+05 -1.875314e+05 -9.177967e+04 -6.537199e+04
## 871 872 873 874 875
## -8.666445e+04 -7.688240e+04 -4.449379e+04 4.256020e+04 7.484639e+04
## 876 877 878 879 880
## 5.891861e+04 4.385776e+04 8.718120e+04 5.102430e+04 4.930085e+04
## 881 882 883 884 885
## -2.008315e+05 -1.839042e+05 -1.634915e+05 -7.236304e+04 6.121900e+04
## 886 887 888 889 890
## 6.526245e+04 6.311053e+04 9.226354e+04 -1.296010e+05 -1.462053e+05
## 891 892 893 894 895
## -9.511426e+04 3.231803e+04 5.927222e+04 -8.114075e+04 -4.162275e+04
## 896 897 898 899 900
## 6.356973e+04 7.891702e+04 -2.038389e+05 -1.790842e+05 -1.803391e+05
## 901 902 903 904 905
## -1.098522e+05 -1.172508e+05 -1.193814e+05 -1.032969e+05 -4.543816e+04
## 906 907 908 909 910
## -4.821740e+04 4.066671e+04 4.727074e+04 7.743764e+04 5.997082e+04
## 911 912 913 914 915
## 5.654608e+04 6.147591e+04 1.005981e+05 1.474607e+05 -1.583145e+05
## 916 917 918 919 920
## 1.003371e+05 7.146025e+04 -3.460877e+04 -1.939239e+05 -1.426780e+05
## 921 922 923 924 925
## -1.811436e+05 -1.455648e+05 -1.325054e+05 -7.667143e+04 -4.102987e+04
## 926 927 928 929 930
## -6.786446e+04 1.733977e+04 -4.311035e+03 6.124700e+04 6.484956e+04
## 931 932 933 934 935
## 6.202523e+04 6.290997e+04 6.459000e+04 7.057471e+04 6.314761e+04
## 936 937 938 939 940
## 6.923073e+04 6.269734e+04 6.404571e+04 6.261229e+04 6.965144e+04
## 941 942 943 944 945
## 5.868619e+04 8.561413e+04 1.247572e+05 1.179504e+05 -1.185704e+05
## 946 947 948 949 950
## -1.581801e+05 -9.421757e+04 -2.059282e+04 4.236431e+04 2.496127e+04
## 951 952 953 954 955
## 2.140393e+04 5.768989e+04 7.643694e+04 5.874076e+04 9.607084e+04
## 956 957 958 959 960
## -2.049316e+05 -2.054315e+05 -1.889757e+05 -1.839778e+05 -1.849154e+05
## 961 962 963 964 965
## -1.462966e+05 -1.294035e+05 -1.207976e+05 -3.923694e+04 -9.280630e+04
## 966 967 968 969 970
## -4.793591e+04 -1.889988e+04 -3.987822e+04 -1.739852e+04 1.109457e+03
## 971 972 973 974 975
## 1.368952e+04 6.155118e+04 6.177924e+04 6.182997e+04 6.422849e+04
## 976 977 978 979 980
## 6.478157e+04 7.122991e+04 7.165102e+04 6.048129e+04 6.414783e+04
## 981 982 983 984 985
## 6.876028e+04 6.735342e+04 6.796037e+04 6.168402e+04 1.097270e+05
## 986 987 988 989 990
## -1.427216e+05 -6.869413e+04 -3.544704e+04 -2.056621e+04 6.183215e+04
## 991 992 993 994 995
## 2.730706e+04 5.525729e+04 4.096683e+04 -1.917126e+05 -1.943836e+05
## 996 997 998 999 1000
## -1.445794e+05 -1.029893e+05 -1.105266e+05 -4.574983e+04 -6.537669e+04
## 1001 1002 1003 1004 1005
## -3.615379e+04 -4.250412e+04 4.849764e+04 3.869260e+04 7.174307e+04
## 1006 1007 1008 1009 1010
## 6.136281e+04 1.014744e+05 1.021379e+05 -1.766729e+05 -1.380409e+05
## 1011 1012 1013 1014 1015
## -4.582746e+04 -5.376089e+04 -4.129058e+03 6.865280e+04 3.687305e+04
## 1016 1017 1018 1019 1020
## 5.035920e+04 7.617799e+04 -2.172169e+05 -1.983192e+05 -1.928495e+05
## 1021 1022 1023 1024 1025
## -1.728806e+05 -1.661862e+05 -1.537673e+05 -1.307246e+05 -8.158538e+04
## 1026 1027 1028 1029 1030
## -5.876840e+04 -4.373610e+04 -2.034668e+04 1.784208e+04 6.254586e+04
## 1031 1032 1033 1034 1035
## 6.019182e+04 6.521234e+04 9.845083e+04 -1.937705e+05 -1.215867e+05
## 1036 1037 1038 1039 1040
## -1.033471e+05 -1.183801e+05 -3.595494e+04 -1.908894e+04 4.389134e+04
## 1041 1042 1043 1044 1045
## 5.885542e+04 2.430785e+04 6.152910e+04 4.381329e+04 4.016748e+04
## 1046 1047 1048 1049 1050
## 5.958719e+03 -1.923325e+05 -1.851902e+05 -1.528083e+05 -1.290897e+05
## 1051 1052 1053 1054 1055
## -4.949782e+04 -3.954499e+04 1.246804e+04 5.488209e+04 4.840853e+04
## 1056 1057 1058 1059 1060
## 7.028955e+04 6.076777e+04 6.357175e+04 5.751190e+04 5.515120e+04
## 1061 1062 1063 1064 1065
## 6.009195e+04 -1.055999e+05 -8.413983e+04 4.433545e+04 3.541810e+04
## 1066 1067 1068 1069 1070
## 5.395034e+04 3.638785e+04 4.705773e+04 8.746807e+04 -2.079357e+05
## 1071 1072 1073 1074 1075
## -1.761557e+05 -1.626108e+05 -9.916001e+04 -7.807685e+04 -4.228109e+04
## 1076 1077 1078 1079 1080
## 2.113056e+04 7.009585e+04 2.011657e+05 -3.780194e+04 2.651923e+04
## 1081 1082 1083 1084 1085
## 6.911859e+04 8.859044e+03 2.752810e+04 6.366753e+04 5.048060e+04
## 1086 1087 1088 1089 1090
## 4.640052e+04 5.459236e+04 -1.981265e+05 -1.601701e+05 -7.669737e+04
## 1091 1092 1093 1094 1095
## -9.281530e+04 -6.815488e+04 -3.416138e+04 -5.456668e+04 -2.098450e+04
## 1096 1097 1098 1099 1100
## 5.095040e+04 5.272996e+04 6.046673e+04 9.093732e+04 1.089026e+05
## 1101 1102 1103 1104 1105
## -1.579097e+05 -1.363580e+05 -1.050256e+05 8.857036e+04 6.440902e+04
## 1106 1107 1108 1109 1110
## 1.015590e+05 6.775214e+04 5.206495e+04 -2.157451e+05 -1.791609e+05
## 1111 1112 1113 1114 1115
## -1.095216e+05 -1.054793e+05 -9.921908e+04 -1.796707e+04 -4.070768e+04
## 1116 1117 1118 1119 1120
## 1.520429e+04 3.178245e+04 6.470705e+04 5.704787e+04 6.479849e+04
## 1121 1122 1123 1124 1125
## -1.706255e+05 -1.420983e+05 -1.196289e+05 -9.819342e+04 -2.959091e+04
## 1126 1127 1128 1129 1130
## 9.113321e+04 4.662224e+04 5.457088e+04 4.630780e+04 5.433912e+04
## 1131 1132 1133 1134 1135
## -1.855351e+05 -1.279847e+05 -1.279031e+05 -6.950893e+04 -6.133964e+04
## 1136 1137 1138 1139 1140
## -1.372079e+04 4.516831e+04 3.778533e+04 6.166266e+04 6.546117e+04
## 1141 1142 1143 1144 1145
## 6.006419e+04 1.011683e+05 -1.959730e+05 -1.572923e+05 -7.800821e+04
## 1146 1147 1148 1149 1150
## -8.272127e+04 -7.617267e+04 1.492660e+04 -6.197851e+02 5.302380e+04
## 1151 1152 1153 1154 1155
## -1.126318e+04 5.808710e+04 7.202604e+04 3.814750e+04 -2.097521e+05
## 1156 1157 1158 1159 1160
## -1.745106e+05 -1.750079e+05 -1.298744e+05 -1.107614e+05 -4.492931e+04
## 1161 1162 1163 1164 1165
## 1.754256e+04 3.331048e+04 4.582594e+04 8.093404e+04 6.339146e+04
## 1166 1167 1168 1169 1170
## 5.915723e+04 6.575293e+04 -1.749869e+05 -1.459479e+05 -6.444810e+04
## 1171 1172 1173 1174 1175
## -6.396408e+04 -3.807790e+04 1.662901e+04 -7.575558e+03 2.168377e+04
## 1176 1177 1178 1179 1180
## 4.132593e+04 4.405865e+04 -1.730644e+05 -9.191721e+04 -8.750883e+04
## 1181 1182 1183 1184 1185
## -6.282959e+04 3.327795e+04 3.957289e+04 1.053373e+05 6.482144e+04
## 1186 1187 1188 1189 1190
## 5.617575e+04 6.575970e+04 1.295099e+05 -1.281279e+05 -1.537797e+04
## 1191 1192 1193 1194 1195
## 3.780005e+04 2.068184e+04 3.399159e+04 9.987232e+04 2.271824e+04
## 1196 1197 1198 1199 1200
## -1.498199e+05 -1.521694e+05 -1.811373e+05 -1.372818e+05 -1.575530e+05
## 1201 1202 1203 1204 1205
## -1.287864e+05 -7.477485e+04 -4.102333e+04 -7.959728e+04 -6.492285e+04
## 1206 1207 1208 1209 1210
## -4.195827e+02 -4.401008e+04 -3.347624e+04 5.077674e+04 5.271711e+04
## 1211 1212 1213 1214 1215
## 5.870181e+04 6.236836e+04 1.069598e+05 5.599131e+04 5.558459e+04
## 1216 1217 1218 1219 1220
## 8.254737e+04 1.355451e+05 -1.475981e+05 5.964894e+04 5.359012e+04
## 1221 1222 1223 1224 1225
## 6.062766e+04 7.848268e+04 -1.546394e+05 4.863539e+04 4.277444e+04
## 1226 1227 1228 1229 1230
## -9.666829e+04 -1.336994e+05 -8.267483e+04 -2.497933e+04 6.287614e+04
## 1231 1232 1233 1234 1235
## 5.858992e+04 1.128733e+05 -3.042799e+04 5.970357e+04 4.855040e+04
## 1236 1237 1238 1239 1240
## 5.075007e+04 6.192999e+04 6.933572e+04 3.901012e+04 8.550459e+04
## 1241 1242 1243 1244 1245
## 4.675665e+04 4.369415e+04 -1.717936e+05 -7.671322e+04 -5.062904e+04
## 1246 1247 1248 1249 1250
## -1.316727e+04 -9.822769e+03 -6.892468e+02 3.042907e+04 9.167035e+04
## 1251 1252 1253 1254 1255
## 5.335906e+04 5.895067e+04 5.494766e+04 6.007511e+04 5.435310e+04
## 1256 1257 1258 1259 1260
## 9.430384e+04 -1.667090e+05 -1.118964e+05 -8.878259e+04 -3.600054e+04
## 1261 1262 1263 1264 1265
## 9.180094e+02 4.425214e+04 3.089941e+04 4.563527e+04 -2.313660e+04
## 1266 1267 1268 1269 1270
## 7.545612e+04 1.032897e+05 5.851154e+02 1.323621e+04 4.577830e+04
## 1271 1272 1273 1274 1275
## 5.975759e+04 -1.958742e+05 -1.549964e+05 -9.197533e+04 -7.855139e+04
## 1276 1277 1278 1279 1280
## -2.548894e+04 -6.021793e+03 7.196113e+04 5.452017e+04 7.766654e+04
## 1281 1282 1283 1284 1285
## 6.189999e+04 6.765588e+04 1.106830e+05 -1.818645e+05 -1.478803e+05
## 1286 1287 1288 1289 1290
## -1.411415e+05 -7.937768e+04 -1.613776e+04 5.133482e+04 -5.515175e+04
## 1291 1292 1293 1294 1295
## 4.670636e+04 4.024099e+04 7.986255e+04 5.102812e+04 4.002309e+04
## 1296 1297 1298 1299 1300
## -1.884117e+05 -1.743706e+05 -1.249768e+05 -7.633966e+04 -4.853814e+04
## 1301 1302 1303 1304 1305
## 4.355393e+04 -4.489846e+04 -3.202138e+04 2.110172e+04 5.118701e+04
## 1306 1307 1308 1309 1310
## 5.142824e+04 1.130040e+05 -2.018553e+05 3.629408e+04 3.708710e+04
## 1311 1312 1313 1314 1315
## 4.052307e+04 3.815025e+04 4.170528e+04 4.909211e+04 -2.197221e+05
## 1316 1317 1318 1319 1320
## -1.877302e+05 -1.724103e+05 -1.660444e+05 -1.558574e+05 -1.419010e+05
## 1321 1322 1323 1324 1325
## -1.222199e+05 -7.793872e+04 -8.441964e+04 -7.125883e+04 -2.343508e+04
## 1326 1327 1328 1329 1330
## 3.549821e+04 4.245953e+04 5.402663e+04 5.862044e+04 4.917327e+04
## 1331 1332 1333 1334 1335
## 5.436268e+04 6.043329e+04 5.646382e+04 5.840781e+04 5.645186e+04
## 1336 1337 1338 1339 1340
## 5.634345e+04 5.225299e+04 6.522867e+04 5.355884e+04 5.722538e+04
## 1341 1342 1343 1344 1345
## 5.579196e+04 8.730676e+04 1.041077e+05 -1.718162e+05 -1.164867e+05
## 1346 1347 1348 1349 1350
## -5.972559e+04 4.340000e+03 4.111647e+04 4.884383e+04 3.467810e+04
## 1351 1352 1353 1354 1355
## 4.966836e+04 2.344622e+04 2.154447e+04 -3.799645e+04 2.488240e+04
## 1356 1357 1358 1359 1360
## -2.145762e+05 -2.045637e+05 -1.079996e+05 -7.114599e+04 -5.318255e+04
## 1361 1362 1363 1364 1365
## 5.464205e+02 5.020519e+04 5.245892e+04 5.345663e+04 5.190510e+04
## 1366 1367 1368 1369 1370
## 5.768755e+04 5.420584e+04 5.805484e+04 5.626268e+04 8.743050e+04
## 1371 1372 1373 1374 1375
## 1.412698e+05 -1.070999e+05 7.737891e+04 4.648567e+03 3.911911e+04
## 1376 1377 1378 1379 1380
## 2.585543e+04 3.167124e+04 -9.227677e+03 5.185934e+04 -2.137453e+05
## 1381 1382 1383 1384 1385
## -1.650863e+05 -3.083872e+04 -1.223312e+05 -1.100074e+05 -7.241279e+04
## 1386 1387 1388 1389 1390
## -8.699513e+04 -6.760602e+04 -3.417562e+04 -3.887605e+04 -3.228397e+04
## 1391 1392 1393 1394 1395
## 2.222885e+04 -2.361024e+03 2.512439e+04 7.288327e+04 4.833096e+04
## 1396 1397 1398 1399 1400
## 4.967934e+04 6.614898e+04 6.117522e+04 5.789716e+04 5.788677e+04
## 1401 1402 1403 1404 1405
## 5.469865e+04 5.550841e+04 5.819069e+04 5.212093e+04 5.360128e+04
## 1406 1407 1408 1409 1410
## 5.481768e+04 5.293263e+04 5.227327e+04 7.597777e+04 1.015371e+05
## 1411 1412 1413 1414 1415
## 1.180242e+05 -1.828093e+05 -1.530081e+05 -8.443452e+04 2.137647e+04
## 1416 1417 1418 1419 1420
## 1.573290e+04 3.152369e+04 1.516909e+04 2.984875e+04 -4.217482e+03
## 1421 1422 1423 1424 1425
## 4.864549e+04 4.040048e+04 2.664742e+04 3.167418e+04 3.747547e+04
## 1426 1427 1428 1429 1430
## -2.021543e+05 -1.542249e+05 -1.281069e+05 -5.165423e+04 -4.298340e+04
## 1431 1432 1433 1434 1435
## 2.413723e+04 4.866330e+04 5.220837e+04 5.533084e+04 5.273313e+04
## 1436 1437 1438 1439 1440
## 5.602571e+04 5.620162e+04 5.884789e+04 5.543450e+04 5.261018e+04
## 1441 1442 1443 1444 1445
## 9.790107e+04 1.240670e+05 -1.968648e+05 -1.293105e+05 -4.754418e+04
## 1446 1447 1448 1449 1450
## 8.326051e+04 4.055741e+04 1.666941e+04 5.832833e+04 4.342375e+04
## 1451 1452 1453 1454 1455
## -2.150459e+05 -1.375315e+05 -9.704370e+04 -2.337025e+04 -7.114313e+03
## 1456 1457 1458 1459 1460
## -3.737728e+03 3.151389e+04 4.863295e+04 5.786309e+04 5.550240e+04
## 1461 1462 1463 1464 1465
## 4.796676e+04 4.647634e+04 5.954752e+04 5.394140e+04 5.885183e+04
## 1466 1467 1468 1469 1470
## 5.731056e+04 5.195928e+04 4.913496e+04 5.112684e+04 4.814710e+04
## 1471 1472 1473 1474 1475
## 4.980267e+04 4.942849e+04 5.998358e+04 1.041289e+05 1.492045e+05
## 1476 1477 1478 1479 1480
## -1.504544e+05 -3.600788e+04 3.571374e+03 2.450335e+04 4.113310e+04
## 1481 1482 1483 1484 1485
## 6.675677e+04 6.664905e+04 4.302421e+04 1.702820e+04 2.443508e+04
## 1486 1487 1488 1489 1490
## 7.939357e+04 -2.092297e+05 -1.671951e+05 -1.571440e+05 -1.390001e+05
## 1491 1492 1493 1494 1495
## -1.079323e+05 -8.298936e+04 -5.592201e+04 1.111059e+04 4.584486e+04
## 1496 1497 1498 1499 1500
## 5.116772e+04 5.989623e+04 7.176139e+04 9.992994e+04 -1.828187e+05
## 1501 1502 1503 1504 1505
## -1.130616e+05 -9.420803e+04 -1.760577e+04 -9.249123e+02 3.054623e+04
## 1506 1507 1508 1509 1510
## 3.857479e+04 3.587946e+04 3.697525e+04 4.432993e+04 -1.592603e+05
## 1511 1512 1513 1514 1515
## -2.176898e+05 -4.208593e+04 -5.551907e+04 -3.906269e+04 6.552671e+04
## 1516 1517 1518 1519 1520
## 4.511311e+04 4.972184e+04 4.508950e+04 5.120618e+04 5.115595e+04
## 1521 1522 1523 1524 1525
## 5.019387e+04 4.711469e+04 4.918155e+04 5.132521e+04 4.686423e+04
## 1526 1527 1528 1529 1530
## 4.849192e+04 5.490670e+04 5.611902e+04 4.935305e+04 5.452055e+04
## 1531 1532 1533 1534 1535
## 5.023224e+04 5.575331e+04 4.445161e+04 4.805671e+04 4.483019e+04
## 1536 1537 1538 1539 1540
## 5.001961e+04 5.124510e+04 4.947092e+04 4.938560e+04 5.083923e+04
## 1541 1542 1543 1544 1545
## 5.202631e+04 5.105730e+04 4.833103e+04 4.537472e+04 4.685507e+04
## 1546 1547 1548 1549 1550
## 4.443549e+04 4.571078e+04 5.715413e+04 -1.990147e+05 -7.541202e+04
## 1551 1552 1553 1554 1555
## -6.799890e+04 3.052082e+04 8.310353e+04 3.576754e+04 6.740562e+04
## 1556 1557 1558 1559 1560
## -1.933093e+05 -1.558279e+05 -1.291732e+05 -7.920907e+04 -2.881954e+04
## 1561 1562 1563 1564 1565
## -5.875669e+04 -3.417326e+03 2.418010e+04 4.161409e+04 5.230678e+04
## 1566 1567 1568 1569 1570
## 4.831387e+04 5.058951e+04 6.264153e+04 5.077093e+04 4.953467e+04
## 1571 1572 1573 1574 1575
## 5.691028e+04 5.501322e+04 5.716598e+04 5.029183e+04 4.640826e+04
## 1576 1577 1578 1579 1580
## 5.716128e+04 4.957774e+04 5.058536e+04 4.590650e+04 5.218328e+04
## 1581 1582 1583 1584 1585
## 6.776115e+04 9.004639e+04 8.861846e+04 1.174703e+05 1.027674e+05
## 1586 1587 1588 1589 1590
## 1.031100e+05 -1.531730e+05 -1.675732e+05 -1.223390e+05 -6.987174e+04
## 1591 1592 1593 1594 1595
## -3.287431e+04 2.798695e+04 9.666473e+03 2.141072e+04 5.313344e+02
## 1596 1597 1598 1599 1600
## 1.252831e+05 2.955177e+04 3.555369e+04 4.440035e+04 3.079095e+04
## 1601 1602 1603 1604 1605
## 4.520090e+04 2.422886e+04 -1.921259e+05 -8.675044e+04 -3.739298e+04
## 1606 1607 1608 1609 1610
## -6.059044e+02 4.306125e+04 4.730113e+04 5.147258e+04 5.038828e+04
## 1611 1612 1613 1614 1615
## 1.013357e+05 -1.396050e+05 6.371253e+04 1.338263e+04 7.635346e+04
## 1616 1617 1618 1619 1620
## -1.827120e+05 -2.150194e+05 -1.432724e+05 -8.260519e+04 -7.465382e+04
## 1621 1622 1623 1624 1625
## -5.238804e+04 -4.143572e+04 -2.911055e+04 -2.184305e+04 -1.136494e+04
## 1626 1627 1628 1629 1630
## -3.965887e+03 2.128232e+04 5.455365e+04 5.881579e+04 5.399307e+04
## 1631 1632 1633 1634 1635
## 6.557970e+04 1.031152e+05 -2.085471e+05 -1.530766e+05 -1.759002e+05
## 1636 1637 1638 1639 1640
## -1.555350e+05 -9.521339e+04 -1.030399e+04 -2.199150e+04 -9.322245e+03
## 1641 1642 1643 1644 1645
## 3.787712e+04 8.376718e+04 2.241768e+04 1.745222e+04 1.600083e+04
## 1646 1647 1648 1649 1650
## 3.159171e+04 2.435872e+04 3.100643e+04 2.969938e+04 2.922359e+04
## 1651 1652 1653 1654 1655
## 2.445158e+04 3.124356e+04 3.459499e+04 -2.040761e+05 -1.453980e+05
## 1656 1657 1658 1659 1660
## -1.064263e+05 -8.013680e+04 8.739045e+03 1.908489e+04 4.488109e+04
## 1661 1662 1663 1664 1665
## 4.795820e+04 4.572330e+04 4.421781e+04 4.345461e+04 5.059284e+04
## 1666 1667 1668 1669 1670
## 4.389754e+04 4.128935e+04 4.642897e+04 4.728015e+04 4.491946e+04
## 1671 1672 1673 1674 1675
## 4.793805e+04 5.558133e+04 5.058362e+04 4.554465e+04 4.174770e+04
## 1676 1677 1678 1679 1680
## 5.022790e+04 5.129252e+04 5.818674e+04 4.957525e+04 5.237597e+04
## 1681 1682 1683 1684 1685
## 4.930588e+04 4.394551e+04 4.098921e+04 4.700202e+04 4.225589e+04
## 1686 1687 1688 1689 1690
## 4.178890e+04 4.280562e+04 5.382988e+04 4.642963e+04 4.314167e+04
## 1691 1692 1693 1694 1695
## 4.496218e+04 4.583842e+04 4.255046e+04 4.204430e+04 3.317732e+04
## 1696 1697 1698 1699 1700
## 6.195935e+04 -3.678913e+03 1.695998e+04 -2.120785e+05 -1.724858e+05
## 1701 1702 1703 1704 1705
## -1.533308e+05 -8.529991e+04 -1.260002e+05 -8.333921e+04 -6.394708e+04
## 1706 1707 1708 1709 1710
## -4.985262e+04 -3.961817e+03 6.682549e+03 2.345096e+04 3.975145e+04
## 1711 1712 1713 1714 1715
## 4.285528e+04 4.442597e+04 5.135694e+04 4.526818e+04 4.382485e+04
## 1716 1717 1718 1719 1720
## 4.703767e+04 1.646828e+03 4.741625e+04 4.134649e+04 4.607227e+04
## 1721 1722 1723 1724 1725
## 4.979581e+04 4.830538e+04 4.228625e+04 4.914760e+04 4.493237e+04
## 1726 1727 1728 1729 1730
## 4.614877e+04 5.275923e+04 4.295026e+04 4.741209e+04 4.139933e+04
## 1731 1732 1733 1734 1735
## 4.977718e+04 4.311181e+04 5.061940e+04 4.950773e+04 4.901147e+04
## 1736 1737 1738 1739 1740
## 4.353732e+04 4.383227e+04 4.480175e+04 4.602295e+04 1.137935e+05
## 1741 1742 1743 1744 1745
## -1.844391e+05 -8.334167e+04 3.628065e+02 1.559228e+04 6.335612e+04
## 1746 1747 1748 1749 1750
## 3.899312e+04 3.417776e+04 2.847187e+04 1.822162e+04 2.045040e+04
## 1751 1752 1753 1754 1755
## 3.974474e+04 2.263730e+04 3.043417e+04 -2.330785e+05 -2.208819e+05
## 1756 1757 1758 1759 1760
## -1.881422e+05 -1.053569e+05 -5.867218e+04 -8.400589e+03 3.995835e+04
## 1761 1762 1763 1764 1765
## 4.386504e+04 4.868233e+04 4.373872e+04 4.346841e+04 5.462173e+04
## 1766 1767 1768 1769 1770
## 4.461338e+04 4.968982e+04 4.403834e+04 3.911198e+04 4.414926e+04
## 1771 1772 1773 1774 1775
## 4.593455e+04 4.343096e+04 3.831737e+04 4.102774e+04 4.247111e+04
## 1776 1777 1778 1779 1780
## 4.418812e+04 3.996978e+04 5.095660e+04 -2.009934e+05 -1.517196e+05
## 1781 1782 1783 1784 1785
## -7.252620e+04 -2.931335e+04 2.882116e+04 3.509112e+04 2.910632e+04
## 1786 1787 1788 1789 1790
## 4.317267e+04 1.194845e+04 6.931871e+04 1.378672e+04 -2.242282e+05
## 1791 1792 1793 1794 1795
## -1.787705e+05 -3.084952e+04 1.438885e+04 3.891907e+04 5.255027e+04
## 1796 1797 1798 1799 1800
## 4.555747e+04 5.537725e+04 4.931346e+04 4.092553e+04 -1.416138e+05
## 1801 1802 1803 1804 1805
## -1.053586e+05 2.735615e+04 2.473624e+04 -1.635171e+05 -2.390614e+04
## 1806 1807 1808 1809 1810
## 4.245309e+04 4.391117e+04 4.011284e+04 4.470665e+04 4.175035e+04
## 1811 1812 1813 1814 1815
## 4.925793e+04 4.162577e+04 3.889797e+04 4.031361e+04 1.021131e+05
## 1816 1817 1818 1819 1820
## -2.082051e+05 -2.748861e+04 -2.518150e+03 -2.118309e+04 3.542834e+04
## 1821 1822 1823 1824 1825
## 2.259216e+04 -1.574515e+05 -1.378395e+05 -6.425312e+03 4.708219e+04
## 1826 1827 1828 1829 1830
## 4.772645e+04 4.697454e+04 4.671413e+04 4.519229e+04 7.116002e+04
## 1831 1832 1833 1834 1835
## -2.136059e+05 -1.421109e+05 -1.197903e+04 -2.422894e+04 1.954450e+04
## 1836 1837 1838 1839 1840
## -2.023015e+05 -1.678807e+05 -8.903441e+04 -5.331778e+04 1.676469e+04
## 1841 1842 1843 1844 1845
## 3.958123e+04 3.780704e+04 4.104351e+04 3.864926e+04 4.324307e+04
## 1846 1847 1848 1849 1850
## 3.902784e+04 4.259050e+04 4.303385e+04 4.650839e+04 4.669962e+04
## 1851 1852 1853 1854 1855
## 4.623334e+04 4.322470e+04 4.090645e+04 3.915126e+04 4.549231e+04
## 1856 1857 1858 1859 1860
## 4.277528e+04 3.809642e+04 3.851753e+04 3.695213e+04 3.949940e+04
## 1861 1862 1863 1864 1865
## 4.441718e+04 3.697516e+04 3.969580e+04 4.079841e+04 3.914711e+04
## 1866 1867 1868 1869 1870
## -2.051144e+05 1.887226e+04 2.412352e+04 2.668302e+04 6.445548e+04
## 1871 1872 1873 1874 1875
## 2.047020e+04 -1.377522e+05 -1.274520e+05 -6.875530e+04 -4.147622e+04
## 1876 1877 1878 1879 1880
## -3.273356e+03 4.098864e+04 4.283865e+04 4.734911e+04 3.887456e+04
## 1881 1882 1883 1884 1885
## 4.609838e+04 4.726688e+04 4.703094e+04 4.658622e+04 4.840475e+04
## 1886 1887 1888 1889 1890
## 4.047393e+04 4.056338e+04 -6.425955e+04 -1.069086e+04 4.146133e+04
## 1891 1892 1893 1894 1895
## 4.296431e+04 -2.208805e+05 -6.197341e+04 -1.365559e+05 -2.000506e+05
## 1896 1897 1898 1899 1900
## -3.572273e+04 2.180900e+04 4.508627e+04 -2.364324e+05 -1.161408e+05
## 1901 1902 1903 1904 1905
## -4.086662e+04 4.002653e+04 4.617299e+04 3.832826e+04 3.989895e+04
## 1906 1907 1908 1909 1910
## 4.041949e+04 3.795936e+04 3.977137e+04 4.109339e+04 4.125709e+04
## 1911 1912 1913 1914 1915
## 4.187264e+04 4.917793e+04 5.305667e+04 3.766168e+04 3.748718e+04
## 1916 1917 1918 1919 1920
## 4.499476e+04 3.972029e+04 3.934611e+04 4.402582e+04 3.833379e+04
## 1921 1922 1923 1924 1925
## 3.908656e+04 3.935588e+04 3.913348e+04 4.063247e+04 4.079326e+04
## 1926 1927 1928 1929 1930
## 4.100778e+04 3.615486e+04 4.339034e+04 4.119649e+04 4.022670e+04
## 1931 1932 1933 1934 1935
## 3.810732e+04 3.630060e+04 -2.111490e+05 -2.042204e+04 -2.100504e+04
## 1936 1937 1938 1939 1940
## 1.850096e+04 2.703981e+04 -2.243752e+05 -1.872609e+05 -1.791372e+05
## 1941 1942 1943 1944 1945
## -1.555919e+05 -7.841079e+04 -2.020292e+04 4.476498e+04 3.624507e+04
## 1946 1947 1948 1949 1950
## 3.973348e+04 3.509088e+04 3.856764e+04 4.977556e+04 3.901603e+04
## 1951 1952 1953 1954 1955
## 4.152753e+04 4.210660e+04 4.360232e+04 4.505923e+04 4.802526e+04
## 1956 1957 1958 1959 1960
## 4.564556e+04 4.467577e+04 4.311037e+04 4.459072e+04 3.786256e+04
## 1961 1962 1963 1964 1965
## 4.298279e+04 4.585404e+04 3.968040e+04 4.020539e+04 3.923559e+04
## 1966 1967 1968 1969 1970
## 4.568394e+04 4.326180e+04 4.281708e+04 3.860186e+04 3.948660e+04
## 1971 1972 1973 1974 1975
## 4.083497e+04 4.728331e+04 4.278433e+04 4.627100e+04 3.649217e+04
## 1976 1977 1978 1979 1980
## 2.437233e+04 4.059882e+04 3.576898e+04 3.433555e+04 3.767044e+04
## 1981 1982 1983 1984 1985
## 3.725018e+04 3.758538e+04 5.670773e+04 7.638210e+04 1.095826e+05
## 1986 1987 1988 1989 1990
## -8.075156e+04 8.381202e+03 2.847996e+04 -5.354218e+03 5.766983e+04
## 1991 1992 1993 1994 1995
## 2.321970e+04 -1.609721e+05 -8.872299e+04 1.650857e+04 5.440646e+04
## 1996 1997 1998 1999 2000
## 8.545097e+04 -1.279755e+05 -1.101263e+05 -7.566620e+04 -1.859403e+04
## 2001 2002 2003 2004 2005
## 1.686839e+04 -5.439526e+04 -1.626632e+05 -9.642406e+04 -7.609540e+04
## 2006 2007 2008 2009 2010
## -1.902070e+04 -1.147074e+04 1.634362e+04 7.056757e+04 8.520932e+04
## 2011 2012 2013 2014 2015
## -1.264641e+05 -5.499436e+04 -3.821244e+04 2.353202e+04 -3.984230e+03
## 2016 2017 2018 2019 2020
## 2.389012e+04 2.408490e+04 1.853224e+04 2.695450e+04 1.656318e+04
## 2021 2022 2023 2024 2025
## 2.195482e+04 4.241381e+03 1.917401e+04 2.448639e+04 1.673104e+03
## 2026 2027 2028 2029 2030
## -1.198100e+05 -5.844199e+04 8.085041e+04 4.655049e+04 -1.417484e+05
## 2031 2032 2033 2034 2035
## -7.411987e+04 2.726009e+04 7.450912e+03 4.444213e+04 4.573919e+04
## 2036 2037 2038 2039 2040
## 6.219906e+04 8.658552e+03 5.225834e+04 3.357151e+04 -1.686466e+05
## 2041 2042 2043 2044 2045
## -7.103731e+04 6.198666e+04 2.441293e+04 -1.450740e+05 3.850860e+04
## 2046 2047 2048 2049 2050
## -1.018174e+05 -5.405090e+04 5.898910e+04 4.386161e+04 5.284699e+04
## 2051 2052 2053
## -3.378014e+04 4.455478e+04 3.427109e+04We could create a linear regression model and find that the DV is most dependent on V2, V5, V8, V9, V10 and V14 and V15.
To better understand the characteristics of the regression model, we can generate its plots -
plot(fit1)
Understanding the flaws and moving to new dataset
We realise that since one field V2 is missing in the test dataset, and from out chi-square and t-tests, the DV values are strong affected by V2, so our data is incomplete and will not prove to be efficient in terms of prediction.
So, we move on to the analysis and understanding of the new datasets - Training dataset and Validation Dataset.
Understanding the dataset 2
We have been provided with 2 sets of data - training data with 16 columns from V1 to V16 which are independent and a dependent variable Target of 2053 records, as well as test data with 16 columns and the dependent variable Target, it contains columns V1-V16. First step is to read the data into R. The dataset is related to loan approved and we must predict the loan value for the next customer.
The validation dataset contains values of Target also, to check accuracy of our model.
setwd("/Volumes/Untitled/My Money Mantra/week 1")train <- read.csv('D1 - Training Dataset.csv')
test <- read.csv('D2 - Validation Dataset.csv')Summarise the data 2
Summarize the dataset Create summary statistics (e.g. mean, standard deviation, median, mode) for the important variables in the dataset using summary() and describe().
summary(train)## Sno Target V1 V2
## Min. : 1 Min. :147000 Min. :721.0 Min. :25.00
## 1st Qu.: 514 1st Qu.:359000 1st Qu.:827.0 1st Qu.:34.00
## Median :1027 Median :429000 Median :846.0 Median :38.00
## Mean :1027 Mean :469864 Mean :841.1 Mean :39.47
## 3rd Qu.:1540 3rd Qu.:632000 3rd Qu.:865.0 3rd Qu.:45.00
## Max. :2053 Max. :750000 Max. :900.0 Max. :55.00
## V3 V4 V5 V6
## Min. :0.0000 Min. : 0 Min. :0.000 Min. : 0
## 1st Qu.:0.0000 1st Qu.: 0 1st Qu.:0.000 1st Qu.: 0
## Median :0.0000 Median : 0 Median :0.000 Median : 0
## Mean :0.4715 Mean : 1437942 Mean :0.227 Mean : 540338
## 3rd Qu.:1.0000 3rd Qu.: 2200000 3rd Qu.:0.000 3rd Qu.: 0
## Max. :4.0000 Max. :65903173 Max. :5.000 Max. :65903173
## V7 V8 V9 V10
## Min. :0.0000 Min. : 0 Min. :0.0000 Min. : 0
## 1st Qu.:0.0000 1st Qu.: 0 1st Qu.:0.0000 1st Qu.: 0
## Median :0.0000 Median : 0 Median :0.0000 Median : 0
## Mean :0.1778 Mean : 70623 Mean :0.2372 Mean : 183748
## 3rd Qu.:0.0000 3rd Qu.: 0 3rd Qu.:0.0000 3rd Qu.: 0
## Max. :4.0000 Max. :3530000 Max. :3.0000 Max. :37000000
## V11 V12 V13
## Min. :0.000000 Min. : 0 Min. :0.00000
## 1st Qu.:0.000000 1st Qu.: 0 1st Qu.:0.00000
## Median :0.000000 Median : 0 Median :0.00000
## Mean :0.004384 Mean : 106259 Mean :0.00341
## 3rd Qu.:0.000000 3rd Qu.: 0 3rd Qu.:0.00000
## Max. :2.000000 Max. :212300000 Max. :3.00000
## V14 V15 V16
## Min. : 0 Min. : 0.000 Min. : 0
## 1st Qu.: 0 1st Qu.: 1.000 1st Qu.: 0
## Median : 0 Median : 1.000 Median : 0
## Mean : 2319 Mean : 1.451 Mean : 67874
## 3rd Qu.: 0 3rd Qu.: 2.000 3rd Qu.: 100000
## Max. :1400000 Max. :15.000 Max. :1133261library(psych)
describe(train)## vars n mean sd median trimmed mad min
## Sno 1 2053 1027.00 592.79 1027 1027.00 760.57 1
## Target 2 2053 469863.61 183152.97 429000 471171.03 169016.40 147000
## V1 3 2053 841.08 32.13 846 845.01 28.17 721
## V2 4 2053 39.47 7.21 38 39.01 7.41 25
## V3 5 2053 0.47 0.68 0 0.35 0.00 0
## V4 6 2053 1437942.14 3286544.02 0 809927.18 0.00 0
## V5 7 2053 0.23 0.55 0 0.10 0.00 0
## V6 8 2053 540338.13 2410844.36 0 101522.75 0.00 0
## V7 9 2053 0.18 0.44 0 0.07 0.00 0
## V8 10 2053 70622.70 260862.51 0 5733.93 0.00 0
## V9 11 2053 0.24 0.51 0 0.13 0.00 0
## V10 12 2053 183747.80 970668.58 0 48248.35 0.00 0
## V11 13 2053 0.00 0.08 0 0.00 0.00 0
## V12 14 2053 106259.13 4685898.74 0 0.00 0.00 0
## V13 15 2053 0.00 0.08 0 0.00 0.00 0
## V14 16 2053 2318.56 50634.20 0 0.00 0.00 0
## V15 17 2053 1.45 0.78 1 1.44 1.48 0
## V16 18 2053 67874.32 118923.12 0 41381.40 0.00 0
## max range skew kurtosis se
## Sno 2053 2052 0.00 -1.20 13.08
## Target 750000 603000 0.24 -0.93 4042.22
## V1 900 179 -1.21 1.62 0.71
## V2 55 30 0.48 -0.76 0.16
## V3 4 4 1.49 2.51 0.01
## V4 65903173 65903173 7.78 104.94 72534.56
## V5 5 5 3.14 13.50 0.01
## V6 65903173 65903173 15.17 335.81 53207.73
## V7 4 4 2.82 9.61 0.01
## V8 3530000 3530000 6.27 53.31 5757.28
## V9 3 3 2.24 5.00 0.01
## V10 37000000 37000000 27.85 1013.96 21422.81
## V11 2 2 20.21 444.30 0.00
## V12 212300000 212300000 45.23 2045.19 103418.55
## V13 3 3 29.90 1027.23 0.00
## V14 1400000 1400000 22.99 542.50 1117.51
## V15 15 15 3.33 48.07 0.02
## V16 1133261 1133261 3.15 14.17 2624.65summary(test)## Sno Target V1 V2
## Min. : 1.0 Min. :147000 Min. :720.0 Min. :25.00
## 1st Qu.: 513.8 1st Qu.:359000 1st Qu.:826.0 1st Qu.:34.00
## Median :1026.5 Median :429000 Median :846.0 Median :38.00
## Mean :1026.5 Mean :469872 Mean :840.8 Mean :39.64
## 3rd Qu.:1539.2 3rd Qu.:631750 3rd Qu.:865.0 3rd Qu.:45.00
## Max. :2052.0 Max. :750000 Max. :898.0 Max. :55.00
## V3 V4 V5 V6
## Min. :0.0000 Min. : 0 Min. :0.0000 Min. : 0
## 1st Qu.:0.0000 1st Qu.: 0 1st Qu.:0.0000 1st Qu.: 0
## Median :0.0000 Median : 0 Median :0.0000 Median : 0
## Mean :0.4669 Mean : 1384357 Mean :0.2271 Mean : 488915
## 3rd Qu.:1.0000 3rd Qu.: 2000000 3rd Qu.:0.0000 3rd Qu.: 0
## Max. :7.0000 Max. :49495493 Max. :5.0000 Max. :30200000
## V7 V8 V9 V10
## Min. :0.0000 Min. : 0 Min. :0.0000 Min. : 0
## 1st Qu.:0.0000 1st Qu.: 0 1st Qu.:0.0000 1st Qu.: 0
## Median :0.0000 Median : 0 Median :0.0000 Median : 0
## Mean :0.1842 Mean : 68918 Mean :0.2485 Mean : 152218
## 3rd Qu.:0.0000 3rd Qu.: 0 3rd Qu.:0.0000 3rd Qu.: 0
## Max. :4.0000 Max. :3280000 Max. :3.0000 Max. :4750000
## V11 V12 V13 V14
## Min. :0.000000 Min. : 0 Min. :0.000000 Min. : 0
## 1st Qu.:0.000000 1st Qu.: 0 1st Qu.:0.000000 1st Qu.: 0
## Median :0.000000 Median : 0 Median :0.000000 Median : 0
## Mean :0.004873 Mean : 6429 Mean :0.002437 Mean : 1462
## 3rd Qu.:0.000000 3rd Qu.: 0 3rd Qu.:0.000000 3rd Qu.: 0
## Max. :4.000000 Max. :5560000 Max. :3.000000 Max. :2000000
## V15 V16
## Min. : 0.000 Min. : 0
## 1st Qu.: 1.000 1st Qu.: 0
## Median : 1.000 Median : 0
## Mean : 1.429 Mean : 70734
## 3rd Qu.: 2.000 3rd Qu.: 100250
## Max. :10.000 Max. :1095000describe(test)## vars n mean sd median trimmed mad min
## Sno 1 2052 1026.50 592.51 1026.5 1026.50 760.57 1
## Target 2 2052 469871.83 183075.55 429000.0 471159.56 169016.40 147000
## V1 3 2052 840.84 31.77 846.0 844.66 28.17 720
## V2 4 2052 39.64 7.17 38.0 39.24 7.41 25
## V3 5 2052 0.47 0.70 0.0 0.34 0.00 0
## V4 6 2052 1384356.67 2966890.18 0.0 750438.05 0.00 0
## V5 7 2052 0.23 0.58 0.0 0.09 0.00 0
## V6 8 2052 488915.05 1668707.79 0.0 97470.86 0.00 0
## V7 9 2052 0.18 0.47 0.0 0.07 0.00 0
## V8 10 2052 68918.06 244940.05 0.0 5823.19 0.00 0
## V9 11 2052 0.25 0.54 0.0 0.13 0.00 0
## V10 12 2052 152217.92 410112.31 0.0 51238.92 0.00 0
## V11 13 2052 0.00 0.10 0.0 0.00 0.00 0
## V12 14 2052 6428.56 168876.55 0.0 0.00 0.00 0
## V13 15 2052 0.00 0.08 0.0 0.00 0.00 0
## V14 16 2052 1461.99 49352.78 0.0 0.00 0.00 0
## V15 17 2052 1.43 0.74 1.0 1.42 0.00 0
## V16 18 2052 70733.52 121828.98 0.0 43620.97 0.00 0
## max range skew kurtosis se
## Sno 2052 2051 0.00 -1.20 13.08
## Target 750000 603000 0.24 -0.93 4041.49
## V1 898 178 -1.16 1.40 0.70
## V2 55 30 0.42 -0.84 0.16
## V3 7 7 1.93 7.05 0.02
## V4 49495493 49495493 5.76 60.36 65495.70
## V5 5 5 3.30 14.10 0.01
## V6 30200000 30200000 7.52 88.14 36837.62
## V7 4 4 2.84 9.34 0.01
## V8 3280000 3280000 5.95 49.77 5407.18
## V9 3 3 2.37 5.98 0.01
## V10 4750000 4750000 4.56 29.02 9053.45
## V11 4 4 30.67 1105.85 0.00
## V12 5560000 5560000 30.28 942.53 3728.04
## V13 3 3 33.76 1171.70 0.00
## V14 2000000 2000000 36.40 1389.13 1089.49
## V15 10 10 1.57 12.72 0.02
## V16 1095000 1095000 3.01 12.93 2689.44Looking at the dependent variable in new dataset
We can now study the dependent variable in the training dataset and try to understand some of its properties, so that we can figure out what the data is trying to hint at.
summary(train$Target)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 147000 359000 429000 469864 632000 750000Generating some plots for new dataset
The next step into data analysis is to generate some plots and find out relations between the fields. Since we are concerned with the dependent variable and we do know that the rest of the variables are independent, we can compare Target with V1-V16.
hist(train$Target, breaks=10,col="yellow",xlab="Target", main="Target")
plot(train$Target,main="Target")
boxplot(train$Target, horizontal =TRUE, main="Boxplot of Target" ,col="lightblue")
We can now generate some scatterplots to understand how the variables are co-related pair wise.
library(car)
scatterplot(train$Target ~ train$V1,
spread=FALSE, smoother.args=list(lty=2),
main="Scatter plot of Target vs V1",
xlab="Target",
ylab="V1")
scatterplot(train$Target ~ train$V3,
spread=FALSE, smoother.args=list(lty=2),
main="Scatter plot of Target vs V3",
xlab="Target",
ylab="V3")
scatterplot(train$Target ~ train$V4,
spread=FALSE, smoother.args=list(lty=2),
main="Scatter plot of Target vs V4",
xlab="Target",
ylab="V4")
scatterplot(train$Target ~ train$V8,
spread=FALSE, smoother.args=list(lty=2),
main="Scatter plot of Target vs V8",
xlab="Target",
ylab="V8")
scatterplot(train$Target ~ train$V12,
spread=FALSE, smoother.args=list(lty=2),
main="Scatter plot of Target vs V12",
xlab="Target",
ylab="V12")
Each graph varies and there does not seem to be a common correlation between the TARGET and the other independent variables.
We now generate a scatterplot matrix to see the relations with all the fields.
scatterplotMatrix(train, spread=FALSE, smoother.args=list(lty=2), main="Scatter Plot Matrix")
CORRGRAM (new dataset)
The next step is to draw a corrgram and create a variance-covariance matrix for the fields.
library(corrgram)
corr.test(train)## Call:corr.test(x = train)
## Correlation matrix
## Sno Target V1 V2 V3 V4 V5 V6 V7 V8 V9
## Sno 1.00 0.96 0.03 0.06 0.35 0.38 0.30 0.23 -0.04 0.08 0.08
## Target 0.96 1.00 0.02 0.08 0.39 0.42 0.33 0.25 -0.03 0.10 0.10
## V1 0.03 0.02 1.00 0.01 0.03 0.00 -0.04 0.00 -0.18 -0.16 -0.23
## V2 0.06 0.08 0.01 1.00 0.01 0.05 0.10 0.07 -0.09 -0.05 0.14
## V3 0.35 0.39 0.03 0.01 1.00 0.57 0.19 0.09 -0.01 -0.06 -0.02
## V4 0.38 0.42 0.00 0.05 0.57 1.00 0.26 0.55 -0.06 -0.05 0.03
## V5 0.30 0.33 -0.04 0.10 0.19 0.26 1.00 0.51 -0.02 -0.02 0.04
## V6 0.23 0.25 0.00 0.07 0.09 0.55 0.51 1.00 -0.04 -0.03 0.05
## V7 -0.04 -0.03 -0.18 -0.09 -0.01 -0.06 -0.02 -0.04 1.00 0.72 -0.02
## V8 0.08 0.10 -0.16 -0.05 -0.06 -0.05 -0.02 -0.03 0.72 1.00 -0.01
## V9 0.08 0.10 -0.23 0.14 -0.02 0.03 0.04 0.05 -0.02 -0.01 1.00
## V10 0.10 0.12 -0.13 0.10 -0.02 0.03 0.02 0.06 -0.03 -0.02 0.45
## V11 -0.03 -0.03 -0.10 0.06 0.07 0.04 0.04 0.02 0.02 0.04 0.02
## V12 -0.01 -0.01 0.02 0.04 -0.01 -0.01 -0.01 0.00 -0.01 -0.01 -0.01
## V13 -0.01 -0.02 -0.10 0.06 0.04 0.07 0.05 0.02 0.05 0.09 0.05
## V14 0.00 -0.01 -0.09 0.06 0.02 0.06 0.02 0.01 0.04 0.06 0.04
## V15 -0.02 -0.02 -0.16 -0.03 -0.06 0.00 0.04 0.02 0.14 0.13 -0.02
## V16 0.05 0.07 -0.08 0.09 0.00 0.04 0.11 0.10 0.02 0.03 0.03
## V10 V11 V12 V13 V14 V15 V16
## Sno 0.10 -0.03 -0.01 -0.01 0.00 -0.02 0.05
## Target 0.12 -0.03 -0.01 -0.02 -0.01 -0.02 0.07
## V1 -0.13 -0.10 0.02 -0.10 -0.09 -0.16 -0.08
## V2 0.10 0.06 0.04 0.06 0.06 -0.03 0.09
## V3 -0.02 0.07 -0.01 0.04 0.02 -0.06 0.00
## V4 0.03 0.04 -0.01 0.07 0.06 0.00 0.04
## V5 0.02 0.04 -0.01 0.05 0.02 0.04 0.11
## V6 0.06 0.02 0.00 0.02 0.01 0.02 0.10
## V7 -0.03 0.02 -0.01 0.05 0.04 0.14 0.02
## V8 -0.02 0.04 -0.01 0.09 0.06 0.13 0.03
## V9 0.45 0.02 -0.01 0.05 0.04 -0.02 0.03
## V10 1.00 0.04 0.00 0.08 0.07 0.01 0.02
## V11 0.04 1.00 0.29 0.54 0.39 0.19 0.06
## V12 0.00 0.29 1.00 0.01 0.01 -0.01 -0.01
## V13 0.08 0.54 0.01 1.00 0.85 0.37 0.11
## V14 0.07 0.39 0.01 0.85 1.00 0.22 0.07
## V15 0.01 0.19 -0.01 0.37 0.22 1.00 0.30
## V16 0.02 0.06 -0.01 0.11 0.07 0.30 1.00
## Sample Size
## [1] 2053
## Probability values (Entries above the diagonal are adjusted for multiple tests.)
## Sno Target V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11
## Sno 0.00 0.00 1.00 0.89 0.00 0.00 0.00 0.00 1.00 0.04 0.05 0.00 1.00
## Target 0.00 0.00 1.00 0.03 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 1.00
## V1 0.14 0.27 0.00 1.00 1.00 1.00 1.00 1.00 0.00 0.00 0.00 0.00 0.00
## V2 0.01 0.00 0.61 0.00 1.00 1.00 0.00 0.18 0.01 1.00 0.00 0.00 0.57
## V3 0.00 0.00 0.14 0.65 0.00 0.00 0.00 0.00 1.00 0.84 1.00 1.00 0.14
## V4 0.00 0.00 1.00 0.02 0.00 0.00 0.00 0.00 0.81 1.00 1.00 1.00 1.00
## V5 0.00 0.00 0.09 0.00 0.00 0.00 0.00 0.00 1.00 1.00 1.00 1.00 1.00
## V6 0.00 0.00 0.92 0.00 0.00 0.00 0.00 0.00 1.00 1.00 1.00 0.44 1.00
## V7 0.05 0.25 0.00 0.00 0.66 0.01 0.37 0.07 0.00 0.00 1.00 1.00 1.00
## V8 0.00 0.00 0.00 0.04 0.01 0.03 0.48 0.15 0.00 0.00 1.00 1.00 1.00
## V9 0.00 0.00 0.00 0.00 0.32 0.20 0.09 0.02 0.46 0.54 0.00 0.00 1.00
## V10 0.00 0.00 0.00 0.00 0.34 0.16 0.30 0.00 0.17 0.42 0.00 0.00 1.00
## V11 0.12 0.22 0.00 0.01 0.00 0.05 0.04 0.36 0.38 0.09 0.31 0.05 0.00
## V12 0.73 0.81 0.41 0.06 0.52 0.69 0.71 0.84 0.70 0.81 0.66 0.88 0.00
## V13 0.57 0.41 0.00 0.01 0.05 0.00 0.03 0.36 0.02 0.00 0.02 0.00 0.00
## V14 0.98 0.59 0.00 0.00 0.43 0.01 0.36 0.75 0.06 0.01 0.06 0.00 0.00
## V15 0.28 0.50 0.00 0.22 0.01 0.97 0.04 0.38 0.00 0.00 0.42 0.52 0.00
## V16 0.02 0.00 0.00 0.00 0.87 0.07 0.00 0.00 0.47 0.17 0.23 0.27 0.00
## V12 V13 V14 V15 V16
## Sno 1.00 1.00 1.00 1.00 1.00
## Target 1.00 1.00 1.00 1.00 0.11
## V1 1.00 0.00 0.00 0.00 0.04
## V2 1.00 0.52 0.31 1.00 0.00
## V3 1.00 1.00 1.00 0.77 1.00
## V4 1.00 0.20 0.48 1.00 1.00
## V5 1.00 1.00 1.00 1.00 0.00
## V6 1.00 1.00 1.00 1.00 0.00
## V7 1.00 1.00 1.00 0.00 1.00
## V8 1.00 0.00 0.96 0.00 1.00
## V9 1.00 1.00 1.00 1.00 1.00
## V10 1.00 0.05 0.25 1.00 1.00
## V11 0.00 0.00 0.00 0.00 0.45
## V12 0.00 1.00 1.00 1.00 1.00
## V13 0.69 0.00 0.00 0.00 0.00
## V14 0.81 0.00 0.00 0.00 0.10
## V15 0.69 0.00 0.00 0.00 0.00
## V16 0.61 0.00 0.00 0.00 0.00
##
## To see confidence intervals of the correlations, print with the short=FALSE optionWe can also understand the correlations in the test dataset as -
library(corrgram)
corr.test(test)## Call:corr.test(x = test)
## Correlation matrix
## Sno Target V1 V2 V3 V4 V5 V6 V7 V8 V9
## Sno 1.00 0.96 0.06 0.03 0.36 0.41 0.29 0.28 -0.04 0.06 0.06
## Target 0.96 1.00 0.04 0.06 0.41 0.45 0.32 0.31 -0.02 0.08 0.09
## V1 0.06 0.04 1.00 0.04 0.05 0.01 0.02 0.00 -0.16 -0.11 -0.26
## V2 0.03 0.06 0.04 1.00 0.01 0.05 0.09 0.11 -0.11 -0.06 0.16
## V3 0.36 0.41 0.05 0.01 1.00 0.66 0.21 0.16 -0.03 -0.05 -0.01
## V4 0.41 0.45 0.01 0.05 0.66 1.00 0.25 0.45 -0.04 0.00 0.02
## V5 0.29 0.32 0.02 0.09 0.21 0.25 1.00 0.68 -0.03 -0.02 -0.01
## V6 0.28 0.31 0.00 0.11 0.16 0.45 0.68 1.00 -0.02 0.03 0.00
## V7 -0.04 -0.02 -0.16 -0.11 -0.03 -0.04 -0.03 -0.02 1.00 0.71 -0.02
## V8 0.06 0.08 -0.11 -0.06 -0.05 0.00 -0.02 0.03 0.71 1.00 -0.02
## V9 0.06 0.09 -0.26 0.16 -0.01 0.02 -0.01 0.00 -0.02 -0.02 1.00
## V10 0.13 0.17 -0.19 0.17 0.00 0.09 0.00 0.09 -0.05 -0.04 0.80
## V11 -0.02 -0.02 -0.08 0.05 0.03 0.13 0.03 0.08 -0.01 0.02 -0.01
## V12 -0.01 -0.01 -0.08 0.05 0.05 0.28 0.06 0.26 0.02 0.08 -0.02
## V13 -0.02 -0.01 -0.05 0.03 0.00 0.03 0.04 0.03 -0.01 -0.01 -0.01
## V14 -0.02 -0.01 -0.05 0.03 0.01 0.05 0.04 0.02 -0.01 -0.01 -0.01
## V15 -0.02 -0.02 -0.20 -0.09 -0.06 0.04 0.04 0.08 0.16 0.13 -0.03
## V16 0.08 0.09 -0.10 0.06 0.02 0.10 0.09 0.09 0.01 0.02 -0.03
## V10 V11 V12 V13 V14 V15 V16
## Sno 0.13 -0.02 -0.01 -0.02 -0.02 -0.02 0.08
## Target 0.17 -0.02 -0.01 -0.01 -0.01 -0.02 0.09
## V1 -0.19 -0.08 -0.08 -0.05 -0.05 -0.20 -0.10
## V2 0.17 0.05 0.05 0.03 0.03 -0.09 0.06
## V3 0.00 0.03 0.05 0.00 0.01 -0.06 0.02
## V4 0.09 0.13 0.28 0.03 0.05 0.04 0.10
## V5 0.00 0.03 0.06 0.04 0.04 0.04 0.09
## V6 0.09 0.08 0.26 0.03 0.02 0.08 0.09
## V7 -0.05 -0.01 0.02 -0.01 -0.01 0.16 0.01
## V8 -0.04 0.02 0.08 -0.01 -0.01 0.13 0.02
## V9 0.80 -0.01 -0.02 -0.01 -0.01 -0.03 -0.03
## V10 1.00 -0.01 -0.01 -0.01 -0.01 -0.02 0.01
## V11 -0.01 1.00 0.83 0.47 0.76 0.02 0.00
## V12 -0.01 0.83 1.00 0.40 0.65 0.08 0.01
## V13 -0.01 0.47 0.40 1.00 0.87 -0.02 0.00
## V14 -0.01 0.76 0.65 0.87 1.00 -0.02 -0.01
## V15 -0.02 0.02 0.08 -0.02 -0.02 1.00 0.31
## V16 0.01 0.00 0.01 0.00 -0.01 0.31 1.00
## Sample Size
## [1] 2052
## Probability values (Entries above the diagonal are adjusted for multiple tests.)
## Sno Target V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11
## Sno 0.00 0.00 0.98 1.00 0.00 0.00 0.00 0.00 1.00 0.33 0.37 0.00 1.00
## Target 0.00 0.00 1.00 1.00 0.00 0.00 0.00 0.00 1.00 0.02 0.00 0.00 1.00
## V1 0.01 0.05 0.00 1.00 1.00 1.00 1.00 1.00 0.00 0.00 0.00 0.00 0.02
## V2 0.15 0.01 0.10 0.00 1.00 1.00 0.00 0.00 0.00 0.69 0.00 0.00 1.00
## V3 0.00 0.00 0.02 0.71 0.00 0.00 0.00 0.00 1.00 1.00 1.00 1.00 1.00
## V4 0.00 0.00 0.57 0.02 0.00 0.00 0.00 0.00 1.00 1.00 1.00 0.00 0.00
## V5 0.00 0.00 0.31 0.00 0.00 0.00 0.00 0.00 1.00 1.00 1.00 1.00 1.00
## V6 0.00 0.00 0.96 0.00 0.00 0.00 0.00 0.00 1.00 1.00 1.00 0.01 0.03
## V7 0.09 0.33 0.00 0.00 0.15 0.07 0.22 0.28 0.00 0.00 1.00 1.00 1.00
## V8 0.00 0.00 0.00 0.01 0.02 0.91 0.31 0.23 0.00 0.00 1.00 1.00 1.00
## V9 0.00 0.00 0.00 0.00 0.77 0.27 0.58 0.88 0.33 0.34 0.00 0.00 1.00
## V10 0.00 0.00 0.00 0.00 0.96 0.00 0.93 0.00 0.02 0.08 0.00 0.00 1.00
## V11 0.31 0.43 0.00 0.03 0.19 0.00 0.17 0.00 0.70 0.49 0.55 0.59 0.00
## V12 0.56 0.68 0.00 0.02 0.03 0.00 0.00 0.00 0.47 0.00 0.44 0.53 0.00
## V13 0.48 0.76 0.01 0.23 0.89 0.23 0.06 0.22 0.58 0.70 0.52 0.61 0.00
## V14 0.49 0.76 0.03 0.13 0.70 0.02 0.07 0.45 0.60 0.71 0.53 0.62 0.00
## V15 0.34 0.27 0.00 0.00 0.01 0.09 0.06 0.00 0.00 0.00 0.16 0.31 0.44
## V16 0.00 0.00 0.00 0.01 0.32 0.00 0.00 0.00 0.72 0.50 0.24 0.56 0.90
## V12 V13 V14 V15 V16
## Sno 1.00 1.00 1.00 1.00 0.03
## Target 1.00 1.00 1.00 1.00 0.01
## V1 0.01 1.00 1.00 0.00 0.00
## V2 1.00 1.00 1.00 0.01 0.49
## V3 1.00 1.00 1.00 0.91 1.00
## V4 0.00 1.00 1.00 1.00 0.00
## V5 0.41 1.00 1.00 1.00 0.00
## V6 0.00 1.00 1.00 0.01 0.00
## V7 1.00 1.00 1.00 0.00 1.00
## V8 0.05 1.00 1.00 0.00 1.00
## V9 1.00 1.00 1.00 1.00 1.00
## V10 1.00 1.00 1.00 1.00 1.00
## V11 0.00 0.00 0.00 1.00 1.00
## V12 0.00 0.00 0.00 0.05 1.00
## V13 0.00 0.00 0.00 1.00 1.00
## V14 0.00 0.00 0.00 1.00 1.00
## V15 0.00 0.42 0.44 0.00 0.00
## V16 0.70 0.90 0.68 0.00 0.00
##
## To see confidence intervals of the correlations, print with the short=FALSE optionThese tables enable us to understand relations between the independent variables. We learn that the Target is most related to V3,V4,V5 and V6 since their correlation values are closer to 1.
We get covariance and correlation matrices as -
cov(train)## Sno Target V1 V2
## Sno 3.514052e+05 1.041758e+08 6.236126e+02 2.415200e+02
## Target 1.041758e+08 3.354501e+10 1.419672e+05 1.063175e+05
## V1 6.236126e+02 1.419672e+05 1.032579e+03 2.574846e+00
## V2 2.415200e+02 1.063175e+05 2.574846e+00 5.202697e+01
## V3 1.394990e+02 4.787477e+04 7.028551e-01 4.896153e-02
## V4 7.384006e+08 2.501741e+11 1.189264e+03 1.240501e+06
## V5 9.787622e+01 3.282434e+04 -6.612605e-01 3.914165e-01
## V6 3.271985e+08 1.103243e+11 -1.786275e+05 1.195588e+06
## V7 -1.137086e+01 -2.068333e+03 -2.571974e+00 -2.872262e-01
## V8 1.213925e+07 4.929926e+09 -1.338522e+06 -8.473785e+04
## V9 2.315936e+01 9.477787e+03 -3.764432e+00 5.264746e-01
## V10 6.014017e+07 2.166705e+10 -3.994135e+06 6.855822e+05
## V11 -1.629142e+00 -3.946260e+02 -2.625400e-01 3.449025e-02
## V12 -2.138991e+07 -4.513383e+09 2.766947e+06 1.420841e+06
## V13 -5.906433e-01 -2.631800e+02 -2.532015e-01 3.494791e-02
## V14 1.614035e+04 -1.114965e+08 -1.467189e+05 2.368660e+04
## V15 -1.093470e+01 -2.138746e+03 -4.057663e+00 -1.509793e-01
## V16 3.748057e+06 1.563396e+09 -2.964646e+05 7.736039e+04
## V3 V4 V5 V6
## Sno 1.394990e+02 7.384006e+08 9.787622e+01 3.271985e+08
## Target 4.787477e+04 2.501741e+11 3.282434e+04 1.103243e+11
## V1 7.028551e-01 1.189264e+03 -6.612605e-01 -1.786275e+05
## V2 4.896153e-02 1.240501e+06 3.914165e-01 1.195588e+06
## V3 4.598358e-01 1.277147e+06 7.128588e-02 1.498863e+05
## V4 1.277147e+06 1.080137e+13 4.614768e+05 4.374216e+12
## V5 7.128588e-02 4.614768e+05 3.003046e-01 6.782443e+05
## V6 1.498863e+05 4.374216e+12 6.782443e+05 5.812171e+12
## V7 -2.972401e-03 -8.394684e+04 -4.799946e-03 -4.325197e+04
## V8 -1.007801e+04 -4.134346e+10 -2.222573e+03 -2.013280e+10
## V9 -7.613543e-03 4.708364e+04 1.045729e-02 6.392140e+04
## V10 -1.381597e+04 9.955212e+10 1.210393e+04 1.457400e+11
## V11 3.779948e-03 1.136948e+04 1.928429e-03 3.863039e+03
## V12 -4.528452e+04 -1.360938e+11 -2.099257e+04 -5.084716e+10
## V13 2.290187e-03 1.772669e+04 2.149662e-03 3.851186e+03
## V14 6.021616e+02 1.023519e+10 5.650838e+02 8.725100e+08
## V15 -3.051352e-02 1.938689e+03 1.891422e-02 3.613014e+04
## V16 -3.020659e+02 1.559843e+10 7.000141e+03 2.809876e+10
## V7 V8 V9 V10
## Sno -1.137086e+01 1.213925e+07 2.315936e+01 6.014017e+07
## Target -2.068333e+03 4.929926e+09 9.477787e+03 2.166705e+10
## V1 -2.571974e+00 -1.338522e+06 -3.764432e+00 -3.994135e+06
## V2 -2.872262e-01 -8.473785e+04 5.264746e-01 6.855822e+05
## V3 -2.972401e-03 -1.007801e+04 -7.613543e-03 -1.381597e+04
## V4 -8.394684e+04 -4.134346e+10 4.708364e+04 9.955212e+10
## V5 -4.799946e-03 -2.222573e+03 1.045729e-02 1.210393e+04
## V6 -4.325197e+04 -2.013280e+10 6.392140e+04 1.457400e+11
## V7 1.979080e-01 8.376531e+04 -3.695443e-03 -1.320706e+04
## V8 8.376531e+04 6.804925e+10 -1.783262e+03 -4.462887e+09
## V9 -3.695443e-03 -1.783262e+03 2.609536e-01 2.245008e+05
## V10 -1.320706e+04 -4.462887e+09 2.245008e+05 9.421975e+11
## V11 6.822137e-04 7.682240e+02 9.089062e-04 3.308362e+03
## V12 -1.772153e+04 -6.367028e+09 -2.342992e+04 -1.550144e+10
## V13 1.830156e-03 1.878967e+03 2.114768e-03 5.905023e+03
## V14 9.326151e+02 7.377368e+08 1.087165e+03 3.261184e+09
## V15 4.696284e-02 2.729794e+04 -7.144254e-03 1.066442e+04
## V16 8.450299e+02 9.498551e+08 1.606986e+03 2.789389e+09
## V11 V12 V13 V14
## Sno -1.629142e+00 -2.138991e+07 -5.906433e-01 1.614035e+04
## Target -3.946260e+02 -4.513383e+09 -2.631800e+02 -1.114965e+08
## V1 -2.625400e-01 2.766947e+06 -2.532015e-01 -1.467189e+05
## V2 3.449025e-02 1.420841e+06 3.494791e-02 2.368660e+04
## V3 3.779948e-03 -4.528452e+04 2.290187e-03 6.021616e+02
## V4 1.136948e+04 -1.360938e+11 1.772669e+04 1.023519e+10
## V5 1.928429e-03 -2.099257e+04 2.149662e-03 5.650838e+02
## V6 3.863039e+03 -5.084716e+10 3.851186e+03 8.725100e+08
## V7 6.822137e-04 -1.772153e+04 1.830156e-03 9.326151e+02
## V8 7.682240e+02 -6.367028e+09 1.878967e+03 7.377368e+08
## V9 9.089062e-04 -2.342992e+04 2.114768e-03 1.087165e+03
## V10 3.308362e+03 -1.550144e+10 5.905023e+03 3.261184e+09
## V11 6.316055e-03 1.077040e+05 3.396351e-03 1.568778e+03
## V12 1.077040e+05 2.195765e+13 3.248629e+03 1.239087e+09
## V13 3.396351e-03 3.248629e+03 6.323651e-03 3.403397e+03
## V14 1.568778e+03 1.239087e+09 3.403397e+03 2.563822e+09
## V15 1.166695e-02 -3.195222e+04 2.282781e-02 8.836752e+03
## V16 5.863212e+02 -6.310535e+09 1.065244e+03 4.362370e+08
## V15 V16
## Sno -1.093470e+01 3.748057e+06
## Target -2.138746e+03 1.563396e+09
## V1 -4.057663e+00 -2.964646e+05
## V2 -1.509793e-01 7.736039e+04
## V3 -3.051352e-02 -3.020659e+02
## V4 1.938689e+03 1.559843e+10
## V5 1.891422e-02 7.000141e+03
## V6 3.613014e+04 2.809876e+10
## V7 4.696284e-02 8.450299e+02
## V8 2.729794e+04 9.498551e+08
## V9 -7.144254e-03 1.606986e+03
## V10 1.066442e+04 2.789389e+09
## V11 1.166695e-02 5.863212e+02
## V12 -3.195222e+04 -6.310535e+09
## V13 2.282781e-02 1.065244e+03
## V14 8.836752e+03 4.362370e+08
## V15 6.054241e-01 2.797963e+04
## V16 2.797963e+04 1.414271e+10cor(train)## Sno Target V1 V2 V3
## Sno 1.0000000000 0.959508202 3.273778e-02 0.05648521 0.347028957
## Target 0.9595082019 1.000000000 2.412196e-02 0.08047787 0.385470662
## V1 0.0327377794 0.024121961 1.000000e+00 0.01110901 0.032255430
## V2 0.0564852060 0.080477867 1.110901e-02 1.00000000 0.010010122
## V3 0.3470289570 0.385470662 3.225543e-02 0.01001012 1.000000000
## V4 0.3790081451 0.415612870 1.126101e-05 0.05232911 0.573060037
## V5 0.3012951344 0.327040187 -3.755173e-02 0.09902476 0.191832024
## V6 0.2289486397 0.249854972 -2.305779e-03 0.06875401 0.091683544
## V7 -0.0431178908 -0.025384864 -1.799175e-01 -0.08951136 -0.009853133
## V8 0.0785011695 0.103184576 -1.596807e-01 -0.04503514 -0.056972027
## V9 0.0764787435 0.101300441 -2.293275e-01 0.14288330 -0.021978789
## V10 0.1045176448 0.121875089 -1.280531e-01 0.09792065 -0.020989831
## V11 -0.0345805571 -0.027111202 -1.028042e-01 0.06016710 0.070139314
## V12 -0.0077003760 -0.005258905 1.837580e-02 0.04203764 -0.014251334
## V13 -0.0125296008 -0.018069866 -9.908791e-02 0.06092884 0.042470331
## V14 0.0005377308 -0.012022735 -9.017383e-02 0.06485516 0.017537501
## V15 -0.0237067961 -0.015007744 -1.622873e-01 -0.02690130 -0.057831043
## V16 0.0531662225 0.071777574 -7.757914e-02 0.09018578 -0.003745708
## V4 V5 V6 V7 V8
## Sno 3.790081e-01 0.301295134 0.228948640 -0.043117891 0.078501169
## Target 4.156129e-01 0.327040187 0.249854972 -0.025384864 0.103184576
## V1 1.126101e-05 -0.037551734 -0.002305779 -0.179917480 -0.159680667
## V2 5.232911e-02 0.099024762 0.068754006 -0.089511362 -0.045035137
## V3 5.730600e-01 0.191832024 0.091683544 -0.009853133 -0.056972027
## V4 1.000000e+00 0.256229680 0.552066738 -0.057416044 -0.048223159
## V5 2.562297e-01 1.000000000 0.513376515 -0.019689001 -0.015547599
## V6 5.520667e-01 0.513376515 1.000000000 -0.040327847 -0.032012772
## V7 -5.741604e-02 -0.019689001 -0.040327847 1.000000000 0.721806676
## V8 -4.822316e-02 -0.015547599 -0.032012772 0.721806676 1.000000000
## V9 2.804458e-02 0.037355656 0.051903351 -0.016261223 -0.013382026
## V10 3.120614e-02 0.022754884 0.062278587 -0.030584644 -0.017625168
## V11 4.352895e-02 0.044279189 0.020162157 0.019295936 0.037055549
## V12 -8.837020e-03 -0.008175075 -0.004500954 -0.008501131 -0.005208734
## V13 6.782724e-02 0.049329323 0.020088214 0.051733572 0.090578185
## V14 6.150529e-02 0.020365162 0.007147551 0.041402526 0.055852911
## V15 7.581215e-04 0.044358579 0.019260636 0.135672831 0.134489477
## V16 3.990939e-02 0.107413656 0.098005781 0.015972545 0.030618179
## V9 V10 V11 V12 V13
## Sno 0.076478743 0.104517645 -0.03458056 -0.007700376 -0.012529601
## Target 0.101300441 0.121875089 -0.02711120 -0.005258905 -0.018069866
## V1 -0.229327544 -0.128053139 -0.10280422 0.018375803 -0.099087914
## V2 0.142883297 0.097920647 0.06016710 0.042037645 0.060928842
## V3 -0.021978789 -0.020989831 0.07013931 -0.014251334 0.042470331
## V4 0.028044578 0.031206142 0.04352895 -0.008837020 0.067827240
## V5 0.037355656 0.022754884 0.04427919 -0.008175075 0.049329323
## V6 0.051903351 0.062278587 0.02016216 -0.004500954 0.020088214
## V7 -0.016261223 -0.030584644 0.01929594 -0.008501131 0.051733572
## V8 -0.013382026 -0.017625168 0.03705555 -0.005208734 0.090578185
## V9 1.000000000 0.452757122 0.02238795 -0.009788052 0.052059144
## V10 0.452757122 1.000000000 0.04288636 -0.003408068 0.076500923
## V11 0.022387955 0.042886357 1.00000000 0.289211853 0.537409953
## V12 -0.009788052 -0.003408068 0.28921185 1.000000000 0.008718128
## V13 0.052059144 0.076500923 0.53740995 0.008718128 1.000000000
## V14 0.042031001 0.066352979 0.38984738 0.005222337 0.845248964
## V15 -0.017974026 0.014120056 0.18867067 -0.008763514 0.368935520
## V16 0.026452346 0.024164168 0.06203636 -0.011324186 0.112641556
## V14 V15 V16
## Sno 0.0005377308 -0.0237067961 0.053166223
## Target -0.0120227352 -0.0150077436 0.071777574
## V1 -0.0901738349 -0.1622873137 -0.077579135
## V2 0.0648551602 -0.0269013027 0.090185776
## V3 0.0175375013 -0.0578310427 -0.003745708
## V4 0.0615052939 0.0007581215 0.039909394
## V5 0.0203651617 0.0443585792 0.107413656
## V6 0.0071475510 0.0192606364 0.098005781
## V7 0.0414025262 0.1356728307 0.015972545
## V8 0.0558529108 0.1344894767 0.030618179
## V9 0.0420310006 -0.0179740263 0.026452346
## V10 0.0663529785 0.0141200561 0.024164168
## V11 0.3898473842 0.1886706744 0.062036362
## V12 0.0052223374 -0.0087635143 -0.011324186
## V13 0.8452489641 0.3689355197 0.112641556
## V14 1.0000000000 0.2242946126 0.072445626
## V15 0.2242946126 1.0000000000 0.302374962
## V16 0.0724456258 0.3023749618 1.000000000library(corrplot)
corrplot(cor(train),method = 'color')
corrgram(train, order=TRUE, lower.panel=panel.shade,
upper.panel=panel.pie, text.panel=panel.txt,
main="Loan Data")
Running some simple tests - chisquare etc (new dataset)
We can test the accuracy of our understanding of the correlations between the Target variable and other fields using the chisquare and t-tests etc.
chisq.test(xtabs(~Target + V1, data = train))##
## Pearson's Chi-squared test
##
## data: xtabs(~Target + V1, data = train)
## X-squared = 83908, df = 79212, p-value < 2.2e-16chisq.test(xtabs(~Target + V2, data = train))##
## Pearson's Chi-squared test
##
## data: xtabs(~Target + V2, data = train)
## X-squared = 14196, df = 14760, p-value = 0.9996chisq.test(xtabs(~Target + V3, data = train))##
## Pearson's Chi-squared test
##
## data: xtabs(~Target + V3, data = train)
## X-squared = 2977.1, df = 1968, p-value < 2.2e-16chisq.test(xtabs(~Target + V4, data = train))##
## Pearson's Chi-squared test
##
## data: xtabs(~Target + V4, data = train)
## X-squared = 363080, df = 268630, p-value < 2.2e-16chisq.test(xtabs(~Target + V5, data = train))##
## Pearson's Chi-squared test
##
## data: xtabs(~Target + V5, data = train)
## X-squared = 1584.7, df = 2460, p-value = 1chisq.test(xtabs(~Target + V6, data = train))##
## Pearson's Chi-squared test
##
## data: xtabs(~Target + V6, data = train)
## X-squared = 138370, df = 126440, p-value < 2.2e-16chisq.test(xtabs(~Target + V7, data = train))##
## Pearson's Chi-squared test
##
## data: xtabs(~Target + V7, data = train)
## X-squared = 2073.2, df = 1968, p-value = 0.04866chisq.test(xtabs(~Target + V8, data = train))##
## Pearson's Chi-squared test
##
## data: xtabs(~Target + V8, data = train)
## X-squared = 101180, df = 64452, p-value < 2.2e-16chisq.test(xtabs(~Target + V9, data = train))##
## Pearson's Chi-squared test
##
## data: xtabs(~Target + V9, data = train)
## X-squared = 2618, df = 1476, p-value < 2.2e-16chisq.test(xtabs(~Target + V10, data = train))##
## Pearson's Chi-squared test
##
## data: xtabs(~Target + V10, data = train)
## X-squared = 168150, df = 122020, p-value < 2.2e-16chisq.test(xtabs(~Target + V11, data = train))##
## Pearson's Chi-squared test
##
## data: xtabs(~Target + V11, data = train)
## X-squared = 857.23, df = 984, p-value = 0.9985chisq.test(xtabs(~Target + V12, data = train))##
## Pearson's Chi-squared test
##
## data: xtabs(~Target + V12, data = train)
## X-squared = 2744.7, df = 3444, p-value = 1chisq.test(xtabs(~Target + V13, data = train))##
## Pearson's Chi-squared test
##
## data: xtabs(~Target + V13, data = train)
## X-squared = 772.88, df = 984, p-value = 1chisq.test(xtabs(~Target + V14, data = train))##
## Pearson's Chi-squared test
##
## data: xtabs(~Target + V14, data = train)
## X-squared = 3085.8, df = 1968, p-value < 2.2e-16chisq.test(xtabs(~Target + V15, data = train))##
## Pearson's Chi-squared test
##
## data: xtabs(~Target + V15, data = train)
## X-squared = 6052.2, df = 3936, p-value < 2.2e-16chisq.test(xtabs(~Target + V16, data = train))##
## Pearson's Chi-squared test
##
## data: xtabs(~Target + V16, data = train)
## X-squared = 171820, df = 176630, p-value = 1We next run t-tests -
attach(train)## The following objects are masked from train (pos = 3):
##
## V1, V10, V11, V12, V13, V14, V15, V16, V2, V3, V4, V5, V6, V7,
## V8, V9t.test(Target,V1, data = train)##
## Welch Two Sample t-test
##
## data: Target and V1
## t = 116.03, df = 2052, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 461095.3 476949.8
## sample estimates:
## mean of x mean of y
## 469863.6142 841.0813t.test(Target,V2, data = train)##
## Welch Two Sample t-test
##
## data: Target and V2
## t = 116.23, df = 2052, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 461896.9 477751.4
## sample estimates:
## mean of x mean of y
## 469863.61422 39.46956t.test(Target,V3, data = train)##
## Welch Two Sample t-test
##
## data: Target and V3
## t = 116.24, df = 2052, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 461935.9 477790.4
## sample estimates:
## mean of x mean of y
## 4.698636e+05 4.715051e-01t.test(Target,V4, data = train)##
## Welch Two Sample t-test
##
## data: Target and V4
## t = -13.326, df = 2064.7, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -1110547.8 -825609.3
## sample estimates:
## mean of x mean of y
## 469863.6 1437942.1t.test(Target,V5, data = train)##
## Welch Two Sample t-test
##
## data: Target and V5
## t = 116.24, df = 2052, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 461936.1 477790.7
## sample estimates:
## mean of x mean of y
## 4.698636e+05 2.269849e-01t.test(Target,V6, data = train)##
## Welch Two Sample t-test
##
## data: Target and V6
## t = -1.3207, df = 2075.7, p-value = 0.1867
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -175121.27 34172.24
## sample estimates:
## mean of x mean of y
## 469863.6 540338.1t.test(Target,V7, data = train)##
## Welch Two Sample t-test
##
## data: Target and V7
## t = 116.24, df = 2052, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 461936.2 477790.7
## sample estimates:
## mean of x mean of y
## 4.698636e+05 1.777886e-01t.test(Target,V8, data = train)##
## Welch Two Sample t-test
##
## data: Target and V8
## t = 56.754, df = 3679.6, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 385448.8 413033.0
## sample estimates:
## mean of x mean of y
## 469863.6 70622.7t.test(Target,V9, data = train)##
## Welch Two Sample t-test
##
## data: Target and V9
## t = 116.24, df = 2052, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 461936.1 477790.6
## sample estimates:
## mean of x mean of y
## 4.698636e+05 2.372138e-01t.test(Target,V10, data = train)##
## Welch Two Sample t-test
##
## data: Target and V10
## t = 13.124, df = 2197.9, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 243363.4 328868.2
## sample estimates:
## mean of x mean of y
## 469863.6 183747.8t.test(Target,V11, data = train)##
## Welch Two Sample t-test
##
## data: Target and V11
## t = 116.24, df = 2052, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 461936.3 477790.9
## sample estimates:
## mean of x mean of y
## 4.698636e+05 4.383829e-03t.test(Target,V12, data = train)##
## Welch Two Sample t-test
##
## data: Target and V12
## t = 3.5132, df = 2058.3, p-value = 0.0004523
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 160633.7 566575.2
## sample estimates:
## mean of x mean of y
## 469863.6 106259.1t.test(Target,V13, data = train)##
## Welch Two Sample t-test
##
## data: Target and V13
## t = 116.24, df = 2052, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 461936.3 477790.9
## sample estimates:
## mean of x mean of y
## 4.698636e+05 3.409644e-03t.test(Target,V14, data = train)##
## Welch Two Sample t-test
##
## data: Target and V14
## t = 111.48, df = 2363.8, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 459321.1 475769.0
## sample estimates:
## mean of x mean of y
## 469863.614 2318.558t.test(Target,V15, data = train)##
## Welch Two Sample t-test
##
## data: Target and V15
## t = 116.24, df = 2052, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 461934.9 477789.4
## sample estimates:
## mean of x mean of y
## 4.698636e+05 1.451047e+00t.test(Target,V16, data = train)##
## Welch Two Sample t-test
##
## data: Target and V16
## t = 83.408, df = 3521.1, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 392539.8 411438.7
## sample estimates:
## mean of x mean of y
## 469863.61 67874.32From the chi-square tests, using the p-value < 0.01, we can reject the null hypothesis and say that the Target is affected by the factors except V2, V5, V7, V11, V12, V13 and V16.
From the t-tests, we see variations between Target and V6 as well as V12.
Running the Regression model (on new dataset)
After understanding relations in the data, we can now move on to creating our model to predict values of DV from V1-V16.
Since we know that these are numerical values, and with our analysis are able to get some understanding of the relations between the data, we will first run a model that depends on all the variables.
fit1 <- lm(Target ~ ., data=train)
summary(fit1)##
## Call:
## lm(formula = Target ~ ., data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -155719 -29168 -389 38523 117700
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.084e+05 3.107e+04 3.490 0.000494 ***
## Sno 2.811e+02 2.118e+00 132.690 < 2e-16 ***
## V1 3.982e+01 3.586e+01 1.110 0.266953
## V2 5.012e+02 1.537e+02 3.260 0.001133 **
## V3 1.228e+04 2.182e+03 5.629 2.07e-08 ***
## V4 2.211e-03 5.272e-04 4.194 2.86e-05 ***
## V5 1.112e+04 2.443e+03 4.550 5.69e-06 ***
## V6 -4.174e-04 6.635e-04 -0.629 0.529435
## V7 -6.722e+03 3.601e+03 -1.867 0.062065 .
## V8 3.613e-02 6.161e-03 5.864 5.25e-09 ***
## V9 8.452e+03 2.440e+03 3.464 0.000543 ***
## V10 3.054e-03 1.256e-03 2.431 0.015144 *
## V11 1.402e+04 1.742e+04 0.805 0.421095
## V12 4.512e-05 2.452e-04 0.184 0.854036
## V13 -4.175e+04 3.017e+04 -1.384 0.166597
## V14 -4.106e-02 4.124e-02 -0.996 0.319501
## V15 1.976e+03 1.615e+03 1.224 0.221160
## V16 2.365e-02 9.626e-03 2.457 0.014089 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 48830 on 2035 degrees of freedom
## Multiple R-squared: 0.9295, Adjusted R-squared: 0.9289
## F-statistic: 1579 on 17 and 2035 DF, p-value: < 2.2e-16We could create a linear regression model and find that the Target is most dependent on V2, V3, V4, V5, V8 and V9.
To better understand the characteristics of the regression model, we can generate its plots with fitted and residual values -
plot(fit1)
fitted(fit1)## 1 2 3 4 5 6 7 8
## 176168.0 168588.6 178928.4 167206.6 176767.1 176253.1 174939.2 165901.4
## 9 10 11 12 13 14 15 16
## 176977.4 169363.4 168692.4 179063.7 172291.4 190661.2 178189.0 168316.8
## 17 18 19 20 21 22 23 24
## 175930.2 175476.1 178616.6 175018.6 178822.9 180125.7 178073.6 181624.8
## 25 26 27 28 29 30 31 32
## 186147.5 172849.8 172522.6 174873.9 179769.1 179823.7 176421.4 182740.7
## 33 34 35 36 37 38 39 40
## 170906.8 177419.0 168454.8 171569.8 193077.5 181555.8 180142.5 185949.7
## 41 42 43 44 45 46 47 48
## 183214.5 173277.4 199763.1 183754.9 188481.3 186935.7 181008.0 191309.0
## 49 50 51 52 53 54 55 56
## 181669.8 173769.3 196120.3 201726.8 189141.0 182156.1 189265.6 189112.5
## 57 58 59 60 61 62 63 64
## 190834.6 181839.0 196402.9 195508.1 192292.0 192041.6 181348.4 183454.8
## 65 66 67 68 69 70 71 72
## 182930.7 192651.9 188039.5 190372.1 195130.2 188980.8 194644.5 199994.0
## 73 74 75 76 77 78 79 80
## 192658.7 190259.2 192158.2 202765.2 184421.7 203957.3 194845.1 199494.9
## 81 82 83 84 85 86 87 88
## 193499.1 183026.0 201594.6 196302.7 191044.9 186503.8 198562.0 193377.1
## 89 90 91 92 93 94 95 96
## 221612.2 182339.0 208033.0 184987.0 198041.6 210258.0 203369.4 193051.0
## 97 98 99 100 101 102 103 104
## 198007.1 212627.2 204275.1 212326.3 217928.9 184340.3 204233.2 199879.4
## 105 106 107 108 109 110 111 112
## 201028.5 208144.2 196578.3 202208.8 208532.6 211256.3 198328.7 207095.3
## 113 114 115 116 117 118 119 120
## 205423.4 205349.3 195237.5 203539.7 206079.3 213265.9 201379.7 213442.3
## 121 122 123 124 125 126 127 128
## 201236.1 213188.3 203509.6 206990.5 198877.3 200512.4 207741.2 210960.1
## 129 130 131 132 133 134 135 136
## 206393.1 209861.9 201385.0 239668.7 219428.4 201025.5 215724.5 207692.5
## 137 138 139 140 141 142 143 144
## 256124.5 218663.5 218518.2 214604.7 214139.6 220994.2 210492.2 214367.9
## 145 146 147 148 149 150 151 152
## 213337.2 214321.9 218575.0 217727.6 223089.8 205817.9 228401.1 223240.2
## 153 154 155 156 157 158 159 160
## 217734.6 218084.4 208808.8 217979.4 222970.4 224630.2 206258.9 224587.8
## 161 162 163 164 165 166 167 168
## 221471.9 208130.4 227036.3 209560.6 213920.7 219877.1 220885.4 215945.4
## 169 170 171 172 173 174 175 176
## 240075.2 219798.3 236052.0 211357.4 218993.0 226432.2 217216.7 214372.5
## 177 178 179 180 181 182 183 184
## 224679.5 229664.2 227131.6 231540.6 214692.6 212614.3 219627.2 231885.7
## 185 186 187 188 189 190 191 192
## 238570.6 232935.6 227187.0 224669.2 225129.3 203497.4 214642.2 224036.1
## 193 194 195 196 197 198 199 200
## 233683.1 245144.2 219509.3 227240.2 229239.0 217513.6 234960.2 219007.6
## 201 202 203 204 205 206 207 208
## 232792.3 235907.4 235323.9 222766.1 234660.1 228925.7 233305.5 248246.5
## 209 210 211 212 213 214 215 216
## 228427.2 242326.7 234531.1 242836.2 246000.7 222135.4 247795.8 237098.3
## 217 218 219 220 221 222 223 224
## 232317.0 229300.3 256375.3 240823.2 258632.9 238655.8 239949.4 239026.6
## 225 226 227 228 229 230 231 232
## 226784.3 238641.2 235197.9 240876.9 244776.0 242694.7 241146.0 244583.3
## 233 234 235 236 237 238 239 240
## 239047.6 245147.0 234744.3 239515.3 240923.3 256821.4 239407.7 239658.7
## 241 242 243 244 245 246 247 248
## 245442.2 234576.5 255294.3 239248.5 237084.3 241639.6 247691.5 245861.0
## 249 250 251 252 253 254 255 256
## 248318.6 237481.0 237625.0 251125.3 230433.2 253187.5 241009.5 256198.7
## 257 258 259 260 261 262 263 264
## 232757.7 241066.3 233454.5 259001.6 253580.7 257560.1 257695.3 241562.5
## 265 266 267 268 269 270 271 272
## 243183.5 237814.4 252426.3 251403.0 255977.3 254035.0 251500.4 263971.2
## 273 274 275 276 277 278 279 280
## 261957.8 252014.2 263415.9 260507.0 260266.3 251841.5 249939.6 259573.2
## 281 282 283 284 285 286 287 288
## 257565.1 258431.9 252098.9 257494.2 262973.9 251283.0 262820.3 266540.0
## 289 290 291 292 293 294 295 296
## 263633.6 239016.7 261795.4 253226.9 250388.8 270310.9 363298.6 258781.3
## 297 298 299 300 301 302 303 304
## 269263.4 260099.1 263566.9 276016.9 253665.8 264124.5 267998.7 268108.4
## 305 306 307 308 309 310 311 312
## 261409.0 274461.0 269002.1 263652.2 257997.8 272421.0 289419.4 275128.4
## 313 314 315 316 317 318 319 320
## 273870.5 258821.9 270227.1 262527.7 265508.2 264212.5 253792.7 263274.5
## 321 322 323 324 325 326 327 328
## 280378.6 288690.4 257783.0 256926.1 253634.1 271328.5 261294.4 275247.3
## 329 330 331 332 333 334 335 336
## 253627.2 281987.0 266848.7 260495.7 259470.5 283346.8 272433.2 261718.6
## 337 338 339 340 341 342 343 344
## 267423.1 283250.8 257303.2 269201.9 271964.4 265269.9 262051.7 278311.2
## 345 346 347 348 349 350 351 352
## 259608.8 259211.2 273515.4 269203.9 278148.2 292010.6 268451.2 280989.1
## 353 354 355 356 357 358 359 360
## 273338.4 286507.3 266173.0 263058.9 285303.5 290517.9 264143.6 283866.1
## 361 362 363 364 365 366 367 368
## 279431.2 283894.3 284320.8 273322.5 312093.0 275981.5 281262.5 273290.6
## 369 370 371 372 373 374 375 376
## 301884.3 282956.4 279802.5 282721.6 292215.1 286021.4 293342.8 292558.4
## 377 378 379 380 381 382 383 384
## 278723.4 287677.5 286182.0 299913.0 269055.8 289893.7 282716.1 299926.7
## 385 386 387 388 389 390 391 392
## 277379.1 299600.7 279956.0 273428.0 287666.6 321524.1 316306.5 299588.3
## 393 394 395 396 397 398 399 400
## 299874.7 301689.5 302269.8 284765.1 281625.5 304049.2 285558.3 283045.1
## 401 402 403 404 405 406 407 408
## 274934.3 281270.0 308467.1 294013.1 310395.0 294548.6 292344.5 283725.3
## 409 410 411 412 413 414 415 416
## 299090.5 305953.8 293935.6 297472.5 289873.7 299716.9 306640.4 279273.9
## 417 418 419 420 421 422 423 424
## 308374.4 283624.2 289524.3 299838.2 292709.6 309017.9 298514.4 309683.3
## 425 426 427 428 429 430 431 432
## 298134.6 295895.8 313458.8 318960.8 297739.8 295262.9 306749.1 294084.0
## 433 434 435 436 437 438 439 440
## 290423.4 307282.8 294447.2 295224.7 312172.4 302483.0 305299.0 285425.4
## 441 442 443 444 445 446 447 448
## 308783.6 314252.0 307338.6 313456.8 306996.8 302642.9 304778.9 328755.9
## 449 450 451 452 453 454 455 456
## 304984.5 315417.2 306102.3 290421.6 300095.9 304689.4 331743.2 323992.6
## 457 458 459 460 461 462 463 464
## 286656.5 290033.3 320040.8 317055.3 312939.2 319636.0 316321.8 315284.6
## 465 466 467 468 469 470 471 472
## 308330.5 317389.4 318056.5 311381.8 312544.4 317418.7 313763.1 309811.4
## 473 474 475 476 477 478 479 480
## 311535.6 307143.6 313635.9 336512.9 313644.4 311871.2 311035.4 317733.1
## 481 482 483 484 485 486 487 488
## 295924.2 336687.3 318055.7 295367.4 321423.6 299383.2 327078.3 334849.5
## 489 490 491 492 493 494 495 496
## 318852.4 311261.1 322143.6 330908.7 335546.3 348664.9 331095.2 317152.3
## 497 498 499 500 501 502 503 504
## 333549.9 313589.9 326059.9 316367.3 312996.3 317036.3 327440.8 326380.7
## 505 506 507 508 509 510 511 512
## 326227.9 319248.2 314326.8 340194.7 305743.2 334950.2 306773.9 322214.8
## 513 514 515 516 517 518 519 520
## 329356.7 324856.4 315783.0 324833.8 330698.8 317769.7 322404.1 312382.9
## 521 522 523 524 525 526 527 528
## 325555.0 325954.8 328214.8 337256.9 327291.6 329195.5 318432.3 338988.5
## 529 530 531 532 533 534 535 536
## 328942.1 328370.4 314991.9 323093.0 329054.3 348781.2 336368.4 332477.4
## 537 538 539 540 541 542 543 544
## 329032.5 342250.6 349265.9 328717.6 333354.2 338935.8 322686.1 339696.9
## 545 546 547 548 549 550 551 552
## 335977.2 333576.8 336474.3 316578.8 335827.2 345037.7 335602.6 354723.8
## 553 554 555 556 557 558 559 560
## 345707.9 319754.0 336894.8 326391.7 335510.3 350247.4 334645.7 349637.8
## 561 562 563 564 565 566 567 568
## 345561.3 345368.1 371716.9 322140.0 342831.5 342294.0 348118.1 342451.1
## 569 570 571 572 573 574 575 576
## 340132.0 344443.1 359737.9 335253.6 362379.6 343518.1 335123.0 338415.8
## 577 578 579 580 581 582 583 584
## 341307.1 361448.8 338890.8 348371.6 341223.6 338361.4 351561.5 378197.9
## 585 586 587 588 589 590 591 592
## 344467.4 352515.8 337656.1 350792.5 349792.4 361541.3 350497.2 343591.7
## 593 594 595 596 597 598 599 600
## 365048.6 348869.8 329878.9 347621.8 351605.0 357148.6 359963.5 361577.3
## 601 602 603 604 605 606 607 608
## 349958.0 356069.5 349706.2 350181.4 353015.1 349676.1 336832.2 365684.4
## 609 610 611 612 613 614 615 616
## 368754.0 369460.5 363285.5 352791.3 352593.6 362071.4 384037.8 347649.6
## 617 618 619 620 621 622 623 624
## 367517.6 347358.6 355053.6 350065.4 348974.7 341124.5 365792.9 355672.2
## 625 626 627 628 629 630 631 632
## 359464.3 372853.1 367914.6 362506.4 358447.3 357296.9 382645.9 366515.0
## 633 634 635 636 637 638 639 640
## 342580.3 360699.0 360354.3 379660.6 376928.2 354045.2 360882.7 361554.6
## 641 642 643 644 645 646 647 648
## 377912.4 342402.6 344003.6 343381.1 344594.4 342406.8 345320.4 343189.7
## 649 650 651 652 653 654 655 656
## 347631.9 342266.0 342672.2 344936.4 344196.9 360954.0 338119.1 346093.6
## 657 658 659 660 661 662 663 664
## 343330.3 344895.1 345948.3 345368.1 348320.0 347762.2 350909.6 349470.9
## 665 666 667 668 669 670 671 672
## 344958.3 348211.0 351275.3 346113.2 352517.8 350375.7 350469.0 357798.9
## 673 674 675 676 677 678 679 680
## 354253.2 350323.7 353932.9 350725.7 361996.1 356913.9 349005.9 356206.3
## 681 682 683 684 685 686 687 688
## 354842.7 365874.6 354651.3 354277.8 352373.3 354060.1 356525.0 359309.3
## 689 690 691 692 693 694 695 696
## 355716.1 355371.4 356221.3 351498.3 360105.5 363142.5 359165.9 355176.1
## 697 698 699 700 701 702 703 704
## 355697.8 378361.8 358969.0 359224.5 361615.6 366459.8 362967.2 360741.4
## 705 706 707 708 709 710 711 712
## 363441.2 366018.6 362056.6 363326.0 368115.1 359971.2 364485.3 363553.8
## 713 714 715 716 717 718 719 720
## 361227.5 362480.8 367877.1 366279.3 373881.8 362515.9 370775.3 362621.2
## 721 722 723 724 725 726 727 728
## 366054.8 366148.1 374256.9 376099.4 373211.8 373912.2 370008.2 375085.5
## 729 730 731 732 733 734 735 736
## 368885.2 375697.0 366661.8 367699.4 363507.1 376844.6 366488.6 365711.0
## 737 738 739 740 741 742 743 744
## 366741.7 372088.1 372184.0 383141.0 370158.1 370147.3 370172.3 378407.2
## 745 746 747 748 749 750 751 752
## 369489.9 373683.2 371597.0 377680.9 374970.6 371969.3 376410.5 375269.3
## 753 754 755 756 757 758 759 760
## 376714.9 376120.5 377903.2 372152.2 382020.7 373606.8 373699.3 375428.8
## 761 762 763 764 765 766 767 768
## 373845.9 376355.8 375086.7 380920.4 375883.3 374651.4 378086.5 382987.8
## 769 770 771 772 773 774 775 776
## 386269.8 375517.8 377659.0 377309.9 395097.9 378947.1 382707.8 376761.8
## 777 778 779 780 781 782 783 784
## 377815.9 380471.3 380511.7 374096.6 381236.7 385761.6 377399.8 380412.2
## 785 786 787 788 789 790 791 792
## 385001.0 378095.1 389368.1 390423.2 382057.9 381670.0 386092.1 387299.1
## 793 794 795 796 797 798 799 800
## 384214.8 380563.5 385521.8 387175.3 385366.1 385460.9 389911.8 386648.1
## 801 802 803 804 805 806 807 808
## 401840.2 397680.1 386824.6 388238.9 394848.1 386494.3 385564.4 392643.8
## 809 810 811 812 813 814 815 816
## 398871.2 391109.9 389424.4 406182.6 394014.5 392093.5 389867.0 396596.6
## 817 818 819 820 821 822 823 824
## 391574.3 393293.4 398248.3 388290.5 390574.5 402429.2 392384.8 389921.1
## 825 826 827 828 829 830 831 832
## 396817.9 392822.9 401132.3 410668.7 397907.6 394186.1 428790.5 401030.4
## 833 834 835 836 837 838 839 840
## 409960.9 412424.6 418190.3 398544.6 406184.0 403507.4 410266.1 413610.7
## 841 842 843 844 845 846 847 848
## 408207.6 407131.9 399783.4 405311.6 421387.2 403512.4 410030.0 417289.4
## 849 850 851 852 853 854 855 856
## 407961.7 417972.0 406622.6 406481.7 413273.2 408352.8 407082.4 410488.2
## 857 858 859 860 861 862 863 864
## 407853.6 411554.7 410669.4 415445.0 428455.0 413560.7 410747.2 409163.9
## 865 866 867 868 869 870 871 872
## 415720.8 463734.4 409382.6 423601.3 410255.9 411070.1 417436.3 417330.4
## 873 874 875 876 877 878 879 880
## 414584.9 413422.5 415351.8 409866.0 417659.0 417399.1 413312.4 410785.6
## 881 882 883 884 885 886 887 888
## 419035.7 415357.1 364307.1 418757.5 429389.0 420490.8 414137.2 442520.0
## 889 890 891 892 893 894 895 896
## 420379.0 422882.1 423502.4 419954.6 426900.4 420132.2 426300.5 422592.7
## 897 898 899 900 901 902 903 904
## 460954.0 418692.7 422008.5 420535.9 420157.1 414278.1 425893.8 420442.4
## 905 906 907 908 909 910 911 912
## 422268.6 425679.8 426603.7 425381.3 427563.7 426259.6 421196.3 420594.5
## 913 914 915 916 917 918 919 920
## 428357.6 421313.7 432820.3 422464.1 435979.6 534087.2 468649.6 428042.6
## 921 922 923 924 925 926 927 928
## 429953.0 426588.0 431679.1 429223.2 422487.9 431137.9 432908.2 429060.8
## 929 930 931 932 933 934 935 936
## 432274.9 427268.9 423749.0 444062.0 424342.6 429120.4 426521.3 435574.6
## 937 938 939 940 941 942 943 944
## 449147.4 433230.1 434727.3 438866.5 430558.2 431150.9 434261.4 438673.2
## 945 946 947 948 949 950 951 952
## 430399.7 426036.9 438293.2 435216.0 434798.2 434931.6 441684.4 433369.6
## 953 954 955 956 957 958 959 960
## 431772.3 445106.8 447821.1 435554.2 435402.5 433655.6 432149.2 441786.3
## 961 962 963 964 965 966 967 968
## 435330.1 438093.3 444671.7 443096.1 443986.4 436016.7 440093.3 440190.0
## 969 970 971 972 973 974 975 976
## 445882.7 435438.4 435691.3 436166.7 440004.5 438138.0 436256.9 446283.3
## 977 978 979 980 981 982 983 984
## 445856.9 440121.8 453997.9 437539.3 434140.7 444407.1 449119.1 451412.8
## 985 986 987 988 989 990 991 992
## 477468.7 441602.0 439979.5 453658.5 450111.3 458000.8 452178.9 445676.2
## 993 994 995 996 997 998 999 1000
## 460383.7 447657.2 452403.9 444307.3 453090.6 451860.4 447428.3 445734.6
## 1001 1002 1003 1004 1005 1006 1007 1008
## 453357.1 454769.6 450425.8 448366.9 444864.0 447389.9 445919.5 443374.5
## 1009 1010 1011 1012 1013 1014 1015 1016
## 444554.9 442941.2 454946.2 454533.5 449660.4 445196.1 455164.0 451824.1
## 1017 1018 1019 1020 1021 1022 1023 1024
## 446517.0 469518.7 448900.5 451138.5 457077.1 454194.4 450604.5 451260.4
## 1025 1026 1027 1028 1029 1030 1031 1032
## 446838.8 463525.3 451379.4 454360.9 454294.9 451583.8 463430.4 453908.9
## 1033 1034 1035 1036 1037 1038 1039 1040
## 456415.4 456232.5 451965.9 449213.9 456612.5 463082.7 456837.3 453206.7
## 1041 1042 1043 1044 1045 1046 1047 1048
## 461567.5 457425.1 452518.8 452710.7 462136.6 456289.4 464712.8 457204.2
## 1049 1050 1051 1052 1053 1054 1055 1056
## 457297.6 460629.3 459909.8 465772.1 461625.8 460646.8 465475.0 461155.9
## 1057 1058 1059 1060 1061 1062 1063 1064
## 460655.4 474521.5 460557.1 459430.7 466529.1 461599.4 461681.4 460960.1
## 1065 1066 1067 1068 1069 1070 1071 1072
## 463342.0 463578.7 474080.3 463760.3 472428.7 460538.9 475511.4 467687.2
## 1073 1074 1075 1076 1077 1078 1079 1080
## 469442.7 462098.5 467500.0 467937.3 464670.4 472213.6 463873.5 468878.3
## 1081 1082 1083 1084 1085 1086 1087 1088
## 475431.2 472836.4 474126.5 475852.7 465916.6 480733.2 470613.9 474192.6
## 1089 1090 1091 1092 1093 1094 1095 1096
## 471040.8 468928.5 468408.1 468682.0 474949.3 470333.3 477294.4 474031.4
## 1097 1098 1099 1100 1101 1102 1103 1104
## 471495.0 474211.6 470797.8 474371.2 469583.7 481136.6 469071.7 482921.4
## 1105 1106 1107 1108 1109 1110 1111 1112
## 474782.7 475469.6 475521.0 475069.8 482449.1 475271.8 476312.8 471012.7
## 1113 1114 1115 1116 1117 1118 1119 1120
## 471915.3 477238.6 479805.5 477119.4 476414.6 486482.8 476618.3 475466.0
## 1121 1122 1123 1124 1125 1126 1127 1128
## 481408.4 475925.1 475306.3 478707.5 490710.6 477703.0 482515.6 487467.0
## 1129 1130 1131 1132 1133 1134 1135 1136
## 503206.3 480386.4 481872.3 479782.8 481778.2 477834.6 488349.9 493348.4
## 1137 1138 1139 1140 1141 1142 1143 1144
## 479743.1 478670.4 482406.0 480715.3 484738.3 482034.1 482265.7 482166.8
## 1145 1146 1147 1148 1149 1150 1151 1152
## 488995.1 484279.2 483448.0 486911.9 502834.1 483254.3 493229.4 515119.1
## 1153 1154 1155 1156 1157 1158 1159 1160
## 486057.2 484809.7 485997.0 506651.0 489264.1 494760.3 486898.8 489791.0
## 1161 1162 1163 1164 1165 1166 1167 1168
## 486147.0 485911.4 491634.9 488845.2 489691.2 494812.0 486655.4 488346.5
## 1169 1170 1171 1172 1173 1174 1175 1176
## 490569.1 489559.5 490962.4 498646.0 498151.4 493110.1 493553.1 496172.9
## 1177 1178 1179 1180 1181 1182 1183 1184
## 495464.0 490311.6 493626.9 491855.0 505918.2 495913.4 488806.9 498045.0
## 1185 1186 1187 1188 1189 1190 1191 1192
## 494751.8 501979.8 503750.2 499714.6 497384.2 498937.7 497953.9 497176.7
## 1193 1194 1195 1196 1197 1198 1199 1200
## 495874.6 495094.4 506398.6 496900.4 499408.7 503173.0 501673.4 496926.3
## 1201 1202 1203 1204 1205 1206 1207 1208
## 501027.2 499076.8 500331.7 502343.1 498584.4 502074.2 506938.6 513132.4
## 1209 1210 1211 1212 1213 1214 1215 1216
## 503506.9 507201.0 498634.7 506751.0 509584.9 504903.4 502096.6 500456.1
## 1217 1218 1219 1220 1221 1222 1223 1224
## 527583.6 504184.3 502920.3 506846.1 509176.7 508637.8 506351.3 510081.4
## 1225 1226 1227 1228 1229 1230 1231 1232
## 504147.1 506391.3 502391.2 506465.2 506803.5 507775.5 509562.5 509445.4
## 1233 1234 1235 1236 1237 1238 1239 1240
## 509674.5 521040.3 504653.6 511659.6 507192.4 507862.5 511122.1 510525.5
## 1241 1242 1243 1244 1245 1246 1247 1248
## 512682.2 528240.1 512394.1 520497.9 513595.8 518056.8 519599.5 511677.4
## 1249 1250 1251 1252 1253 1254 1255 1256
## 523181.6 509431.6 512616.7 518638.5 521108.4 516437.7 524003.9 515509.4
## 1257 1258 1259 1260 1261 1262 1263 1264
## 516939.0 518233.5 513924.4 516648.1 526763.1 516530.7 531106.1 569490.0
## 1265 1266 1267 1268 1269 1270 1271 1272
## 523436.7 519713.5 515671.8 520477.2 523187.2 509205.7 516053.4 529959.4
## 1273 1274 1275 1276 1277 1278 1279 1280
## 525315.5 538627.9 533381.9 538710.2 558354.7 551957.7 547365.6 543290.6
## 1281 1282 1283 1284 1285 1286 1287 1288
## 541339.6 539068.9 544293.2 528056.8 540821.2 564562.6 560742.5 544912.1
## 1289 1290 1291 1292 1293 1294 1295 1296
## 567020.4 546155.3 543779.9 548603.6 552934.6 550087.6 543025.8 543086.7
## 1297 1298 1299 1300 1301 1302 1303 1304
## 553139.3 599718.6 530422.8 549688.8 528822.2 543956.3 552722.0 537280.0
## 1305 1306 1307 1308 1309 1310 1311 1312
## 539788.3 547959.7 544857.6 447552.1 547725.1 548363.6 553334.3 547968.4
## 1313 1314 1315 1316 1317 1318 1319 1320
## 565567.6 553663.6 545610.9 551776.0 559364.6 563283.4 575042.7 548086.4
## 1321 1322 1323 1324 1325 1326 1327 1328
## 567775.8 542594.7 554373.8 562024.7 563907.0 550157.3 555259.6 568305.1
## 1329 1330 1331 1332 1333 1334 1335 1336
## 557365.5 565935.6 551453.2 568990.5 556710.8 554063.5 559626.2 551614.8
## 1337 1338 1339 1340 1341 1342 1343 1344
## 571675.6 569164.6 556895.8 556932.9 547163.0 550940.7 561910.2 557181.2
## 1345 1346 1347 1348 1349 1350 1351 1352
## 559174.5 558020.2 566312.7 561036.6 563366.1 561405.8 562121.7 553908.9
## 1353 1354 1355 1356 1357 1358 1359 1360
## 561014.8 562213.8 553083.6 571288.4 585335.0 580334.2 571169.1 545755.6
## 1361 1362 1363 1364 1365 1366 1367 1368
## 569374.4 554633.9 574808.4 571492.7 571143.1 568414.1 569657.3 570923.1
## 1369 1370 1371 1372 1373 1374 1375 1376
## 564637.9 564464.0 566685.6 565333.6 559099.4 572051.9 570796.8 560075.0
## 1377 1378 1379 1380 1381 1382 1383 1384
## 587703.2 568490.5 561314.0 563983.8 564427.7 572876.5 581090.1 584287.2
## 1385 1386 1387 1388 1389 1390 1391 1392
## 562794.4 579373.2 553122.0 560826.1 577523.5 576694.4 577190.8 578072.6
## 1393 1394 1395 1396 1397 1398 1399 1400
## 590894.1 573461.6 573995.0 584902.2 584699.3 605576.9 587613.1 582095.5
## 1401 1402 1403 1404 1405 1406 1407 1408
## 581268.5 562697.9 575132.3 574281.0 592028.1 568142.4 598932.9 561343.7
## 1409 1410 1411 1412 1413 1414 1415 1416
## 580008.8 566904.5 568757.3 595817.6 579938.9 581567.3 580054.0 577648.2
## 1417 1418 1419 1420 1421 1422 1423 1424
## 584211.6 580054.2 581515.1 590296.7 570524.2 583622.9 589532.8 602518.9
## 1425 1426 1427 1428 1429 1430 1431 1432
## 580325.2 561196.3 598961.4 591299.2 584195.3 580717.1 570670.5 581262.5
## 1433 1434 1435 1436 1437 1438 1439 1440
## 573087.9 582469.0 573836.5 589345.1 587079.1 592389.8 588424.8 593202.6
## 1441 1442 1443 1444 1445 1446 1447 1448
## 591896.5 570833.3 583381.3 597658.6 583082.0 589878.7 601053.0 598185.4
## 1449 1450 1451 1452 1453 1454 1455 1456
## 602925.0 590688.9 598778.8 598150.0 594057.7 577954.2 601852.4 592057.9
## 1457 1458 1459 1460 1461 1462 1463 1464
## 588759.8 593848.4 605705.3 591262.4 600093.2 604157.2 591281.1 589450.2
## 1465 1466 1467 1468 1469 1470 1471 1472
## 598869.1 605632.8 601667.2 585530.8 605777.2 600710.0 589125.3 591759.0
## 1473 1474 1475 1476 1477 1478 1479 1480
## 605864.7 618950.6 590456.0 601190.2 597876.6 599366.4 603792.5 611870.2
## 1481 1482 1483 1484 1485 1486 1487 1488
## 599076.6 577056.0 613806.2 621122.6 599548.0 594583.9 616348.0 617130.4
## 1489 1490 1491 1492 1493 1494 1495 1496
## 597725.7 602326.6 603830.7 612676.3 596516.6 601965.3 603527.5 599830.6
## 1497 1498 1499 1500 1501 1502 1503 1504
## 629735.7 641632.6 605981.1 609628.1 614402.8 597606.7 590229.7 612370.0
## 1505 1506 1507 1508 1509 1510 1511 1512
## 671509.8 629212.1 599128.8 609407.8 604615.5 616350.4 603451.5 616805.7
## 1513 1514 1515 1516 1517 1518 1519 1520
## 620957.5 614940.5 621618.6 624673.0 598957.7 610145.7 607877.8 608255.3
## 1521 1522 1523 1524 1525 1526 1527 1528
## 600336.0 598470.0 612649.6 637724.0 610424.9 629267.1 615679.8 608736.7
## 1529 1530 1531 1532 1533 1534 1535 1536
## 620863.5 613492.3 622864.6 630272.0 621825.2 604670.0 616439.1 612221.8
## 1537 1538 1539 1540 1541 1542 1543 1544
## 615949.2 633589.6 627362.3 635863.9 614354.2 615117.0 602803.5 619040.9
## 1545 1546 1547 1548 1549 1550 1551 1552
## 650962.8 627143.3 656828.9 624615.5 601642.0 622399.1 641339.1 636842.2
## 1553 1554 1555 1556 1557 1558 1559 1560
## 626022.6 648108.0 616136.3 603999.5 623591.0 597305.5 621663.3 620340.2
## 1561 1562 1563 1564 1565 1566 1567 1568
## 644072.2 622822.4 637188.6 634606.4 664090.4 666570.7 636967.7 605294.1
## 1569 1570 1571 1572 1573 1574 1575 1576
## 625740.6 625689.4 636399.1 646292.1 619640.0 632341.9 626173.6 620653.5
## 1577 1578 1579 1580 1581 1582 1583 1584
## 628905.2 633562.2 622172.7 631734.6 615467.7 632112.7 611166.0 623200.1
## 1585 1586 1587 1588 1589 1590 1591 1592
## 609337.0 661703.1 633682.5 627916.5 638488.7 644901.8 638823.5 635040.6
## 1593 1594 1595 1596 1597 1598 1599 1600
## 634794.9 629473.6 644488.7 630660.3 621374.2 638144.6 644182.5 631399.0
## 1601 1602 1603 1604 1605 1606 1607 1608
## 636272.5 638671.3 650523.5 631687.7 662817.2 655221.0 654405.2 633825.2
## 1609 1610 1611 1612 1613 1614 1615 1616
## 630930.3 655020.2 636255.1 660523.4 637295.1 660034.3 647920.4 668959.3
## 1617 1618 1619 1620 1621 1622 1623 1624
## 642240.5 651101.3 680456.1 661002.9 660717.3 629992.4 651475.9 647406.2
## 1625 1626 1627 1628 1629 1630 1631 1632
## 633845.4 669495.9 629399.5 648751.1 656034.2 633121.8 651312.6 653595.1
## 1633 1634 1635 1636 1637 1638 1639 1640
## 668192.6 642450.4 646645.0 630666.6 666789.8 668624.0 661881.3 657459.2
## 1641 1642 1643 1644 1645 1646 1647 1648
## 644583.2 631681.5 635168.4 652534.9 647900.8 667635.6 662607.4 672627.0
## 1649 1650 1651 1652 1653 1654 1655 1656
## 643590.6 695995.9 657538.9 660700.3 679272.6 676648.5 685510.8 668350.3
## 1657 1658 1659 1660 1661 1662 1663 1664
## 658154.2 673782.1 691122.8 662185.3 715757.3 673309.1 709158.2 664568.0
## 1665 1666 1667 1668 1669 1670 1671 1672
## 660616.1 658576.8 665411.2 701668.8 680015.3 673507.9 643386.6 681947.4
## 1673 1674 1675 1676 1677 1678 1679 1680
## 732387.0 666141.7 680001.8 667067.8 664654.1 661909.8 681925.4 714762.8
## 1681 1682 1683 1684 1685 1686 1687 1688
## 670964.8 658563.3 677601.0 640365.7 678488.3 657586.7 664073.2 689433.1
## 1689 1690 1691 1692 1693 1694 1695 1696
## 677109.2 703890.4 661822.3 632300.1 693546.0 679970.7 681817.0 678831.8
## 1697 1698 1699 1700 1701 1702 1703 1704
## 672304.7 692982.4 695981.3 668937.5 670884.0 666230.6 684720.0 674030.4
## 1705 1706 1707 1708 1709 1710 1711 1712
## 696075.4 740080.5 666145.4 678635.1 697430.8 676082.9 733287.3 682672.8
## 1713 1714 1715 1716 1717 1718 1719 1720
## 676572.0 664275.9 724277.5 683723.6 661115.2 679412.8 698891.1 685628.9
## 1721 1722 1723 1724 1725 1726 1727 1728
## 714635.7 739283.1 665527.5 714247.1 718212.6 681832.9 684744.1 676485.4
## 1729 1730 1731 1732 1733 1734 1735 1736
## 735099.2 664939.7 655677.3 682338.4 704966.5 686012.4 681982.3 677195.6
## 1737 1738 1739 1740 1741 1742 1743 1744
## 696339.3 692587.3 702090.0 678344.2 831281.2 712182.0 679224.7 688815.5
## 1745 1746 1747 1748 1749 1750 1751 1752
## 756047.1 694812.0 698070.0 714664.6 700712.8 657146.1 680503.1 685961.9
## 1753 1754 1755 1756 1757 1758 1759 1760
## 708436.6 690859.1 684906.4 677510.2 666814.7 715215.0 686444.7 790687.3
## 1761 1762 1763 1764 1765 1766 1767 1768
## 673446.7 703339.9 699252.0 697875.1 700749.7 660665.7 679013.6 665419.9
## 1769 1770 1771 1772 1773 1774 1775 1776
## 702659.7 679116.7 678956.7 685716.5 729789.6 677712.3 692672.8 742535.9
## 1777 1778 1779 1780 1781 1782 1783 1784
## 689333.9 700782.2 698215.9 706170.2 697740.3 698167.7 690021.5 697758.1
## 1785 1786 1787 1788 1789 1790 1791 1792
## 716596.2 718029.2 686768.1 711692.4 705623.9 762422.3 684450.9 726443.5
## 1793 1794 1795 1796 1797 1798 1799 1800
## 711090.7 708266.5 723119.0 763006.0 696551.3 709135.3 697540.5 673707.2
## 1801 1802 1803 1804 1805 1806 1807 1808
## 669002.4 706535.8 682350.5 720139.3 713853.4 769900.8 715220.4 697893.0
## 1809 1810 1811 1812 1813 1814 1815 1816
## 711521.9 775374.8 712954.8 718806.3 714106.3 698321.0 692414.8 699127.4
## 1817 1818 1819 1820 1821 1822 1823 1824
## 697856.1 672529.3 709635.9 705663.3 695902.0 677045.2 721884.9 708038.5
## 1825 1826 1827 1828 1829 1830 1831 1832
## 725803.8 697613.4 742519.9 735232.4 726271.6 722286.5 702155.6 678892.1
## 1833 1834 1835 1836 1837 1838 1839 1840
## 725619.5 711941.1 767385.5 687298.5 726865.6 742142.6 738019.2 736818.3
## 1841 1842 1843 1844 1845 1846 1847 1848
## 691286.1 713207.8 683158.5 734730.5 699484.8 742526.3 816870.0 760272.6
## 1849 1850 1851 1852 1853 1854 1855 1856
## 717566.2 711272.2 699053.7 725368.6 810735.5 708570.8 750295.6 725335.2
## 1857 1858 1859 1860 1861 1862 1863 1864
## 713875.5 708881.3 712720.6 721991.1 732005.5 754144.3 729749.5 743183.3
## 1865 1866 1867 1868 1869 1870 1871 1872
## 835624.3 709863.7 722789.3 733702.9 729715.2 716985.5 705564.8 701469.5
## 1873 1874 1875 1876 1877 1878 1879 1880
## 707224.1 734030.1 780122.8 732521.4 728621.4 723148.5 729612.1 746119.2
## 1881 1882 1883 1884 1885 1886 1887 1888
## 721776.3 721626.2 721565.4 722175.9 823901.8 720615.7 749124.3 725457.5
## 1889 1890 1891 1892 1893 1894 1895 1896
## 734865.5 759120.2 729616.2 747345.4 732541.9 750383.6 723006.2 752682.5
## 1897 1898 1899 1900 1901 1902 1903 1904
## 763067.9 750824.9 743408.1 731790.5 701932.1 712992.5 745835.2 724142.5
## 1905 1906 1907 1908 1909 1910 1911 1912
## 716407.8 762928.3 734851.5 704561.8 748165.8 757004.1 721880.2 715144.6
## 1913 1914 1915 1916 1917 1918 1919 1920
## 731824.3 770228.4 746948.1 728807.0 746724.9 757152.9 745476.4 731400.2
## 1921 1922 1923 1924 1925 1926 1927 1928
## 711739.6 744844.7 741526.6 750744.2 741977.9 749912.3 761128.5 762951.5
## 1929 1930 1931 1932 1933 1934 1935 1936
## 758611.2 743684.6 761431.0 769098.7 743476.0 749093.6 772659.4 740109.2
## 1937 1938 1939 1940 1941 1942 1943 1944
## 741085.8 731571.8 783515.2 736069.7 766065.5 739284.7 745109.8 742358.3
## 1945 1946 1947 1948 1949 1950 1951 1952
## 765596.3 741351.3 746642.2 737469.8 742695.9 784661.1 757086.2 732993.2
## 1953 1954 1955 1956 1957 1958 1959 1960
## 740462.1 754576.0 722640.3 746029.0 729480.2 737358.7 796958.0 746048.3
## 1961 1962 1963 1964 1965 1966 1967 1968
## 761806.6 781602.7 741598.7 749377.6 783861.7 758616.2 742601.0 753596.7
## 1969 1970 1971 1972 1973 1974 1975 1976
## 781489.7 748169.7 775784.9 800697.0 756548.7 769154.9 771200.1 760433.6
## 1977 1978 1979 1980 1981 1982 1983 1984
## 717469.3 771111.9 745627.1 806217.6 726388.3 763791.3 748329.0 770991.5
## 1985 1986 1987 1988 1989 1990 1991 1992
## 777205.3 740464.0 750933.5 757132.8 805722.9 766136.9 734175.9 755915.6
## 1993 1994 1995 1996 1997 1998 1999 2000
## 743813.0 764103.9 742596.2 753273.7 752856.6 764840.1 764394.2 744382.9
## 2001 2002 2003 2004 2005 2006 2007 2008
## 761296.0 739336.9 755292.3 765588.5 748393.0 755612.6 769476.7 752550.1
## 2009 2010 2011 2012 2013 2014 2015 2016
## 775971.0 751226.0 765279.2 771071.5 830200.4 755779.0 766303.1 759493.8
## 2017 2018 2019 2020 2021 2022 2023 2024
## 768094.4 768010.8 769717.7 794461.6 758668.0 739232.5 750977.4 762869.7
## 2025 2026 2027 2028 2029 2030 2031 2032
## 778326.1 767345.9 758778.4 773732.6 777584.0 754739.9 778051.7 761093.2
## 2033 2034 2035 2036 2037 2038 2039 2040
## 803351.0 737404.1 764959.0 775434.4 772120.4 761235.0 763275.8 785589.4
## 2041 2042 2043 2044 2045 2046 2047 2048
## 824890.4 778196.2 764707.7 774095.4 788124.8 777976.6 790104.3 769438.5
## 2049 2050 2051 2052 2053
## 803173.0 776892.5 762600.3 778233.5 788305.9residuals(fit1)## 1 2 3 4 5
## -29167.99856 -21588.61298 -31928.44015 -20206.59376 -28767.08160
## 6 7 8 9 10
## -28253.13527 -26939.22639 -17901.38954 -28977.39667 -20363.40379
## 11 12 13 14 15
## -18692.43635 -29063.69807 -22291.36865 -38661.21867 -26188.95629
## 16 17 18 19 20
## -15316.79736 -22930.22568 -22476.08796 -25616.64354 -22018.58253
## 21 22 23 24 25
## -25822.88523 -27125.70267 -25073.56730 -28624.84930 -33147.51675
## 26 27 28 29 30
## -19849.75593 -19522.58047 -21873.87837 -26769.10598 -26823.70545
## 31 32 33 34 35
## -23421.36139 -29740.73368 -17906.82104 -24418.96156 -15454.76561
## 36 37 38 39 40
## -18569.83738 -39077.46745 -26555.76613 -25142.50992 -30949.70227
## 41 42 43 44 45
## -27214.50170 -17277.42503 -42763.05447 -25754.94453 -30481.33262
## 46 47 48 49 50
## -27935.70974 -21008.01299 -30308.97504 -19669.75804 -11769.32796
## 51 52 53 54 55
## -34120.30401 -38726.79154 -26140.95452 -19156.06997 -26265.62415
## 56 57 58 59 60
## -26112.45638 -27834.56957 -18838.99929 -33402.87170 -32508.09546
## 61 62 63 64 65
## -29291.95003 -29041.64661 -17348.42871 -19454.75284 -18930.68038
## 66 67 68 69 70
## -28651.93731 -24039.52142 -26372.06737 -31130.15630 -24980.82887
## 71 72 73 74 75
## -30644.51948 -35994.02219 -28658.69749 -26259.21771 -28158.22888
## 76 77 78 79 80
## -37765.21821 -19421.65979 -37957.26563 -28845.14972 -32494.91577
## 81 82 83 84 85
## -26499.11925 -15026.00437 -33594.60634 -27302.70073 -22044.89080
## 86 87 88 89 90
## -17503.79496 -29561.99106 -24377.12460 -51612.16146 -11339.01595
## 91 92 93 94 95
## -36033.02079 -12987.00880 -26041.59329 -37257.97251 -30369.43832
## 96 97 98 99 100
## -20050.96096 -24007.14538 -37627.16554 -29275.12462 -36326.29313
## 101 102 103 104 105
## -41928.94866 -7340.32101 -27233.17023 -21879.40340 -23028.45962
## 106 107 108 109 110
## -30144.19757 -18578.31267 -23208.77917 -29532.55601 -32256.30632
## 111 112 113 114 115
## -18328.67613 -27095.28832 -24423.41090 -24349.28460 -14237.50804
## 116 117 118 119 120
## -21539.65747 -24079.31672 -30265.87597 -17379.73693 -29442.34116
## 121 122 123 124 125
## -17236.08529 -29188.28278 -19509.55218 -22990.51768 -14877.31986
## 126 127 128 129 130
## -16512.39102 -22741.22401 -24960.05321 -20393.12614 -22861.89661
## 131 132 133 134 135
## -14384.99174 -51668.66887 -31428.42751 -13025.48192 -27724.48941
## 136 137 138 139 140
## -18692.45444 -67124.50897 -28663.50366 -27518.24873 -22604.70842
## 141 142 143 144 145
## -21139.59603 -27994.17904 -17492.23645 -20367.86811 -19337.22061
## 146 147 148 149 150
## -19321.94735 -22574.99040 -21727.55179 -27089.84885 -9817.86531
## 151 152 153 154 155
## -31401.07852 -26240.16419 -20734.58920 -21084.39535 -11808.84653
## 156 157 158 159 160
## -19979.39487 -23970.41242 -24630.24106 -6258.85674 -23587.80272
## 161 162 163 164 165
## -20471.94728 -6130.43110 -24036.27426 -6560.61889 -10920.68226
## 166 167 168 169 170
## -15877.13240 -16885.39168 -10945.41933 -33075.19198 -12798.28189
## 171 172 173 174 175
## -29051.99960 -4357.37526 -11993.02216 -18432.19829 -9216.67618
## 176 177 178 179 180
## -5372.47366 -15679.46406 -20664.18897 -18131.64975 -20540.56040
## 181 182 183 184 185
## -3692.63685 -1614.26022 -7627.24920 -19885.69734 -26570.55335
## 186 187 188 189 190
## -20935.59612 -15186.95928 -11669.23071 -12129.33328 10502.59146
## 191 192 193 194 195
## -642.19476 -9036.06287 -18683.14312 -30144.19955 -4509.25674
## 196 197 198 199 200
## -12240.19579 -14238.95839 -2513.60329 -18960.21267 -2007.61786
## 201 202 203 204 205
## -15792.33624 -17907.43399 -16323.90147 -3766.11292 -14660.07506
## 206 207 208 209 210
## -8925.72151 -13305.45924 -27246.46012 -6427.15860 -19326.71308
## 211 212 213 214 215
## -11531.05057 -19836.16724 -22000.65165 1864.56555 -22795.81144
## 216 217 218 219 220
## -11098.31961 -6316.98276 -3300.31666 -29375.33204 -13823.23365
## 221 222 223 224 225
## -30632.92941 -10655.78297 -10949.39553 -10026.63941 3215.74081
## 226 227 228 229 230
## -8641.16622 -5197.92931 -10876.88465 -14776.01323 -12694.66324
## 231 232 233 234 235
## -11145.97010 -13583.32930 -7047.60431 -13147.00119 -2744.33678
## 236 237 238 239 240
## -7515.28677 -8923.27150 -24821.39336 -7407.74640 -6658.72357
## 241 242 243 244 245
## -12442.18202 -576.45481 -21294.30895 -4248.50448 -2084.32709
## 246 247 248 249 250
## -6639.61191 -10691.50991 -8860.95766 -11318.63947 519.00858
## 251 252 253 254 255
## 374.96287 -13125.29297 8566.83132 -13187.50848 -1009.49909
## 256 257 258 259 260
## -15198.65741 10242.28910 1933.74451 9545.47077 -16001.55266
## 261 262 263 264 265
## -8580.73827 -12560.07666 -12695.32369 3437.53511 1816.49824
## 266 267 268 269 270
## 7185.58339 -7426.34073 -6402.99101 -10977.33682 -9034.98805
## 271 272 273 274 275
## -6500.35786 -18971.17382 -15957.80882 -6014.16010 -17415.92583
## 276 277 278 279 280
## -14507.04719 -14266.29943 -4841.54711 -2939.55873 -12573.20767
## 281 282 283 284 285
## -10565.08847 -9431.86306 -3098.89917 -7494.16514 -10973.93103
## 286 287 288 289 290
## 1716.97904 -9820.27465 -12539.97504 -9633.57591 14983.31786
## 291 292 293 294 295
## -6795.35521 1773.12148 4611.16316 -14310.93190 -107298.56585
## 296 297 298 299 300
## -1781.31831 -11263.44352 -2099.14405 -3566.85564 -16016.89965
## 301 302 303 304 305
## 7334.24731 -3124.49767 -6998.69956 -7108.35570 -408.98526
## 306 307 308 309 310
## -13460.97379 -8002.08128 -2652.17901 3002.15942 -9420.99902
## 311 312 313 314 315
## -25419.37955 -11128.41761 -9870.53051 6178.14736 -4227.10668
## 316 317 318 319 320
## 3472.28327 2491.75542 3787.49678 15207.34896 5725.51945
## 321 322 323 324 325
## -10378.61252 -17690.38627 14216.95564 17073.90365 20365.92551
## 326 327 328 329 330
## 3671.49737 13705.56811 752.73495 22372.75143 -4987.02678
## 331 332 333 334 335
## 10151.32459 16504.28171 17529.49270 -6346.83988 4566.78803
## 336 337 338 339 340
## 15281.38217 10576.86811 -5250.81599 20696.76550 8798.07060
## 341 342 343 344 345
## 6035.55203 13730.06465 16948.34013 1688.78832 20391.24425
## 346 347 348 349 350
## 20788.78861 6484.58777 11796.11593 2851.78687 -11010.56612
## 351 352 353 354 355
## 13548.77895 2010.93551 10661.58523 -2507.32426 17827.01487
## 356 357 358 359 360
## 21941.05865 696.46590 -4517.90474 22856.39124 3133.91502
## 361 362 363 364 365
## 8568.75600 4105.66614 4679.17936 16677.51983 -21092.99940
## 366 367 368 369 370
## 16018.54260 10737.49441 18709.36584 -9884.30027 10043.58106
## 371 372 373 374 375
## 13197.49346 11278.38540 1784.85658 7978.58187 657.16702
## 376 377 378 379 380
## 1441.61204 16276.56728 7322.47450 9818.00099 -3913.02806
## 381 382 383 384 385
## 27944.24700 8106.28618 16283.92603 -926.74584 22620.92389
## 386 387 388 389 390
## 399.28649 21043.98181 27572.03012 13333.35672 -19524.05717
## 391 392 393 394 395
## -14306.53577 3411.69151 4125.34946 2310.50292 1730.18571
## 396 397 398 399 400
## 20234.88037 24374.47025 1950.82895 21441.66419 23954.90978
## 401 402 403 404 405
## 32065.65672 25729.95097 -1467.11292 13986.90317 -1394.99499
## 406 407 408 409 410
## 14451.36844 17655.53091 26274.65435 10909.52093 4046.20717
## 411 412 413 414 415
## 16064.42726 13527.46182 22126.30137 12283.12996 6359.58407
## 416 417 418 419 420
## 34726.11881 5625.61882 31375.82415 26475.66403 17161.76674
## 421 422 423 424 425
## 24290.41045 7982.11782 19485.55462 8316.65484 20865.39141
## 426 427 428 429 430
## 23104.18200 5541.22690 39.21894 22260.20506 24737.11359
## 431 432 433 434 435
## 14250.87514 27915.99894 32576.63958 15717.18404 29552.83202
## 436 437 438 439 440
## 30775.27591 14827.56714 24517.02170 21700.97373 41574.59376
## 441 442 443 444 445
## 18216.44820 12748.04200 19661.44633 13543.17277 20003.18877
## 446 447 448 449 450
## 24357.10561 22221.06624 -1755.91604 22015.54960 11582.75258
## 451 452 453 454 455
## 20897.67770 37578.43455 28904.12669 24310.62403 -2743.24737
## 456 457 458 459 460
## 5007.40141 42343.49009 38966.68491 8959.17145 12944.71589
## 461 462 463 464 465
## 18060.79121 11363.99822 15678.23819 16715.39796 24669.47903
## 466 467 468 469 470
## 15610.60190 15943.50208 22618.19015 22455.64121 17581.28441
## 471 472 473 474 475
## 22236.86801 27188.55603 25464.43703 30856.39155 24364.09750
## 476 477 478 479 480
## 1487.11473 24355.59691 26128.76131 26964.58438 20266.91456
## 481 482 483 484 485
## 43075.79774 2312.71127 21944.26602 47632.60544 21576.41979
## 486 487 488 489 490
## 43616.80995 15921.66944 8150.51722 24147.59012 32738.85495
## 491 492 493 494 495
## 22856.44635 14091.29831 11453.71256 -1664.91038 16904.82907
## 496 497 498 499 500
## 30847.74298 15450.10479 36410.13700 23940.05757 34632.73050
## 501 502 503 504 505
## 38003.65017 33963.68468 24559.21410 25619.26572 25772.12150
## 506 507 508 509 510
## 32751.77254 39673.24622 14805.25636 50256.79682 21049.83552
## 511 512 513 514 515
## 50226.08857 35785.16522 29643.30334 34143.56548 44216.95891
## 516 517 518 519 520
## 35166.18489 29301.16852 43230.33589 38595.92196 50617.13987
## 521 522 523 524 525
## 38444.98260 39045.21803 36785.23478 27743.09930 38708.44733
## 526 527 528 529 530
## 37804.49290 49567.69335 29011.45770 40057.91771 40629.56957
## 531 532 533 534 535
## 54008.11857 45907.02057 39945.70847 21218.82652 33631.61852
## 536 537 538 539 540
## 38522.61550 42967.45394 29749.36846 23734.05048 44282.36999
## 541 542 543 544 545
## 39645.81891 35064.15845 51313.89082 35303.10979 39022.77794
## 546 547 548 549 550
## 42423.18423 39525.70368 60421.21685 42172.81482 33962.27306
## 551 552 553 554 555
## 44397.42261 25276.22710 34292.06282 62245.98567 46105.17640
## 556 557 558 559 560
## 57608.33011 48489.73201 34752.63453 51354.31106 37362.17800
## 561 562 563 564 565
## 42438.69258 43631.89082 18283.08765 68860.03889 49168.45378
## 566 567 568 569 570
## 49705.95267 43881.86495 49548.85876 51868.02823 48556.92757
## 571 572 573 574 575
## 34262.09659 59746.43921 32620.36642 52481.93225 62876.98547
## 576 577 578 579 580
## 60584.19353 57692.93365 37551.23013 60109.21283 51628.37824
## 581 582 583 584 585
## 58776.35784 61638.58918 49438.51105 22802.12405 57532.58108
## 586 587 588 589 590
## 49484.17002 65343.93808 53207.50569 55207.60720 43458.71916
## 591 592 593 594 595
## 54502.76986 61408.26461 40951.35051 58130.24021 78121.14802
## 596 597 598 599 600
## 60378.15722 56394.98157 50851.38567 48036.54735 46422.70594
## 601 602 603 604 605
## 58042.02201 51930.51385 58293.82311 57818.57651 54984.89997
## 606 607 608 609 610
## 58323.94437 72167.77647 43315.61521 42246.01260 41539.45130
## 611 612 613 614 615
## 48714.53279 59208.73051 60406.40199 50928.63004 29962.22341
## 616 617 618 619 620
## 66350.41294 46482.41127 67641.38971 59946.37029 65934.64817
## 621 622 623 624 625
## 68025.25523 75875.46537 51207.06999 62327.78622 59535.67421
## 626 627 628 629 630
## 47146.90129 52085.38672 58493.55011 63552.67090 64703.09991
## 631 632 633 634 635
## 39354.09827 56484.95085 80419.70710 63300.96758 64645.73318
## 636 637 638 639 640
## 45339.41316 48071.80869 71954.78072 66117.32462 66445.44322
## 641 642 643 644 645
## 50087.59681 86597.39820 84996.36398 85618.89394 84405.56736
## 646 647 648 649 650
## 86593.16774 83679.57555 85810.29152 81368.13184 86734.04071
## 651 652 653 654 655
## 86327.76412 84063.64408 84803.08940 68046.02356 90880.90201
## 656 657 658 659 660
## 82906.43062 85669.66058 84104.87608 83051.73560 83631.91112
## 661 662 663 664 665
## 80680.00509 81237.81486 78090.44367 79529.12888 84041.68110
## 666 667 668 669 670
## 80789.03011 77724.73803 82886.82082 76482.17956 78624.29289
## 671 672 673 674 675
## 78531.03098 71201.11662 74746.82043 78676.33596 75067.13001
## 676 677 678 679 680
## 78274.34168 67003.92414 72086.12553 79994.07951 72793.65593
## 681 682 683 684 685
## 74157.31512 63125.44725 74348.65719 74722.15052 76626.66637
## 686 687 688 689 690
## 74939.89278 72475.02034 69690.68688 73283.86174 73628.59178
## 691 692 693 694 695
## 72778.67481 77501.71163 68894.47735 65857.53070 69834.09505
## 696 697 698 699 700
## 73823.94696 73302.20827 50638.19400 70030.99478 69775.48265
## 701 702 703 704 705
## 67384.38819 62540.21651 66032.79385 68258.55322 65558.77488
## 706 707 708 709 710
## 62981.42904 66943.44226 65674.00959 60884.86932 69028.75402
## 711 712 713 714 715
## 64514.71593 65446.18220 67772.47449 66519.24473 61122.91976
## 716 717 718 719 720
## 62720.71561 55118.18305 66484.05717 58224.71336 66378.76803
## 721 722 723 724 725
## 62945.20891 62851.94700 54743.09999 52900.64736 55788.23568
## 726 727 728 729 730
## 55087.79122 58991.80786 53914.51575 60114.82595 53303.04936
## 731 732 733 734 735
## 62338.22597 61300.61911 65492.90870 52155.38670 62511.44443
## 736 737 738 739 740
## 63288.98416 62258.28258 56911.87162 56815.96421 45858.96884
## 741 742 743 744 745
## 58841.94777 58852.65631 58827.69063 50592.79115 59510.10072
## 746 747 748 749 750
## 55316.83969 57403.02886 51319.07918 54029.38577 57030.70699
## 751 752 753 754 755
## 52589.51347 53730.68840 52285.07198 52879.53686 51096.76660
## 756 757 758 759 760
## 56847.76734 46979.25474 55393.17672 55300.69260 53571.17179
## 761 762 763 764 765
## 55154.11778 52644.18776 53913.34746 48079.57631 53116.66066
## 766 767 768 769 770
## 54348.64841 50913.51871 46012.18691 42730.23489 53482.24464
## 771 772 773 774 775
## 51341.02303 51690.12161 33902.10014 50052.89982 46292.17279
## 776 777 778 779 780
## 52238.15319 51184.09024 48528.70100 48488.25341 54903.41488
## 781 782 783 784 785
## 47763.29258 43238.39434 51600.17101 48587.81954 43999.04640
## 786 787 788 789 790
## 50904.90536 39631.90792 38576.82654 46942.10777 47330.04908
## 791 792 793 794 795
## 42907.92981 41700.86254 44785.19829 48436.49967 43478.18943
## 796 797 798 799 800
## 41824.72749 43633.94488 43539.09147 39088.15879 42351.94917
## 801 802 803 804 805
## 27159.82679 31319.86273 42175.41450 40761.11232 34151.87310
## 806 807 808 809 810
## 42505.72823 43435.63247 36356.24656 30128.76943 37890.08718
## 811 812 813 814 815
## 39575.60692 22817.38488 34985.50515 36906.47708 39132.97860
## 816 817 818 819 820
## 32403.42349 37425.67271 35706.64794 30751.65891 40709.54214
## 821 822 823 824 825
## 38425.50681 26570.78124 36615.20466 39078.88784 32182.13309
## 826 827 828 829 830
## 36177.05847 27867.72108 18331.34290 31092.44940 34813.85248
## 831 832 833 834 835
## 209.46989 27969.60638 19039.13145 16575.36646 10809.70528
## 836 837 838 839 840
## 30455.37165 22816.00470 25492.58571 18733.94121 15389.34502
## 841 842 843 844 845
## 20792.35816 21868.09995 29216.64601 23688.44009 7612.83637
## 846 847 848 849 850
## 25487.57086 18969.99779 11710.56702 21038.33554 11028.00431
## 851 852 853 854 855
## 22377.42799 22518.33222 15726.77556 20647.23501 21917.55750
## 856 857 858 859 860
## 18511.77867 21146.38406 17445.26546 18330.57858 13554.97880
## 861 862 863 864 865
## 545.01638 15439.26727 18252.80480 19836.13555 13279.23212
## 866 867 868 869 870
## -34734.42199 19617.38468 5398.74400 18744.11628 17929.88050
## 871 872 873 874 875
## 11563.74947 11669.57481 14415.12721 15577.51821 13648.20550
## 876 877 878 879 880
## 19134.02462 11340.99236 11600.90525 15687.55306 18214.41506
## 881 882 883 884 885
## 9964.34582 13642.89832 64692.91107 10242.48477 -388.96307
## 886 887 888 889 890
## 8509.23094 14862.82786 -13519.99690 8621.02763 6117.92331
## 891 892 893 894 895
## 5497.64265 9045.35993 2099.57956 8867.75539 2699.54050
## 896 897 898 899 900
## 6407.34718 -31954.04429 10307.30447 6991.47467 8464.09016
## 901 902 903 904 905
## 8842.90963 14721.88843 3106.20555 8557.57111 6731.42185
## 906 907 908 909 910
## 3320.23491 2396.28807 3618.72503 1436.34842 2740.43327
## 911 912 913 914 915
## 7803.66276 8405.47661 642.36807 7686.26156 -3820.30114
## 916 917 918 919 920
## 6535.91761 -6979.59342 -105087.22649 -39649.58423 957.35299
## 921 922 923 924 925
## -952.98994 2411.97293 -2679.10672 -223.22183 6512.09351
## 926 927 928 929 930
## -2137.93811 -3908.19242 -60.79842 -3274.92445 1731.10073
## 931 932 933 934 935
## 5251.02942 -15061.95966 4657.40563 -120.39597 2478.66409
## 936 937 938 939 940
## -6574.60666 -20147.37503 -4230.08350 -5727.32063 -9866.48076
## 941 942 943 944 945
## -1558.20885 -2150.91848 -5261.35216 -9673.18626 -1399.72344
## 946 947 948 949 950
## 2963.10978 -9293.22832 -6216.02396 -5798.15680 -5931.57697
## 951 952 953 954 955
## -12684.40107 -4369.59222 -2772.34214 -16106.84860 -18821.08667
## 956 957 958 959 960
## -6554.23161 -6402.51197 -4655.55761 -3149.18679 -12786.33149
## 961 962 963 964 965
## -6330.13162 -9093.30607 -15671.68868 -14096.07692 -14986.37800
## 966 967 968 969 970
## -7016.67779 -11093.29892 -11190.02004 -16882.70051 -6438.37955
## 971 972 973 974 975
## -6691.32548 -7166.70529 -11004.45118 -9138.00028 -7256.91089
## 976 977 978 979 980
## -17283.31937 -16856.90537 -11121.82937 -24997.90598 -8539.32398
## 981 982 983 984 985
## -5140.73788 -15407.10532 -20119.05314 -22412.80619 -48468.69956
## 986 987 988 989 990
## -12602.00150 -10979.47839 -24658.47531 -21111.27195 -29000.76594
## 991 992 993 994 995
## -23178.90468 -16676.23852 -31383.72621 -18657.24824 -23403.86072
## 996 997 998 999 1000
## -15307.33856 -24090.64596 -22860.42544 -18428.31537 -16734.64584
## 1001 1002 1003 1004 1005
## -24357.14249 -25769.56247 -21425.83084 -19366.90136 -15863.99516
## 1006 1007 1008 1009 1010
## -18389.90891 -16919.52445 -14374.48333 -15554.90391 -13941.19775
## 1011 1012 1013 1014 1015
## -25946.16530 -25533.47369 -20660.44190 -16196.10651 -26163.98403
## 1016 1017 1018 1019 1020
## -22824.13477 -17516.95660 -40518.69345 -19900.50484 -22138.47172
## 1021 1022 1023 1024 1025
## -28077.07977 -25194.38864 -21604.54304 -22260.43149 -17838.78800
## 1026 1027 1028 1029 1030
## -34525.33197 -22379.40657 -25360.87221 -25294.90879 -22583.81558
## 1031 1032 1033 1034 1035
## -34430.36428 -24908.93161 -27415.41555 -27232.49206 -22965.85859
## 1036 1037 1038 1039 1040
## -20213.90247 -27612.51199 -34082.67831 -27837.25991 -24206.70386
## 1041 1042 1043 1044 1045
## -32567.53845 -28425.12510 -23518.76693 -23710.65656 -33136.62648
## 1046 1047 1048 1049 1050
## -27289.38257 -35712.80840 -28204.23488 -28297.60635 -31629.34647
## 1051 1052 1053 1054 1055
## -30909.80331 -36772.11807 -32625.76752 -31646.80636 -36475.02407
## 1056 1057 1058 1059 1060
## -32155.91013 -31655.36951 -45521.49096 -31557.07959 -30430.73361
## 1061 1062 1063 1064 1065
## -37529.11235 -32599.39281 -32681.38089 -31960.11469 -34341.96403
## 1066 1067 1068 1069 1070
## -34578.74458 -45080.28773 -34760.33318 -43428.72398 -31538.88731
## 1071 1072 1073 1074 1075
## -46511.44057 -38687.17843 -40442.69138 -33098.53504 -38499.96911
## 1076 1077 1078 1079 1080
## -38937.30487 -35670.36742 -43213.64339 -34873.54254 -39878.34349
## 1081 1082 1083 1084 1085
## -46431.18328 -43836.42720 -45126.47927 -46852.67082 -36916.62848
## 1086 1087 1088 1089 1090
## -51733.17636 -41613.88607 -45192.59873 -42040.77454 -39928.51365
## 1091 1092 1093 1094 1095
## -39408.05774 -39681.99575 -45949.29598 -41333.26013 -48294.35060
## 1096 1097 1098 1099 1100
## -45031.43848 -42495.02569 -45211.63869 -41797.75100 -45371.15224
## 1101 1102 1103 1104 1105
## -40583.65004 -52136.56832 -40071.65202 -53921.43077 -45782.65491
## 1106 1107 1108 1109 1110
## -46469.57307 -46521.01827 -46069.84589 -53449.11493 -46271.83688
## 1111 1112 1113 1114 1115
## -47312.78773 -42012.69651 -42915.31741 -48238.64323 -50805.49303
## 1116 1117 1118 1119 1120
## -48119.36123 -47414.55111 -57482.84662 -47618.34471 -46465.99186
## 1121 1122 1123 1124 1125
## -52408.40796 -46925.14624 -46306.28043 -49707.52326 -61710.55879
## 1126 1127 1128 1129 1130
## -48702.98280 -53515.58706 -58467.01480 -74206.25476 -51386.42366
## 1131 1132 1133 1134 1135
## -52872.29266 -50782.84120 -52778.18938 -48834.63955 -59349.94960
## 1136 1137 1138 1139 1140
## -64348.38247 -50743.10159 -49670.38364 -53406.04100 -51715.33070
## 1141 1142 1143 1144 1145
## -55738.32380 -53034.10077 -53265.71997 -53166.79992 -59995.08562
## 1146 1147 1148 1149 1150
## -55279.18559 -54448.01783 -57911.85833 -73834.05745 -54254.26708
## 1151 1152 1153 1154 1155
## -64229.35197 -86119.06083 -57057.17640 -55809.65503 -56997.03957
## 1156 1157 1158 1159 1160
## -77650.95364 -60264.07259 -65760.27622 -57898.83357 -60790.98436
## 1161 1162 1163 1164 1165
## -57147.00839 -56911.40212 -62634.90169 -59845.19840 -60691.22774
## 1166 1167 1168 1169 1170
## -65812.04890 -57655.39293 -59346.53506 -61569.11461 -60559.51063
## 1171 1172 1173 1174 1175
## -61962.44467 -69645.99761 -69151.39612 -64110.09567 -64553.08630
## 1176 1177 1178 1179 1180
## -67172.93261 -66464.01544 -61311.57106 -64626.94324 -62854.99183
## 1181 1182 1183 1184 1185
## -76918.19140 -66913.37378 -59806.90897 -69044.98430 -65751.84357
## 1186 1187 1188 1189 1190
## -72979.80068 -74750.19888 -70714.64235 -68384.22209 -69937.73276
## 1191 1192 1193 1194 1195
## -68953.91810 -68176.66076 -66874.58890 -66094.40367 -77398.61909
## 1196 1197 1198 1199 1200
## -67900.44604 -70408.66775 -74172.98554 -72673.40320 -67926.31483
## 1201 1202 1203 1204 1205
## -72027.21979 -70076.79491 -71331.66814 -73343.07290 -69584.40672
## 1206 1207 1208 1209 1210
## -73074.23936 -77938.63982 -84132.43238 -74506.89932 -78200.99528
## 1211 1212 1213 1214 1215
## -69634.70879 -77751.02133 -80584.91166 -75903.44504 -73096.63943
## 1216 1217 1218 1219 1220
## -71456.12211 -98583.55812 -75184.25869 -73920.28124 -77846.05003
## 1221 1222 1223 1224 1225
## -80176.66985 -79637.77358 -77351.34910 -81081.36015 -75147.10291
## 1226 1227 1228 1229 1230
## -77391.32079 -73391.21316 -77465.18073 -77803.46010 -78775.48323
## 1231 1232 1233 1234 1235
## -80562.47575 -80445.37658 -80674.54692 -92040.28879 -75653.62632
## 1236 1237 1238 1239 1240
## -82659.64281 -78192.38929 -78862.53789 -82122.09416 -81525.46256
## 1241 1242 1243 1244 1245
## -83682.21779 -99240.08865 -83394.05061 -91497.86836 -84595.78798
## 1246 1247 1248 1249 1250
## -89056.77302 -90599.51143 -82677.35568 -94181.55197 -80431.56901
## 1251 1252 1253 1254 1255
## -83616.67263 -89638.49778 -92108.44343 -87437.74002 -95003.94866
## 1256 1257 1258 1259 1260
## -86509.36694 -87938.95598 -89233.48590 -84924.38948 -87648.13979
## 1261 1262 1263 1264 1265
## -97763.06117 -87530.74829 -102106.14380 -140490.03013 -94436.73092
## 1266 1267 1268 1269 1270
## -90713.46942 -86671.82130 -91477.24405 -94187.18379 -80205.69870
## 1271 1272 1273 1274 1275
## -87053.40163 -100959.43919 -96315.54964 -108627.87701 -102381.93510
## 1276 1277 1278 1279 1280
## -107710.24166 -126354.74686 -119957.67279 -114365.64141 -110290.59923
## 1281 1282 1283 1284 1285
## -106339.63280 -103068.85260 -108293.21595 -91056.77528 -102821.19256
## 1286 1287 1288 1289 1290
## -126562.55232 -122742.50562 -105912.10906 -128020.39306 -106155.28770
## 1291 1292 1293 1294 1295
## -102779.85384 -107603.61547 -111934.55835 -109087.61361 -101025.77810
## 1296 1297 1298 1299 1300
## -101086.66306 -110139.33345 -155718.64742 -86422.81341 -105688.76830
## 1301 1302 1303 1304 1305
## -83822.18729 -97956.33220 -105721.96132 -88279.99618 -90788.26169
## 1306 1307 1308 1309 1310
## -96959.67654 -93857.59945 4447.90690 -93725.08938 -94363.64145
## 1311 1312 1313 1314 1315
## -97334.25382 -90968.38289 -108567.61033 -96663.63300 -88610.91530
## 1316 1317 1318 1319 1320
## -94775.98691 -102364.60841 -105283.40382 -117042.74583 -89086.38429
## 1321 1322 1323 1324 1325
## -108775.83746 -82594.71278 -93373.84325 -101024.72960 -102907.01796
## 1326 1327 1328 1329 1330
## -89157.30471 -92259.61432 -105305.10426 -93365.49382 -98935.55329
## 1331 1332 1333 1334 1335
## -83453.16048 -99990.50966 -86710.84157 -84063.50067 -89626.23023
## 1336 1337 1338 1339 1340
## -80614.80896 -100675.55217 -96164.58302 -82895.83735 -82932.93024
## 1341 1342 1343 1344 1345
## -73163.02024 -76940.68440 -87910.18019 -83181.24764 -85174.47329
## 1346 1347 1348 1349 1350
## -82020.15058 -88312.73946 -83036.55659 -84366.06928 -82405.79095
## 1351 1352 1353 1354 1355
## -83121.73411 -73908.88366 -80014.76708 -80213.79169 -70083.62900
## 1356 1357 1358 1359 1360
## -87288.38931 -101334.97043 -96334.21298 -86169.14291 -60755.63315
## 1361 1362 1363 1364 1365
## -84374.37951 -68633.90341 -87808.37059 -84492.66891 -84143.13155
## 1366 1367 1368 1369 1370
## -79414.08603 -79657.25673 -80923.08416 -74637.86868 -74464.00802
## 1371 1372 1373 1374 1375
## -76685.62229 -75333.60203 -69099.35793 -82051.92435 -80796.79252
## 1376 1377 1378 1379 1380
## -70074.98663 -96703.17554 -77490.54683 -70314.02355 -71983.75835
## 1381 1382 1383 1384 1385
## -72427.68471 -77876.47260 -85090.07222 -88287.21114 -66794.40977
## 1386 1387 1388 1389 1390
## -81373.18919 -52121.95325 -59826.13129 -75523.47450 -73694.44761
## 1391 1392 1393 1394 1395
## -74190.79227 -74072.57909 -84894.14430 -66461.57084 -66994.96721
## 1396 1397 1398 1399 1400
## -77902.17055 -75699.28666 -96576.86104 -78613.13689 -72095.46653
## 1401 1402 1403 1404 1405
## -70268.50430 -50697.93057 -63132.26511 -61280.97879 -79028.12180
## 1406 1407 1408 1409 1410
## -54142.39893 -83932.93944 -46343.69334 -64008.77046 -49904.54875
## 1411 1412 1413 1414 1415
## -50757.25276 -75817.55213 -58938.86338 -58567.28052 -57054.03387
## 1416 1417 1418 1419 1420
## -54648.23850 -61211.56832 -57054.18812 -58515.05388 -67296.73801
## 1421 1422 1423 1424 1425
## -46524.16605 -57622.91993 -62532.77355 -74518.90207 -52325.24366
## 1426 1427 1428 1429 1430
## -32196.31863 -68961.44806 -60299.19716 -53195.27454 -48717.13414
## 1431 1432 1433 1434 1435
## -37670.50033 -47262.50941 -38087.92891 -47469.03527 -35836.46803
## 1436 1437 1438 1439 1440
## -51345.11285 -49079.14233 -53389.76584 -49424.81629 -54202.55279
## 1441 1442 1443 1444 1445
## -50896.48150 -29833.31209 -41381.33398 -55658.62095 -39081.95534
## 1446 1447 1448 1449 1450
## -44878.73195 -55053.00486 -50185.37840 -52925.03774 -39688.85191
## 1451 1452 1453 1454 1455
## -46778.82345 -45149.95756 -40057.70181 -23954.23847 -47852.40060
## 1456 1457 1458 1459 1460
## -37057.85688 -33759.75367 -37848.43888 -47705.25946 -32262.35640
## 1461 1462 1463 1464 1465
## -40093.15315 -43157.17126 -29281.06766 -26450.18501 -34869.07738
## 1466 1467 1468 1469 1470
## -40632.77130 -34667.20303 -18530.83868 -37777.22104 -31709.95932
## 1471 1472 1473 1474 1475
## -20125.34386 -21758.99665 -33864.69757 -46950.59520 -18455.97886
## 1476 1477 1478 1479 1480
## -29190.21554 -25876.55535 -25366.42091 -29792.46361 -35870.20936
## 1481 1482 1483 1484 1485
## -22076.59618 944.01091 -34806.17225 -42122.58646 -20548.02404
## 1486 1487 1488 1489 1490
## -13583.85556 -35347.97217 -35130.39456 -14725.74860 -18326.56124
## 1491 1492 1493 1494 1495
## -16830.66381 -24676.34162 -8516.58208 -13965.31667 -15527.46863
## 1496 1497 1498 1499 1500
## -10830.55821 -40735.74436 -51632.62346 -15981.05340 -16628.13245
## 1501 1502 1503 1504 1505
## -21402.81568 -4606.73517 4770.33841 -14370.01199 -72509.77942
## 1506 1507 1508 1509 1510
## -29212.05544 871.17090 -9407.75393 -4615.53678 -15350.44848
## 1511 1512 1513 1514 1515
## -451.48185 -12805.73757 -15957.53402 -7940.45002 -13618.64509
## 1516 1517 1518 1519 1520
## -13672.95381 13042.33515 2854.26047 5122.15478 4744.74549
## 1521 1522 1523 1524 1525
## 13663.97906 16529.97154 2350.37466 -21723.95359 5575.08632
## 1526 1527 1528 1529 1530
## -10267.11714 4320.17684 12263.31712 136.50557 7507.65703
## 1531 1532 1533 1534 1535
## 135.36957 -7272.03403 2174.82822 20330.01583 9560.87820
## 1536 1537 1538 1539 1540
## 14778.22218 12050.81324 -4589.62313 3637.69439 -3863.90869
## 1541 1542 1543 1544 1545
## 19645.80338 18882.97453 33196.45014 16959.08333 -13962.83680
## 1546 1547 1548 1549 1550
## 12856.73352 -12828.92991 21384.50324 44357.95442 23600.94852
## 1551 1552 1553 1554 1555
## 6660.85474 12157.78290 22977.41394 1892.01985 34863.68637
## 1556 1557 1558 1559 1560
## 48000.46867 29408.97923 56694.52942 32336.70205 33659.81795
## 1561 1562 1563 1564 1565
## 9927.82452 31177.63388 17811.37277 20393.55935 -8090.38577
## 1566 1567 1568 1569 1570
## -9570.73732 20032.29086 53705.89349 33259.38173 34310.63665
## 1571 1572 1573 1574 1575
## 25600.89600 16707.94217 46360.02109 35658.12559 42826.42754
## 1576 1577 1578 1579 1580
## 48346.53784 41094.77869 39437.83373 52827.26489 43265.38497
## 1581 1582 1583 1584 1585
## 60532.32585 44887.31471 66833.96048 54799.86100 69662.97384
## 1586 1587 1588 1589 1590
## 18296.93913 46317.50971 55083.53381 46511.27403 40098.24867
## 1591 1592 1593 1594 1595
## 47176.48205 50959.43107 53205.09989 59526.37166 45511.28843
## 1596 1597 1598 1599 1600
## 60339.67475 72625.77372 56855.37738 51817.48385 67601.02147
## 1601 1602 1603 1604 1605
## 64727.54500 62328.67643 50476.53908 70312.33026 40182.79668
## 1606 1607 1608 1609 1610
## 47778.97298 51594.81285 73174.82516 77069.73266 52979.84120
## 1611 1612 1613 1614 1615
## 73744.92090 50476.63896 74704.92611 51965.73559 65079.55481
## 1616 1617 1618 1619 1620
## 45040.74194 76759.51951 67898.68827 38543.88039 58997.11221
## 1621 1622 1623 1624 1625
## 60282.74263 92007.56963 71524.07758 76593.83893 92154.61592
## 1626 1627 1628 1629 1630
## 56504.07430 98600.51945 81248.86920 74965.77755 99878.15849
## 1631 1632 1633 1634 1635
## 82687.43781 81404.91112 67807.37294 94549.61807 92354.96489
## 1636 1637 1638 1639 1640
## 109333.42013 74210.24059 74375.99273 82118.74884 89540.83968
## 1641 1642 1643 1644 1645
## 103416.76333 116318.53013 113831.58308 96465.13210 102099.18255
## 1646 1647 1648 1649 1650
## 82364.40149 87392.55467 77372.96359 106409.39273 54004.09775
## 1651 1652 1653 1654 1655
## 92461.07795 89299.71464 70727.39508 73351.47234 64489.17517
## 1656 1657 1658 1659 1660
## 81649.68146 91845.83874 76217.90160 58877.22820 87814.66533
## 1661 1662 1663 1664 1665
## 34242.73425 76690.86129 40841.77406 85431.99539 89383.89616
## 1666 1667 1668 1669 1670
## 91423.18973 84588.76942 48331.23064 69984.66960 76492.14709
## 1671 1672 1673 1674 1675
## 106613.43941 68052.55408 17613.00696 83858.29896 69998.19561
## 1676 1677 1678 1679 1680
## 82932.15490 85345.94830 88090.17520 68074.56398 35237.24215
## 1681 1682 1683 1684 1685
## 79035.15685 91436.68970 72398.96189 109634.32760 71511.67289
## 1686 1687 1688 1689 1690
## 92413.30861 85926.77512 60566.94509 72890.82503 46109.64003
## 1691 1692 1693 1694 1695
## 88177.66866 117699.92825 56454.00287 70029.33214 68183.01863
## 1696 1697 1698 1699 1700
## 71168.24506 77695.26556 57017.60948 54018.72172 81062.47227
## 1701 1702 1703 1704 1705
## 79116.03833 83769.43650 65279.97190 75969.64091 53924.56268
## 1706 1707 1708 1709 1710
## 9919.53486 83854.60997 71364.94204 52569.17318 73917.07129
## 1711 1712 1713 1714 1715
## 16712.69751 67327.16141 73427.96457 85724.11744 25722.46727
## 1716 1717 1718 1719 1720
## 66276.38223 88884.77959 70587.18912 51108.89388 64371.11635
## 1721 1722 1723 1724 1725
## 35364.29371 10716.90123 84472.54826 35752.93083 31787.44739
## 1726 1727 1728 1729 1730
## 68167.12578 65255.88891 73514.61229 14900.79684 85060.32936
## 1731 1732 1733 1734 1735
## 94322.72834 67661.58531 45033.54488 63987.60223 68017.73339
## 1736 1737 1738 1739 1740
## 72804.37199 53660.70243 57412.65971 47910.03501 71655.75758
## 1741 1742 1743 1744 1745
## -81281.17829 37818.02617 70775.25982 61184.48944 -6047.10240
## 1746 1747 1748 1749 1750
## 55188.03925 51930.02642 35335.40699 49287.23348 92853.87295
## 1751 1752 1753 1754 1755
## 69496.93639 64038.06277 41563.41800 59140.85033 65093.55511
## 1756 1757 1758 1759 1760
## 72489.81143 83185.33085 34785.04934 63555.33894 -40687.32760
## 1761 1762 1763 1764 1765
## 76553.26506 46660.10037 50747.99197 52124.91796 49250.28925
## 1766 1767 1768 1769 1770
## 89334.34714 70986.37146 84580.09047 47340.34938 70883.29077
## 1771 1772 1773 1774 1775
## 71043.33316 64283.48626 20210.37891 72287.70893 57327.15240
## 1776 1777 1778 1779 1780
## 7464.11694 60666.11974 49217.78468 51784.11842 43829.80784
## 1781 1782 1783 1784 1785
## 52259.69875 51832.25698 59978.53032 52241.94400 33403.79587
## 1786 1787 1788 1789 1790
## 31970.75430 63231.92841 38307.59547 44376.14191 -12422.33364
## 1791 1792 1793 1794 1795
## 65549.12030 23556.45191 38909.30512 41733.45010 26880.98636
## 1796 1797 1798 1799 1800
## -13005.95393 53448.65216 40864.71170 52459.48318 76292.84342
## 1801 1802 1803 1804 1805
## 80997.57760 43464.19343 67649.52276 29860.73609 36146.55280
## 1806 1807 1808 1809 1810
## -19900.83825 34779.56502 52106.98885 38478.10163 -25374.77640
## 1811 1812 1813 1814 1815
## 37045.20045 31193.72582 35893.70740 51679.00472 57585.15616
## 1816 1817 1818 1819 1820
## 50872.62743 52143.92386 77470.69642 40364.07802 44336.70592
## 1821 1822 1823 1824 1825
## 54097.99645 72954.80382 28115.12329 41961.49919 24196.17920
## 1826 1827 1828 1829 1830
## 52386.57484 7480.11070 14767.63500 23728.39319 27713.46737
## 1831 1832 1833 1834 1835
## 47844.41252 71107.87809 24380.45115 38058.93515 -17385.53401
## 1836 1837 1838 1839 1840
## 62701.49412 23134.38502 7857.41997 11980.84963 13181.68078
## 1841 1842 1843 1844 1845
## 58713.94333 36792.19892 66841.46147 15269.54486 50515.15289
## 1846 1847 1848 1849 1850
## 7473.74487 -66869.98299 -10272.56304 32433.81882 38727.80809
## 1851 1852 1853 1854 1855
## 50946.34338 24631.35183 -60735.45245 41429.16859 -295.62957
## 1856 1857 1858 1859 1860
## 24664.77746 36124.46582 41118.70042 37279.35572 28008.86856
## 1861 1862 1863 1864 1865
## 17994.46948 -4144.31856 20250.47534 6816.65253 -85624.27841
## 1866 1867 1868 1869 1870
## 40136.29126 27210.68379 16297.13205 20284.75101 33014.47353
## 1871 1872 1873 1874 1875
## 44435.19506 48530.45111 42775.90144 15969.93197 -30122.82736
## 1876 1877 1878 1879 1880
## 17478.62435 21378.62011 26851.48608 20387.90603 3880.79009
## 1881 1882 1883 1884 1885
## 28223.71357 28373.80319 28434.60728 27824.11602 -73901.81165
## 1886 1887 1888 1889 1890
## 29384.31611 875.66470 24542.52410 15134.54598 -9120.22453
## 1891 1892 1893 1894 1895
## 20383.82577 2654.56480 17458.13137 -383.55121 26993.76318
## 1896 1897 1898 1899 1900
## -2682.47795 -13067.87265 -824.87095 6591.86474 18209.53604
## 1901 1902 1903 1904 1905
## 48067.87411 37007.45804 4164.82340 25857.51492 33592.18828
## 1906 1907 1908 1909 1910
## -12928.33139 15148.47233 45438.18325 1834.15323 -7004.13859
## 1911 1912 1913 1914 1915
## 28119.82199 34855.36534 18175.72656 -20228.37932 3051.88719
## 1916 1917 1918 1919 1920
## 21192.99056 3275.05543 -7152.93019 4523.64891 18599.76371
## 1921 1922 1923 1924 1925
## 38260.37431 5155.31006 8473.41204 -744.16371 8022.05748
## 1926 1927 1928 1929 1930
## 87.66946 -11128.48575 -12951.48736 -8611.17860 6315.42620
## 1931 1932 1933 1934 1935
## -11431.00174 -19098.71244 6523.97501 906.37791 -22659.44660
## 1936 1937 1938 1939 1940
## 9890.78497 8914.19623 18428.15586 -33515.19541 13930.30816
## 1941 1942 1943 1944 1945
## -16065.48890 10715.27993 4890.17000 7641.70041 -15596.25872
## 1946 1947 1948 1949 1950
## 8648.71431 3357.81362 12530.22571 7304.11764 -34661.13890
## 1951 1952 1953 1954 1955
## -7086.20904 17006.81043 9537.85732 -4576.02817 27359.70696
## 1956 1957 1958 1959 1960
## 3971.00306 20519.81761 12641.26833 -46958.03595 3951.66970
## 1961 1962 1963 1964 1965
## -11806.60226 -31602.71460 8401.30991 622.37077 -33861.67928
## 1966 1967 1968 1969 1970
## -8616.20870 7399.00433 -3596.68704 -31489.73469 1830.34283
## 1971 1972 1973 1974 1975
## -25784.90000 -50697.01079 -6548.65974 -19154.88270 -21200.06263
## 1976 1977 1978 1979 1980
## -10433.55234 32530.66223 -21111.94907 4372.90440 -56217.57181
## 1981 1982 1983 1984 1985
## 23611.70747 -13791.33913 1671.03767 -20991.53769 -27205.28097
## 1986 1987 1988 1989 1990
## 9535.95349 -933.49668 -7132.82592 -55722.93719 -16136.87120
## 1991 1992 1993 1994 1995
## 15824.08647 -5915.62760 6186.95622 -14103.92606 7403.83776
## 1996 1997 1998 1999 2000
## -3273.71349 -2856.64567 -14840.12546 -14394.19648 5617.06412
## 2001 2002 2003 2004 2005
## -11296.00281 10663.08430 -5292.25501 -15588.52423 1607.04035
## 2006 2007 2008 2009 2010
## -5612.64597 -19476.68244 -2550.05023 -25971.04242 -1226.00847
## 2011 2012 2013 2014 2015
## -15279.16296 -21071.54845 -80200.44887 -5779.04617 -16303.08078
## 2016 2017 2018 2019 2020
## -9493.78260 -18094.35732 -18010.80005 -19717.72228 -44461.63468
## 2021 2022 2023 2024 2025
## -8668.02045 10767.47728 -977.41599 -12869.70815 -28326.07458
## 2026 2027 2028 2029 2030
## -17345.92083 -8778.35065 -23732.62727 -27584.04280 -4739.92123
## 2031 2032 2033 2034 2035
## -28051.71417 -11093.16089 -53350.96397 12595.87536 -14959.02396
## 2036 2037 2038 2039 2040
## -25434.35271 -22120.37053 -11234.96339 -13275.76806 -35589.35369
## 2041 2042 2043 2044 2045
## -74890.40295 -28196.15259 -14707.68248 -24095.40315 -38124.83254
## 2046 2047 2048 2049 2050
## -27976.58893 -40104.30009 -19438.47760 -53172.96513 -26892.52865
## 2051 2052 2053
## -12600.30960 -28233.54226 -38305.87451Creating an alternate model
We now try a linear regression model with fields V2, V3, V4, V5, V8 and V9.
fit2 <- lm(Target ~ V3+V4+V5+V6, data=train)
summary(fit2)##
## Call:
## lm(formula = Target ~ V3 + V4 + V5 + V6, data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -730534 -115655 21453 83453 342453
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.075e+05 4.376e+03 93.141 < 2e-16 ***
## V3 5.134e+04 6.880e+03 7.463 1.25e-13 ***
## V4 1.483e-02 1.672e-03 8.867 < 2e-16 ***
## V5 8.100e+04 7.683e+03 10.543 < 2e-16 ***
## V6 -2.953e-03 2.140e-03 -1.380 0.168
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 158400 on 2048 degrees of freedom
## Multiple R-squared: 0.2534, Adjusted R-squared: 0.2519
## F-statistic: 173.8 on 4 and 2048 DF, p-value: < 2.2e-16Since the adjusted R-squared values decrease, it is more efficient to use the first model.
Predicting Values
We add a new column to the Validation dataset with our predicted values.
new.Predictions <- predict(fit1,test)
results <- cbind(test$Target,new.Predictions)
colnames(results) <- c('Actual','Predicted')
results <- as.data.frame(results)
test$Predictions <- new.Predictionshead(results)## Actual Predicted
## 1 147000 168258.6
## 2 147000 183460.0
## 3 147000 161938.6
## 4 148000 165909.0
## 5 148000 167563.3
## 6 148000 166709.4head(test)## Sno Target V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12 V13 V14 V15
## 1 1 147000 865 39 0 0 0 0 2 400000 0 0 0 0 0 0 2
## 2 2 147000 871 54 0 0 1 900000 0 0 0 0 0 0 0 0 1
## 3 3 147000 829 37 0 0 0 0 2 348000 0 0 0 0 0 0 1
## 4 4 148000 846 31 0 0 0 0 0 0 0 0 0 0 0 0 1
## 5 5 148000 721 31 0 0 0 0 1 300000 0 0 0 0 0 0 3
## 6 6 148000 807 31 0 0 0 0 1 200000 0 0 0 0 0 0 3
## V16 Predictions
## 1 25000 168258.6
## 2 0 183460.0
## 3 0 161938.6
## 4 217687 165909.0
## 5 145000 167563.3
## 6 105000 166709.4We look at the multiple R-squared, adjusted R-Squared values and the F-tests to find that the accuracy of our model is about 92 percent.
Finding Error percentages
## mean((results$Actual - results$Predicted)^2)
SSE <- sum((results$Predicted - results$Actual)^2)
SST <- sum((mean(results$Actual)-results$Actual)^2)
R2 <- 1-SSE/SST
R2## [1] 0.9275589Using decision trees for predicting values
We can also use decision trees to predict the housing values. Let us see the tree we get for it.
library(rpart)
tree <- rpart(Target ~ .,method = 'class',data = train)
library(rpart.plot)
prp(tree)
predicted.val <- predict(tree,test)Storing the saved predicted values into the csv file
We use the model we build using linear regression to get the final predicted values of housing prices and save it in the CSV file for further use.
new.Predictions <- round(new.Predictions,2)
test$Predictions <- new.Predictions
write.csv(test,file = 'week1Predictions.csv')