library(ggplot2)
library(tidyverse)
library(dplyr)
library(tidyr)
library(plotly)https://www.kaggle.com/c/house-prices-advanced-regression-techniques
take a glance of data, I see that there are NAs in some numerical and categorical variable. Combine with the description of data, NA is meaningful in categorical data, not in numerical data. Therefore, I am going to deal with NA first.
# read data
data = read.csv('train2.csv')
# check number of observations
dim(data)## [1] 1460 81# variables
colnames(data)## [1] "Id" "MSSubClass" "MSZoning" "LotFrontage"
## [5] "LotArea" "Street" "Alley" "LotShape"
## [9] "LandContour" "Utilities" "LotConfig" "LandSlope"
## [13] "Neighborhood" "Condition1" "Condition2" "BldgType"
## [17] "HouseStyle" "OverallQual" "OverallCond" "YearBuilt"
## [21] "YearRemodAdd" "RoofStyle" "RoofMatl" "Exterior1st"
## [25] "Exterior2nd" "MasVnrType" "MasVnrArea" "ExterQual"
## [29] "ExterCond" "Foundation" "BsmtQual" "BsmtCond"
## [33] "BsmtExposure" "BsmtFinType1" "BsmtFinSF1" "BsmtFinType2"
## [37] "BsmtFinSF2" "BsmtUnfSF" "TotalBsmtSF" "Heating"
## [41] "HeatingQC" "CentralAir" "Electrical" "X1stFlrSF"
## [45] "X2ndFlrSF" "LowQualFinSF" "GrLivArea" "BsmtFullBath"
## [49] "BsmtHalfBath" "FullBath" "HalfBath" "BedroomAbvGr"
## [53] "KitchenAbvGr" "KitchenQual" "TotRmsAbvGrd" "Functional"
## [57] "Fireplaces" "FireplaceQu" "GarageType" "GarageYrBlt"
## [61] "GarageFinish" "GarageCars" "GarageArea" "GarageQual"
## [65] "GarageCond" "PavedDrive" "WoodDeckSF" "OpenPorchSF"
## [69] "EnclosedPorch" "X3SsnPorch" "ScreenPorch" "PoolArea"
## [73] "PoolQC" "Fence" "MiscFeature" "MiscVal"
## [77] "MoSold" "YrSold" "SaleType" "SaleCondition"
## [81] "SalePrice"# double check NAs
summary(data)## Id MSSubClass MSZoning LotFrontage
## Min. : 1.0 Min. : 20.0 Length:1460 Min. : 21.00
## 1st Qu.: 365.8 1st Qu.: 20.0 Class :character 1st Qu.: 59.00
## Median : 730.5 Median : 50.0 Mode :character Median : 69.00
## Mean : 730.5 Mean : 56.9 Mean : 70.05
## 3rd Qu.:1095.2 3rd Qu.: 70.0 3rd Qu.: 80.00
## Max. :1460.0 Max. :190.0 Max. :313.00
## NA's :259
## LotArea Street Alley LotShape
## Min. : 1300 Length:1460 Length:1460 Length:1460
## 1st Qu.: 7554 Class :character Class :character Class :character
## Median : 9478 Mode :character Mode :character Mode :character
## Mean : 10517
## 3rd Qu.: 11602
## Max. :215245
##
## LandContour Utilities LotConfig LandSlope
## Length:1460 Length:1460 Length:1460 Length:1460
## Class :character Class :character Class :character Class :character
## Mode :character Mode :character Mode :character Mode :character
##
##
##
##
## Neighborhood Condition1 Condition2 BldgType
## Length:1460 Length:1460 Length:1460 Length:1460
## Class :character Class :character Class :character Class :character
## Mode :character Mode :character Mode :character Mode :character
##
##
##
##
## HouseStyle OverallQual OverallCond YearBuilt
## Length:1460 Min. : 1.000 Min. :1.000 Min. :1872
## Class :character 1st Qu.: 5.000 1st Qu.:5.000 1st Qu.:1954
## Mode :character Median : 6.000 Median :5.000 Median :1973
## Mean : 6.099 Mean :5.575 Mean :1971
## 3rd Qu.: 7.000 3rd Qu.:6.000 3rd Qu.:2000
## Max. :10.000 Max. :9.000 Max. :2010
##
## YearRemodAdd RoofStyle RoofMatl Exterior1st
## Min. :1950 Length:1460 Length:1460 Length:1460
## 1st Qu.:1967 Class :character Class :character Class :character
## Median :1994 Mode :character Mode :character Mode :character
## Mean :1985
## 3rd Qu.:2004
## Max. :2010
##
## Exterior2nd MasVnrType MasVnrArea ExterQual
## Length:1460 Length:1460 Min. : 0.0 Length:1460
## Class :character Class :character 1st Qu.: 0.0 Class :character
## Mode :character Mode :character Median : 0.0 Mode :character
## Mean : 103.7
## 3rd Qu.: 166.0
## Max. :1600.0
## NA's :8
## ExterCond Foundation BsmtQual BsmtCond
## Length:1460 Length:1460 Length:1460 Length:1460
## Class :character Class :character Class :character Class :character
## Mode :character Mode :character Mode :character Mode :character
##
##
##
##
## BsmtExposure BsmtFinType1 BsmtFinSF1 BsmtFinType2
## Length:1460 Length:1460 Min. : 0.0 Length:1460
## Class :character Class :character 1st Qu.: 0.0 Class :character
## Mode :character Mode :character Median : 383.5 Mode :character
## Mean : 443.6
## 3rd Qu.: 712.2
## Max. :5644.0
##
## BsmtFinSF2 BsmtUnfSF TotalBsmtSF Heating
## Min. : 0.00 Min. : 0.0 Min. : 0.0 Length:1460
## 1st Qu.: 0.00 1st Qu.: 223.0 1st Qu.: 795.8 Class :character
## Median : 0.00 Median : 477.5 Median : 991.5 Mode :character
## Mean : 46.55 Mean : 567.2 Mean :1057.4
## 3rd Qu.: 0.00 3rd Qu.: 808.0 3rd Qu.:1298.2
## Max. :1474.00 Max. :2336.0 Max. :6110.0
##
## HeatingQC CentralAir Electrical X1stFlrSF
## Length:1460 Length:1460 Length:1460 Min. : 334
## Class :character Class :character Class :character 1st Qu.: 882
## Mode :character Mode :character Mode :character Median :1087
## Mean :1163
## 3rd Qu.:1391
## Max. :4692
##
## X2ndFlrSF LowQualFinSF GrLivArea BsmtFullBath
## Min. : 0 Min. : 0.000 Min. : 334 Min. :0.0000
## 1st Qu.: 0 1st Qu.: 0.000 1st Qu.:1130 1st Qu.:0.0000
## Median : 0 Median : 0.000 Median :1464 Median :0.0000
## Mean : 347 Mean : 5.845 Mean :1515 Mean :0.4253
## 3rd Qu.: 728 3rd Qu.: 0.000 3rd Qu.:1777 3rd Qu.:1.0000
## Max. :2065 Max. :572.000 Max. :5642 Max. :3.0000
##
## BsmtHalfBath FullBath HalfBath BedroomAbvGr
## Min. :0.00000 Min. :0.000 Min. :0.0000 Min. :0.000
## 1st Qu.:0.00000 1st Qu.:1.000 1st Qu.:0.0000 1st Qu.:2.000
## Median :0.00000 Median :2.000 Median :0.0000 Median :3.000
## Mean :0.05753 Mean :1.565 Mean :0.3829 Mean :2.866
## 3rd Qu.:0.00000 3rd Qu.:2.000 3rd Qu.:1.0000 3rd Qu.:3.000
## Max. :2.00000 Max. :3.000 Max. :2.0000 Max. :8.000
##
## KitchenAbvGr KitchenQual TotRmsAbvGrd Functional
## Min. :0.000 Length:1460 Min. : 2.000 Length:1460
## 1st Qu.:1.000 Class :character 1st Qu.: 5.000 Class :character
## Median :1.000 Mode :character Median : 6.000 Mode :character
## Mean :1.047 Mean : 6.518
## 3rd Qu.:1.000 3rd Qu.: 7.000
## Max. :3.000 Max. :14.000
##
## Fireplaces FireplaceQu GarageType GarageYrBlt
## Min. :0.000 Length:1460 Length:1460 Min. :1900
## 1st Qu.:0.000 Class :character Class :character 1st Qu.:1961
## Median :1.000 Mode :character Mode :character Median :1980
## Mean :0.613 Mean :1979
## 3rd Qu.:1.000 3rd Qu.:2002
## Max. :3.000 Max. :2010
## NA's :81
## GarageFinish GarageCars GarageArea GarageQual
## Length:1460 Min. :0.000 Min. : 0.0 Length:1460
## Class :character 1st Qu.:1.000 1st Qu.: 334.5 Class :character
## Mode :character Median :2.000 Median : 480.0 Mode :character
## Mean :1.767 Mean : 473.0
## 3rd Qu.:2.000 3rd Qu.: 576.0
## Max. :4.000 Max. :1418.0
##
## GarageCond PavedDrive WoodDeckSF OpenPorchSF
## Length:1460 Length:1460 Min. : 0.00 Min. : 0.00
## Class :character Class :character 1st Qu.: 0.00 1st Qu.: 0.00
## Mode :character Mode :character Median : 0.00 Median : 25.00
## Mean : 94.24 Mean : 46.66
## 3rd Qu.:168.00 3rd Qu.: 68.00
## Max. :857.00 Max. :547.00
##
## EnclosedPorch X3SsnPorch ScreenPorch PoolArea
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.000
## 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.000
## Median : 0.00 Median : 0.00 Median : 0.00 Median : 0.000
## Mean : 21.95 Mean : 3.41 Mean : 15.06 Mean : 2.759
## 3rd Qu.: 0.00 3rd Qu.: 0.00 3rd Qu.: 0.00 3rd Qu.: 0.000
## Max. :552.00 Max. :508.00 Max. :480.00 Max. :738.000
##
## PoolQC Fence MiscFeature MiscVal
## Length:1460 Length:1460 Length:1460 Min. : 0.00
## Class :character Class :character Class :character 1st Qu.: 0.00
## Mode :character Mode :character Mode :character Median : 0.00
## Mean : 43.49
## 3rd Qu.: 0.00
## Max. :15500.00
##
## MoSold YrSold SaleType SaleCondition
## Min. : 1.000 Min. :2006 Length:1460 Length:1460
## 1st Qu.: 5.000 1st Qu.:2007 Class :character Class :character
## Median : 6.000 Median :2008 Mode :character Mode :character
## Mean : 6.322 Mean :2008
## 3rd Qu.: 8.000 3rd Qu.:2009
## Max. :12.000 Max. :2010
##
## SalePrice
## Min. : 34900
## 1st Qu.:129975
## Median :163000
## Mean :180921
## 3rd Qu.:214000
## Max. :755000
## reduce NA
# numerical variables contains NA
summary(data$GarageYrBlt)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 1900 1961 1980 1979 2002 2010 81summary(data$MasVnrArea)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 0.0 0.0 0.0 103.7 166.0 1600.0 8summary(data$LotFrontage)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 21.00 59.00 69.00 70.05 80.00 313.00 259variable: garage year built
the plot is left skewed, as we can see that mostly garage built between 1950 and 2021. The missing value could be year was too old to recorded, or, for some reasons, they were forgotten to be recorded. Anyhow, consider it only takes 5% of data, I’m going to drop these rows.
# garage year built
ggplot(data, aes(x = GarageYrBlt)) + geom_bar()## Warning: Removed 81 rows containing non-finite values (stat_count).
# garage year built vs sale price
ggplot(data, aes(x = GarageYrBlt, y = SalePrice)) + geom_point()## Warning: Removed 81 rows containing missing values (geom_point).
# drop NA in the variable
data <- data %>% drop_na(GarageYrBlt)
# check NA amount: it helps a little
summary(data$MasVnrArea)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 0.0 0.0 0.0 109.0 171.5 1600.0 8summary(data$LotFrontage)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 21.00 60.00 70.00 70.68 80.00 313.00 252variable: Masonry veneer area in square feet
there is only 8 NAs, I guess I will just drop them.
data <- data %>% drop_na(MasVnrArea)variable: Linear feet of street connected to property
with no NA, the distribution looks roughly normal without outliers. since most data is centered between first and third quantile, so I am going to replace NA with random number between the range.
ggplot(data, aes(x = LotFrontage)) + geom_boxplot()## Warning: Removed 250 rows containing non-finite values (stat_boxplot).
ggplot(data, aes(x = LotFrontage)) + geom_histogram()## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## Warning: Removed 250 rows containing non-finite values (stat_bin).
set.seed(100)
data$LotFrontage <- data$LotFrontage %>% replace_na(round(runif(1, 60.0, 80.0),2))
# double check NA values in these numerical variable
sum(is.na(data$GarageYrBlt)) == 0## [1] TRUEsum(is.na(data$MasVnrArea)) == 0## [1] TRUEsum(is.na(data$LotFrontage)) == 0## [1] TRUEDescriptive and inferential statisctics
Descriptive statistics
provide univariate descriptive statistics and appropriate plots.
If I am the one wants to buy a house, I am interested in the following features:
qualitative:
* ExterCond: Evaluates the present condition of the material on the exterior
* Utilities: Type of utilities available
* HouseStyle: Style of dwelling
* BldgType: Type of dwelling
* Neighborhood: Physical locations within Ames city limitsquantitative:
* OverallCond: Rates the overall condition of the house
* OverallQual: Rates the overall material and finish of the house
* YearBuilt: Original construction date
* TotalBsmtSF: Total square feet of basement area
* GrLivArea: Above grade (ground) living area square feet
* GarageCars: Size of garage in car capacity
* SalePrice: the property's sale price in dollarsthe plots below are just some kind of idea of features influence sales price.
# qualitative plots
qualitative <- data %>% select(ExterCond, Utilities,HouseStyle,BldgType,Neighborhood)
ggplot(qualitative, aes(x = ExterCond, y = data$SalePrice)) + geom_point() + labs(x = 'the material on the exterior', y = 'sale price', title = 'relationshiop between sale price and condition of the material on the exterior')
ggplot(qualitative, aes(x = Utilities, y = data$SalePrice)) + geom_point() + labs(x = 'public Utilities', y = 'sale price', title = 'relationshiop between sale price and house around public Utilities')
ggplot(qualitative, aes(x = HouseStyle, y = data$SalePrice)) + geom_boxplot() + labs(x = 'house style', y = 'sale price', title = 'relationshiop between sale price and house style')
ggplot(qualitative, aes(x = BldgType, y = data$SalePrice)) + geom_point() + labs(x = 'Type of dwelling', y = 'sale price', title = 'relationshiop between sale price and dwelling type')
ggplot(qualitative, aes(x = Neighborhood, y = data$SalePrice)) + geom_boxplot() + labs(x = 'Type of dwelling', y = 'sale price', title = 'relationshiop between sale price and dwelling type')+ coord_flip()
scatterplot matrix for at least two of the independent variables
from the plot created with quantitative data, the OverallQual, TotalBsmtSF and GrLivArea have strong positive relationship with SalePrice compared to others.
# quantitative plot
quantitative <- data %>% select(OverallCond, OverallQual,YearBuilt,TotalBsmtSF,GrLivArea,GarageCars,SalePrice)
pairs(quantitative)
derive a correlation matrix for any three quantitative variables
# select variables with strong relationship and subset
positive_relation <- quantitative %>% select(OverallQual, TotalBsmtSF,GrLivArea,SalePrice)
# correlation matrix
correlation <- cor(positive_relation)
correlation## OverallQual TotalBsmtSF GrLivArea SalePrice
## OverallQual 1.0000000 0.5313612 0.5912377 0.7862117
## TotalBsmtSF 0.5313612 1.0000000 0.4410784 0.6029809
## GrLivArea 0.5912377 0.4410784 1.0000000 0.7097950
## SalePrice 0.7862117 0.6029809 0.7097950 1.0000000inferencial statistics
hypotheses
null hypo: there is 0 relationship between these variables
alter hypo: there are some relationship between these variables
p is less than significant level, therefore, reject the null hypo. confidence interval is [182450.7, 187913.1]
library(infer)
t_result <- positive_relation %>% t_test(response = SalePrice, conf_level = 0.8)
t_result ## # A tibble: 1 × 7
## statistic t_df p_value alternative estimate lower_ci upper_ci
## <dbl> <dbl> <dbl> <chr> <dbl> <dbl> <dbl>
## 1 86.9 1370 0 two.sided 185182. 182451. 187913.meaning of analysis
would you be worried about familywise error?
I only pick 3 independent variables to see if there is relationship between sales price and these variables for my personal preference. And I see positive trend in pairs plot, therefore, I am not worried about familywise error so far.
Linear Algebra and Correlation
library(matrixcalc)
# invert correlation matrix
inv_cor <- solve(correlation)
# correction * precision
cor_pre <- round(correlation %*% inv_cor,3)
# precision * correlation
pre_cor <- round(inv_cor%*%correlation, 3)
cor_pre %>% lu.decomposition()## $L
## [,1] [,2] [,3] [,4]
## [1,] 1 0 0 0
## [2,] 0 1 0 0
## [3,] 0 0 1 0
## [4,] 0 0 0 1
##
## $U
## [,1] [,2] [,3] [,4]
## [1,] 1 0 0 0
## [2,] 0 1 0 0
## [3,] 0 0 1 0
## [4,] 0 0 0 1pre_cor %>% lu.decomposition()## $L
## [,1] [,2] [,3] [,4]
## [1,] 1 0 0 0
## [2,] 0 1 0 0
## [3,] 0 0 1 0
## [4,] 0 0 0 1
##
## $U
## [,1] [,2] [,3] [,4]
## [1,] 1 0 0 0
## [2,] 0 1 0 0
## [3,] 0 0 1 0
## [4,] 0 0 0 1inv_cor %>% lu.decomposition()## $L
## [,1] [,2] [,3] [,4]
## [1,] 1.00000000 0.00000000 0.000000 0
## [2,] -0.08869378 1.00000000 0.000000 0
## [3,] -0.06454766 -0.02637211 1.000000 0
## [4,] -0.68691543 -0.58426210 -0.709795 1
##
## $U
## [,1] [,2] [,3] [,4]
## [1,] 2.669175e+00 -0.2367392 -0.17228900 -1.8334974
## [2,] 2.775558e-17 1.5721566 -0.04146109 -0.9185515
## [3,] 7.319731e-19 0.0000000 2.01535257 -1.4304871
## [4,] 2.387807e-16 0.0000000 0.00000000 1.0000000Calculus-Based Probability & Statistics
# pick a right skewed variable
library(MASS)
plot(density(data$X1stFlrSF), main = "density function of first floor sf")
# run fitdistr with exponential function
fit <- data$X1stFlrSF %>% fitdistr('exponential')
fit## rate
## 8.505005e-04
## (2.296973e-05)# find lambda
lamda <- fit$estimate
# take sample from this exp distribution
exp_df <- rexp(1000, lamda)
# histogram of orig. data
hist(data$X1stFlrSF, main = 'distribution of first floor square feet', xlab = 'first floor square feet')
# histogram of sample exp data
hist(exp_df, main = 'distribution of sample exponential data', xlab = 'x')
# 5th and 95th percentiles using CDF
qexp(0.05, rate = lamda) ## [1] 60.30954qexp(0.95, rate = lamda)## [1] 3522.317# 95% of confidence interval from empirical data
library(Rmisc)
CI(data$X1stFlrSF)## upper mean lower
## 1196.197 1175.778 1155.359# 5 percentile of data
quantile(data$X1stFlrSF, 0.05)## 5%
## 687.5# 95% percentile of data
quantile(data$X1stFlrSF, 0.95)## 95%
## 1837Modeling
multiple regression model
according to summary, there are some variables are not so important in modeling. So, I will reduce some features
library(purrr)
# select all quantitative variable
mask <- data %>% select_all() %>% map_lgl(is.numeric)
df <- data %>% select_if(mask)
lm <- lm(SalePrice ~ ., data = df)
summary(lm)##
## Call:
## lm(formula = SalePrice ~ ., data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -459477 -16340 -2188 14573 299895
##
## Coefficients: (2 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.678e+05 1.457e+06 0.252 0.800729
## Id -5.073e-01 2.264e+00 -0.224 0.822773
## MSSubClass -1.903e+02 2.930e+01 -6.496 1.16e-10 ***
## LotFrontage -8.570e+01 5.354e+01 -1.601 0.109700
## LotArea 4.277e-01 1.027e-01 4.163 3.34e-05 ***
## OverallQual 1.827e+04 1.256e+03 14.550 < 2e-16 ***
## OverallCond 5.323e+03 1.116e+03 4.772 2.03e-06 ***
## YearBuilt 3.649e+02 7.658e+01 4.765 2.10e-06 ***
## YearRemodAdd 1.199e+02 7.358e+01 1.630 0.103330
## MasVnrArea 2.851e+01 6.036e+00 4.722 2.58e-06 ***
## BsmtFinSF1 1.813e+01 4.861e+00 3.730 0.000200 ***
## BsmtFinSF2 8.758e+00 7.254e+00 1.207 0.227519
## BsmtUnfSF 7.393e+00 4.423e+00 1.671 0.094882 .
## TotalBsmtSF NA NA NA NA
## X1stFlrSF 4.784e+01 6.061e+00 7.892 6.13e-15 ***
## X2ndFlrSF 4.946e+01 5.149e+00 9.605 < 2e-16 ***
## LowQualFinSF 3.194e+01 2.461e+01 1.298 0.194570
## GrLivArea NA NA NA NA
## BsmtFullBath 8.117e+03 2.743e+03 2.959 0.003144 **
## BsmtHalfBath 1.651e+03 4.237e+03 0.390 0.696754
## FullBath 2.165e+03 3.003e+03 0.721 0.471031
## HalfBath -3.548e+03 2.798e+03 -1.268 0.205005
## BedroomAbvGr -9.982e+03 1.834e+03 -5.443 6.24e-08 ***
## KitchenAbvGr -2.069e+04 5.971e+03 -3.465 0.000547 ***
## TotRmsAbvGrd 5.331e+03 1.277e+03 4.175 3.17e-05 ***
## Fireplaces 3.526e+03 1.824e+03 1.933 0.053419 .
## GarageYrBlt -5.806e+01 8.070e+01 -0.719 0.472034
## GarageCars 1.590e+04 3.028e+03 5.251 1.76e-07 ***
## GarageArea 5.572e+00 1.030e+01 0.541 0.588718
## WoodDeckSF 2.287e+01 8.186e+00 2.793 0.005290 **
## OpenPorchSF -4.545e+00 1.614e+01 -0.282 0.778294
## EnclosedPorch 1.034e+01 1.762e+01 0.587 0.557506
## X3SsnPorch 2.166e+01 3.151e+01 0.687 0.491969
## ScreenPorch 5.487e+01 1.728e+01 3.176 0.001528 **
## PoolArea -2.790e+01 2.401e+01 -1.162 0.245601
## MiscVal -7.401e-01 1.894e+00 -0.391 0.696008
## MoSold -8.483e+01 3.580e+02 -0.237 0.812715
## YrSold -6.343e+02 7.245e+02 -0.875 0.381504
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 34800 on 1335 degrees of freedom
## Multiple R-squared: 0.8103, Adjusted R-squared: 0.8053
## F-statistic: 162.9 on 35 and 1335 DF, p-value: < 2.2e-16# update multiple regression
updated_lm <- lm(SalePrice ~ MSSubClass+
LotArea +
OverallQual +
OverallCond +
YearBuilt+
MasVnrArea+
BsmtFinSF1+
X1stFlrSF+
X2ndFlrSF+
BsmtFullBath+
BedroomAbvGr+
KitchenAbvGr+
TotRmsAbvGrd+
GarageCars+
WoodDeckSF+
ScreenPorch, df)
summary(updated_lm)##
## Call:
## lm(formula = SalePrice ~ MSSubClass + LotArea + OverallQual +
## OverallCond + YearBuilt + MasVnrArea + BsmtFinSF1 + X1stFlrSF +
## X2ndFlrSF + BsmtFullBath + BedroomAbvGr + KitchenAbvGr +
## TotRmsAbvGrd + GarageCars + WoodDeckSF + ScreenPorch, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -477089 -16199 -2083 14188 280797
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7.712e+05 9.392e+04 -8.212 5.04e-16 ***
## MSSubClass -1.751e+02 2.726e+01 -6.424 1.83e-10 ***
## LotArea 4.377e-01 9.959e-02 4.396 1.19e-05 ***
## OverallQual 1.951e+04 1.176e+03 16.587 < 2e-16 ***
## OverallCond 5.834e+03 9.881e+02 5.905 4.46e-09 ***
## YearBuilt 3.537e+02 4.757e+01 7.435 1.84e-13 ***
## MasVnrArea 2.770e+01 5.891e+00 4.701 2.85e-06 ***
## BsmtFinSF1 1.085e+01 3.009e+00 3.606 0.000322 ***
## X1stFlrSF 5.578e+01 4.619e+00 12.075 < 2e-16 ***
## X2ndFlrSF 4.785e+01 4.155e+00 11.514 < 2e-16 ***
## BsmtFullBath 8.050e+03 2.456e+03 3.278 0.001071 **
## BedroomAbvGr -1.034e+04 1.757e+03 -5.887 4.95e-09 ***
## KitchenAbvGr -2.339e+04 5.765e+03 -4.058 5.24e-05 ***
## TotRmsAbvGrd 5.408e+03 1.250e+03 4.326 1.63e-05 ***
## GarageCars 1.714e+04 2.072e+03 8.272 3.12e-16 ***
## WoodDeckSF 2.383e+01 8.013e+00 2.975 0.002986 **
## ScreenPorch 5.493e+01 1.675e+01 3.280 0.001063 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 34810 on 1354 degrees of freedom
## Multiple R-squared: 0.8075, Adjusted R-squared: 0.8053
## F-statistic: 355.1 on 16 and 1354 DF, p-value: < 2.2e-16\(SalePrice = -771200-175.1MSSubClass + 0.4377LotArea + 19510OverallQual + 5834OverallCond + 353.7YearBuilt + 27.7MasVnrArea + 10.85BsmtFinSF1 + 55.78X1stFlrSF + 47.85X2ndFlrSF + 805BsmtFullBath -10340BedroomAbvGr -23390KitchenAbvGr + 5408TotRmsAbvGrd + 17140GarageCars + 23.83WoodDeckSF + 54.93ScreenPorch\)
# read test data
test <- as.data.frame(read.csv('test2.csv'))
# synchronize variables from formula and drop na
syn_test <- test %>% dplyr::select(Id,MSSubClass,
LotArea,
OverallQual,
OverallCond,
YearBuilt,
MasVnrArea,
BsmtFinSF1,
X1stFlrSF,
X2ndFlrSF,
BsmtFullBath,
BedroomAbvGr,
KitchenAbvGr,
TotRmsAbvGrd,
GarageCars,
WoodDeckSF,
ScreenPorch) %>% drop_na()
summary(syn_test)## Id MSSubClass LotArea OverallQual
## Min. :1461 Min. : 20.00 Min. : 1470 Min. : 1.000
## 1st Qu.:1823 1st Qu.: 20.00 1st Qu.: 7379 1st Qu.: 5.000
## Median :2188 Median : 50.00 Median : 9399 Median : 6.000
## Mean :2189 Mean : 57.51 Mean : 9791 Mean : 6.069
## 3rd Qu.:2554 3rd Qu.: 70.00 3rd Qu.:11500 3rd Qu.: 7.000
## Max. :2919 Max. :190.00 Max. :56600 Max. :10.000
## OverallCond YearBuilt MasVnrArea BsmtFinSF1
## Min. :1.000 Min. :1879 Min. : 0.0 Min. : 0.0
## 1st Qu.:5.000 1st Qu.:1953 1st Qu.: 0.0 1st Qu.: 0.0
## Median :5.000 Median :1973 Median : 0.0 Median : 353.0
## Mean :5.557 Mean :1971 Mean : 100.9 Mean : 440.8
## 3rd Qu.:6.000 3rd Qu.:2000 3rd Qu.: 164.0 3rd Qu.: 758.0
## Max. :9.000 Max. :2010 Max. :1290.0 Max. :4010.0
## X1stFlrSF X2ndFlrSF BsmtFullBath BedroomAbvGr
## Min. : 407 Min. : 0.0 Min. :0.0000 Min. :0.000
## 1st Qu.: 873 1st Qu.: 0.0 1st Qu.:0.0000 1st Qu.:2.000
## Median :1080 Median : 0.0 Median :0.0000 Median :3.000
## Mean :1155 Mean : 324.6 Mean :0.4365 Mean :2.854
## 3rd Qu.:1380 3rd Qu.: 672.0 3rd Qu.:1.0000 3rd Qu.:3.000
## Max. :5095 Max. :1862.0 Max. :3.0000 Max. :6.000
## KitchenAbvGr TotRmsAbvGrd GarageCars WoodDeckSF
## Min. :0.000 Min. : 3.000 Min. :0.000 Min. : 0.00
## 1st Qu.:1.000 1st Qu.: 5.000 1st Qu.:1.000 1st Qu.: 0.00
## Median :1.000 Median : 6.000 Median :2.000 Median : 0.00
## Mean :1.043 Mean : 6.384 Mean :1.763 Mean : 93.51
## 3rd Qu.:1.000 3rd Qu.: 7.000 3rd Qu.:2.000 3rd Qu.: 168.00
## Max. :2.000 Max. :15.000 Max. :5.000 Max. :1424.00
## ScreenPorch
## Min. : 0.00
## 1st Qu.: 0.00
## Median : 0.00
## Mean : 17.28
## 3rd Qu.: 0.00
## Max. :576.00# formula
salesprice <- -771200-175.1*syn_test$MSSubClass + 0.4377*syn_test$LotArea + 19510*syn_test$OverallQual + 5834*syn_test$OverallCond + 353.7*syn_test$YearBuilt + 27.7*syn_test$MasVnrArea + 10.85*syn_test$BsmtFinSF1 + 55.78*syn_test$X1stFlrSF + 47.85*syn_test$X2ndFlrSF + 805*syn_test$BsmtFullBath -10340*syn_test$BedroomAbvGr -23390*syn_test$KitchenAbvGr + 5408*syn_test$TotRmsAbvGrd + 17140*syn_test$GarageCars + 23.83*syn_test$WoodDeckSF + 54.93*syn_test$ScreenPorch
syn_test <- syn_test %>% mutate(predicted_saleprice = salesprice)
result <- syn_test %>% dplyr::select(Id, predicted_saleprice)
result$predicted_saleprice <- round(result$predicted_saleprice,2)
result## Id predicted_saleprice
## 1 1461 121639.13
## 2 1462 167832.23
## 3 1463 168665.29
## 4 1464 198903.05
## 5 1465 199210.96
## 6 1466 180534.75
## 7 1467 192247.75
## 8 1468 168977.18
## 9 1469 203697.83
## 10 1470 109261.24
## 11 1471 192012.05
## 12 1472 118266.83
## 13 1473 93858.89
## 14 1474 150870.70
## 15 1475 120251.54
## 16 1476 322858.18
## 17 1477 254851.71
## 18 1478 296653.60
## 19 1479 274754.66
## 20 1480 397527.24
## 21 1481 292706.65
## 22 1482 212809.08
## 23 1483 175819.92
## 24 1484 173922.65
## 25 1485 191265.13
## 26 1486 207401.23
## 27 1487 291634.59
## 28 1488 262108.93
## 29 1489 185436.75
## 30 1490 217820.91
## 31 1491 213984.08
## 32 1492 93103.25
## 33 1493 199522.86
## 34 1494 290123.73
## 35 1495 277856.85
## 36 1496 209009.46
## 37 1497 170360.52
## 38 1498 157128.01
## 39 1499 155270.11
## 40 1500 143906.41
## 41 1501 189278.03
## 42 1502 146407.19
## 43 1503 272159.80
## 44 1504 240787.14
## 45 1505 214632.72
## 46 1506 202101.21
## 47 1507 240388.84
## 48 1508 200008.76
## 49 1509 168746.42
## 50 1510 145775.78
## 51 1511 143776.60
## 52 1512 184755.46
## 53 1513 177365.00
## 54 1514 108879.94
## 55 1515 218503.41
## 56 1516 176595.04
## 57 1517 163735.71
## 58 1518 115800.05
## 59 1519 237083.49
## 60 1520 121621.92
## 61 1521 124735.61
## 62 1522 198791.81
## 63 1523 83104.21
## 64 1524 116631.28
## 65 1525 105123.20
## 66 1526 82540.47
## 67 1527 91771.25
## 68 1528 147012.96
## 69 1529 138685.14
## 70 1530 231122.71
## 71 1531 134882.59
## 72 1532 86484.64
## 73 1533 149649.31
## 74 1534 128905.69
## 75 1535 147959.94
## 76 1536 100375.86
## 77 1537 22285.49
## 78 1538 185541.74
## 79 1539 232986.11
## 80 1540 83759.64
## 81 1541 161825.80
## 82 1542 139303.69
## 83 1543 195587.40
## 84 1544 68921.55
## 85 1545 131200.34
## 86 1546 140048.84
## 87 1547 140299.01
## 88 1548 147217.23
## 89 1549 127573.67
## 90 1550 125240.69
## 91 1551 123524.86
## 92 1552 131071.58
## 93 1553 143898.89
## 94 1554 124502.92
## 95 1555 161826.52
## 96 1556 77289.18
## 97 1557 64279.19
## 98 1558 97574.59
## 99 1559 49263.14
## 100 1560 114744.77
## 101 1561 77582.00
## 102 1562 106710.92
## 103 1563 109022.92
## 104 1564 141241.17
## 105 1565 135481.57
## 106 1566 240128.66
## 107 1567 66473.64
## 108 1568 215310.93
## 109 1569 79682.48
## 110 1570 134954.48
## 111 1571 99119.42
## 112 1572 131004.15
## 113 1573 239049.02
## 114 1574 119231.48
## 115 1575 237065.62
## 116 1576 260219.73
## 117 1577 198494.03
## 118 1578 150088.74
## 119 1579 129088.49
## 120 1580 209459.51
## 121 1581 132939.31
## 122 1582 120408.68
## 123 1583 306561.95
## 124 1584 229234.29
## 125 1585 150045.14
## 126 1586 44678.39
## 127 1587 104793.50
## 128 1588 138759.55
## 129 1589 107335.32
## 130 1590 125611.88
## 131 1591 54037.06
## 132 1592 118210.99
## 133 1593 136984.11
## 134 1594 103862.50
## 135 1595 87622.75
## 136 1596 205861.64
## 137 1597 166314.18
## 138 1598 204459.25
## 139 1599 196219.89
## 140 1600 185434.93
## 141 1601 22208.91
## 142 1602 122906.14
## 143 1603 59726.00
## 144 1604 245003.39
## 145 1605 262721.01
## 146 1606 176464.27
## 147 1607 162476.69
## 148 1608 216708.66
## 149 1609 196286.99
## 150 1610 153930.86
## 151 1611 153567.93
## 152 1612 162751.10
## 153 1613 164772.55
## 154 1614 112873.66
## 155 1615 52984.63
## 156 1616 28992.61
## 157 1617 61693.53
## 158 1618 107482.40
## 159 1619 148103.86
## 160 1620 158723.87
## 161 1621 137536.39
## 162 1622 122754.89
## 163 1623 251473.79
## 164 1624 202876.80
## 165 1625 124486.16
## 166 1626 185627.66
## 167 1627 192676.01
## 168 1628 287033.15
## 169 1629 198528.26
## 170 1630 315999.73
## 171 1631 211161.96
## 172 1632 231641.32
## 173 1633 189091.46
## 174 1634 184026.91
## 175 1635 176842.98
## 176 1636 159568.12
## 177 1637 188163.11
## 178 1638 226990.40
## 179 1639 205439.58
## 180 1640 276876.29
## 181 1641 201958.28
## 182 1642 219044.98
## 183 1643 230013.59
## 184 1644 235252.03
## 185 1645 221134.89
## 186 1646 170441.56
## 187 1647 175741.42
## 188 1648 140712.59
## 189 1649 129461.13
## 190 1650 107001.85
## 191 1651 107731.92
## 192 1652 114289.28
## 193 1653 116018.88
## 194 1654 151002.67
## 195 1655 148493.11
## 196 1656 140295.46
## 197 1657 151886.48
## 198 1658 142965.23
## 199 1659 135326.30
## 200 1660 144689.47
## 201 1661 365675.06
## 202 1662 330360.94
## 203 1663 324447.36
## 204 1664 413295.05
## 205 1665 293022.54
## 206 1666 287380.88
## 207 1667 305849.92
## 208 1668 306011.77
## 209 1669 289356.62
## 210 1670 307775.12
## 211 1671 256450.85
## 212 1672 376128.09
## 213 1673 290031.35
## 214 1674 259428.19
## 215 1675 184909.58
## 216 1676 184021.53
## 217 1677 206082.67
## 218 1678 404189.96
## 219 1679 324353.37
## 220 1680 277281.05
## 221 1681 247909.43
## 222 1682 288220.53
## 223 1683 192583.14
## 224 1684 198945.33
## 225 1685 173384.14
## 226 1686 172390.66
## 227 1687 179822.88
## 228 1688 207347.74
## 229 1689 205137.19
## 230 1690 205072.51
## 231 1691 192096.60
## 232 1693 185594.04
## 233 1694 180496.24
## 234 1695 183259.79
## 235 1696 271928.96
## 236 1697 189136.69
## 237 1698 321152.08
## 238 1699 295735.67
## 239 1700 243296.75
## 240 1701 275158.23
## 241 1702 264653.69
## 242 1703 264169.33
## 243 1704 276708.26
## 244 1705 238569.16
## 245 1706 370383.43
## 246 1708 205864.04
## 247 1709 274036.91
## 248 1710 233633.39
## 249 1711 266640.09
## 250 1712 257857.59
## 251 1713 258515.06
## 252 1714 216012.90
## 253 1715 199159.00
## 254 1716 191210.05
## 255 1717 185533.89
## 256 1718 120848.79
## 257 1719 217725.09
## 258 1720 255514.58
## 259 1721 185941.17
## 260 1722 106731.33
## 261 1723 150260.98
## 262 1724 229032.07
## 263 1725 227993.89
## 264 1726 189796.63
## 265 1727 152570.46
## 266 1728 189816.83
## 267 1729 175477.32
## 268 1730 162331.94
## 269 1731 113362.17
## 270 1732 118247.63
## 271 1733 111041.04
## 272 1734 107759.04
## 273 1735 120867.98
## 274 1736 104171.32
## 275 1737 321179.32
## 276 1738 244329.99
## 277 1739 276982.31
## 278 1740 192614.27
## 279 1741 181966.16
## 280 1742 166428.55
## 281 1743 175470.09
## 282 1744 290114.81
## 283 1745 230335.01
## 284 1746 236634.18
## 285 1747 233620.11
## 286 1748 231648.45
## 287 1749 156475.91
## 288 1750 146207.83
## 289 1751 262451.27
## 290 1752 112035.42
## 291 1753 160949.66
## 292 1754 232411.00
## 293 1755 169587.85
## 294 1756 116568.96
## 295 1757 102477.08
## 296 1758 147911.28
## 297 1759 179235.05
## 298 1760 162032.02
## 299 1761 156342.07
## 300 1762 170331.72
## 301 1763 172265.94
## 302 1764 103325.75
## 303 1765 196695.16
## 304 1766 199904.98
## 305 1767 235950.47
## 306 1768 139107.48
## 307 1769 185990.76
## 308 1770 148465.57
## 309 1771 114630.38
## 310 1772 128135.94
## 311 1773 93498.03
## 312 1774 142310.25
## 313 1775 140637.29
## 314 1776 144433.75
## 315 1777 95094.74
## 316 1778 131805.83
## 317 1779 134221.13
## 318 1780 189833.73
## 319 1781 121117.00
## 320 1782 46816.58
## 321 1783 129129.55
## 322 1784 83867.69
## 323 1785 108746.17
## 324 1786 105520.10
## 325 1787 169148.84
## 326 1788 -7942.20
## 327 1789 104798.04
## 328 1790 29949.66
## 329 1791 212358.34
## 330 1792 178305.87
## 331 1793 147050.85
## 332 1794 175507.61
## 333 1795 135420.72
## 334 1796 139928.06
## 335 1797 146136.79
## 336 1798 106858.67
## 337 1799 100433.30
## 338 1800 104580.69
## 339 1801 94356.07
## 340 1802 147739.53
## 341 1803 181223.78
## 342 1804 133594.20
## 343 1805 138383.89
## 344 1806 139202.17
## 345 1807 158786.78
## 346 1808 127921.78
## 347 1809 100222.15
## 348 1810 151449.86
## 349 1811 36265.12
## 350 1812 82302.93
## 351 1813 119753.64
## 352 1814 84212.31
## 353 1815 13853.73
## 354 1816 95951.06
## 355 1817 94273.11
## 356 1818 160820.33
## 357 1819 111530.94
## 358 1820 24586.89
## 359 1821 106988.90
## 360 1822 163161.69
## 361 1823 3146.54
## 362 1824 140065.23
## 363 1825 133225.34
## 364 1826 100936.96
## 365 1827 95263.32
## 366 1828 126973.36
## 367 1829 165644.10
## 368 1830 165528.68
## 369 1831 191139.27
## 370 1832 79350.14
## 371 1833 150923.51
## 372 1834 129048.30
## 373 1835 103801.01
## 374 1836 129575.25
## 375 1837 70170.34
## 376 1838 112779.93
## 377 1839 79988.68
## 378 1840 105150.66
## 379 1841 104491.78
## 380 1842 67733.62
## 381 1843 123009.07
## 382 1844 133444.05
## 383 1845 124084.45
## 384 1846 152337.50
## 385 1847 170012.63
## 386 1848 -11636.00
## 387 1849 136325.28
## 388 1850 111599.82
## 389 1851 152973.10
## 390 1852 113251.00
## 391 1853 107647.18
## 392 1854 184823.73
## 393 1855 166250.15
## 394 1856 230660.73
## 395 1857 145507.72
## 396 1858 128712.49
## 397 1859 117831.38
## 398 1860 132959.03
## 399 1861 116599.40
## 400 1862 255573.18
## 401 1863 253859.15
## 402 1864 253875.35
## 403 1865 323085.87
## 404 1866 309060.20
## 405 1867 240713.21
## 406 1868 274643.32
## 407 1869 213082.97
## 408 1870 247782.17
## 409 1871 249035.08
## 410 1872 170999.25
## 411 1873 218352.68
## 412 1874 133849.73
## 413 1875 203816.63
## 414 1876 199200.31
## 415 1877 216490.45
## 416 1878 213695.46
## 417 1879 109722.21
## 418 1880 144549.73
## 419 1881 244007.67
## 420 1882 253231.29
## 421 1884 212095.72
## 422 1885 250876.36
## 423 1886 268668.74
## 424 1887 224478.30
## 425 1888 281652.65
## 426 1889 165565.84
## 427 1890 106080.88
## 428 1891 140291.16
## 429 1892 70447.44
## 430 1893 130869.76
## 431 1894 78350.25
## 432 1895 160046.82
## 433 1896 115578.43
## 434 1897 108481.47
## 435 1898 123092.93
## 436 1899 149760.00
## 437 1900 150942.53
## 438 1901 157768.69
## 439 1902 143410.27
## 440 1903 211632.37
## 441 1904 122986.13
## 442 1905 187601.31
## 443 1906 140093.15
## 444 1907 209897.63
## 445 1908 131304.18
## 446 1909 144441.11
## 447 1910 138055.77
## 448 1911 213756.24
## 449 1912 283148.16
## 450 1913 150892.73
## 451 1914 48536.20
## 452 1915 239271.28
## 453 1916 24062.68
## 454 1917 266509.66
## 455 1918 138003.97
## 456 1919 187933.24
## 457 1920 168700.89
## 458 1921 334257.69
## 459 1922 297167.99
## 460 1923 234609.58
## 461 1924 215213.04
## 462 1925 232870.90
## 463 1926 334973.84
## 464 1927 130896.09
## 465 1928 161672.26
## 466 1929 109203.80
## 467 1930 138194.30
## 468 1931 131879.66
## 469 1932 140153.44
## 470 1933 159700.85
## 471 1934 184152.45
## 472 1935 180212.10
## 473 1936 188827.00
## 474 1937 185864.55
## 475 1938 164803.98
## 476 1939 236861.21
## 477 1940 196385.86
## 478 1941 179367.65
## 479 1942 192795.11
## 480 1943 195245.62
## 481 1944 280879.47
## 482 1945 324519.61
## 483 1946 158059.11
## 484 1947 264690.93
## 485 1948 178474.90
## 486 1949 244433.36
## 487 1950 208783.91
## 488 1951 260900.99
## 489 1952 234929.83
## 490 1953 183689.84
## 491 1954 228827.33
## 492 1955 140609.21
## 493 1956 321824.10
## 494 1957 176111.60
## 495 1958 300520.91
## 496 1959 124160.58
## 497 1960 91305.38
## 498 1961 109669.78
## 499 1962 112920.34
## 500 1963 129063.87
## 501 1964 101869.04
## 502 1965 139354.56
## 503 1966 154525.04
## 504 1967 274225.47
## 505 1968 342631.99
## 506 1969 332958.89
## 507 1970 348696.52
## 508 1971 398323.84
## 509 1972 335099.97
## 510 1973 271302.03
## 511 1974 292114.06
## 512 1975 417388.39
## 513 1976 289195.19
## 514 1977 341429.18
## 515 1978 310078.06
## 516 1979 294963.83
## 517 1980 191197.02
## 518 1981 304879.55
## 519 1982 217665.51
## 520 1983 208495.81
## 521 1984 185513.41
## 522 1985 232707.09
## 523 1986 233854.06
## 524 1987 192226.65
## 525 1988 179362.44
## 526 1989 205625.12
## 527 1990 224407.64
## 528 1991 210600.95
## 529 1992 243089.47
## 530 1994 241530.17
## 531 1995 198401.84
## 532 1996 290354.99
## 533 1997 293321.55
## 534 1998 304594.45
## 535 1999 253416.08
## 536 2000 308483.66
## 537 2001 263911.72
## 538 2002 245490.08
## 539 2003 260011.50
## 540 2004 276369.68
## 541 2006 217889.55
## 542 2007 263793.05
## 543 2008 215206.83
## 544 2009 187992.09
## 545 2010 214051.32
## 546 2011 135160.81
## 547 2012 182101.36
## 548 2013 174123.55
## 549 2014 191587.00
## 550 2015 207164.58
## 551 2016 186431.02
## 552 2017 208647.92
## 553 2018 99807.09
## 554 2019 116874.95
## 555 2020 71906.86
## 556 2021 92384.44
## 557 2022 185810.76
## 558 2023 128227.89
## 559 2024 263094.29
## 560 2025 333398.57
## 561 2026 181142.80
## 562 2027 142038.89
## 563 2028 167223.78
## 564 2029 160254.62
## 565 2030 255282.13
## 566 2031 246207.39
## 567 2032 233580.88
## 568 2033 248834.04
## 569 2034 167806.05
## 570 2035 229096.01
## 571 2036 219863.45
## 572 2037 222772.15
## 573 2038 295053.39
## 574 2039 205785.39
## 575 2040 357508.23
## 576 2041 264252.14
## 577 2043 175984.26
## 578 2044 196705.54
## 579 2045 214868.94
## 580 2046 124929.57
## 581 2047 141972.85
## 582 2048 129947.70
## 583 2049 115555.55
## 584 2050 193178.08
## 585 2051 120327.61
## 586 2052 128819.37
## 587 2053 132882.56
## 588 2054 71031.14
## 589 2055 163833.20
## 590 2056 139752.98
## 591 2057 104730.25
## 592 2058 217665.53
## 593 2059 119748.75
## 594 2060 182007.10
## 595 2061 198224.74
## 596 2062 108972.24
## 597 2063 101083.62
## 598 2064 137059.02
## 599 2065 125396.68
## 600 2066 192092.33
## 601 2067 125051.21
## 602 2068 123609.86
## 603 2069 79886.82
## 604 2070 101578.46
## 605 2071 65249.78
## 606 2072 161982.14
## 607 2073 136372.11
## 608 2074 196095.99
## 609 2075 143211.73
## 610 2076 127706.62
## 611 2077 125459.18
## 612 2078 107585.06
## 613 2079 147204.27
## 614 2080 123139.72
## 615 2081 120620.81
## 616 2082 82756.84
## 617 2083 147672.56
## 618 2084 98687.74
## 619 2085 107137.50
## 620 2086 151694.16
## 621 2087 134601.63
## 622 2088 101492.72
## 623 2089 64898.12
## 624 2090 119215.84
## 625 2091 37686.30
## 626 2092 148458.94
## 627 2093 129363.51
## 628 2094 116844.64
## 629 2095 120368.38
## 630 2096 84881.32
## 631 2097 70914.68
## 632 2098 152612.62
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## 1356 2833 275959.10
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## 1438 2916 60106.18
## 1439 2917 166733.54
## 1440 2918 87484.38
## 1441 2919 257807.92write_csv(result, file = 'result.csv')