221207_Final_Project_DS101_rja
Jerome
2022-12-12
### Setup
library(lsr)## Warning: package 'lsr' was built under R version 4.2.2library(RColorBrewer)
library(tidyverse)## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.2 ──
## ✔ ggplot2 3.3.6 ✔ purrr 0.3.5
## ✔ tibble 3.1.8 ✔ dplyr 1.0.10
## ✔ tidyr 1.2.1 ✔ stringr 1.4.1
## ✔ readr 2.1.3 ✔ forcats 0.5.2
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()library(dplyr)
library(infer)
library(car) #Need this for qqPlot## Warning: package 'car' was built under R version 4.2.2## Loading required package: carData
##
## Attaching package: 'car'
##
## The following object is masked from 'package:dplyr':
##
## recode
##
## The following object is masked from 'package:purrr':
##
## somegetwd()## [1] "C:/Users/Jerome/Documents/0000_Work_Files/0000_Montgomery_College/Data_Science_101/Data_101_Fall_2022/Final_Project/Melbourne_Housing_Data_C2/Data_and_Documentation"### Question 1 - Dataset Description
https://www.kaggle.com/datasets/dansbecker/melbourne-housing-snapshot
Melbourne Housing Snapshot–NB: This is the Snapshot file. There are other Melbourne Housing Data Files that are much larger. Snapshot of Tony Pino’s Melbourne Housing Dataset 21 variables. 13,580 observations.
Data items and descriptions:
- Suburb - Text - Name of the suburb in which the property is located.
- Address - Text - Street address of the property.
- Rooms - Discrete - # of rooms in the unit.
- Type - Categorical - Type of unit. In this dataset, there are only houses, townhouses, and units in multi-unit buildings.
- Price - Continuous - Sales price (in Australian dollars, I assume)
- Method - Categorical - Type or method of sale. In this dataset, there are only 5 types of sales. PI “passed in” (?); S “sold;” SA “sold after auction;” SP “sold prior” (prior to auction?); VB “vendor bid.”
- SellerG - Text - Name of Real Estate Agent.
- Date - Date - Date of sale.
- Distance - Continuous - Distance from center of Melbourne. Unit not given. Kilometers?
- Postcode - Discrete - Postal code of the property.
- Bedroom2 - Discrete - Number of bedrooms in the property.
- Bathroom - Discrete - Number of bathrooms in the property.
- Car - Discrete - Number of parking places attached to the property.
- Landsize - Continuous - land area of the property (unit not given).
- BuildingArea - Continuous - area of the building (unit not given).
- YearBuilt - Discrete - Year the unit was constructed.
- CouncilArea - Text - There are 33 council areas in Melbourne.
- Latitude - Continuous.
- Longtitude - Continuous.
- Regionname - Text - Eight regions are identified.
- Propertycount - Discrete - This variable is not explained in the documentation.
Question 2 - Read data, calculate # and % of missing values, check that all missing values are NA
mhd_all <- read_csv("melb_data.csv")## Rows: 13580 Columns: 21
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (8): Suburb, Address, Type, Method, SellerG, Date, CouncilArea, Regionname
## dbl (13): Rooms, Price, Distance, Postcode, Bedroom2, Bathroom, Car, Landsiz...
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.### Code for calculating # of NA
mhd_all %>%
select(everything()) %>%
summarise_all(funs(sum(is.na(.))))## Warning: `funs()` was deprecated in dplyr 0.8.0.
## ℹ Please use a list of either functions or lambdas:
##
## # Simple named list: list(mean = mean, median = median)
##
## # Auto named with `tibble::lst()`: tibble::lst(mean, median)
##
## # Using lambdas list(~ mean(., trim = .2), ~ median(., na.rm = TRUE))## # A tibble: 1 × 21
## Suburb Address Rooms Type Price Method SellerG Date Distance Postc…¹ Bedro…²
## <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int>
## 1 0 0 0 0 0 0 0 0 0 0 0
## # … with 10 more variables: Bathroom <int>, Car <int>, Landsize <int>,
## # BuildingArea <int>, YearBuilt <int>, CouncilArea <int>, Lattitude <int>,
## # Longtitude <int>, Regionname <int>, Propertycount <int>, and abbreviated
## # variable names ¹Postcode, ²Bedroom2### Four variables have missing data: Car, 62; BuildingArea, 6,450; YearBuilt, 5,375; CouncilArea, 1,369.### Calculate % missing data
#### I tried using prop.table but all I got was a list of NA values for the numeric variables. Prop.table doesn't work for categorical values. I calculated the percentages by hand.
#prop.table(mhd_all$BuildingArea)
#prop.table(mhd_all$YearBuilt)
#prop.table(mhd_all$CouncilArea)
#prop.table(mhd_all$Car)
62+6450+5375+1369## [1] 1325613580*21## [1] 28518013256/285180## [1] 0.0464829262/13580## [1] 0.0045655386450/13580## [1] 0.47496325375/13580## [1] 0.39580271369/13580## [1] 0.10081### In the entire dataset, just 4.6% of the data are missing. By variable, only 0.46% of the Car data are missing. 47.49% of the BuildingArea data are missing, 39.6% of YearBuild data are missing, and 10% of the CouncilArea data are missing.
### All missing data are coded as NA.### Remove NAs for processing the statistics in later steps.
mhd_nona <- na.omit(mhd_all)
write.csv(mhd_nona,"mhd_nona.csv")
mhd <- read_csv("mhd_nona.csv")## New names:
## Rows: 6196 Columns: 22
## ── Column specification
## ──────────────────────────────────────────────────────── Delimiter: "," chr
## (8): Suburb, Address, Type, Method, SellerG, Date, CouncilArea, Regionname dbl
## (14): ...1, Rooms, Price, Distance, Postcode, Bedroom2, Bathroom, Car, L...
## ℹ Use `spec()` to retrieve the full column specification for this data. ℹ
## Specify the column types or set `show_col_types = FALSE` to quiet this message.
## • `` -> `...1`Question 3 - Two questions about the dataset to be answered w/ EDA
If my research gave me the correct answers, for regression, neither the independent nor the dependent variables need be normally distributed. However, for ANOVA, the continuous (dependent) variable should be normally distributed. Therefore, I need to determine if the prices at which the properties was sold are normally distributed. That’s one question. NB: I wrote this prior to reading your comment about normality and the CLT on my Final Project Outline. The non-nomality of the dependent variable should not be an issue.
The second question I have goes to the issue of variability. How much variation is in the sales price, given the different types of housing units sold and the regions in which the properties are located? While the degree of variation should not affect any statistical analysis (assuming normality is met), I am curious as to the degree to which the prices vary by housing type and region of Melbourne.
In addition to answering these questions, I need to perform additional tasks in the EDA stage. There are 3 housing types in the data: stand-alone, single-family houses; townhouses; and units in multi-unit buildings. Each one of those housing types must be analyzed separately in the regression analyses. In this step, I create separate files for each housing type and analyze the separate files for normality. In the regression step the data will be analyzed to determine the variables that most affect their sales prices.
In addition, I will shorten the names of Melbourne’s regions so I can display the abbreviated names on the boxplot. The original names were too long to fully display in the boxplot.
### Question 4 EDA Coding
#### Basic "check the packaging" commands
str(mhd)## spec_tbl_df [6,196 × 22] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
## $ ...1 : num [1:6196] 1 2 3 4 5 6 7 8 9 10 ...
## $ Suburb : chr [1:6196] "Abbotsford" "Abbotsford" "Abbotsford" "Abbotsford" ...
## $ Address : chr [1:6196] "25 Bloomburg St" "5 Charles St" "55a Park St" "124 Yarra St" ...
## $ Rooms : num [1:6196] 2 3 4 3 2 2 3 2 2 3 ...
## $ Type : chr [1:6196] "h" "h" "h" "h" ...
## $ Price : num [1:6196] 1035000 1465000 1600000 1876000 1636000 ...
## $ Method : chr [1:6196] "S" "SP" "VB" "S" ...
## $ SellerG : chr [1:6196] "Biggin" "Biggin" "Nelson" "Nelson" ...
## $ Date : chr [1:6196] "4/02/2016" "4/03/2017" "4/06/2016" "7/05/2016" ...
## $ Distance : num [1:6196] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 ...
## $ Postcode : num [1:6196] 3067 3067 3067 3067 3067 ...
## $ Bedroom2 : num [1:6196] 2 3 3 4 2 3 3 2 2 3 ...
## $ Bathroom : num [1:6196] 1 2 1 2 1 1 2 2 1 2 ...
## $ Car : num [1:6196] 0 0 2 0 2 2 2 1 2 1 ...
## $ Landsize : num [1:6196] 156 134 120 245 256 220 214 0 238 113 ...
## $ BuildingArea : num [1:6196] 79 150 142 210 107 75 190 94 97 110 ...
## $ YearBuilt : num [1:6196] 1900 1900 2014 1910 1890 ...
## $ CouncilArea : chr [1:6196] "Yarra" "Yarra" "Yarra" "Yarra" ...
## $ Lattitude : num [1:6196] -37.8 -37.8 -37.8 -37.8 -37.8 ...
## $ Longtitude : num [1:6196] 145 145 145 145 145 ...
## $ Regionname : chr [1:6196] "Northern Metropolitan" "Northern Metropolitan" "Northern Metropolitan" "Northern Metropolitan" ...
## $ Propertycount: num [1:6196] 4019 4019 4019 4019 4019 ...
## - attr(*, "spec")=
## .. cols(
## .. ...1 = col_double(),
## .. Suburb = col_character(),
## .. Address = col_character(),
## .. Rooms = col_double(),
## .. Type = col_character(),
## .. Price = col_double(),
## .. Method = col_character(),
## .. SellerG = col_character(),
## .. Date = col_character(),
## .. Distance = col_double(),
## .. Postcode = col_double(),
## .. Bedroom2 = col_double(),
## .. Bathroom = col_double(),
## .. Car = col_double(),
## .. Landsize = col_double(),
## .. BuildingArea = col_double(),
## .. YearBuilt = col_double(),
## .. CouncilArea = col_character(),
## .. Lattitude = col_double(),
## .. Longtitude = col_double(),
## .. Regionname = col_character(),
## .. Propertycount = col_double()
## .. )
## - attr(*, "problems")=<externalptr>head(mhd)## # A tibble: 6 × 22
## ...1 Suburb Address Rooms Type Price Method SellerG Date Dista…¹ Postc…²
## <dbl> <chr> <chr> <dbl> <chr> <dbl> <chr> <chr> <chr> <dbl> <dbl>
## 1 1 Abbotsf… 25 Blo… 2 h 1.03e6 S Biggin 4/02… 2.5 3067
## 2 2 Abbotsf… 5 Char… 3 h 1.46e6 SP Biggin 4/03… 2.5 3067
## 3 3 Abbotsf… 55a Pa… 4 h 1.6 e6 VB Nelson 4/06… 2.5 3067
## 4 4 Abbotsf… 124 Ya… 3 h 1.88e6 S Nelson 7/05… 2.5 3067
## 5 5 Abbotsf… 98 Cha… 2 h 1.64e6 S Nelson 8/10… 2.5 3067
## 6 6 Abbotsf… 10 Val… 2 h 1.10e6 S Biggin 8/10… 2.5 3067
## # … with 11 more variables: Bedroom2 <dbl>, Bathroom <dbl>, Car <dbl>,
## # Landsize <dbl>, BuildingArea <dbl>, YearBuilt <dbl>, CouncilArea <chr>,
## # Lattitude <dbl>, Longtitude <dbl>, Regionname <chr>, Propertycount <dbl>,
## # and abbreviated variable names ¹Distance, ²Postcodetail(mhd)## # A tibble: 6 × 22
## ...1 Suburb Address Rooms Type Price Method SellerG Date Dista…¹ Postc…²
## <dbl> <chr> <chr> <dbl> <chr> <dbl> <chr> <chr> <chr> <dbl> <dbl>
## 1 6191 Westmea… 4 Pers… 3 h 6.35e5 S Barry 29/0… 16.5 3049
## 2 6192 Whittle… 30 She… 3 h 6.01e5 S Ray 29/0… 35.5 3757
## 3 6193 William… 75 Cec… 3 h 1.05e6 VB Willia… 29/0… 6.8 3016
## 4 6194 William… 2/29 D… 1 u 3.85e5 SP Willia… 29/0… 6.8 3016
## 5 6195 Windsor 201/15… 2 u 5.6 e5 PI hockin… 29/0… 4.6 3181
## 6 6196 Yarravi… 54 Pen… 6 h 2.45e6 VB Village 29/0… 6.3 3013
## # … with 11 more variables: Bedroom2 <dbl>, Bathroom <dbl>, Car <dbl>,
## # Landsize <dbl>, BuildingArea <dbl>, YearBuilt <dbl>, CouncilArea <chr>,
## # Lattitude <dbl>, Longtitude <dbl>, Regionname <chr>, Propertycount <dbl>,
## # and abbreviated variable names ¹Distance, ²Postcodesummary(mhd)## ...1 Suburb Address Rooms
## Min. : 1 Length:6196 Length:6196 Min. :1.000
## 1st Qu.:1550 Class :character Class :character 1st Qu.:2.000
## Median :3098 Mode :character Mode :character Median :3.000
## Mean :3098 Mean :2.931
## 3rd Qu.:4647 3rd Qu.:4.000
## Max. :6196 Max. :8.000
## Type Price Method SellerG
## Length:6196 Min. : 131000 Length:6196 Length:6196
## Class :character 1st Qu.: 620000 Class :character Class :character
## Mode :character Median : 880000 Mode :character Mode :character
## Mean :1068828
## 3rd Qu.:1325000
## Max. :9000000
## Date Distance Postcode Bedroom2
## Length:6196 Min. : 0.000 Min. :3000 Min. :0.000
## Class :character 1st Qu.: 5.900 1st Qu.:3044 1st Qu.:2.000
## Mode :character Median : 9.000 Median :3081 Median :3.000
## Mean : 9.751 Mean :3102 Mean :2.902
## 3rd Qu.:12.400 3rd Qu.:3147 3rd Qu.:3.000
## Max. :47.400 Max. :3977 Max. :9.000
## Bathroom Car Landsize BuildingArea
## Min. :1.000 Min. : 0.000 Min. : 0 Min. : 0.0
## 1st Qu.:1.000 1st Qu.: 1.000 1st Qu.: 152 1st Qu.: 91.0
## Median :1.000 Median : 1.000 Median : 373 Median : 124.0
## Mean :1.576 Mean : 1.574 Mean : 471 Mean : 141.6
## 3rd Qu.:2.000 3rd Qu.: 2.000 3rd Qu.: 628 3rd Qu.: 170.0
## Max. :8.000 Max. :10.000 Max. :37000 Max. :3112.0
## YearBuilt CouncilArea Lattitude Longtitude
## Min. :1196 Length:6196 Min. :-38.16 Min. :144.5
## 1st Qu.:1940 Class :character 1st Qu.:-37.86 1st Qu.:144.9
## Median :1970 Mode :character Median :-37.80 Median :145.0
## Mean :1964 Mean :-37.81 Mean :145.0
## 3rd Qu.:2000 3rd Qu.:-37.76 3rd Qu.:145.1
## Max. :2018 Max. :-37.46 Max. :145.5
## Regionname Propertycount
## Length:6196 Min. : 389
## Class :character 1st Qu.: 4384
## Mode :character Median : 6567
## Mean : 7435
## 3rd Qu.:10175
## Max. :21650fivenum(mhd$Price)## [1] 131000 620000 880000 1325000 9000000mean(mhd$Price)## [1] 1068828median(mhd$Price)## [1] 880000mode<-function(x){which.max(tabulate(x))}
mode(mhd$Price)## [1] 600000### Question 4 - Part 1 - Check for normality in Price
ks.test(mhd$Price, pnorm)## Warning in ks.test.default(mhd$Price, pnorm): ties should not be present for the
## Kolmogorov-Smirnov test##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: mhd$Price
## D = 1, p-value < 2.2e-16
## alternative hypothesis: two-sidedqqPlot(mhd$Price)
## [1] 6142 4108options(scipen = 999)
hist(mhd$Price, main = "Histogram of Price of Melbourne Housing", xlab = "Price", ylab = "Number of Occurrences", col = "orange")
type_h <- filter(mhd, Type == 'h')
ks.test(type_h$Price, pnorm)## Warning in ks.test.default(type_h$Price, pnorm): ties should not be present for
## the Kolmogorov-Smirnov test##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: type_h$Price
## D = 1, p-value < 0.00000000000000022
## alternative hypothesis: two-sidedtype_u <- filter(mhd, Type == "u")
ks.test(type_u$Price, pnorm)## Warning in ks.test.default(type_u$Price, pnorm): ties should not be present for
## the Kolmogorov-Smirnov test##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: type_u$Price
## D = 1, p-value < 0.00000000000000022
## alternative hypothesis: two-sidedtype_t <- filter(mhd, Type == "t")
ks.test(type_t$Price, pnorm)## Warning in ks.test.default(type_t$Price, pnorm): ties should not be present for
## the Kolmogorov-Smirnov test##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: type_t$Price
## D = 1, p-value < 0.00000000000000022
## alternative hypothesis: two-sided### The null hypothesis of the K-S test is the data are normally distributed. Given the p-value of the test, I reject the null hypothesis and conclude the Price is not normally distributed. This may affect the results of the ANOVA. The qqPlot and the histogram likewise confirm the non-normality of Price. NB: I ran the ks.test for each of the subgroups of Type to determine if each group was not normally distributed. The distribution was not normal in any of the groups. I tried using group_by to do this, but using group_by only gave me counts for each of the types, which is not what I wanted. ### Question 4 - Part 2 - Check for Variation in Price by Housing Type and Melbourne's regions
#### First simplify the Region Names so they all appear on the abscissa of the boxplot.
table(mhd$Regionname)##
## Eastern Metropolitan Eastern Victoria
## 571 23
## Northern Metropolitan Northern Victoria
## 1854 19
## South-Eastern Metropolitan Southern Metropolitan
## 157 2166
## Western Metropolitan Western Victoria
## 1392 14mhd$Regionname[mhd$Regionname == "Eastern Metropolitan"] <- "EM"
mhd$Regionname[mhd$Regionname == "Eastern Victoria"] <- "EV"
mhd$Regionname[mhd$Regionname == "Northern Metropolitan"] <- "NM"
mhd$Regionname[mhd$Regionname == "Northern Victoria"] <- "NV"
mhd$Regionname[mhd$Regionname == "South-Eastern Metropolitan"] <- "SEM"
mhd$Regionname[mhd$Regionname == "Southern Metropolitan"] <- "SM"
mhd$Regionname[mhd$Regionname == "Western Metropolitan"] <- "WM"
mhd$Regionname[mhd$Regionname == "Western Victoria"] <- "WV"
table(mhd$Regionname)##
## EM EV NM NV SEM SM WM WV
## 571 23 1854 19 157 2166 1392 14### Generate the boxplots
options(scipen = 999)
boxplot (mhd$Price ~ mhd$Regionname, xlab = "Region", ylab = "Sales Price", main = "Price by Region", col=brewer.pal(8,"Accent"))
boxplot(mhd$Price ~ (mhd$Type), ylab = "Range of Price", xlab = "Housing Type", main = "Boxplot of Price by Housing Type",col=brewer.pal(8,"Accent") )
Question 5 - What does the EDA tell me about my data?
The exploratory data analysis tells me several things. One thing is the sales prices of houses in Melbourne in 2017 are not normally distributed; in fact, they are heavily right-skewed. This is shown by the qqPlot, the Kolmogorov-Smirnov normality test, and the histogram. Diving deeper, I checked to see if the non-normality holds across all housing types (stand-alone houses, townhouses, and units in buildings). The K-S test shows the skewness across all housing types.
I will conduct an ANOVA using Price as the dependent variable. According to https://usq.pressbooks.pub/statisticsforresearchstudents/chapter/one-way-anova-assumptions/#:~:text=The%20data%20should%20have%20independence,normally%20distributed%20for%20each%20group, “The dependent variable should be normally or near-to-normally distributed for each group.” I don’t know what negative affect this may have on the ANOVA results. I wrote this before you posted your comment on my Final Project Outline. Based on your comment, I shouldn’t be concerned about normality because I have 6,196 observations.
The second thing the EDA tells me is housing prices vary a great deal across both housing types and Melbourne’s regions. As could be expected, single-family stand-alone homes are most expensive, followed by townhomes, followed by units in multi-unit buildings. The EDA also shows that the 3 Victoria areas - Eastern, Western, and Northern - have the lowest values in Melbourne. While the Southern Metropolitan region has the highest values overall, South-Eastern Metropolitan has one very high-value property, the highest in this dataset.
### Question 6 - ANOVA to determine if there are statistically-significant differences among the mean sales prices of the three housing types and statistically significant differences among the mean sales prices of properties in the 8 regions. NB: From the boxplots, it appears there are large differences in the means of the sale price of the 3 housing types and the regions.The ANOVA will quantify and confirm the visual analyses.
anova_type <- aov(Price ~ Type, data = mhd)
summary(anova_type)## Df Sum Sq Mean Sq F value Pr(>F)
## Type 2 538603361430103 269301680715051 729.8 <0.0000000000000002
## Residuals 6193 2285301907461460 369013710231
##
## Type ***
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1etaSquared(anova_type)## eta.sq eta.sq.part
## Type 0.19073 0.19073TukeyHSD(anova_type, conf.level=.95)## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Price ~ Type, data = mhd)
##
## $Type
## diff lwr upr p adj
## t-h -388834.6 -451001.8 -326667.5 0
## u-h -684641.7 -727567.8 -641715.6 0
## u-t -295807.0 -364474.8 -227139.3 0anova_region <- aov(Price ~ Regionname, data = mhd)
summary(anova_region)## Df Sum Sq Mean Sq F value Pr(>F)
## Regionname 7 355032128709868 50718875529981 127.1 <0.0000000000000002
## Residuals 6188 2468873140181730 398977559823
##
## Regionname ***
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1etaSquared(anova_region)## eta.sq eta.sq.part
## Regionname 0.1257238 0.1257238TukeyHSD(anova_region, conf.level=.95)## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Price ~ Regionname, data = mhd)
##
## $Regionname
## diff lwr upr p adj
## EV-EM -440342.268 -847631.95 -33052.587 0.0233983
## NM-EM -238078.027 -329737.03 -146419.028 0.0000000
## NV-EM -553446.748 -1000051.47 -106842.029 0.0043020
## SEM-EM -179856.804 -352436.61 -7277.002 0.0340272
## SM-EM 268312.500 178221.32 358403.680 0.0000000
## WM-EM -242840.413 -338013.60 -147667.221 0.0000000
## WV-EM -719270.057 -1237339.55 -201200.565 0.0006832
## NM-EV 202264.241 -199531.67 604060.149 0.7933989
## NV-EV -113104.481 -706816.83 480607.870 0.9991313
## SEM-EV 260485.464 -167091.86 688062.788 0.5876487
## SM-EV 708654.767 307213.61 1110095.922 0.0000025
## WM-EV 197501.855 -205110.26 600113.972 0.8145283
## WV-EV -278927.789 -928107.72 370252.138 0.8981554
## NV-NM -315368.721 -756969.04 126231.599 0.3731651
## SEM-NM 58221.224 -100960.61 217403.056 0.9550884
## SM-NM 506390.527 445797.72 566983.337 0.0000000
## WM-NM -4762.385 -72681.49 63156.716 0.9999990
## WV-NM -481192.029 -994953.71 32569.652 0.0856212
## SEM-NV 373589.945 -91590.94 838770.833 0.2245552
## SM-NV 821759.248 380481.68 1263036.815 0.0000005
## WM-NV 310606.336 -131736.75 752949.424 0.3961507
## WV-NV -165823.308 -840364.24 508717.623 0.9955769
## SM-SEM 448169.303 289885.05 606453.556 0.0000000
## WM-SEM -62983.609 -224214.56 98247.344 0.9365612
## WV-SEM -539413.253 -1073579.41 -5247.098 0.0457992
## WM-SM -511152.912 -576940.85 -445364.973 0.0000000
## WV-SM -987582.556 -1501066.84 -474098.268 0.0000002
## WV-WM -476429.644 -990829.91 37970.618 0.0930889### As predicted, the differences in mean sales prices for the 3 housing types and the 8 regions are statistically significant. Query, however, how much of that statistical significance is due to the large number of observations. Also note the etaSquared value is above 0.14 for Type, suggesting a highly significant result. https://finnstats.com/index.php/2022/01/03/how-to-perform-eta-squared-in-r/ The etaSquared value is slightly below 0.14 for the Regions, suggesting a less strong effect size for the Regions. ### The more interesting question is whether there is an interaction effect between Type and Region. A 2-way ANOVA will show any interaction effect.
tapply(mhd$Price, INDEX = list(mhd$Type, mhd$Regionname), FUN=mean)## EM EV NM NV SEM SM WM WV
## h 1217287.9 680135.5 1017514 556894.7 967620.0 1861503.5 976162.9 391071.4
## t 812892.1 NA 734746 NA 897479.2 1160534.3 711452.1 NA
## u 674204.3 447000.0 540825 NA 583884.6 644718.7 473205.5 NAmhd.means <- aggregate(mhd$Price,
by=list(mhd$Type, mhd$Regionname), FUN = mean)
mhd.means ## Group.1 Group.2 x
## 1 h EM 1217287.9
## 2 t EM 812892.1
## 3 u EM 674204.3
## 4 h EV 680135.5
## 5 u EV 447000.0
## 6 h NM 1017514.0
## 7 t NM 734746.0
## 8 u NM 540825.0
## 9 h NV 556894.7
## 10 h SEM 967620.0
## 11 t SEM 897479.2
## 12 u SEM 583884.6
## 13 h SM 1861503.5
## 14 t SM 1160534.3
## 15 u SM 644718.7
## 16 h WM 976162.9
## 17 t WM 711452.1
## 18 u WM 473205.5
## 19 h WV 391071.4 anova_interact <- (aov(Price~Type+Regionname+Type:Regionname, data = mhd))
summary(anova_interact)## Df Sum Sq Mean Sq F value
## Type 2 538603361430103 269301680715051 1026.76
## Regionname 7 522215750763151 74602250109022 284.44
## Type:Regionname 9 142970752663295 15885639184811 60.57
## Residuals 6177 1620115404035031 262281917441
## Pr(>F)
## Type <0.0000000000000002 ***
## Regionname <0.0000000000000002 ***
## Type:Regionname <0.0000000000000002 ***
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1etaSquared(anova_interact)## eta.sq eta.sq.part
## Type 0.24993295 0.30344652
## Regionname 0.18492680 0.24376052
## Type:Regionname 0.05062874 0.08109119TukeyHSD(anova_interact, conf.level=.95)## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Price ~ Type + Regionname + Type:Regionname, data = mhd)
##
## $Type
## diff lwr upr p adj
## t-h -388834.6 -441245.8 -336423.5 0
## u-h -684641.7 -720831.3 -648452.0 0
## u-t -295807.0 -353698.7 -237915.4 0
##
## $Regionname
## diff lwr upr p adj
## EV-EM -533322.159 -863549.945 -203094.373 0.0000274
## NM-EM -153953.643 -228270.154 -79637.131 0.0000000
## NV-EM -676193.670 -1038297.829 -314089.510 0.0000004
## SEM-EM -216193.804 -356120.369 -76267.240 0.0000780
## SM-EM 416722.732 343677.397 489768.066 0.0000000
## WM-EM -214765.826 -291931.622 -137600.030 0.0000000
## WV-EM -842016.978 -1262064.303 -421969.653 0.0000000
## NM-EV 379368.517 53595.045 705141.988 0.0099120
## NV-EV -142871.510 -624249.567 338506.546 0.9861482
## SEM-EV 317128.355 -29548.518 663805.228 0.1018594
## SM-EV 950044.891 624559.051 1275530.731 0.0000000
## WM-EV 318556.333 -7878.915 644991.581 0.0617238
## WV-EV -308694.818 -835045.620 217655.983 0.6350427
## NV-NM -522240.027 -880286.653 -164193.401 0.0002660
## SEM-NM -62240.162 -191303.742 66823.418 0.8275794
## SM-NM 570676.374 521548.124 619804.625 0.0000000
## WM-NM -60812.183 -115880.543 -5743.824 0.0185781
## WV-NM -688063.335 -1104617.917 -271508.753 0.0000156
## SEM-NV 459999.865 82834.270 837165.460 0.0053866
## SM-NV 1092916.401 735131.461 1450701.342 0.0000000
## WM-NV 461427.843 102778.986 820076.701 0.0024587
## WV-NV -165823.308 -712736.645 381090.029 0.9843038
## SM-SEM 632916.536 504580.709 761252.364 0.0000000
## WM-SEM 1427.978 -129297.015 132152.971 1.0000000
## WV-SEM -625823.173 -1058921.568 -192724.779 0.0003205
## WM-SM -631488.558 -684828.985 -578148.131 0.0000000
## WV-SM -1258739.710 -1675069.383 -842410.037 0.0000000
## WV-WM -627251.152 -1044323.491 -210178.813 0.0001410
##
## $`Type:Regionname`
## diff lwr upr p adj
## t:EM-h:EM -404395.818 -666604.728 -142186.91 0.0000056
## u:EM-h:EM -543083.638 -782745.290 -303421.99 0.0000000
## h:EV-h:EM -537152.378 -944202.255 -130102.50 0.0004110
## t:EV-h:EM NA NA NA NA
## u:EV-h:EM -770287.923 -2636005.985 1095430.14 0.9985916
## h:NM-h:EM -199773.973 -303144.532 -96403.41 0.0000000
## t:NM-h:EM -482541.934 -645006.961 -320076.91 0.0000000
## u:NM-h:EM -676462.970 -800850.330 -552075.61 0.0000000
## h:NV-h:EM -660393.187 -1096989.139 -223797.23 0.0000104
## t:NV-h:EM NA NA NA NA
## u:NV-h:EM NA NA NA NA
## h:SEM-h:EM -249667.886 -434420.370 -64915.40 0.0002329
## t:SEM-h:EM -319808.757 -865011.219 225393.71 0.9006330
## u:SEM-h:EM -633403.308 -1157790.933 -109015.68 0.0026830
## h:SM-h:EM 644215.587 540924.522 747506.65 0.0000000
## t:SM-h:EM -56753.610 -214383.448 100876.23 0.9998376
## u:SM-h:EM -572569.260 -684385.891 -460752.63 0.0000000
## h:WM-h:EM -241124.985 -347020.864 -135229.11 0.0000000
## t:WM-h:EM -505835.811 -685503.775 -326167.85 0.0000000
## u:WM-h:EM -744082.419 -896364.636 -591800.20 0.0000000
## h:WV-h:EM -826216.495 -1332081.610 -320351.38 0.0000008
## t:WV-h:EM NA NA NA NA
## u:WV-h:EM NA NA NA NA
## u:EM-t:EM -138687.820 -471173.471 193797.83 0.9983601
## h:EV-t:EM -132756.560 -600515.690 335002.57 0.9999977
## t:EV-t:EM NA NA NA NA
## u:EV-t:EM -365892.105 -2245789.146 1514004.94 1.0000000
## h:NM-t:EM 204621.845 -47953.833 457197.52 0.3287286
## t:NM-t:EM -78146.116 -360110.450 203818.22 0.9999985
## u:NM-t:EM -272067.152 -533947.308 -10187.00 0.0307675
## h:NV-t:EM -255997.368 -749682.518 237687.78 0.9716464
## t:NV-t:EM NA NA NA NA
## u:NV-t:EM NA NA NA NA
## h:SEM-t:EM 154727.933 -140640.449 450096.31 0.9682212
## t:SEM-t:EM 84587.061 -507320.639 676494.76 1.0000000
## u:SEM-t:EM -229007.490 -801800.107 343785.13 0.9991334
## h:SM-t:EM 1048611.405 796068.251 1301154.56 0.0000000
## t:SM-t:EM 347642.208 68435.893 626848.52 0.0014679
## u:SM-t:EM -168173.442 -424321.758 87974.87 0.7574517
## h:WM-t:EM 163270.833 -90348.839 416890.51 0.7886942
## t:WM-t:EM -101439.993 -393654.944 190774.96 0.9999121
## u:WM-t:EM -339686.601 -615909.110 -63464.09 0.0018876
## h:WV-t:EM -421820.677 -977706.021 134064.67 0.4673419
## t:WV-t:EM NA NA NA NA
## u:WV-t:EM NA NA NA NA
## h:EV-u:EM 5931.260 -449571.538 461434.06 1.0000000
## t:EV-u:EM NA NA NA NA
## u:EV-u:EM -227204.286 -2104089.226 1649680.66 1.0000000
## h:NM-u:EM 343309.665 114227.434 572391.90 0.0000138
## t:NM-u:EM 60541.704 -200586.772 321670.18 1.0000000
## u:NM-u:EM -133379.332 -372681.257 105922.59 0.9388449
## h:NV-u:EM -117309.549 -599397.945 364778.85 0.9999999
## t:NV-u:EM NA NA NA NA
## u:NV-u:EM NA NA NA NA
## h:SEM-u:EM 293415.752 17867.796 568963.71 0.0218865
## t:SEM-u:EM 223274.881 -358995.607 805545.37 0.9995483
## u:SEM-u:EM -90319.670 -653147.865 472508.52 1.0000000
## h:SM-u:EM 1187299.225 958252.854 1416345.60 0.0000000
## t:SM-u:EM 486330.028 228182.082 744477.97 0.0000000
## u:SM-u:EM -29485.623 -262500.976 203529.73 1.0000000
## h:WM-u:EM 301958.653 71725.872 532191.43 0.0004738
## t:WM-u:EM 37247.827 -234917.147 309412.80 1.0000000
## u:WM-u:EM -200998.781 -455916.552 53918.99 0.3847267
## h:WV-u:EM -283132.857 -828745.092 262479.38 0.9714090
## t:WV-u:EM NA NA NA NA
## u:WV-u:EM NA NA NA NA
## t:EV-h:EV NA NA NA NA
## u:EV-h:EV -233135.545 -2138640.459 1672369.37 1.0000000
## h:NM-h:EV 337378.405 -63533.759 738290.57 0.2559437
## t:NM-h:EV 54610.444 -365437.144 474658.03 1.0000000
## u:NM-h:EV -139310.592 -546148.774 267527.59 0.9999304
## h:NV-h:EV -123240.809 -706902.626 460421.01 1.0000000
## t:NV-h:EV NA NA NA NA
## u:NV-h:EV NA NA NA NA
## h:SEM-h:EV 287484.492 -141675.817 716644.80 0.7229107
## t:SEM-h:EV 217343.621 -451454.417 886141.66 0.9999720
## u:SEM-h:EV -96250.930 -748192.240 555690.38 1.0000000
## h:SM-h:EV 1181367.965 780476.290 1582259.64 0.0000000
## t:SM-h:EV 480398.768 62197.553 898599.98 0.0066767
## u:SM-h:EV -35416.882 -438589.364 367755.60 1.0000000
## h:WM-h:EV 296027.393 -105543.308 697598.09 0.5303824
## t:WM-h:EV 31316.567 -395679.531 458312.67 1.0000000
## u:WM-h:EV -206930.041 -623145.087 209285.01 0.9826480
## h:WV-h:EV -289064.117 -926201.940 348073.71 0.9946155
## t:WV-h:EV NA NA NA NA
## u:WV-h:EV NA NA NA NA
## u:EV-t:EV NA NA NA NA
## h:NM-t:EV NA NA NA NA
## t:NM-t:EV NA NA NA NA
## u:NM-t:EV NA NA NA NA
## h:NV-t:EV NA NA NA NA
## t:NV-t:EV NA NA NA NA
## u:NV-t:EV NA NA NA NA
## h:SEM-t:EV NA NA NA NA
## t:SEM-t:EV NA NA NA NA
## u:SEM-t:EV NA NA NA NA
## h:SM-t:EV NA NA NA NA
## t:SM-t:EV NA NA NA NA
## u:SM-t:EV NA NA NA NA
## h:WM-t:EV NA NA NA NA
## t:WM-t:EV NA NA NA NA
## u:WM-t:EV NA NA NA NA
## h:WV-t:EV NA NA NA NA
## t:WV-t:EV NA NA NA NA
## u:WV-t:EV NA NA NA NA
## h:NM-u:EV 570513.951 -1293874.648 2434902.55 0.9999905
## t:NM-u:EV 287745.989 -1580850.879 2156342.86 1.0000000
## u:NM-u:EV 93824.954 -1771846.933 1959496.84 1.0000000
## h:NV-u:EV 109894.737 -1802139.624 2021929.10 1.0000000
## t:NV-u:EV NA NA NA NA
## u:NV-u:EV NA NA NA NA
## h:SEM-u:EV 520620.038 -1350046.382 2391286.46 0.9999984
## t:SEM-u:EV 450479.167 -1489238.622 2390196.95 1.0000000
## u:SEM-u:EV 136884.615 -1797085.848 2070855.08 1.0000000
## h:SM-u:EV 1414503.511 -449880.682 3278887.70 0.4677134
## t:SM-u:EV 713534.314 -1154648.370 2581717.00 0.9995758
## u:SM-u:EV 197718.663 -1667157.293 2062594.62 1.0000000
## h:WM-u:EV 529162.938 -1335367.380 2393693.26 0.9999977
## t:WM-u:EV 264452.113 -1605718.989 2134623.21 1.0000000
## u:WM-u:EV 26205.504 -1841533.569 1893944.58 1.0000000
## h:WV-u:EV -55928.571 -1984959.128 1873101.99 1.0000000
## t:WV-u:EV NA NA NA NA
## u:WV-u:EV NA NA NA NA
## t:NM-h:NM -282767.961 -429177.816 -136358.11 0.0000000
## u:NM-h:NM -476688.997 -579222.777 -374155.22 0.0000000
## h:NV-h:NM -460619.214 -891498.531 -29739.90 0.0206936
## t:NV-h:NM NA NA NA NA
## u:NV-h:NM NA NA NA NA
## h:SEM-h:NM -49893.913 -220699.185 120911.36 0.9999960
## t:SEM-h:NM -120034.784 -660670.230 420600.66 1.0000000
## u:SEM-h:NM -433629.335 -953267.038 86008.37 0.2713413
## h:SM-h:NM 843989.560 768424.987 919554.13 0.0000000
## t:SM-h:NM 143020.363 1995.094 284045.63 0.0420555
## u:SM-h:NM -372795.287 -459651.027 -285939.55 0.0000000
## h:WM-h:NM -41351.012 -120438.924 37736.90 0.9688892
## t:WM-h:NM -306061.838 -471354.118 -140769.56 0.0000000
## u:WM-h:NM -544308.446 -679330.053 -409286.84 0.0000000
## h:WV-h:NM -626442.522 -1127382.115 -125502.93 0.0013419
## t:WV-h:NM NA NA NA NA
## u:WV-h:NM NA NA NA NA
## u:NM-t:NM -193921.036 -355854.937 -31987.13 0.0031608
## h:NV-t:NM -177851.252 -626589.928 270887.42 0.9992423
## t:NV-t:NM NA NA NA NA
## u:NV-t:NM NA NA NA NA
## h:SEM-t:NM 232874.049 21015.951 444732.15 0.0136694
## t:SEM-t:NM 162733.177 -392240.784 717707.14 0.9999957
## u:SEM-t:NM -150861.374 -685401.133 383678.39 0.9999979
## h:SM-t:NM 1126757.521 980403.781 1273111.26 0.0000000
## t:SM-t:NM 425788.324 237115.224 614461.43 0.0000000
## u:SM-t:NM -90027.326 -242517.759 62463.11 0.8947311
## h:WM-t:NM 241416.949 93213.338 389620.56 0.0000009
## t:WM-t:NM -23293.877 -230732.905 184145.15 1.0000000
## u:WM-t:NM -261540.485 -445769.274 -77311.70 0.0000653
## h:WV-t:NM -343674.561 -860056.094 172706.97 0.7343404
## t:WV-t:NM NA NA NA NA
## u:WV-t:NM NA NA NA NA
## h:NV-u:NM 16069.783 -420328.807 452468.37 1.0000000
## t:NV-u:NM NA NA NA NA
## u:NV-u:NM NA NA NA NA
## h:SEM-u:NM 426795.084 242509.480 611080.69 0.0000000
## t:SEM-u:NM 356654.213 -188390.215 901698.64 0.7629398
## u:SEM-u:NM 43059.662 -481163.654 567282.98 1.0000000
## h:SM-u:NM 1320678.557 1218224.920 1423132.19 0.0000000
## t:SM-u:NM 619709.360 462626.995 776791.73 0.0000000
## u:SM-u:NM 103893.709 -7149.807 214937.23 0.1041288
## h:WM-u:NM 435337.985 330258.773 540417.20 0.0000000
## t:WM-u:NM 170627.159 -8560.678 349815.00 0.0869265
## u:WM-u:NM -67619.449 -219334.898 84096.00 0.9957759
## h:WV-u:NM -149753.525 -655448.313 355941.26 0.9999948
## t:WV-u:NM NA NA NA NA
## u:WV-u:NM NA NA NA NA
## t:NV-h:NV NA NA NA NA
## u:NV-h:NV NA NA NA NA
## h:SEM-h:NV 410725.301 -46554.695 868005.30 0.1527897
## t:SEM-h:NV 340584.430 -346596.215 1027765.07 0.9832871
## u:SEM-h:NV 26989.879 -643796.149 697775.91 1.0000000
## h:SM-h:NV 1304608.774 873748.520 1735469.03 0.0000000
## t:SM-h:NV 603639.577 156628.749 1050650.40 0.0002371
## u:SM-h:NV 87823.926 -345159.299 520807.15 1.0000000
## h:WM-h:NV 419268.202 -12223.920 850760.32 0.0698190
## t:WM-h:NV 154557.376 -300692.107 609806.86 0.9999400
## u:WM-h:NV -83689.232 -528842.451 361463.99 1.0000000
## h:WV-h:NV -165823.308 -822230.978 490584.36 0.9999998
## t:WV-h:NV NA NA NA NA
## u:WV-h:NV NA NA NA NA
## u:NV-t:NV NA NA NA NA
## h:SEM-t:NV NA NA NA NA
## t:SEM-t:NV NA NA NA NA
## u:SEM-t:NV NA NA NA NA
## h:SM-t:NV NA NA NA NA
## t:SM-t:NV NA NA NA NA
## u:SM-t:NV NA NA NA NA
## h:WM-t:NV NA NA NA NA
## t:WM-t:NV NA NA NA NA
## u:WM-t:NV NA NA NA NA
## h:WV-t:NV NA NA NA NA
## t:WV-t:NV NA NA NA NA
## u:WV-t:NV NA NA NA NA
## h:SEM-u:NV NA NA NA NA
## t:SEM-u:NV NA NA NA NA
## u:SEM-u:NV NA NA NA NA
## h:SM-u:NV NA NA NA NA
## t:SM-u:NV NA NA NA NA
## u:SM-u:NV NA NA NA NA
## h:WM-u:NV NA NA NA NA
## t:WM-u:NV NA NA NA NA
## u:WM-u:NV NA NA NA NA
## h:WV-u:NV NA NA NA NA
## t:WV-u:NV NA NA NA NA
## u:WV-u:NV NA NA NA NA
## t:SEM-h:SEM -70140.871 -632043.615 491761.87 1.0000000
## u:SEM-h:SEM -383735.422 -925465.383 157994.54 0.6150017
## h:SM-h:SEM 893883.473 723126.298 1064640.65 0.0000000
## t:SM-h:SEM 192914.276 -15259.052 401087.60 0.1144243
## u:SM-h:SEM -322901.375 -498946.617 -146856.13 0.0000000
## h:WM-h:SEM 8542.901 -163802.409 180888.21 1.0000000
## t:WM-h:SEM -256167.925 -481488.909 -30846.94 0.0079537
## u:WM-h:SEM -494414.533 -698568.501 -290260.57 0.0000000
## h:WV-h:SEM -576548.609 -1100369.651 -52727.57 0.0133919
## t:WV-h:SEM NA NA NA NA
## u:WV-h:SEM NA NA NA NA
## u:SEM-t:SEM -313594.551 -1059639.854 432450.75 0.9981639
## h:SM-t:SEM 964024.344 423404.092 1504644.60 0.0000000
## t:SM-t:SEM 263055.147 -290522.651 816632.95 0.9900997
## u:SM-t:SEM -252760.504 -795074.225 289553.22 0.9922941
## h:WM-t:SEM 78683.772 -462440.198 619807.74 1.0000000
## t:WM-t:SEM -186027.054 -746278.596 374224.49 0.9999592
## u:WM-t:SEM -424273.662 -976352.540 127805.22 0.4397836
## h:WV-t:SEM -506407.738 -1239552.150 226736.67 0.6656019
## t:WV-t:SEM NA NA NA NA
## u:WV-t:SEM NA NA NA NA
## h:SM-u:SEM 1277618.895 757997.001 1797240.79 0.0000000
## t:SM-u:SEM 576649.698 43559.617 1109739.78 0.0174183
## u:SM-u:SEM 60834.048 -460549.524 582217.62 1.0000000
## h:WM-u:SEM 392278.323 -127867.624 912424.27 0.4807680
## t:WM-u:SEM 127567.497 -412449.583 667584.58 0.9999999
## u:WM-u:SEM -110679.111 -642212.499 420854.28 1.0000000
## h:WV-u:SEM -192813.187 -910613.566 524987.19 0.9999992
## t:WV-u:SEM NA NA NA NA
## u:WV-u:SEM NA NA NA NA
## t:SM-h:SM -700969.197 -841936.208 -560002.19 0.0000000
## u:SM-h:SM -1216784.848 -1303545.963 -1130023.73 0.0000000
## h:WM-h:SM -885340.572 -964324.555 -806356.59 0.0000000
## t:WM-h:SM -1150051.398 -1315293.976 -984808.82 0.0000000
## u:WM-h:SM -1388298.006 -1523258.764 -1253337.25 0.0000000
## h:WV-h:SM -1470432.082 -1971355.277 -969508.89 0.0000000
## t:WV-h:SM NA NA NA NA
## u:WV-h:SM NA NA NA NA
## u:SM-t:SM -515815.651 -663143.900 -368487.40 0.0000000
## h:WM-t:SM -184371.375 -327258.013 -41484.74 0.0006848
## t:WM-t:SM -449082.201 -652756.528 -245407.87 0.0000000
## u:WM-t:SM -687328.809 -867308.052 -507349.57 0.0000000
## h:WV-t:SM -769462.885 -1284343.618 -254582.15 0.0000150
## t:WV-t:SM NA NA NA NA
## u:WV-t:SM NA NA NA NA
## h:WM-u:SM 331444.275 241597.827 421290.72 0.0000000
## t:WM-u:SM 66733.450 -103968.116 237435.01 0.9993877
## u:WM-u:SM -171513.159 -313105.252 -29921.07 0.0025405
## h:WV-u:SM -253647.235 -756397.632 249103.16 0.9793365
## t:WV-u:SM NA NA NA NA
## u:WV-u:SM NA NA NA NA
## t:WM-h:WM -264710.826 -431594.026 -97827.63 0.0000022
## u:WM-h:WM -502957.434 -639922.025 -365992.84 0.0000000
## h:WV-h:WM -585091.510 -1086558.299 -83624.72 0.0050887
## t:WV-h:WM NA NA NA NA
## u:WV-h:WM NA NA NA NA
## u:WM-t:WM -238246.608 -437810.982 -38682.23 0.0033498
## h:WV-t:WM -320380.684 -842430.088 201668.72 0.8535967
## t:WV-t:WM NA NA NA NA
## u:WV-t:WM NA NA NA NA
## h:WV-u:WM -82134.076 -595402.891 431134.74 1.0000000
## t:WV-u:WM NA NA NA NA
## u:WV-u:WM NA NA NA NA
## t:WV-h:WV NA NA NA NA
## u:WV-h:WV NA NA NA NA
## u:WV-t:WV NA NA NA NAinteraction.plot(x.factor = mhd.means[,1],trace.factor = mhd.means[,2],
response =mhd.means$x, trace.label = "Region", xlab = "Housing Type", ylab = "Sales Price",col=brewer.pal(8,"Accent") )
### According to this website: https://finnstats.com/index.php/2022/01/03/how-to-perform-eta-squared-in-r/, the effect size is large if it is 0.14 or greater. That seems wrong to me; I'm used to Cohen's d of something over .6 to be meaningful. A second web site, https://www.spss-tutorials.com/effect-size/#:~:text=ANOVA%20%2D%20(Partial)%20Eta%20Squared&text=%CE%B72%20%3D%200.01%20indicates%20a,0.14%20indicates%20a%20large%20effect., said the same thing, so I guess 0.14 is OK.
### What I don't understand are all the NAs in the TukeyHSD output. I thought by running na.omit on the original file I could eliminate NAs in the post-hoc output. ### Calculate the variance of Price for each of the 3 housing types.
var(type_h$Price)## [1] 518486487083var(type_t$Price)## [1] 132101270583var(type_u$Price)## [1] 57710811385Answers to Question 6:
Visualization: See the interaction plot, above.
Assumptions
ANOVA has 3 underlying assumptions: (1) the data are independent; (2) for the categorical variables, the variances of the dependent variables are equal; and (3) the dependent variable is normally distributed. As noted above, the 3rd assumption is not met, but given the large n with which I am working, the CLT should take care of that problem. I must assume the data are independent. As far as equal variances go, the variances of houses and units are somewhat close together (sort of), but the variance of the price of townhomes is very low compared to the other two. I do not know how this will affect the ANOVA.
- Hypotheses
The null hypotheses are there are no statistically significant differences among the mean sales prices of the three housing types; there are no statistically significant differences among the mean sales prices in the eight Melbourne regions; and there are no significant differences among the mean sales prices based on housing type and Melbourne region.
The alternative hypotheses are there are statistically significant differences among the mean sales prices of the three housing types; there are statistically significant differences among the mean sales prices in the eight Melbourne regions; and there are significant differences among the mean sales prices based on housing type and Melbourne region.
See the ANOVA output above for the results and the confidence intervals.
Report the p-values and whether the null hypothesis is rejected.
For the two one-way ANOVA runs, both were statistically significant w/ infinitely small p-values. The very small p-values may have resulted from the large dataset used for the analysis; given a sufficiently large dataset, almost any relationship could be statistically significant. But it does appear in this dataset that housing type has a statistically significant affect on the value, as does the region in which the housing unit is located. In the two-way ANOVA, the results were statistically significant for all 3 terms, leading to a rejection of the null hypotheses. The interesting, and to me unexplainable, result is the low etaSquared value for region in the one-way ANOVA (.1257) and the higher etaSquared value for region in the two-way ANOVA (.1849). Also interesting is the very low etaSquared value for the interaction term in the two-way ANOVA.
6, Real world conclusion
In Melbourne, in 2017, with these data points, in a one-way ANOVA, housing type has a statistically significant affect on sales price, as does the region in which the housing unit is located, although region has a less than strong effect size. In a two-way ANOVA, Both housing type and region had etaSquared values in excess of 0.14; type had an especially high eta squared value. The surprising result was the weak effect size for the interaction effect. While there does seem to be at least some interaction effect, both the plot of the interaction and the effect size of the interaction effect size suggest the interaction effect is minimal at best. Perhaps the conclusion to be drawn from this is there is a mix of housing types across all the regions, so there is little concentration of one housing type in a particular region.
Question 7 - Correlation, Regression, Scatterplot
The basic question in this part of the analysis is this: “What are the factors that most influence the value of properties in Melbourne?” To do this, I need to build multiple regression models for each of the three housing types. I already know, from the ANOVAs, Housing Type is strongly correlated w/ sales prices. Running a regression model against all sales prices w/ housing type as a predictor variable would make no sense. Therefore, I must analyze each housing type separately.
Before I do the multiple regressions on each housing type, I will do a simple linear regression on Price vs. Building Area for all the properties to answer the questions in Question 7.
plot(mhd$BuildingArea, mhd$Price, pch = 16, col = "red", xlab = "Building Area", ylab = "Sales Price",
main = "Sales Price as a Function of Building Area, Sales in Melbourne, 2017")
abline(lm(Price ~ BuildingArea, data = mhd), lwd = 2, col = "blue")
lin_model <- lm(formula = Price ~ BuildingArea, data = mhd)
lin_model##
## Call:
## lm(formula = Price ~ BuildingArea, data = mhd)
##
## Coefficients:
## (Intercept) BuildingArea
## 510532 3944summary(lin_model)##
## Call:
## lm(formula = Price ~ BuildingArea, data = mhd)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10175155 -312714 -133445 227808 8028062
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 510531.73 13464.92 37.92 <0.0000000000000002 ***
## BuildingArea 3943.64 80.05 49.26 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 572300 on 6194 degrees of freedom
## Multiple R-squared: 0.2815, Adjusted R-squared: 0.2814
## F-statistic: 2427 on 1 and 6194 DF, p-value: < 0.00000000000000022### Plot the residuals
res <- residuals(lin_model); res## 1 2 3 4 5
## 212920.3199 362921.5252 529470.6852 537302.8255 703498.2600
## 6 7 8 9 10
## 290694.8998 90175.7254 -131234.3551 416934.7099 255667.3250
## 11 12 13 14 15
## 251885.5500 91582.1898 287076.2001 -247150.4252 57076.2001
## 16 17 18 19 20
## 469258.4499 250774.0453 119681.7151 290456.2951 -237713.9753
## 21 22 23 24 25
## 310596.5799 179681.7151 178589.3849 200033.0299 -557851.8495
## 26 27 28 29 30
## -352360.2498 -312360.2498 -238797.9051 -338980.1549 -367994.5450
## 31 32 33 34 35
## -349685.1951 -519049.6946 -415459.7751 -283417.8102 -351234.3551
## 36 37 38 39 40
## -140036.5099 -119614.4500 -271205.5749 -335036.5099 -126163.6100
## 41 42 43 44 45
## -229896.2250 -154725.9547 -956118.0291 -457711.5646 -292430.9949
## 46 47 48 49 50
## -368839.8700 -87783.5150 -271163.6100 -186303.8948 441089.3849
## 51 52 53 54 55
## 1558626.5654 814963.4901 606033.0299 1079612.1753 662428.7202
## 56 57 58 59 60
## 1187498.2600 808343.5851 1390668.5303 524258.4499 425491.0649
## 61 62 63 64 65
## 724645.7399 909752.4602 1923696.1052 1287782.4457 1104399.9401
## 66 67 68 69 70
## 972850.7801 -202115.6554 3408133.7605 1057639.7502 201300.4148
## 71 72 73 74 75
## 701019.8451 261511.4447 452289.6407 406408.3404 1678766.8503
## 76 77 78 79 80
## -221650.4252 -257642.0249 877780.0350 520740.4808 -162149.2199
## 81 82 83 84 85
## -357150.4252 -239094.0702 316796.8358 611302.8255 -944893.8144
## 86 87 88 89 90
## -42428.5842 -283487.3499 136230.8750 401866.3755 -251234.3551
## 91 92 93 94 95
## -335600.0599 -297290.7101 737708.0846 -300248.7452 -310319.4903
## 96 97 98 99 100
## -375868.6502 -178205.5749 -336585.6699 -367192.3902 -175628.8401
## 101 102 103 104 105
## -230248.7452 -206867.4449 -379163.6100 -47896.2250 207637.3395
## 106 107 108 109 110
## -333803.4201 -415386.6193 -190938.1900 -393192.3902 -486120.4397
## 111 112 113 114 115
## -303205.5749 -387881.8350 -257994.5450 -302007.7297 -265389.0300
## 116 117 118 119 120
## -185065.2901 -487951.3747 -284896.2250 -401183.9898 -210514.9248
## 121 122 123 124 125
## -208205.5749 66372.3652 -494586.8752 -211248.7452 90103.7750
## 126 127 128 129 130
## 280385.5500 836921.5252 902005.4550 756766.8503 1082005.4550
## 131 132 133 134 135
## 169257.2445 502498.2600 -380390.2353 -205917.8102 320878.3549
## 136 137 138 139 140
## 1414979.0855 812287.2301 1046654.1403 2979547.4569 -279544.9103
## 141 142 143 144 145
## 371441.9050 -98361.4552 -277008.9351 963554.6150 -116023.3251
## 146 147 148 149 150
## -259572.4851 458976.6749 -290248.7452 2124613.3807 2376234.4911
## 151 152 153 154 155
## 578637.3395 1878029.4508 -403.4201 -152544.9103 3554.6150
## 156 157 158 159 160
## -288037.7152 183274.0453 -265037.7152 274684.1258 -44318.2849
## 161 162 163 164 165
## -104192.3902 198982.7015 -123347.0651 112610.9700 203935.9153
## 166 167 168 169 170
## -33487.3499 -71079.6801 37216.4850 -180459.7751 135808.8152
## 171 172 173 174 175
## -83628.8401 -350106.0496 412850.7801 16230.8750 344752.4602
## 176 177 178 179 180
## -349263.1352 366301.6201 -85457.3644 -16938.1900 -179542.4996
## 181 182 183 184 185
## -323037.7152 324964.6954 -208414.1942 -310670.8050 -71374.6399
## 186 187 188 189 190
## -54332.6750 81865.1702 259612.1753 -166092.8649 -313037.7152
## 191 192 193 194 195
## 93167.3250 -91514.9248 -326868.6502 296372.3652 316.0102
## 196 197 198 199 200
## 214329.1950 -140247.5398 -392643.2302 223203.3002 208435.9153
## 201 202 203 204 205
## -248838.6647 -213556.8897 -197769.1250 -231445.3850 -54192.3902
## 206 207 208 209 210
## -78416.6048 139823.2053 14330.4003 -245530.5202 117853.1908
## 211 212 213 214 215
## 565953.9214 291866.3755 297220.1010 456865.1702 -112500.5347
## 216 217 218 219 220
## 384780.0350 2295.6674 435639.7502 801160.1300 545034.2352
## 221 222 223 224 225
## 329612.1753 252317.2156 582639.7502 1248489.8966 -44332.6750
## 226 227 228 229 230
## 703446.7263 441301.6201 477077.4055 656935.9153 466723.6800
## 231 232 233 234 235
## 519329.1950 -45317.0796 40458.7057 268909.5458 332993.4756
## 236 237 238 239 240
## 343134.9658 492710.4953 -103204.3696 114892.7450 188908.3404
## 241 242 243 244 245
## -244332.6750 -120234.3551 -2268898.5618 -9965.7648 -175459.7751
## 246 247 248 249 250
## 272584.6005 -16161.1993 -231167.1890 -226023.3251 -27711.5646
## 251 252 253 254 255
## -157572.4851 260314.8049 321230.8750 9258.4499 -138480.1549
## 256 257 258 259 260
## -91373.4346 -193205.5749 -125881.8350 -166727.1600 -373331.4697
## 261 262 263 264 265
## -242851.8495 -303769.1250 -446972.9598 -668695.9692 -223558.0950
## 266 267 268 269 270
## -968271.4986 -83381.8350 -386339.8700 -382642.0249 -96938.1900
## 271 272 273 274 275
## -340078.4748 -434741.5501 -111727.1600 -479909.4098 598612.1753
## 276 277 278 279 280
## -341094.0702 31230.8750 -264368.6502 -219263.1352 -309094.0702
## 281 282 283 284 285
## 288103.7750 -287770.3303 -269206.7802 139202.0949 552428.7202
## 286 287 288 289 290
## -171657.6203 1104399.9401 429753.6655 235738.0701 117780.0350
## 291 292 293 294 295
## 403137.3765 998204.5056 -87065.2901 1718771.6716 335530.6562
## 296 297 298 299 300
## 913136.1711 684823.2053 -244332.6750 -294474.1652 620669.7357
## 301 302 303 304 305
## 500739.2754 -151586.8752 -272417.8102 -197078.4748 24825.6159
## 306 307 308 309 310
## -144896.2250 209710.4953 -57006.5244 1809049.8306 -295670.8050
## 311 312 313 314 315
## 894403.5561 -362079.6801 155991.0649 291048.6253 -103572.4851
## 316 317 318 319 320
## 679726.0907 -118347.0651 1399192.5261 1083133.7605 -452078.4748
## 321 322 323 324 325
## 341867.5809 778203.3002 2235823.2053 478344.7904 853137.3765
## 326 327 328 329 330
## 914120.5757 -96023.3251 240175.7254 735949.1000 145879.5603
## 331 332 333 334 335
## 382146.9452 1634965.9008 664893.9504 908349.6117 541584.6005
## 336 337 338 339 340
## 1200188.9101 850528.2455 123485.0752 509893.9504 450456.2951
## 341 342 343 344 345
## 1511921.5252 427148.1505 688772.8769 71583.3952 -239934.5740
## 346 347 348 349 350
## -199962.1488 337782.4457 534965.9008 2572146.9452 144965.9008
## 351 352 353 354 355
## 664474.3012 -95812.0393 638766.8503 1425387.9607 289474.3012
## 356 357 358 359 360
## 526935.9153 -21936.9846 3280.0720 524542.6356 569048.6253
## 361 362 363 364 365
## 527218.8956 512005.4550 952540.2249 1241513.8554 1193137.3765
## 366 367 368 369 370
## -1446956.1221 539048.6253 371795.6304 380739.2754 1446660.1669
## 371 372 373 374 375
## 708557.0257 899330.4003 -160741.5501 126443.1103 738766.8503
## 376 377 378 379 380
## 87780.0350 136090.5902 575739.2754 238626.5654 499330.4003
## 381 382 383 384 385
## 544977.8802 9474.3012 264682.9204 -40416.6048 388344.7904
## 386 387 388 389 390
## 679752.4602 -221283.5150 -112712.7699 350527.0402 -645442.9743
## 391 392 393 394 395
## -1831.4697 306125.3601 -422643.2302 88415.5355 -47289.5047
## 396 397 398 399 400
## 938557.0257 113979.0855 24401.1454 157005.4550 375780.0350
## 401 402 403 404 405
## 297076.2001 -163978.9495 220245.2651 -61727.1600 -223347.0651
## 406 407 408 409 410
## 385598.9906 352361.5912 -1528763.0983 572570.2104 -179896.2250
## 411 412 413 414 415
## 356554.6150 -148724.7494 -269161.1993 295527.0402 -85951.3747
## 416 417 418 419 420
## -132572.4851 -273134.8298 93485.0752 161512.6501 279473.0958
## 421 422 423 424 425
## -120389.0300 256935.9153 20878.3549 585812.4312 403557.0257
## 426 427 428 429 430
## -195459.7751 -252501.7400 -58133.6245 304965.9008 432921.5252
## 431 432 433 434 435
## 178921.5252 172499.4653 685812.4312 -178487.3499 -139178.0001
## 436 437 438 439 440
## 15175.7254 41230.8750 -327079.6801 7499.4653 -59332.6750
## 441 442 443 444 445
## -236585.6699 -176020.9145 -60387.8247 270667.3250 -63767.9196
## 446 447 448 449 450
## -12642.0249 -136303.8948 -438136.0352 129443.1103 -451078.4748
## 451 452 453 454 455
## 414118.1650 -53345.8597 151245.2651 -319805.1002 206443.1103
## 456 457 458 459 460
## -141866.2395 -105176.7947 -237360.2498 -111938.1900 -141642.0249
## 461 462 463 464 465
## -300423.7999 -63769.1250 -210783.5150 -166938.1900 -159824.2746
## 466 467 468 469 470
## 22850.7801 -100079.6801 -105036.5099 -58825.4800 -106514.9248
## 471 472 473 474 475
## 68513.8554 -313978.9495 -152779.8990 216230.8750 -227430.9949
## 476 477 478 479 480
## -171513.7194 -94613.2447 528766.8503 -200656.4149 -162642.0249
## 481 482 483 484 485
## -155740.3448 -251472.9598 -214824.2746 -171023.3251 25951.5107
## 486 487 488 489 490
## -89614.4500 -55104.8443 20878.3549 -75600.0599 -206514.9248
## 491 492 493 494 495
## -176345.8597 360343.5851 -26514.9248 106752.4602 -352854.2601
## 496 497 498 499 500
## 258977.8802 -140652.0889 344046.2146 -232078.4748 -12064.0847
## 501 502 503 504 505
## 179696.1052 -599260.7246 -230597.6493 -261092.8649 -520952.5801
## 506 507 508 509 510
## 41372.3652 216230.8750 86513.8554 189450.3054 -167149.2199
## 511 512 513 514 515
## -245107.2550 -254050.9000 -127850.6441 -114896.2250 -58416.6048
## 516 517 518 519 520
## -105656.4149 -276373.4346 85879.5603 438765.6449 -165036.5099
## 521 522 523 524 525
## 98310.0205 -335881.8350 103838.8007 -184966.9701 390879.5603
## 526 527 528 529 530
## 534048.6253 255667.3250 653977.8802 11554.6150 -301868.6502
## 531 532 533 534 535
## -158627.6348 286019.8451 227637.3395 262428.7202 571441.9050
## 536 537 538 539 540
## 320457.5004 24111.7006 -161445.3850 520597.7852 3016230.8750
## 541 542 543 544 545
## -558.0950 -197910.6151 284821.9999 248486.2806 -122825.4800
## 546 547 548 549 550
## -200705.5749 -161305.1002 -426558.0950 -504543.7049 53807.6098
## 551 552 553 554 555
## -472853.0548 -430360.2498 -607006.5244 -322008.9351 -480359.0445
## 556 557 558 559 560
## -312923.7999 -507853.0548 -169459.7751 -499416.6048 -159614.4500
## 561 562 563 564 565
## -445670.8050 -591514.9248 -559754.7349 -253136.0352 509259.6552
## 566 567 568 569 570
## 2064473.0958 -250586.8752 2215387.9607 983343.5851 339188.9101
## 571 572 573 574 575
## 1369120.5757 268907.1351 327148.1505 765246.4705 -2361.4552
## 576 577 578 579 580
## 718076.2001 117604.9803 894685.3311 19152.9349 857570.2104
## 581 582 583 584 585
## 1319628.9761 -182361.4552 321654.1403 701723.6800 255351.9854
## 586 587 588 589 590
## 506233.2857 1373981.4962 254258.4499 575527.0402 621723.6800
## 591 592 593 594 595
## 809118.1650 694048.6253 298005.4550 551306.4415 1456347.9111
## 596 597 598 599 600
## -293277.5253 -70023.3251 725810.0205 673487.4859 401230.8750
## 601 602 603 604 605
## 51694.8998 1386373.5706 1986656.5509 883909.5458 876234.4911
## 606 607 608 609 610
## 2162994.6810 -196305.1002 370766.8503 518580.9845 1281445.5210
## 611 612 613 614 615
## 346513.8554 1159331.6056 -131361.4552 631304.0308 1754541.4302
## 616 617 618 619 620
## 1334470.6852 408167.3250 1395600.1959 220457.5004 482993.4756
## 621 622 623 624 625
## 282571.4158 -41938.1900 -40528.1095 1271781.2403 437569.0051
## 626 627 628 629 630
## -1028056.8527 108909.5458 -37288.2994 90317.2156 171724.8853
## 631 632 633 634 635
## 123275.2506 800174.5200 -375315.8742 -90459.7751 405527.0402
## 636 637 638 639 640
## 117218.8956 1248909.5458 -27149.2199 104965.9008 1623796.8358
## 641 642 643 644 645
## 235384.3446 608908.3404 313287.2301 1120598.9906 465880.7656
## 646 647 648 649 650
## 303415.5355 321443.1103 620598.9906 674967.1061 27709.2899
## 651 652 653 654 655
## 248977.8802 762639.7502 320881.9709 300317.2156 -86020.9145
## 656 657 658 659 660
## 561585.8058 752148.1505 -66150.4252 -186442.9743 -395319.4903
## 661 662 663 664 665
## -78812.2952 840693.6945 -5839.8700 980459.9111 841061.8100
## 666 667 668 669 670
## 8698.5158 -41655.2096 286921.5252 1286794.4251 -13149.2199
## 671 672 673 674 675
## 89554.6150 925209.2899 165246.4705 587642.1608 -360812.2952
## 676 677 678 679 680
## -395777.5253 -224896.2250 -351094.0702 60878.3549 -19959.7751
## 681 682 683 684 685
## -213136.0352 -306094.0702 -186241.5501 -206305.1002 56301.6201
## 686 687 688 689 690
## 255596.5799 -38065.2901 -122642.0249 -107572.4851 119554.6150
## 691 692 693 694 695
## -229965.7648 215069.0051 10667.3250 -179868.6502 72287.2301
## 696 697 698 699 700
## 12709.2899 -219896.2250 -173402.2148 -311219.9650 -83628.8401
## 701 702 703 704 705
## -432157.6203 579612.1753 243977.8802 194259.6552 -198205.5749
## 706 707 708 709 710
## 356103.7750 120385.5500 198258.4499 42569.0051 581534.2352
## 711 712 713 714 715
## 138554.6150 -325023.3251 362991.0649 583414.3301 -134319.4903
## 716 717 718 719 720
## 165314.8049 -335107.2550 420457.5004 -300319.4903 940458.7057
## 721 722 723 724 725
## 2427.5149 -279812.2952 123483.8699 100597.7852 -311219.9650
## 726 727 728 729 730
## -60670.8050 -73699.5852 -91938.1900 -170614.4500 -212361.4552
## 731 732 733 734 735
## -195812.2952 407921.5252 -52628.8401 -187430.9949 -317995.7503
## 736 737 738 739 740
## 249329.1950 770738.0701 -335881.8350 548133.7605 -3562866.1656
## 741 742 743 744 745
## -243276.3200 205625.3601 40174.5200 308907.1351 55528.2455
## 746 747 748 749 750
## 542569.0051 -251656.4149 -269016.1301 -353488.5553 -218769.1250
## 751 752 753 754 755
## -61910.6151 186794.4251 459682.9204 28272.8400 -374683.9898
## 756 757 758 759 760
## -261143.2302 210174.5200 -276150.4252 -411164.8153 77709.2899
## 761 762 763 764 765
## -426441.7690 -465741.5501 -356446.5903 -75178.0001 -186825.4800
## 766 767 768 769 770
## -362925.0052 -386086.8752 -324296.6998 257076.2001 421160.1300
## 771 772 773 774 775
## -437357.8392 -375037.7152 -78064.0847 -153910.6151 -142628.8401
## 776 777 778 779 780
## -306305.1002 -370037.7152 -373206.7802 -360108.4603 -346164.8153
## 781 782 783 784 785
## -71655.2096 -233812.2952 -156585.6699 -402995.7503 -239733.1497
## 786 787 788 789 790
## 347005.4550 -396868.6502 -205389.0300 -94191.1848 -435995.7503
## 791 792 793 794 795
## 463837.5954 -77008.9351 -396868.6502 -282868.6502 -180600.0599
## 796 797 798 799 800
## -27007.7297 -344797.9051 -315037.7152 -148050.9000 -132078.4748
## 801 802 803 804 805
## -211642.0249 79612.1753 -119471.7545 15570.2104 -379824.2746
## 806 807 808 809 810
## -426795.4944 -230387.8247 87428.7202 -219399.8041 -256233.1497
## 811 812 813 814 815
## -312851.8495 -117896.2250 185878.3549 -174724.7494 -2296012.4771
## 816 817 818 819 820
## -346584.4645 -393625.2241 -210669.5997 -246584.4645 -159642.0249
## 821 822 823 824 825
## 81726.0907 941723.6800 -705.5749 672639.7502 253132.5551
## 826 827 828 829 830
## 211723.6800 586373.5706 -126727.1600 485274.0453 -339050.9000
## 831 832 833 834 835
## -333769.1250 -278697.1745 -83697.1745 -240347.0651 516089.3849
## 836 837 838 839 840
## -382219.9650 -262430.9949 140883.1763 -127347.0651 556230.8750
## 841 842 843 844 845
## -76584.4645 -304613.2447 -128133.6245 181724.8853 -302078.4748
## 846 847 848 849 850
## -226558.0950 1394119.3704 -124628.8401 717079.8161 394119.3704
## 851 852 853 854 855
## -163699.5852 829710.4953 -166685.1951 572146.9452 -301375.8453
## 856 857 858 859 860
## 1174542.6356 1297850.7801 -379192.3902 1075385.5500 337949.1000
## 861 862 863 864 865
## 480485.0752 -312192.3902 -379192.3902 -270516.1301 -10175154.9507
## 866 867 868 869 870
## 744963.4901 852148.1505 9821.9999 449471.8905 42427.5149
## 871 872 873 874 875
## 939332.8110 -280248.7452 1074654.1403 689716.4850 1153794.4251
## 876 877 878 879 880
## 2313696.1052 947710.4953 483485.0752 1921866.3755 -162966.9701
## 881 882 883 884 885
## 932639.7502 -106305.1002 1649684.1258 1204404.7614 502360.3858
## 886 887 888 889 890
## 691302.8255 1225951.5107 420740.4808 -47002.9084 797925.1412
## 891 892 893 894 895
## 1591584.6005 564294.4251 -7854.2601 961373.5706 1218205.7109
## 896 897 898 899 900
## 1105808.8152 1182711.7006 384329.1950 -134642.0249 1543979.0855
## 901 902 903 904 905
## 1757217.6903 -151347.0651 727360.3858 313133.7605 392570.2104
## 906 907 908 909 910
## 1355531.8615 1268630.1814 487640.9555 1546022.2558 401794.4251
## 911 912 913 914 915
## 1792710.4953 1021654.1403 -120670.8050 1647470.6852 1211161.3353
## 916 917 918 919 920
## 1346935.9153 955808.8152 800597.7852 -294375.8453 -329685.1951
## 921 922 923 924 925
## -240248.7452 -69121.6451 -125670.8050 -151094.0702 129823.2053
## 926 927 928 929 930
## -272643.2302 -353826.6853 -96163.6100 -132896.2250 190964.6954
## 931 932 933 934 935
## -257501.7400 -249755.9402 -417713.9753 -426586.8752 3449.1000
## 936 937 938 939 940
## -310672.0104 931722.4747 -15205.5749 -10951.3747 384824.4106
## 941 942 943 944 945
## -394615.6554 -250951.3747 -266375.8453 514963.4901 -182121.6451
## 946 947 948 949 950
## -45685.1951 197795.6304 -419964.5595 -95283.5150 150739.2754
## 951 952 953 954 955
## -73558.0950 -190459.7751 -202530.5202 -343417.8102 -576442.9743
## 956 957 958 959 960
## -177910.6151 -14332.6750 -347925.0052 -176023.3251 131724.8853
## 961 962 963 964 965
## -369544.9103 264823.2053 320879.5603 141230.8750 -389474.1652
## 966 967 968 969 970
## 272922.7305 -159994.5450 -408699.5852 304684.1258 -189755.9402
## 971 972 973 974 975
## -344474.1652 -182923.7999 -181586.8752 -77034.0992 -264508.9351
## 976 977 978 979 980
## -312150.4252 -338055.1002 692794.4251 -334826.6853 -182396.2250
## 981 982 983 984 985
## -268136.0352 -990796.6998 5107.3910 -198699.5852 559824.4106
## 986 987 988 989 990
## -311375.8453 -390108.4603 341301.6201 -308981.3602 -297910.6151
## 991 992 993 994 995
## -224755.9402 811584.6005 499083.3952 472287.2301 -408552.1053
## 996 997 998 999 1000
## 104892.7450 -131233.1497 324047.4199 466230.8750 254395.1557
## 1001 1002 1003 1004 1005
## -300523.3251 -20741.5501 -321203.1642 368061.8100 157076.2001
## 1006 1007 1008 1009 1010
## 155258.4499 334399.9401 211584.6005 597021.0505 -243627.6348
## 1011 1012 1013 1014 1015
## -181234.3551 -209472.9598 -99014.9248 108934.7099 -258839.8700
## 1016 1017 1018 1019 1020
## -263275.1147 443427.5149 258210.4953 -342921.3892 75385.5500
## 1021 1022 1023 1024 1025
## -103276.3200 -169811.0899 -65741.5501 162991.0649 -37994.5450
## 1026 1027 1028 1029 1030
## 229258.4499 263202.0949 315934.7099 1513557.0257 545878.3549
## 1031 1032 1033 1034 1035
## 389047.4199 -212713.9753 327076.2001 517498.2600 -161367.4449
## 1036 1037 1038 1039 1040
## -154825.4800 328992.2703 384118.1650 -27290.7101 -160332.6750
## 1041 1042 1043 1044 1045
## -256445.3850 -397613.2447 -320600.0599 139357.9751 149612.1753
## 1046 1047 1048 1049 1050
## 55667.3250 -1012289.5047 -80389.0300 44160.1300 -142290.7101
## 1051 1052 1053 1054 1055
## -56487.3499 -302361.4552 -289037.7152 -417289.5047 -211205.5749
## 1056 1057 1058 1059 1060
## -233543.7049 -150881.8350 -562625.2241 -148500.5347 206512.6501
## 1061 1062 1063 1064 1065
## -392023.3251 -279501.7400 -300389.0300 118625.3601 -181332.6750
## 1066 1067 1068 1069 1070
## 21765.6449 28061.8100 221895.1557 -138487.3499 -404121.6451
## 1071 1072 1073 1074 1075
## 152259.6552 -350389.0300 49696.1052 -250178.0001 144119.3704
## 1076 1077 1078 1079 1080
## -157570.0744 -56008.9351 -260917.8102 -306896.2250 -100387.8247
## 1081 1082 1083 1084 1085
## -34896.2250 -114474.1652 -202149.2199 -302149.2199 -242499.3293
## 1086 1087 1088 1089 1090
## 146483.8699 -80529.3148 -343474.1652 -463134.8298 -618414.1942
## 1091 1092 1093 1094 1095
## 72780.0350 -212783.5150 303976.6749 -172993.3396 -285178.0001
## 1096 1097 1098 1099 1100
## -168978.9495 -271586.8752 -310643.2302 -31501.7400 43200.8895
## 1101 1102 1103 1104 1105
## -375642.0249 -336091.6596 346794.4251 -173347.0651 -217149.2199
## 1106 1107 1108 1109 1110
## -252247.5398 -7289.5047 -210514.9248 -514037.7152 20892.7450
## 1111 1112 1113 1114 1115
## -279685.1951 -286586.8752 -242008.9351 -352769.1250 -324614.4500
## 1116 1117 1118 1119 1120
## -268769.1250 -100050.9000 -236445.3850 -258685.1951 -222360.2498
## 1121 1122 1123 1124 1125
## -202994.5450 -429754.7349 -120459.7751 -477992.1343 2498.2600
## 1126 1127 1128 1129 1130
## -163769.1250 -109121.6451 -312261.9299 -256065.2901 -471513.7194
## 1131 1132 1133 1134 1135
## -178980.1549 515553.4097 -235178.0001 -235149.2199 -204614.4500
## 1136 1137 1138 1139 1140
## -49261.9299 103413.1248 240738.0701 -136656.4149 18977.8802
## 1141 1142 1143 1144 1145
## 16934.7099 -267544.9103 -340037.7152 -394868.6502 66175.7254
## 1146 1147 1148 1149 1150
## 116090.5902 28976.6749 -246770.3303 63589.3849 312780.0350
## 1151 1152 1153 1154 1155
## 154329.1950 -318052.1053 48498.2600 -190347.0651 150314.8049
## 1156 1157 1158 1159 1160
## 53589.3849 -144072.4851 362428.7202 -75150.4252 -69403.4201
## 1161 1162 1163 1164 1165
## 1126580.9845 -100107.2550 407399.9401 485949.1000 341245.2651
## 1166 1167 1168 1169 1170
## -67782.3097 -279825.4800 -52613.2447 497753.6655 -225598.8546
## 1171 1172 1173 1174 1175
## -132923.7999 775527.0402 -15106.0496 194203.3002 -372498.1240
## 1176 1177 1178 1179 1180
## 99728.5014 249048.6253 -168389.0300 287048.6253 -171614.4500
## 1181 1182 1183 1184 1185
## -182558.0950 422357.9751 127357.9751 -202078.4748 147921.5252
## 1186 1187 1188 1189 1190
## 125103.7750 -156514.9248 320174.5200 320985.0752 -29542.4996
## 1191 1192 1193 1194 1195
## -252543.4491 133238.0701 -552355.4285 190330.4003 -326699.5852
## 1196 1197 1198 1199 1200
## -98469.5997 -138823.0693 64712.9059 -75034.0992 -275345.8597
## 1201 1202 1203 1204 1205
## -168014.9248 -231969.1250 -77007.7297 99921.5252 330907.1351
## 1206 1207 1208 1209 1210
## 352993.4756 503148.1505 -150103.6390 595612.1753 -261586.8752
## 1211 1212 1213 1214 1215
## 395811.2259 488768.0556 819614.5860 -285178.0001 554132.5551
## 1216 1217 1218 1219 1220
## -593625.2241 154405.9667 95808.8152 535275.2506 650867.5809
## 1221 1222 1223 1224 1225
## -44332.6750 400668.5303 -37571.2798 562217.6903 297921.5252
## 1226 1227 1228 1229 1230
## 244399.9401 -164037.7152 -285079.6801 -152219.9650 -14825.4800
## 1231 1232 1233 1234 1235
## 109188.9101 297637.3395 1363837.5954 67512.6501 575668.5303
## 1236 1237 1238 1239 1240
## 1029964.6954 -5925561.5631 -278896.2250 409893.9504 -220529.3148
## 1241 1242 1243 1244 1245
## 423133.7605 513554.6150 1289838.8007 -103178.0001 -292260.7246
## 1246 1247 1248 1249 1250
## 182288.4354 -243206.7802 1012853.1908 65033.0299 474684.1258
## 1251 1252 1253 1254 1255
## 495034.2352 -191657.6203 -315079.6801 -312854.2601 -40530.5202
## 1256 1257 1258 1259 1260
## -237150.4252 -340672.0104 387569.0051 9258.4499 -55741.5501
## 1261 1262 1263 1264 1265
## -228699.5852 -350713.9753 336652.9349 -24685.1951 -4754.7349
## 1266 1267 1268 1269 1270
## -91488.5553 -195108.4603 -160319.4903 -224192.3902 258174.5200
## 1271 1272 1273 1274 1275
## -245037.7152 682217.6903 -124896.2250 -113156.4149 2245133.7605
## 1276 1277 1278 1279 1280
## -226586.8752 -92572.4851 -171797.9051 589963.4901 201329.1950
## 1281 1282 1283 1284 1285
## 1159893.9504 -131586.8752 -213008.9351 -258981.3602 -94755.9402
## 1286 1287 1288 1289 1290
## -206305.1002 -341657.6203 -305883.0403 -156586.8752 -186023.3251
## 1291 1292 1293 1294 1295
## -12332.6750 -161305.1002 -309446.5903 37145.7399 -184368.6502
## 1296 1297 1298 1299 1300
## -137713.9753 532359.1805 -336164.8153 829753.6655 -95143.2302
## 1301 1302 1303 1304 1305
## -115741.5501 -169883.0403 338482.6646 680597.7852 334752.4602
## 1306 1307 1308 1309 1310
## -296163.6100 -287854.2601 370385.5500 -266516.1301 13991.0649
## 1311 1312 1313 1314 1315
## -438697.1745 -165248.7452 -111692.3902 31441.9050 437781.2403
## 1316 1317 1318 1319 1320
## -424048.4893 441584.6005 -313484.9393 225103.7750 -357432.2003
## 1321 1322 1323 1324 1325
## 282104.9803 798770.4663 -206302.6895 709474.3012 222512.6501
## 1326 1327 1328 1329 1330
## 130344.7904 -112994.5450 133485.0752 6796.8358 -271290.7101
## 1331 1332 1333 1334 1335
## 334188.9101 -369261.9299 -334474.1652 -393908.2045 -278417.8102
## 1336 1337 1338 1339 1340
## -350529.3148 229260.8606 -313417.8102 -725946.5534 -423770.3303
## 1341 1342 1343 1344 1345
## 384639.7502 -46445.3850 -113769.1250 173892.7450 -395101.2653
## 1346 1347 1348 1349 1350
## -9472.9598 113557.0257 -2501.7400 -383699.5852 486230.8750
## 1351 1352 1353 1354 1355
## -332360.2498 -380812.2952 -50387.8247 229753.6655 129260.8606
## 1356 1357 1358 1359 1360
## -335812.2952 405245.2651 -192558.0950 -316868.6502 -180670.8050
## 1361 1362 1363 1364 1365
## -135023.3251 767853.1908 463766.8503 67639.7502 -418699.5852
## 1366 1367 1368 1369 1370
## -212572.4851 -753487.3499 -170923.7999 -207854.2601 -374192.3902
## 1371 1372 1373 1374 1375
## 180473.0958 240175.7254 258907.1351 -2171083.2222 -289541.2943
## 1376 1377 1378 1379 1380
## 271935.9153 101625.3601 -373206.7802 -335375.8453 -293206.7802
## 1381 1382 1383 1384 1385
## 76513.8554 -426868.6502 -273980.1549 -208670.8050 171583.3952
## 1386 1387 1388 1389 1390
## 405667.3250 346652.9349 77639.7502 -281586.8752 -212192.3902
## 1391 1392 1393 1394 1395
## -86501.7400 -378699.5852 -286375.8453 328204.5056 -268699.5852
## 1396 1397 1398 1399 1400
## 409610.9700 385247.6758 286580.9845 -7642.0249 -230699.5852
## 1401 1402 1403 1404 1405
## 492569.0051 -206305.1002 -269192.3902 383343.5851 201188.9101
## 1406 1407 1408 1409 1410
## 19469.4798 176687.7048 535385.5500 -44614.4500 1651867.5809
## 1411 1412 1413 1414 1415
## 325385.5500 840034.2352 -250601.2653 458766.8503 -114050.9000
## 1416 1417 1418 1419 1420
## 213160.1300 355667.3250 -256164.8153 -87361.4552 -254754.7349
## 1421 1422 1423 1424 1425
## -155459.7751 -156586.8752 2415965.9008 -145741.5501 73413.1248
## 1426 1427 1428 1429 1430
## 107074.9948 249330.4003 -309777.5253 -336022.1198 193807.6098
## 1431 1432 1433 1434 1435
## -67360.2498 355681.7151 318005.4550 580738.0701 587640.9555
## 1436 1437 1438 1439 1440
## 2199330.4003 623766.8503 234118.1650 330667.3250 416652.9349
## 1441 1442 1443 1444 1445
## -135178.0001 -198347.0651 365246.4705 44963.4901 297885.5500
## 1446 1447 1448 1449 1450
## 143025.8348 355667.3250 257076.2001 428769.2609 549907.1351
## 1451 1452 1453 1454 1455
## -97826.6853 -156305.1002 533272.8400 -382150.4252 -333981.3602
## 1456 1457 1458 1459 1460
## -352206.7802 67357.9751 82850.7801 99863.9648 -167008.9351
## 1461 1462 1463 1464 1465
## 9258.4499 99216.4850 -352150.4252 -266079.6801 -346939.3953
## 1466 1467 1468 1469 1470
## -2078.4748 -312713.9753 273202.0949 -295101.2653 201794.4251
## 1471 1472 1473 1474 1475
## 105991.0649 -37290.7101 236259.6552 -168458.5698 -491713.9753
## 1476 1477 1478 1479 1480
## -52558.0950 -488601.2653 -300514.9248 -248628.8401 -343559.3004
## 1481 1482 1483 1484 1485
## -326305.1002 -65881.8350 -400939.3953 -145008.9351 171230.8750
## 1486 1487 1488 1489 1490
## -213585.6699 -385459.7751 -78628.8401 -485868.6502 40175.7254
## 1491 1492 1493 1494 1495
## 191637.3395 76652.9349 -204050.9000 -386305.1002 -91205.5749
## 1496 1497 1498 1499 1500
## -239261.9299 -487643.2302 -337812.2952 -416023.3251 253272.8400
## 1501 1502 1503 1504 1505
## -332713.9753 -236769.1250 -125952.5801 -247136.0352 -481586.8752
## 1506 1507 1508 1509 1510
## -549182.7844 -436305.1002 -154459.7751 -206508.9351 -134234.3551
## 1511 1512 1513 1514 1515
## -19290.7101 -308430.9949 -105389.0300 -176854.2601 -178945.3850
## 1516 1517 1518 1519 1520
## -394164.8153 -257163.6100 -50952.5801 -487361.4552 -141234.3551
## 1521 1522 1523 1524 1525
## -137853.0548 -411432.2003 -26586.8752 -438064.0847 201794.4251
## 1526 1527 1528 1529 1530
## -129508.9351 -427079.6801 -291022.1198 -155783.5150 308485.0752
## 1531 1532 1533 1534 1535
## -57361.4552 -879034.0992 554048.6253 1844402.3507 1827361.5912
## 1536 1537 1538 1539 1540
## 433697.3105 765781.2403 -174741.5501 271654.1403 554118.1650
## 1541 1542 1543 1544 1545
## 115670.9410 321019.8451 374896.3610 576163.7460 789163.7460
## 1546 1547 1548 1549 1550
## 787782.4457 -208981.3602 561019.8451 985316.0102 448063.0154
## 1551 1552 1553 1554 1555
## 1002527.0402 1136656.5509 -355868.6502 125248.8811 663415.5355
## 1556 1557 1558 1559 1560
## 2346158.9246 -263601.2653 773132.5551 -369390.2353 958429.9256
## 1561 1562 1563 1564 1565
## 385470.6852 -339052.1053 511444.3157 -256797.9051 140458.7057
## 1566 1567 1568 1569 1570
## 170386.7553 -44050.9000 -258672.0104 284399.9401 1502077.4055
## 1571 1572 1573 1574 1575
## 1458697.3105 1211933.5046 1288840.0060 363837.5954 516903.5561
## 1576 1577 1578 1579 1580
## 1298772.8769 828840.0060 828203.3002 1129470.6852 688357.9751
## 1581 1582 1583 1584 1585
## 538021.0505 -82361.4552 567498.2600 1244331.6056 1686090.5902
## 1586 1587 1588 1589 1590
## 590527.0402 -226023.3251 -1484324.2376 503417.9462 737640.9555
## 1591 1592 1593 1594 1595
## 1276093.0009 1789684.1258 659344.7904 317498.2600 -760661.1623
## 1596 1597 1598 1599 1600
## -365881.8350 -468416.6048 -204874.6399 -504754.7349 -102614.4500
## 1601 1602 1603 1604 1605
## -66867.4449 -474896.2250 -420107.2550 -156065.2901 -62362.6605
## 1606 1607 1608 1609 1610
## -478205.5749 -392642.0249 -297543.7049 -234050.9000 -118466.9701
## 1611 1612 1613 1614 1615
## -394613.2447 -501094.0702 -468558.0950 -190769.1250 -462361.4552
## 1616 1617 1618 1619 1620
## -575705.5749 -415487.3499 -469121.6451 -419966.9701 -320741.5501
## 1621 1622 1623 1624 1625
## -209783.5150 -494078.4748 -420149.2199 -454887.8247 -430952.5801
## 1626 1627 1628 1629 1630
## -490529.3148 -249153.4201 -210670.8050 -393205.5749 -458698.3799
## 1631 1632 1633 1634 1635
## -469261.9299 -537571.2798 -50211.5646 -502078.4748 -516303.8948
## 1636 1637 1638 1639 1640
## -142196.2250 -396516.1301 -116322.4851 -709399.8041 -590387.8247
## 1641 1642 1643 1644 1645
## -372923.7999 -397192.3902 -474472.9598 -547712.7699 -307994.5450
## 1646 1647 1648 1649 1650
## -851796.6998 -450598.8546 -889992.1343 -423754.7349 -53460.9804
## 1651 1652 1653 1654 1655
## -554698.3799 -586754.7349 -749154.0043 -641528.1095 -553980.1549
## 1656 1657 1658 1659 1660
## -526585.6699 -656867.4449 -700386.6193 -610528.1095 -362994.5450
## 1661 1662 1663 1664 1665
## -231227.1600 -287008.9351 -322219.9650 -697428.5842 -209261.9299
## 1666 1667 1668 1669 1670
## -402121.6451 -473064.0847 -544958.5698 -308980.1549 -167994.5450
## 1671 1672 1673 1674 1675
## -750386.6193 -224050.9000 -282558.0950 -411163.6100 -427613.2447
## 1676 1677 1678 1679 1680
## -194727.1600 -367783.5150 -454050.9000 -253678.0001 -520529.3148
## 1681 1682 1683 1684 1685
## -188419.0155 -157459.0651 -476332.6750 -307079.6801 41371.1599
## 1686 1687 1688 1689 1690
## -215361.4552 1027501.8760 1556374.7759 892006.6604 135106.1856
## 1691 1692 1693 1694 1695
## 63110.9700 -43741.5501 556512.6501 -89685.1951 -304670.8050
## 1696 1697 1698 1699 1700
## 814540.2249 163836.3900 1407783.6510 -128133.6245 511444.3157
## 1701 1702 1703 1704 1705
## 411091.7955 1450597.7852 1330742.8914 66230.8750 -154050.9000
## 1706 1707 1708 1709 1710
## 409188.9101 1759964.6954 -100381.8350 811727.2960 -241018.5038
## 1711 1712 1713 1714 1715
## -1412986.1076 1195670.9410 486656.5509 37357.9751 1619543.8409
## 1716 1717 1718 1719 1720
## -336586.8752 -251094.0702 50317.2156 405246.4705 563837.5954
## 1721 1722 1723 1724 1725
## 738486.2806 714120.5757 878063.0154 -406305.1002 -136642.0249
## 1726 1727 1728 1729 1730
## 141441.9050 -131501.7400 627637.3395 -306699.5852 197921.5252
## 1731 1732 1733 1734 1735
## 82146.9452 311302.8255 1232711.7006 -371544.9103 197343.5851
## 1736 1737 1738 1739 1740
## -223910.6151 -266981.3602 43074.9948 795386.7553 -104572.4851
## 1741 1742 1743 1744 1745
## -385601.2653 483554.6150 -252150.4252 -439375.8453 -230248.7452
## 1746 1747 1748 1749 1750
## 178203.3002 434540.2249 -275601.2653 -82360.2498 800610.9700
## 1751 1752 1753 1754 1755
## -163136.0352 -247319.4903 962921.5252 -361657.6203 688794.4251
## 1756 1757 1758 1759 1760
## -227713.9753 1846866.3755 -272221.1703 429612.1753 2098628.9761
## 1761 1762 1763 1764 1765
## -206974.1652 -226586.8752 743217.6903 2023982.7015 -176305.1002
## 1766 1767 1768 1769 1770
## 465808.8152 -17572.4851 567499.4653 -62290.7101 691513.8554
## 1771 1772 1773 1774 1775
## -140917.8102 3068488.6912 -270601.2653 306652.9349 -316586.8752
## 1776 1777 1778 1779 1780
## -325248.7452 666372.3652 851512.6501 -121586.8752 634272.8400
## 1781 1782 1783 1784 1785
## -178030.5202 1225104.9803 -118910.6151 -51022.1198 380965.9008
## 1786 1787 1788 1789 1790
## -232375.8453 -350741.5501 1882854.3961 392569.0051 -314052.1053
## 1791 1792 1793 1794 1795
## -234016.1301 -168769.1250 -367501.7400 -273711.5646 -238205.5749
## 1796 1797 1798 1799 1800
## -355881.8350 -296737.3499 -257797.9051 -129980.1549 -59458.5698
## 1801 1802 1803 1804 1805
## -138136.0352 -195741.5501 -298838.6647 -215459.7751 -248628.8401
## 1806 1807 1808 1809 1810
## -194050.9000 -25881.8350 -474809.8845 -699260.7246 6160.1300
## 1811 1812 1813 1814 1815
## -437854.2601 -315459.7751 -236023.3251 26934.7099 -362079.6801
## 1816 1817 1818 1819 1820
## -263267.9196 -269952.5801 -158685.1951 -293628.8401 -495459.7751
## 1821 1822 1823 1824 1825
## -317685.1951 -432776.3200 -57572.4851 -237572.4851 -485741.5501
## 1826 1827 1828 1829 1830
## -389466.9701 -351965.7648 -81799.1105 -568486.1446 64732.6646
## 1831 1832 1833 1834 1835
## 446441.9050 -178952.5801 -89192.3902 -380741.5501 656934.7099
## 1836 1837 1838 1839 1840
## -294248.7452 324681.7151 308569.0051 -147881.8350 161934.7099
## 1841 1842 1843 1844 1845
## -242459.7751 367220.1010 504893.9504 479612.1753 -366586.8752
## 1846 1847 1848 1849 1850
## 432103.7750 -292150.4252 -457572.4851 218343.5851 -68662.4046
## 1851 1852 1853 1854 1855
## -217853.0548 -160354.2601 934190.1155 -1020229.5337 1096795.6304
## 1856 1857 1858 1859 1860
## -172642.0249 -130403.4201 -159332.6750 -25951.3747 201863.9648
## 1861 1862 1863 1864 1865
## 457569.0051 -168205.5749 -330206.7802 275667.3250 443766.8503
## 1866 1867 1868 1869 1870
## -231136.0352 472357.9751 103697.3105 352372.3652 67923.9359
## 1871 1872 1873 1874 1875
## 424542.6356 468630.1814 -286586.8752 137949.1000 97992.2703
## 1876 1877 1878 1879 1880
## -257923.7999 176632.5551 290598.9906 201794.4251 235668.5303
## 1881 1882 1883 1884 1885
## -318263.1352 337220.1010 -244332.6750 479404.7614 -273769.1250
## 1886 1887 1888 1889 1890
## -239121.6451 -445107.2550 -662049.6946 -608345.8597 -962343.4491
## 1891 1892 1893 1894 1895
## -404896.2250 -561796.6998 -596260.7246 -270670.8050 -533204.3696
## 1896 1897 1898 1899 1900
## -103487.3499 -267994.5450 -435936.9846 -162430.9949 -259092.8649
## 1901 1902 1903 1904 1905
## -306163.6100 -305642.0249 -404191.1848 -452036.5099 -115600.0599
## 1906 1907 1908 1909 1910
## -474754.7349 -638048.4893 -308275.1147 -370584.4645 -76442.9743
## 1911 1912 1913 1914 1915
## -111374.6399 -352783.5150 -557428.5842 -401162.4046 -420740.3448
## 1916 1917 1918 1919 1920
## -437853.0548 -281585.6699 -422853.0548 -343741.5501 -426725.9547
## 1921 1922 1923 1924 1925
## -413769.1250 -461373.4346 -403487.3499 -182430.9949 -501162.4046
## 1926 1927 1928 1929 1930
## -148205.5749 -489047.5398 -244614.4500 -598204.3696 -325036.5099
## 1931 1932 1933 1934 1935
## -697401.0094 -280600.0599 -202754.7349 108441.9050 482287.2301
## 1936 1937 1938 1939 1940
## -337466.9701 -307432.2003 -406023.3251 314836.3900 89329.1950
## 1941 1942 1943 1944 1945
## -202219.9650 -102430.9949 165525.8348 130047.4199 -15178.0001
## 1946 1947 1948 1949 1950
## 122076.2001 134684.1258 471230.8750 -330883.0403 -348530.5202
## 1951 1952 1953 1954 1955
## -45248.7452 -314966.9701 -337713.9753 223125.3601 -207347.0651
## 1956 1957 1958 1959 1960
## -32572.4851 -10079.6801 324684.1258 -329755.9402 -291205.5749
## 1961 1962 1963 1964 1965
## 169752.4602 -31092.8649 246160.1300 -256867.4449 -193065.2901
## 1966 1967 1968 1969 1970
## 289610.9700 -381797.9051 -431023.3251 -15459.7751 -48727.1600
## 1971 1972 1973 1974 1975
## -92459.7751 -250144.3551 -439685.1951 -318206.7802 -184474.1652
## 1976 1977 1978 1979 1980
## -184585.6699 1564545.0463 499976.6749 449613.3807 1171866.3755
## 1981 1982 1983 1984 1985
## -312524.4935 614682.9204 398625.3601 1109330.4003 1082781.2403
## 1986 1987 1988 1989 1990
## -93065.2901 2762010.2764 4550037.8512 -285459.7751 645175.7254
## 1991 1992 1993 1994 1995
## -233657.6203 -142192.3902 840824.4106 748976.6749 -236023.3251
## 1996 1997 1998 1999 2000
## 427643.3662 91612.1753 36371.1599 469483.8699 552006.6604
## 2001 2002 2003 2004 2005
## 164908.3404 1231584.6005 1227148.1505 800106.1856 -2565936.9107
## 2006 2007 2008 2009 2010
## 690741.6861 93837.5954 134964.6954 2027360.3858 -298685.1951
## 2011 2012 2013 2014 2015
## 793980.2909 1361444.3157 979824.4106 -184474.1652 -32712.7699
## 2016 2017 2018 2019 2020
## -142185.1951 -212332.6750 2009540.2249 476794.4251 332429.9256
## 2021 2022 2023 2024 2025
## 135949.1000 416794.4251 684967.1061 981304.0308 2189752.4602
## 2026 2027 2028 2029 2030
## -332219.9650 -671083.2222 1339049.8306 306090.5902 741301.6201
## 2031 2032 2033 2034 2035
## -332432.2003 528769.2609 441726.0907 -232854.2601 810034.2352
## 2036 2037 2038 2039 2040
## 603625.3601 343994.6810 15739.2754 608485.0752 169756.0762
## 2041 2042 2043 2044 2045
## -433061.6740 15739.2754 450879.5603 -530458.5698 -300318.2849
## 2046 2047 2048 2049 2050
## -414106.0496 -483981.3602 -71643.2302 -304543.7049 -379403.4201
## 2051 2052 2053 2054 2055
## -320079.6801 -266712.7699 10033.0299 -451586.8752 -171487.3499
## 2056 2057 2058 2059 2060
## -239178.0001 -259501.7400 -391303.8948 -433643.2302 -432712.7699
## 2061 2062 2063 2064 2065
## -418312.2952 -572356.6338 -359403.4201 -336023.3251 -151023.3251
## 2066 2067 2068 2069 2070
## -122712.7699 -352219.9650 -277811.0899 829612.1753 1730881.9709
## 2071 2072 2073 2074 2075
## 1120457.5004 1100385.5500 -167699.5852 1743559.4363 165668.5303
## 2076 2077 2078 2079 2080
## 1399681.7151 -260023.3251 405907.1351 -223488.5553 1552572.6211
## 2081 2082 2083 2084 2085
## 917711.7006 2467501.8760 421103.7750 3387428.7202 724893.9504
## 2086 2087 2088 2089 2090
## 1981444.3157 -129403.4201 895598.9906 1041441.9050 589821.9999
## 2091 2092 2093 2094 2095
## -218361.4552 439188.9101 123696.1052 965035.4405 123216.4850
## 2096 2097 2098 2099 2100
## 760782.4457 549896.3610 841584.6005 -150389.0300 -35387.8247
## 2101 2102 2103 2104 2105
## 553513.8554 210076.2001 -132754.7349 3239015.0607 -621938.1900
## 2106 2107 2108 2109 2110
## 452921.5252 610782.4457 755667.3250 170174.5200 532162.5406
## 2111 2112 2113 2114 2115
## 907569.0051 111794.4251 19612.1753 13977.8802 338766.8503
## 2116 2117 2118 2119 2120
## -130354.2601 -140881.8350 760034.2352 44120.5757 -100670.8050
## 2121 2122 2123 2124 2125
## -322361.4552 376795.6304 -376164.8153 92569.0051 -287390.2353
## 2126 2127 2128 2129 2130
## 720459.9111 -107.2550 -376939.3953 206752.4602 -23980.1549
## 2131 2132 2133 2134 2135
## -232037.7152 299963.4901 -310319.4903 548203.3002 484540.2249
## 2136 2137 2138 2139 2140
## 689892.7450 -81092.8649 775069.0051 -333769.1250 -142853.0548
## 2141 2142 2143 2144 2145
## -404050.9000 -502572.4851 -504754.7349 -496727.1600 -320544.9103
## 2146 2147 2148 2149 2150
## 34470.6852 -301092.8649 -325212.7699 -380530.5202 -24332.6750
## 2151 2152 2153 2154 2155
## -22640.8195 -488414.1942 -452260.7246 -453628.8401 -128669.5997
## 2156 2157 2158 2159 2160
## -560529.3148 342637.3395 -445318.2849 -85454.9537 -428572.4851
## 2161 2162 2163 2164 2165
## -429178.0001 -260023.3251 -433797.9051 -352079.6801 -456162.4046
## 2166 2167 2168 2169 2170
## -405741.5501 -428024.7494 -445741.5501 144470.6852 14823.2053
## 2171 2172 2173 2174 2175
## -209866.2395 -358699.5852 -651513.7194 -274457.3644 -92543.7049
## 2176 2177 2178 2179 2180
## -745035.3046 -321514.9248 -126585.6699 -253486.1446 -128415.3995
## 2181 2182 2183 2184 2185
## -548844.6544 -384613.2447 -65741.5501 -306797.9051 -277432.2003
## 2186 2187 2188 2189 2190
## -410812.2952 -161023.3251 -376925.0052 -84206.7802 -229755.9402
## 2191 2192 2193 2194 2195
## -285319.4903 -279657.6203 -241656.4149 -320883.0403 -232783.5150
## 2196 2197 2198 2199 2200
## -257432.2003 -295699.5852 -62925.0052 -258699.5852 -326868.6502
## 2201 2202 2203 2204 2205
## -148234.3551 -101516.1301 -422643.2302 1564963.4901 1318907.1351
## 2206 2207 2208 2209 2210
## -204263.1352 -74755.9402 2215103.7750 226582.1898 1086089.3849
## 2211 2212 2213 2214 2215
## 1276415.5355 338766.8503 673836.3900 906512.6501 355949.1000
## 2216 2217 2218 2219 2220
## -76023.3251 1190148.1505 790877.1496 904682.9204 215808.8152
## 2221 2222 2223 2224 2225
## 1154048.6253 488133.7605 -242994.5450 2099896.3610 90034.2352
## 2226 2227 2228 2229 2230
## 592061.8100 -353347.0651 -313769.1250 -200880.6296 -410981.3602
## 2231 2232 2233 2234 2235
## 476795.6304 156513.8554 241230.8750 232499.4653 57498.2600
## 2236 2237 2238 2239 2240
## 22007.8657 257216.4850 65245.2651 420034.2352 -116276.3200
## 2241 2242 2243 2244 2245
## -413910.6151 674825.6159 -399050.9000 -295741.5501 124696.1052
## 2246 2247 2248 2249 2250
## 334682.9204 124963.4901 279139.7502 51934.7099 -363488.5553
## 2251 2252 2253 2254 2255
## 33976.6749 377175.7254 331935.9153 -433276.3200 -334333.8803
## 2256 2257 2258 2259 2260
## 54288.4354 11512.6501 -206867.4449 360176.9307 362432.3362
## 2261 2262 2263 2264 2265
## 258485.0752 -167990.9290 409470.6852 -333206.7802 -193064.0847
## 2266 2267 2268 2269 2270
## -283240.3448 73344.7904 -407221.1703 -36178.0001 287428.7202
## 2271 2272 2273 2274 2275
## -297357.8392 -393488.5553 -356360.2498 -136020.9145 -239965.7648
## 2276 2277 2278 2279 2280
## 413908.3404 -229966.9701 347710.4953 -224472.9598 -395995.7503
## 2281 2282 2283 2284 2285
## 618203.3002 -296868.6502 47639.7502 -101092.8649 -371713.9753
## 2286 2287 2288 2289 2290
## -183769.1250 149527.0402 -102078.4748 -331157.6203 -51514.9248
## 2291 2292 2293 2294 2295
## -325233.1497 196862.1753 143694.8998 -324893.8144 -245600.0599
## 2296 2297 2298 2299 2300
## -137571.2798 -154471.7545 34780.0350 16329.1950 55753.6655
## 2301 2302 2303 2304 2305
## -235936.9846 -134036.5099 115104.9803 -12712.7699 7357.9751
## 2306 2307 2308 2309 2310
## -183079.6801 -173699.5852 -4050.9000 -325811.0899 -132501.7400
## 2311 2312 2313 2314 2315
## -192965.7648 -70107.2550 -133514.9248 297934.7099 -132839.8700
## 2316 2317 2318 2319 2320
## -110458.5698 -135317.0796 -440108.4603 -142993.3396 -78896.2250
## 2321 2322 2323 2324 2325
## -304613.2447 -254444.1797 1582.1898 -226445.3850 -248838.6647
## 2326 2327 2328 2329 2330
## -256983.5150 -79233.1497 131583.3952 -68276.3200 -372713.9753
## 2331 2332 2333 2334 2335
## 122428.7202 120457.5004 19118.1650 80765.6449 -254754.7349
## 2336 2337 2338 2339 2340
## 352780.0350 -281868.6502 -31797.9051 190598.9906 -52881.8350
## 2341 2342 2343 2344 2345
## -16867.4449 42512.6501 -271374.6399 -136022.1198 -414402.2148
## 2346 2347 2348 2349 2350
## -273981.3602 -132360.2498 166090.5902 -251373.4346 -38345.8597
## 2351 2352 2353 2354 2355
## 227723.6800 24893.9504 -127558.0950 -261092.8649 -140627.6348
## 2356 2357 2358 2359 2360
## -105037.7152 -131705.5749 -115670.8050 -228839.8700 -269642.0249
## 2361 2362 2363 2364 2365
## -433951.3747 10821.9999 24540.2249 -321936.9846 167230.8750
## 2366 2367 2368 2369 2370
## -495035.3046 -104670.8050 -314824.2746 -44295.7503 -180389.0300
## 2371 2372 2373 2374 2375
## -378824.2746 -273064.0847 -611231.9444 23921.5252 -80035.3046
## 2376 2377 2378 2379 2380
## -404516.1301 -296163.6100 -312360.2498 -114893.8144 -400387.8247
## 2381 2382 2383 2384 2385
## -67698.3799 -263670.8050 -352642.0249 -380387.8247 -254188.7741
## 2386 2387 2388 2389 2390
## -69402.2148 11512.6501 -152851.8495 125174.5200 1321022.2558
## 2391 2392 2393 2394 2395
## -226868.6502 -36925.0052 320738.0701 125174.5200 330468.2745
## 2396 2397 2398 2399 2400
## -273861.4552 -317432.2003 -173488.5553 -265319.4903 -201797.9051
## 2401 2402 2403 2404 2405
## -177008.9351 266301.6201 -347601.2653 -340530.5202 282921.5252
## 2406 2407 2408 2409 2410
## 6230.8750 -235797.9051 -297150.4252 592709.2899 105103.7750
## 2411 2412 2413 2414 2415
## 337441.9050 -162643.2302 -176305.1002 -218699.5852 -223621.6451
## 2416 2417 2418 2419 2420
## -216813.6502 -322108.4603 -367995.7503 -180951.3747 -247741.5501
## 2421 2422 2423 2424 2425
## 86582.1898 72658.6295 349554.6150 196512.6501 130563.0154
## 2426 2427 2428 2429 2430
## 383555.8203 568485.0752 475951.5107 -199643.2302 -254896.2250
## 2431 2432 2433 2434 2435
## 329753.6655 567569.0051 151582.1898 746160.1300 129259.6552
## 2436 2437 2438 2439 2440
## 55949.1000 -292432.2003 -28136.0352 -161868.6502 -287221.1703
## 2441 2442 2443 2444 2445
## 186512.6501 -71445.3850 930950.3054 -352333.8803 16652.9349
## 2446 2447 2448 2449 2450
## 884121.7810 200047.4199 121441.9050 10456.2951 703274.0453
## 2451 2452 2453 2454 2455
## -24783.5150 126934.7099 -84558.0950 -154754.7349 257076.2001
## 2456 2457 2458 2459 2460
## -169825.4800 -239389.0300 -145248.7452 1240527.0402 292709.2899
## 2461 2462 2463 2464 2465
## 640527.0402 -246277.5253 446850.7801 122216.4850 -306868.6502
## 2466 2467 2468 2469 2470
## 539612.1753 245314.8049 182076.2001 306103.7750 -194050.9000
## 2471 2472 2473 2474 2475
## -27149.2199 145103.7750 144402.3507 1294540.2249 -280108.4603
## 2476 2477 2478 2479 2480
## 369188.9101 887357.9751 402429.9256 56794.4251 20031.8245
## 2481 2482 2483 2484 2485
## 403554.6150 918486.2806 693610.9700 80033.0299 476935.9153
## 2486 2487 2488 2489 2490
## 348766.8503 -276514.9248 -369741.5501 -242276.3200 -296444.1797
## 2491 2492 2493 2494 2495
## -347403.4201 -360811.0899 -284754.7349 -289964.5595 -481163.6100
## 2496 2497 2498 2499 2500
## -305163.6100 -345733.1497 -422782.3097 -264185.1951 -443486.1446
## 2501 2502 2503 2504 2505
## -340248.7452 -67290.7101 -376885.7597 -635879.4243 -49614.4500
## 2506 2507 2508 2509 2510
## -604880.6296 -181769.1250 -553062.8794 16230.8750 -355942.5047
## 2511 2512 2513 2514 2515
## -98261.9299 675668.5303 -199719.9650 75343.5851 327998.2600
## 2516 2517 2518 2519 2520
## -125381.8350 -120838.6647 -464295.4944 -338893.8144 -83516.1301
## 2521 2522 2523 2524 2525
## -262499.3293 892216.4850 1011161.3353 352216.4850 683950.3054
## 2526 2527 2528 2529 2530
## -181713.9753 952513.8554 371907.1351 53414.3301 -213769.1250
## 2531 2532 2533 2534 2535
## -162571.2798 -184050.9000 -399543.7049 -87923.7999 -422695.9692
## 2536 2537 2538 2539 2540
## -217276.3200 -312008.9351 -401234.3551 -524683.9898 -190558.0950
## 2541 2542 2543 2544 2545
## -388755.9402 -401628.8401 -465212.7699 -952625.2241 -367008.9351
## 2546 2547 2548 2549 2550
## -66234.3551 -141727.1600 -215176.7947 -158698.3799 -196092.8649
## 2551 2552 2553 2554 2555
## -410669.5997 -280247.5398 -440389.0300 -317361.4552 -353797.9051
## 2556 2557 2558 2559 2560
## -273064.0847 -205178.0001 -480529.3148 -229543.7049 -131022.1198
## 2561 2562 2563 2564 2565
## -147853.0548 -332501.7400 -359403.4201 -336303.8948 -453598.8546
## 2566 2567 2568 2569 2570
## -498558.0950 -292357.8392 -71234.3551 -354396.2250 -330389.0300
## 2571 2572 2573 2574 2575
## -415276.3200 -447572.4851 -348276.3200 -320445.3850 11723.6800
## 2576 2577 2578 2579 2580
## -243275.1147 -412360.2498 -401585.6699 -48558.0950 -220670.8050
## 2581 2582 2583 2584 2585
## -458698.3799 14402.3507 -316297.9051 -418592.8649 -455270.3303
## 2586 2587 2588 2589 2590
## -1526297.8681 -416585.6699 -373347.0651 -305896.2250 111019.8451
## 2591 2592 2593 2594 2595
## -184120.4397 141301.6201 585247.6758 880668.5303 -185319.4903
## 2596 2597 2598 2599 2600
## 469824.4106 587076.2001 63554.6150 529610.9700 -128628.8401
## 2601 2602 2603 2604 2605
## -202361.4552 291188.9101 -247150.4252 -46797.9051 -196586.8752
## 2606 2607 2608 2609 2610
## 155667.3250 310949.1000 71441.9050 686372.3652 -182854.2601
## 2611 2612 2613 2614 2615
## 468765.6449 532850.7801 273413.1248 689329.1950 310469.4798
## 2616 2617 2618 2619 2620
## 42145.7399 293413.1248 304751.2548 -270586.8752 639090.5902
## 2621 2622 2623 2624 2625
## 113413.1248 1157217.6903 492992.2703 473441.9050 227359.1805
## 2626 2627 2628 2629 2630
## 284540.2249 479103.7750 -194685.1951 -302981.3602 -266586.8752
## 2631 2632 2633 2634 2635
## -285037.7152 -194474.1652 -120530.5202 487216.4850 378485.0752
## 2636 2637 2638 2639 2640
## -158981.3602 1547216.4850 2244049.8306 -88980.1549 295245.2651
## 2641 2642 2643 2644 2645
## -169896.2250 -362925.0052 18765.6449 341019.8451 194821.9999
## 2646 2647 2648 2649 2650
## -302615.6554 -37712.7699 -17417.8102 -161857.6203 -195995.7503
## 2651 2652 2653 2654 2655
## -262425.0052 353132.5551 -188347.0651 -250107.2550 -381657.6203
## 2656 2657 2658 2659 2660
## 206019.8451 388025.8348 161485.0752 -225213.9753 -268628.8401
## 2661 2662 2663 2664 2665
## 63076.2001 657498.2600 209258.4499 199047.4199 -280248.7452
## 2666 2667 2668 2669 2670
## 563554.6150 -67839.8700 -248136.0352 -230530.5202 24469.4798
## 2671 2672 2673 2674 2675
## 119469.4798 552991.0649 619329.1950 807512.6501 -178415.3995
## 2676 2677 2678 2679 2680
## 420739.2754 26794.4251 590343.5851 -204178.0001 482920.3199
## 2681 2682 2683 2684 2685
## 255456.2951 1066090.5902 566654.1403 315103.7750 553301.6201
## 2686 2687 2688 2689 2690
## 183414.3301 -290387.8247 228637.3395 -272712.7699 -52121.6451
## 2691 2692 2693 2694 2695
## -270387.8247 -401008.9351 -62783.5150 -353065.2901 75527.0402
## 2696 2697 2698 2699 2700
## -238628.8401 -146234.3551 -296022.1198 -328558.0950 630738.0701
## 2701 2702 2703 2704 2705
## -308839.8700 -135572.4851 157921.5252 -313417.8102 -183347.0651
## 2706 2707 2708 2709 2710
## 104892.7450 216230.8750 -272361.4552 -190247.5398 -145741.5501
## 2711 2712 2713 2714 2715
## 26934.7099 -7712.7699 12652.9349 -175880.6296 33697.3105
## 2716 2717 2718 2719 2720
## -205459.7751 -330868.6502 30258.4499 -6727.1600 -250050.9000
## 2721 2722 2723 2724 2725
## -249261.9299 -83065.2901 64357.9751 -14474.1652 -72698.3799
## 2726 2727 2728 2729 2730
## -854752.3242 -1383016.0931 -474755.9402 4821.9999 -357643.2302
## 2731 2732 2733 2734 2735
## -232150.4252 52287.2301 -14896.2250 -114896.2250 -194754.7349
## 2736 2737 2738 2739 2740
## -203910.6151 -215247.5398 -52881.8350 -316162.4046 -231078.4748
## 2741 2742 2743 2744 2745
## -112642.0249 -101938.1900 348145.7399 -212079.6801 166899.9401
## 2746 2747 2748 2749 2750
## 985.0752 -144472.9598 -104825.4800 -143769.1250 -261374.6399
## 2751 2752 2753 2754 2755
## -352078.4748 -457501.7400 -426797.9051 -323754.7349 -403037.7152
## 2756 2757 2758 2759 2760
## -126685.1951 -438755.9402 -160741.5501 -558203.1642 -351797.9051
## 2761 2762 2763 2764 2765
## -170881.8350 -1347213.9383 -338347.0651 -380951.3747 -532923.7999
## 2766 2767 2768 2769 2770
## -309107.2550 -472854.2601 -476234.3551 -351438.1900 -566023.3251
## 2771 2772 2773 2774 2775
## -619049.6946 -414297.9051 -621781.1044 -115909.4098 -229824.2746
## 2776 2777 2778 2779 2780
## -341094.0702 -27923.7999 -198909.4098 -406586.8752 -493205.5749
## 2781 2782 2783 2784 2785
## -549514.9248 -397854.2601 -310107.2550 -370586.8752 -457981.3602
## 2786 2787 2788 2789 2790
## -79332.6750 -247008.9351 -413192.3902 -386290.7101 -1901085.6329
## 2791 2792 2793 2794 2795
## -318347.0651 -444474.1652 -546303.8948 -234727.1600 -465741.5501
## 2796 2797 2798 2799 2800
## -337995.7503 -537429.7896 -303417.8102 -440389.0300 -424755.9402
## 2801 2802 2803 2804 2805
## -388488.5553 -295797.9051 -493065.2901 -406868.6502 -514614.4500
## 2806 2807 2808 2809 2810
## -151712.7699 -397854.2601 -438192.3902 -443868.6502 -406303.8948
## 2811 2812 2813 2814 2815
## -398558.0950 -410725.9547 -412361.4552 -223347.0651 -337571.2798
## 2816 2817 2818 2819 2820
## -432925.0052 -421107.2550 -258734.3551 -251761.9299 -223487.3499
## 2821 2822 2823 2824 2825
## -430134.8298 -423065.2901 -395811.0899 -437290.7101 -280769.1250
## 2826 2827 2828 2829 2830
## -405966.9701 -485134.8298 -560036.5099 -33769.1250 -379965.7648
## 2831 2832 2833 2834 2835
## -82712.7699 -602360.2498 -122121.6451 -486445.3850 -287056.8897
## 2836 2837 2838 2839 2840
## -379403.4201 -188881.8350 -427432.2003 -388488.5553 -429896.2250
## 2841 2842 2843 2844 2845
## -413628.8401 -471995.7503 -467995.7503 -486023.3251 -312713.9753
## 2846 2847 2848 2849 2850
## -103065.2901 -311783.5150 -455037.7152 -512501.7400 -658766.7143
## 2851 2852 2853 2854 2855
## -1892141.9879 -160423.7999 -222318.2849 -465318.2849 -361474.1652
## 2856 2857 2858 2859 2860
## -193347.0651 -57839.8700 -13980.1549 -365402.2148 -65936.9846
## 2861 2862 2863 2864 2865
## -181585.6699 -316536.5099 -871970.5492 -306727.1600 -358980.1549
## 2866 2867 2868 2869 2870
## -376868.6502 20272.8400 430033.0299 -50491.5501 -224305.1002
## 2871 2872 2873 2874 2875
## -290390.2353 -314319.4903 1664120.5757 -276037.7152 -127643.2302
## 2876 2877 2878 2879 2880
## -209812.2952 -175248.7452 85385.5500 151652.9349 -228699.5852
## 2881 2882 2883 2884 2885
## 241372.3652 478850.7801 382005.4550 -314544.9103 -353108.4603
## 2886 2887 2888 2889 2890
## 592765.6449 590949.1000 -215601.2653 -342995.7503 259681.7151
## 2891 2892 2893 2894 2895
## 276652.9349 -49543.7049 -477150.4252 -292375.8453 -83699.5852
## 2896 2897 2898 2899 2900
## -239094.0702 -109050.9000 154821.9999 -172475.3705 -26713.9753
## 2901 2902 2903 2904 2905
## 141018.6398 242569.0051 183694.8998 244667.3250 362427.5149
## 2906 2907 2908 2909 2910
## 270033.0299 -320812.2952 11357.9751 426512.6501 284048.6253
## 2911 2912 2913 2914 2915
## -320657.6203 84258.4499 237667.3250 -32748.7452 131230.8750
## 2916 2917 2918 2919 2920
## -223769.1250 -142643.2302 440174.5200 -278277.5253 -304052.1053
## 2921 2922 2923 2924 2925
## -35601.2653 116949.1000 -25178.0001 181511.4447 -154741.5501
## 2926 2927 2928 2929 2930
## 104230.8750 -33332.6750 1540049.8306 -176192.3902 152849.5748
## 2931 2932 2933 2934 2935
## 719118.1650 420667.3250 179540.2249 508639.7502 389821.9999
## 2936 2937 2938 2939 2940
## 325104.9803 739751.2548 389414.3301 124118.1650 215033.0299
## 2941 2942 2943 2944 2945
## 779612.1753 -140586.8752 -150248.7452 318976.6749 -94543.7049
## 2946 2947 2948 2949 2950
## -170670.8050 -202305.1002 290528.2455 -362277.5253 357216.4850
## 2951 2952 2953 2954 2955
## 897780.0350 583414.3301 344118.1650 702723.6800 528344.7904
## 2956 2957 2958 2959 2960
## -129170.8050 521583.3952 338483.8699 397710.4953 345837.5954
## 2961 2962 2963 2964 2965
## 1067287.2301 329681.7151 -337150.4252 -82699.5852 153274.0453
## 2966 2967 2968 2969 2970
## -121558.0950 -322713.9753 323976.6749 696583.3952 396652.9349
## 2971 2972 2973 2974 2975
## 33025.8348 -226586.8752 -79403.4201 276054.6150 322638.5448
## 2976 2977 2978 2979 2980
## 615103.7750 -225366.2395 -204331.4697 -392219.9650 -268978.9495
## 2981 2982 2983 2984 2985
## -330516.1301 -418980.1549 -337853.0548 -273191.1848 -325106.0496
## 2986 2987 2988 2989 2990
## -338275.1147 -407854.2601 -58529.3148 -46585.6699 -147570.0744
## 2991 2992 2993 2994 2995
## -385952.5801 155342.3797 -97923.7999 -271121.6451 -469529.3148
## 2996 2997 2998 2999 3000
## -95487.3499 177005.4550 72991.0649 -17640.8195 -316868.6502
## 3001 3002 3003 3004 3005
## 82006.6604 12357.9751 7359.1805 67372.3652 -48980.1549
## 3006 3007 3008 3009 3010
## -291374.6399 -123487.3499 -111092.8649 273203.3002 44329.1950
## 3011 3012 3013 3014 3015
## -178134.8298 -242853.0548 -125776.3200 131723.6800 -95246.3345
## 3016 3017 3018 3019 3020
## 160525.8348 163626.5654 -222037.7152 -41374.6399 -435530.5202
## 3021 3022 3023 3024 3025
## -14867.4449 167921.5252 -14966.9701 -244854.2601 722709.2899
## 3026 3027 3028 3029 3030
## 506090.5902 349329.1950 1653174.5200 433061.8100 834542.6356
## 3031 3032 3033 3034 3035
## 587569.0051 -215248.7452 -241375.8453 293836.3900 1066090.5902
## 3036 3037 3038 3039 3040
## 119751.2548 216230.8750 933414.3301 897921.5252 58343.5851
## 3041 3042 3043 3044 3045
## 246512.6501 370457.5004 -257136.0352 711090.5902 377920.3199
## 3046 3047 3048 3049 3050
## 335245.2651 236866.3755 764120.5757 -123459.7751 921654.1403
## 3051 3052 3053 3054 3055
## -127685.1951 314.8049 175245.2651 -227925.0052 329609.7647
## 3056 3057 3058 3059 3060
## -127079.6801 -141727.1600 -226417.8102 365808.8152 -182805.1002
## 3061 3062 3063 3064 3065
## -278995.7503 274118.1650 -155192.3902 -26305.1002 573765.6449
## 3066 3067 3068 3069 3070
## -323552.1053 367498.2600 367498.2600 -292221.1703 4116796.8358
## 3071 3072 3073 3074 3075
## -169052.1053 1395739.2754 -358277.5253 -218241.5501 -306375.8453
## 3076 3077 3078 3079 3080
## -365883.0403 -69925.0052 1242076.2001 1799330.4003 -251868.6502
## 3081 3082 3083 3084 3085
## -194474.1652 1588625.3601 -375883.0403 -287995.7503 1228482.6646
## 3086 3087 3088 3089 3090
## -163875.8453 -179544.9103 683133.7605 850808.8152 48427.5149
## 3091 3092 3093 3094 3095
## -309164.8153 315807.6098 -298417.8102 -346446.5903 270033.0299
## 3096 3097 3098 3099 3100
## -289826.6853 263483.8699 -33347.0651 211161.3353 -106086.8752
## 3101 3102 3103 3104 3105
## -368559.3004 -235037.7152 358202.0949 -271094.0702 750880.7656
## 3106 3107 3108 3109 3110
## 511161.3353 350314.8049 477357.9751 3920.3199 605808.8152
## 3111 3112 3113 3114 3115
## -289474.1652 -208558.0950 -92107.2550 -311797.9051 -294332.6750
## 3116 3117 3118 3119 3120
## -198838.6647 -312396.2250 -300952.5801 -331586.8752 45386.7553
## 3121 3122 3123 3124 3125
## -310319.4903 -184614.4500 -154192.3902 -152255.9402 1582.1898
## 3126 3127 3128 3129 3130
## -337290.7101 -341657.6203 -97219.9650 -135494.5450 -70670.8050
## 3131 3132 3133 3134 3135
## 194821.9999 -100149.2199 -283627.6348 -109389.0300 -762921.3892
## 3136 3137 3138 3139 3140
## 276019.8451 -280231.9444 -22980.1549 -1863339.8331 58625.3601
## 3141 3142 3143 3144 3145
## -262127.6348 -327713.9753 -360530.5202 -168812.2952 -231305.1002
## 3146 3147 3148 3149 3150
## -307361.4552 -286586.8752 895399.9401 858485.0752 295386.7553
## 3151 3152 3153 3154 3155
## 732288.4354 -239263.1352 -227783.5150 -323770.3303 -348050.9000
## 3156 3157 3158 3159 3160
## -319544.9103 -221221.1703 167781.2403 -284206.7802 -207432.2003
## 3161 3162 3163 3164 3165
## -321439.3953 3044770.4663 -334544.9103 908343.5851 -408417.8102
## 3166 3167 3168 3169 3170
## -235319.4903 -328981.3602 -288108.4603 592851.9854 -246586.8752
## 3171 3172 3173 3174 3175
## -362854.2601 -216586.8752 -366868.6502 -118980.1549 -290974.1652
## 3176 3177 3178 3179 3180
## -305178.0001 -4260.7246 -270094.0702 84963.4901 -315601.2653
## 3181 3182 3183 3184 3185
## 506229.6697 -112008.9351 -301094.0702 96300.4148 -136586.8752
## 3186 3187 3188 3189 3190
## -359530.5202 -306939.3953 -243136.0352 2659051.0360 -251586.8752
## 3191 3192 3193 3194 3195
## 362645.7399 -245248.7452 -238981.3602 -34445.3850 1077637.3395
## 3196 3197 3198 3199 3200
## -174614.4500 369399.9401 607359.1805 493104.9803 -374755.9402
## 3201 3202 3203 3204 3205
## -420670.8050 -125178.0001 -332783.5150 -328981.3602 33414.3301
## 3206 3207 3208 3209 3210
## -347643.2302 -337939.3953 -195387.8247 296372.3652 192428.7202
## 3211 3212 3213 3214 3215
## -46794.2891 119527.0402 -438976.5389 158485.0752 -476866.2395
## 3216 3217 3218 3219 3220
## -7289.5047 -61938.1900 36091.7955 -388874.6399 216513.8554
## 3221 3222 3223 3224 3225
## 670877.1496 -464962.1488 388060.6047 -167920.1839 700037.8512
## 3226 3227 3228 3229 3230
## -298558.0950 39190.1155 -361233.1497 -132360.2498 -184050.9000
## 3231 3232 3233 3234 3235
## 126168.5303 -246656.4149 -310494.5450 -699118.0291 -484332.6750
## 3236 3237 3238 3239 3240
## -474050.9000 -121374.6399 -401023.3251 -205670.8050 -140163.6100
## 3241 3242 3243 3244 3245
## -368974.1652 -365881.8350 -407430.9949 -203192.3902 -258558.0950
## 3246 3247 3248 3249 3250
## -315670.8050 -266725.9547 -52501.7400 -354614.4500 -106305.1002
## 3251 3252 3253 3254 3255
## -358769.1250 -276938.1900 -2163900.9724 -384656.4149 -323987.3499
## 3256 3257 3258 3259 3260
## -637571.2798 -183416.6048 -435741.5501 -297501.7400 -420952.5801
## 3261 3262 3263 3264 3265
## -394966.9701 -368558.0950 -396405.5749 -479311.0899 -430036.5099
## 3266 3267 3268 3269 3270
## -352219.9650 -302219.9650 -299036.5099 -568204.3696 -248276.3200
## 3271 3272 3273 3274 3275
## 123414.3301 -2573604.8073 -243839.8700 -501796.6998 -362459.7751
## 3276 3277 3278 3279 3280
## -673906.9991 -404050.9000 -494965.7648 -762500.5347 -398416.6048
## 3281 3282 3283 3284 3285
## -383487.3499 -482149.2199 -583613.2447 -225783.5150 -680176.7947
## 3286 3287 3288 3289 3290
## -596022.1198 -535036.5099 -614191.1848 -402205.5749 -297712.7699
## 3291 3292 3293 3294 3295
## -479649.2199 -407995.7503 -373558.0950 -525740.3448 -404649.2199
## 3296 3297 3298 3299 3300
## -476023.3251 -555500.5347 -439796.6998 -660951.3747 -446727.1600
## 3301 3302 3303 3304 3305
## -397769.1250 -655107.2550 -586373.4346 -713415.3995 -440389.0300
## 3306 3307 3308 3309 3310
## -556585.6699 -473831.4697 -635303.8948 888345.9957 90738.0701
## 3311 3312 3313 3314 3315
## 387051.0360 762711.7006 -170248.7452 479612.1753 979895.1557
## 3316 3317 3318 3319 3320
## 616796.8358 1308345.9957 559753.6655 394929.9256 -66023.3251
## 3321 3322 3323 3324 3325
## 8626.5654 767217.6903 691868.7862 -64332.6750 617428.7202
## 3326 3327 3328 3329 3330
## 625527.0402 336585.8058 -208136.0352 187923.9359 383980.2909
## 3331 3332 3333 3334 3335
## 497078.6108 67639.7502 -102847.0651 -324614.4500 671937.1206
## 3336 3337 3338 3339 3340
## -154248.7452 96486.2806 225246.4705 -43839.8700 718768.0556
## 3341 3342 3343 3344 3345
## 925810.0205 -226023.3251 1164681.7151 -91640.8195 -23906.9991
## 3346 3347 3348 3349 3350
## 594893.9504 -39636.0352 -181077.2695 -15951.3747 -272818.2849
## 3351 3352 3353 3354 3355
## 58076.2001 78203.3002 -265880.6296 -16161.1993 286512.6501
## 3356 3357 3358 3359 3360
## -430387.8247 -428133.6245 -114879.4243 -19529.3148 -200525.6988
## 3361 3362 3363 3364 3365
## 146372.3652 -1081652.7989 -157289.5047 -187459.7751 -190669.5997
## 3366 3367 3368 3369 3370
## 171019.8451 -279331.4697 -199614.4500 215399.9401 -195317.0796
## 3371 3372 3373 3374 3375
## -194725.9547 67485.0752 149756.0762 -161542.4996 305708.0846
## 3376 3377 3378 3379 3380
## 184963.4901 35247.6758 80421.5252 -62360.2498 -333769.1250
## 3381 3382 3383 3384 3385
## 375372.3652 -202044.9103 -385037.7152 -80178.0001 314978.5902
## 3386 3387 3388 3389 3390
## -4332.6750 -370672.0104 -303277.5253 -268974.1652 125863.9648
## 3391 3392 3393 3394 3395
## -132261.9299 -89530.5202 185385.5500 -367826.6853 371934.7099
## 3396 3397 3398 3399 3400
## 172216.4850 -38445.3850 199963.4901 -167916.6048 105878.3549
## 3401 3402 3403 3404 3405
## -46305.1002 -321023.3251 262428.7202 -15740.3448 -671089.2489
## 3406 3407 3408 3409 3410
## -265601.2653 355580.9845 415625.3601 -301052.1053 235245.2651
## 3411 3412 3413 3414 3415
## -293206.7802 -332812.2952 -183344.6544 7357.9751 -427285.8887
## 3416 3417 3418 3419 3420
## -284812.2952 317934.7099 256794.4251 368034.2352 566415.5355
## 3421 3422 3423 3424 3425
## -173578.4748 -298875.8453 -338277.5253 256090.5902 -368721.1703
## 3426 3427 3428 3429 3430
## 61865.1702 364681.7151 392076.2001 3514545.0463 3680178.1361
## 3431 3432 3433 3434 3435
## 713118.1650 92569.0051 -15389.0300 -305037.7152 -311390.2353
## 3436 3437 3438 3439 3440
## 991867.5809 1501021.0505 -71234.3551 1430317.2156 1321866.3755
## 3441 3442 3443 3444 3445
## 4390741.6861 2542150.5612 -194319.4903 195528.2455 964893.9504
## 3446 3447 3448 3449 3450
## 17498.2600 -282559.3004 981585.8058 841301.6201 2184121.7810
## 3451 3452 3453 3454 3455
## 2384121.7810 -147854.2601 -267699.5852 -136867.4449 931021.0505
## 3456 3457 3458 3459 3460
## -308910.6151 1911584.6005 -272218.7597 -143345.8597 -289120.4397
## 3461 3462 3463 3464 3465
## -272923.7999 -458838.6647 -227218.7597 -310459.7751 -358896.2250
## 3466 3467 3468 3469 3470
## -289754.7349 -154472.9598 -404401.0094 313482.6646 -388556.8897
## 3471 3472 3473 3474 3475
## -180811.0899 -257148.0146 -339543.7049 -323896.2250 -419261.9299
## 3476 3477 3478 3479 3480
## -329261.9299 -283459.7751 -180670.8050 -482345.8597 -175727.1600
## 3481 3482 3483 3484 3485
## -348178.0001 12850.7801 -621216.3490 -298107.2550 -191909.4098
## 3486 3487 3488 3489 3490
## -229747.5398 -191065.2901 -261621.6451 -312516.1301 -196008.9351
## 3491 3492 3493 3494 3495
## -303276.3200 -21092.8649 -19542.4996 -255601.2653 755247.6758
## 3496 3497 3498 3499 3500
## -61516.1301 -776866.2395 -244896.2250 -62853.0548 -118909.4098
## 3501 3502 3503 3504 3505
## -296263.1352 128343.5851 -273037.7152 -217854.2601 -228966.9701
## 3506 3507 3508 3509 3510
## 258485.0752 290950.3054 -58276.3200 295669.7357 1626513.8554
## 3511 3512 3513 3514 3515
## 1271585.8058 3274.0453 527498.2600 -429263.1352 -99260.7246
## 3516 3517 3518 3519 3520
## 343555.8203 216584.6005 -114332.6750 592709.2899 883415.5355
## 3521 3522 3523 3524 3525
## 239612.1753 -229541.2943 -305035.3046 -280974.1652 663485.0752
## 3526 3527 3528 3529 3530
## 23921.5252 -340598.8546 -328770.3303 415529.4508 251301.6201
## 3531 3532 3533 3534 3535
## -259594.0702 -199650.4252 364258.4499 -354868.6502 342570.2104
## 3536 3537 3538 3539 3540
## 423801.6201 -196442.9743 730951.5107 529048.6253 833134.9658
## 3541 3542 3543 3544 3545
## -382925.0052 -383594.0702 217569.0051 -238136.0352 1223583.3952
## 3546 3547 3548 3549 3550
## -195305.1002 -73347.0651 -409052.1053 449752.4602 417780.0350
## 3551 3552 3553 3554 3555
## -239939.3953 -210657.6203 -410530.5202 185343.5851 -237854.2601
## 3556 3557 3558 3559 3560
## 610878.3549 -122219.9650 251723.6800 -289121.6451 -296812.2952
## 3561 3562 3563 3564 3565
## 441160.1300 1048483.8699 -530175.5894 -382782.3097 -364853.0548
## 3566 3567 3568 3569 3570
## -460142.0249 -229938.1900 -149078.4748 -369261.9299 -394740.3448
## 3571 3572 3573 3574 3575
## -254050.9000 -489457.3644 -270656.4149 -90247.5398 -26727.1600
## 3576 3577 3578 3579 3580
## 240385.5500 120598.9906 -288698.3799 -33896.2250 -203769.1250
## 3581 3582 3583 3584 3585
## 131580.9845 -63910.6151 -87922.5945 75385.5500 135104.9803
## 3586 3587 3588 3589 3590
## 80738.0701 -91347.0651 -30389.0300 -48896.2250 -313769.1250
## 3591 3592 3593 3594 3595
## -171290.7101 18907.1351 135104.9803 626161.3353 -192079.6801
## 3596 3597 3598 3599 3600
## 700879.5603 910738.0701 -327854.2601 -385868.6502 -69965.7648
## 3601 3602 3603 3604 3605
## -367854.2601 -293130.1652 -187769.1250 87005.4550 -446585.6699
## 3606 3607 3608 3609 3610
## -350883.0403 108202.0949 70316.0102 40949.1000 139330.4003
## 3611 3612 3613 3614 3615
## 11371.1599 -249592.8649 365963.4901 -357712.7699 -335281.1044
## 3616 3617 3618 3619 3620
## 268878.3549 -237782.3097 160329.1950 -290318.2849 -59023.3251
## 3621 3622 3623 3624 3625
## 107359.1805 241161.3353 259681.7151 393499.4653 -180107.2550
## 3626 3627 3628 3629 3630
## -309825.4800 301583.3952 -286368.6502 378485.0752 -63528.1095
## 3631 3632 3633 3634 3635
## -302078.4748 480174.5200 -171374.6399 -4396.2250 -146303.8948
## 3636 3637 3638 3639 3640
## -284333.8803 516316.0102 -320530.5202 30964.6954 -163134.8298
## 3641 3642 3643 3644 3645
## 1910601.4013 501440.6996 673132.5551 677850.7801 225949.1000
## 3646 3647 3648 3649 3650
## 255387.9607 551440.6996 -222276.3200 -18978.9495 -246727.1600
## 3651 3652 3653 3654 3655
## 129612.1753 -104290.7101 -295389.0300 -362360.2498 -252290.7101
## 3656 3657 3658 3659 3660
## 231583.3952 -250022.1198 -186868.6502 -27994.5450 471794.4251
## 3661 3662 3663 3664 3665
## 286232.0804 499964.6954 542639.7502 -100543.7049 -292432.2003
## 3666 3667 3668 3669 3670
## 171160.1300 -166079.6801 247133.7605 -224121.6451 -200530.5202
## 3671 3672 3673 3674 3675
## 703118.1650 -56022.1198 -142994.5450 22118.1650 -25036.5099
## 3676 3677 3678 3679 3680
## 58343.5851 643836.3900 282076.2001 378836.3900 -155107.2550
## 3681 3682 3683 3684 3685
## 251184.5200 -234.3551 388307.6098 522216.4850 -80389.0300
## 3686 3687 3688 3689 3690
## 661441.9050 -184224.1652 -70530.5202 10033.0299 -81586.8752
## 3691 3692 3693 3694 3695
## 350557.5004 -266868.6502 262849.5748 340033.0299 -174755.9402
## 3696 3697 3698 3699 3700
## 557301.6201 -169981.3602 243652.9349 832921.5252 -66868.6502
## 3701 3702 3703 3704 3705
## 58060.6047 -409652.7989 41795.6304 -137114.4500 -489014.9248
## 3706 3707 3708 3709 3710
## 63837.5954 -245881.8350 -456723.5440 -419964.5595 -152711.5646
## 3711 3712 3713 3714 3715
## -489079.6801 -599754.7349 -526896.2250 -331727.1600 -337219.9650
## 3716 3717 3718 3719 3720
## -382839.8700 -341234.3551 -617289.5047 -232572.4851 -432909.4098
## 3721 3722 3723 3724 3725
## -253065.2901 -181050.9000 -332994.5450 -341107.2550 -492219.9650
## 3726 3727 3728 3729 3730
## -165727.1600 -374769.1250 -290423.7999 -243065.2901 -624189.9795
## 3731 3732 3733 3734 3735
## -389727.1600 -417501.7400 -343107.2550 -443769.1250 -404036.5099
## 3736 3737 3738 3739 3740
## -402923.7999 -365389.0300 -484867.4449 -639824.2746 -303663.6100
## 3741 3742 3743 3744 3745
## -833483.7339 -440501.7400 -446903.4201 881230.8750 388908.3404
## 3746 3747 3748 3749 3750
## 245386.7553 -67007.7297 1674542.6356 -227643.2302 290317.2156
## 3751 3752 3753 3754 3755
## 672216.4850 2498.2600 -267432.2003 1615104.9803 -174150.4252
## 3756 3757 3758 3759 3760
## -264332.6750 481445.5210 1215823.2053 277049.8306 -150178.0001
## 3761 3762 3763 3764 3765
## 396794.4251 -347150.4252 548413.1248 841230.8750 -60952.5801
## 3766 3767 3768 3769 3770
## 1569756.0762 -334699.5852 170597.7852 697217.6903 1261161.3353
## 3771 3772 3773 3774 3775
## 365668.5303 693276.4560 -159459.7751 1042993.4756 971866.3755
## 3776 3777 3778 3779 3780
## 428836.3900 -127393.2302 374626.5654 -309263.1352 -313136.0352
## 3781 3782 3783 3784 3785
## 685949.1000 -313052.1053 660949.1000 -8769.1250 -236143.2302
## 3786 3787 3788 3789 3790
## 173132.5551 -445600.0599 -239332.6750 -371516.1301 -149824.2746
## 3791 3792 3793 3794 3795
## -353065.2901 -312642.0249 14979.0855 57428.7202 -167572.4851
## 3796 3797 3798 3799 3800
## 410949.1000 459610.9700 -303699.5852 -888412.9888 121512.6501
## 3801 3802 3803 3804 3805
## 1742292.0514 633061.8100 -296868.6502 247500.6707 -92779.8990
## 3806 3807 3808 3809 3810
## 715387.9607 110389.1660 300557.0257 -111233.1497 -436712.7699
## 3811 3812 3813 3814 3815
## -594332.6750 -440459.7751 -592782.3097 -413347.0651 -266290.7101
## 3816 3817 3818 3819 3820
## -378347.0651 -385072.4851 -464332.6750 -181233.1497 -373769.1250
## 3821 3822 3823 3824 3825
## -506409.4098 -539244.1797 159399.9401 -107614.4500 -47360.2498
## 3826 3827 3828 3829 3830
## -184016.1301 -200107.2550 -293205.5749 -362361.4552 -689189.9795
## 3831 3832 3833 3834 3835
## -442502.9454 308907.1351 398693.6945 86161.3353 20103.7750
## 3836 3837 3838 3839 3840
## 395610.9700 -460390.2353 -41514.9248 -28838.6647 -112501.7400
## 3841 3842 3843 3844 3845
## -121516.1301 34610.9700 36794.4251 -201234.3551 276654.1403
## 3846 3847 3848 3849 3850
## 196935.9153 -189474.1652 440879.5603 -399946.5903 -89964.5595
## 3851 3852 3853 3854 3855
## -85670.8050 -141987.3499 -286586.8752 187499.4653 -270347.0651
## 3856 3857 3858 3859 3860
## -77007.7297 35245.2651 236515.0607 -198832.6750 298921.5252
## 3861 3862 3863 3864 3865
## 812711.7006 313204.5056 -402502.9454 -1776996.8817 768597.7852
## 3866 3867 3868 3869 3870
## 30596.5799 699470.6852 -1936.9846 -54790.7101 -55459.7751
## 3871 3872 3873 3874 3875
## 196259.6552 589119.3704 472357.9751 733344.7904 58652.9349
## 3876 3877 3878 3879 3880
## 386090.5902 256372.3652 -59543.7049 -356502.9454 -240601.2653
## 3881 3882 3883 3884 3885
## -191374.6399 -110811.0899 316654.1403 -352643.2302 -322052.1053
## 3886 3887 3888 3889 3890
## -356868.6502 252385.5500 -251903.4201 -373699.5852 -275317.0796
## 3891 3892 3893 3894 3895
## 15491.0649 -317149.2199 -261134.8298 -366444.1797 -664895.0197
## 3896 3897 3898 3899 3900
## -384375.8453 -368305.1002 -347925.0052 -280487.3499 -654895.0197
## 3901 3902 3903 3904 3905
## 10836.3900 -155600.0599 -239402.2148 -207149.2199 -1174243.9238
## 3906 3907 3908 3909 3910
## -474191.1848 -6234.3551 -248416.6048 26580.9845 23878.3549
## 3911 3912 3913 3914 3915
## -58839.8700 -115178.0001 -2776083.2222 729258.4499 -396052.1053
## 3916 3917 3918 3919 3920
## 195336.3900 -230247.5398 -84121.6451 -415459.7751 -413910.6151
## 3921 3922 3923 3924 3925
## -133374.6399 -183276.3200 -332642.0249 -151234.3551 -319783.5150
## 3926 3927 3928 3929 3930
## -309740.3448 -265459.7751 -344332.6750 -495108.4603 -499136.0352
## 3931 3932 3933 3934 3935
## -542078.4748 -273909.4098 -346628.8401 109188.9101 125386.7553
## 3936 3937 3938 3939 3940
## -142199.5852 696023.4611 -108136.0352 -304332.6750 -521023.3251
## 3941 3942 3943 3944 3945
## -453628.8401 -95881.8350 112498.2600 -226727.1600 -36303.8948
## 3946 3947 3948 3949 3950
## -197642.0249 68949.1000 -304754.7349 -33698.3799 -251678.0001
## 3951 3952 3953 3954 3955
## -52218.7597 272780.0350 -113343.4491 -193276.3200 -282361.4552
## 3956 3957 3958 3959 3960
## 39892.7450 -290601.2653 118766.8503 313766.8503 188976.6749
## 3961 3962 3963 3964 3965
## 151300.4148 734823.2053 -143805.1002 -96022.1198 395103.7750
## 3966 3967 3968 3969 3970
## 363554.6150 -144472.9598 -262783.5150 -14543.7049 -640597.6493
## 3971 3972 3973 3974 3975
## -365347.0651 -603205.5749 -331854.2601 -375037.7152 -293896.2250
## 3976 3977 3978 3979 3980
## -342921.3892 -335712.5646 143090.5902 294288.4354 275106.1856
## 3981 3982 3983 3984 3985
## -396657.6203 4190.1155 -329892.6090 -311092.8649 -524896.2250
## 3986 3987 3988 3989 3990
## -530092.8649 -344585.6699 -450725.9547 -591867.4449 -486303.8948
## 3991 3992 3993 3994 3995
## -357501.7400 -453261.9299 -21655.2096 -373868.6502 -211305.1002
## 3996 3997 3998 3999 4000
## 782429.9256 782259.6552 -157006.5244 -325657.2587 594541.4302
## 4001 4002 4003 4004 4005
## 732005.4550 337074.9948 1304258.4499 403413.1248 -24389.0300
## 4006 4007 4008 4009 4010
## -121092.8649 -291719.3336 49638.5448 -294826.6853 508909.5458
## 4011 4012 4013 4014 4015
## 313203.3002 122991.0649 23982.7015 -237571.2798 609821.9999
## 4016 4017 4018 4019 4020
## 78793.2198 -133205.5749 -337078.4748 -480385.4140 -140952.5801
## 4021 4022 4023 4024 4025
## 876794.4251 -283769.1250 484260.8606 374471.8905 -16851.1290
## 4026 4027 4028 4029 4030
## 99401.1454 -239050.9000 215739.2754 81103.7750 4612.1753
## 4031 4032 4033 4034 4035
## -114614.4500 -244133.3861 146541.4302 -20825.4800 -46023.3251
## 4036 4037 4038 4039 4040
## 650034.2352 946372.3652 -192361.4552 -73910.6151 -490801.7400
## 4041 4042 4043 4044 4045
## -768554.4790 1295457.5004 1237923.9359 1055879.5603 -253275.1147
## 4046 4047 4048 4049 4050
## 2401234.4911 1017639.7502 -278417.8102 373416.7408 734119.3704
## 4051 4052 4053 4054 4055
## 1745457.5004 280610.9700 817077.4055 607850.7801 724118.1650
## 4056 4057 4058 4059 4060
## 320740.4808 -169514.9248 365358.9394 -79192.3902 257780.0350
## 4061 4062 4063 4064 4065
## -211263.1352 147005.4550 -379826.6853 276230.8750 -89260.7246
## 4066 4067 4068 4069 4070
## 190443.0501 -81642.0249 -293657.6203 -942992.1343 553415.5355
## 4071 4072 4073 4074 4075
## 77694.8998 -255319.4903 172428.7202 342610.9700 240244.0598
## 4076 4077 4078 4079 4080
## -351586.8752 -54121.6451 496512.6501 -367255.9402 10807.6098
## 4081 4082 4083 4084 4085
## -295389.0300 263836.3900 41301.6201 -250670.8050 -95319.4903
## 4086 4087 4088 4089 4090
## -198206.7802 63485.0752 -84332.6750 -210348.7452 -125036.5099
## 4091 4092 4093 4094 4095
## 25527.0402 489893.9504 256246.4705 -127078.4748 531513.8554
## 4096 4097 4098 4099 4100
## 372372.7268 439766.8503 -3275.1147 962005.4550 1011386.7553
## 4101 4102 4103 4104 4105
## 1007921.5252 859836.7516 498203.3002 2049613.3807 822639.7502
## 4106 4107 4108 4109 4110
## 1375247.6758 -10741.5501 5658433.9032 2138908.3404 -163417.8102
## 4111 4112 4113 4114 4115
## -386939.3953 74259.6552 40103.7750 395344.7904 -361939.3953
## 4116 4117 4118 4119 4120
## -264797.9051 -375108.4603 -103241.5501 -160530.5202 330738.0701
## 4121 4122 4123 4124 4125
## -261094.0702 -251219.9650 -126092.8649 -11543.7049 -144050.9000
## 4126 4127 4128 4129 4130
## 488625.3601 -224459.7751 364821.9999 471548.6253 -222995.7503
## 4131 4132 4133 4134 4135
## -287643.2302 653.1760 -174769.2455 -85149.0052 -394472.9598
## 4136 4137 4138 4139 4140
## -135160.7802 252006.6604 -37923.7999 -94600.0599 -124303.7743
## 4141 4142 4143 4144 4145
## -179470.5492 155808.8152 853554.6150 -179966.9701 -232219.9650
## 4146 4147 4148 4149 4150
## -232219.9650 -223981.3602 47991.0649 -16896.2250 -94191.1848
## 4151 4152 4153 4154 4155
## 259752.4602 59893.9504 297921.5252 -80951.3747 371230.8750
## 4156 4157 4158 4159 4160
## 368513.8554 88076.2001 -377995.7503 -283769.1250 -196305.1002
## 4161 4162 4163 4164 4165
## -177571.2798 -293044.9103 -177628.8401 397921.5252 -197572.4851
## 4166 4167 4168 4169 4170
## -274318.2849 -786978.9495 16230.8750 -446755.9402 -373227.1600
## 4171 4172 4173 4174 4175
## -306728.3654 -133825.4800 208469.7209 187357.9751 36272.8400
## 4176 4177 4178 4179 4180
## -286121.6451 -4332.6750 250739.2754 -298023.4457 -305037.7152
## 4181 4182 4183 4184 4185
## -337432.2003 53907.1351 253694.8998 -129867.4449 -17924.4025
## 4186 4187 4188 4189 4190
## -301586.8752 237637.3395 -37839.8700 55976.6749 -33558.0950
## 4191 4192 4193 4194 4195
## -424052.1053 215837.5954 745245.2651 225850.7801 618485.0752
## 4196 4197 4198 4199 4200
## 1754402.3507 688216.4850 16934.7099 -128839.8700 -413910.6151
## 4201 4202 4203 4204 4205
## -199191.1848 -197360.2498 -244297.9051 -112079.1980 -464965.7648
## 4206 4207 4208 4209 4210
## -477895.5018 -529259.5192 -239332.6750 -385881.8350 -355036.5099
## 4211 4212 4213 4214 4215
## -269613.2447 -342360.2498 -36347.0651 739332.8110 -5459.7751
## 4216 4217 4218 4219 4220
## 668907.1351 -271657.6203 -172713.9753 -183136.0352 -409932.2003
## 4221 4222 4223 4224 4225
## -456164.2127 871441.9050 -353841.0754 486019.8451 -275093.7086
## 4226 4227 4228 4229 4230
## 16006.6604 1866938.3260 164893.9504 -207925.0052 86104.9803
## 4231 4232 4233 4234 4235
## -176797.9051 -294403.4201 -250163.6100 -228178.0001 -365600.0599
## 4236 4237 4238 4239 4240
## -179966.9701 -45952.5801 -189361.4552 -659260.7246 -179276.6789
## 4241 4242 4243 4244 4245
## -94330.2643 409893.9504 492584.6005 532783.6510 942993.4756
## 4246 4247 4248 4249 4250
## -645373.4346 -361613.2447 -172430.9949 -329050.9000 -293980.1549
## 4251 4252 4253 4254 4255
## -7276.3200 1617362.7965 -160783.5150 167637.3395 1354530.5932
## 4256 4257 4258 4259 4260
## 2072082.2268 -65178.0001 -256036.2688 -196586.8752 418230.8750
## 4261 4262 4263 4264 4265
## 265385.5500 122639.7502 -313064.0847 -389016.1301 -340318.2849
## 4266 4267 4268 4269 4270
## -401305.1002 72427.5149 -326939.3953 986232.0804 1069048.6253
## 4271 4272 4273 4274 4275
## 1845528.2455 736513.8554 310047.4199 167499.4653 573642.0752
## 4276 4277 4278 4279 4280
## 181019.8451 28909.5458 -128978.9495 499471.8905 -339221.1703
## 4281 4282 4283 4284 4285
## -295150.4252 -440601.2653 -174572.4851 -130812.2952 520740.4808
## 4286 4287 4288 4289 4290
## -347586.8752 154821.9999 504823.2053 530317.2156 -198981.3602
## 4291 4292 4293 4294 4295
## 203908.3404 519614.5860 124258.4499 46794.4251 -291910.6151
## 4296 4297 4298 4299 4300
## 311441.9050 -525668.3944 360682.9204 -295290.7101 318554.6150
## 4301 4302 4303 4304 4305
## -279192.3902 -220305.1002 143696.1052 122711.7006 -292711.5646
## 4306 4307 4308 4309 4310
## 406373.5706 -115318.2849 -163.6100 457217.6903 950979.0855
## 4311 4312 4313 4314 4315
## -11303.8948 -248698.3799 -272643.2302 -414263.1352 -306022.1198
## 4316 4317 4318 4319 4320
## -381234.3551 -106586.8752 363554.6150 50667.3250 352148.1505
## 4321 4322 4323 4324 4325
## 204258.4499 223625.3601 -352219.9650 -264459.7751 -425951.3747
## 4326 4327 4328 4329 4330
## -233234.3551 319682.9204 -265670.8050 150330.4003 249471.8905
## 4331 4332 4333 4334 4335
## 453979.0855 840317.2156 -364861.4552 -209120.4397 169119.3704
## 4336 4337 4338 4339 4340
## 1806230.8750 -189332.6750 113821.9999 -227149.2199 -253205.5749
## 4341 4342 4343 4344 4345
## -434261.9299 -173234.3551 -378805.1002 -321234.3551 -313910.6151
## 4346 4347 4348 4349 4350
## -207176.7947 475385.5500 -203488.5553 -64459.7751 998204.5056
## 4351 4352 4353 4354 4355
## -176094.0702 1574259.6552 -151094.0702 129047.4199 -196797.9051
## 4356 4357 4358 4359 4360
## -232643.2302 -113206.7802 -168628.8401 136511.4447 214118.1650
## 4361 4362 4363 4364 4365
## 125399.9401 -78100.0599 -199543.7049 -11303.8948 -82360.2498
## 4366 4367 4368 4369 4370
## 44540.2249 -175459.7751 100456.2951 -381868.6502 -372994.5450
## 4371 4372 4373 4374 4375
## -165529.3148 -59896.2250 300524.6295 -580528.1095 -302783.5150
## 4376 4377 4378 4379 4380
## -43396.2250 -163050.9000 -355741.5501 -347219.9650 -225290.7101
## 4381 4382 4383 4384 4385
## -399755.9402 -9475.3705 -25881.8350 325047.4199 285441.9050
## 4386 4387 4388 4389 4390
## -75459.7751 39188.9101 820949.1000 -206868.6502 288258.0883
## 4391 4392 4393 4394 4395
## 147103.7750 1684964.6954 444821.9999 96807.6098 -309614.4500
## 4396 4397 4398 4399 4400
## -161023.3251 1066935.9153 -216164.8153 131580.9845 293694.8998
## 4401 4402 4403 4404 4405
## 895385.5500 -267763.6461 -392078.4748 380089.3849 -313417.8102
## 4406 4407 4408 4409 4410
## 627639.7502 -136058.0950 -301439.3953 -231297.9051 317638.5448
## 4411 4412 4413 4414 4415
## 179991.0649 407934.7099 487780.0350 35949.1000 127357.9751
## 4416 4417 4418 4419 4420
## -241488.5553 -240811.0899 -211218.7597 -405035.3046 -319824.2746
## 4421 4422 4423 4424 4425
## -159178.0001 -265880.6296 -170603.3719 -96445.3850 -315247.5398
## 4426 4427 4428 4429 4430
## -592360.2498 -267769.1250 -622571.2798 -449825.4800 -551162.4046
## 4431 4432 4433 4434 4435
## -480318.3452 -333896.2250 -20741.5501 245457.5004 260456.2951
## 4436 4437 4438 4439 4440
## 804402.3507 360878.3549 355950.3054 676374.7759 167850.7801
## 4441 4442 4443 4444 4445
## -137628.8401 -167176.7947 -143206.7802 322794.4251 310949.1000
## 4446 4447 4448 4449 4450
## -91938.1900 -75036.5099 370878.3549 68907.1351 -211302.6895
## 4451 4452 4453 4454 4455
## -205092.8649 -234600.0599 -287887.8247 -37781.1044 -344192.3902
## 4456 4457 4458 4459 4460
## -320079.6801 -340670.8050 -104472.9598 73063.0154 -500868.6502
## 4461 4462 4463 4464 4465
## -71357.9624 22216.4850 905175.7254 273061.8100 661373.5706
## 4466 4467 4468 4469 4470
## -275136.0352 166230.8750 393698.5158 -353136.0352 -216868.6502
## 4471 4472 4473 4474 4475
## -63767.9196 10174.5200 731795.6304 37991.0649 -39555.2652
## 4476 4477 4478 4479 4480
## -73198.3799 -223347.0651 -381699.5852 -179966.9701 -257430.9949
## 4481 4482 4483 4484 4485
## -72923.7999 307723.6800 -60951.3747 46866.3755 26758.4499
## 4486 4487 4488 4489 4490
## 392357.9751 -392488.5553 -391378.8531 102991.0649 20314.8049
## 4491 4492 4493 4494 4495
## 34681.7151 344991.0649 204892.7450 -326867.4449 -856302.6895
## 4496 4497 4498 4499 4500
## -393347.0651 -215318.2849 -437572.4851 -439261.9299 -448559.3004
## 4501 4502 4503 4504 4505
## -419261.9299 176795.6304 747218.8956 467499.4653 -120740.3448
## 4506 4507 4508 4509 4510
## 94540.2249 50667.3250 -221657.6203 383697.3105 -232360.2498
## 4511 4512 4513 4514 4515
## -153065.2901 -177748.7452 256512.6501 -306305.7028 465245.2651
## 4516 4517 4518 4519 4520
## -73347.0651 -310248.7452 -229544.9103 161316.0102 53132.5551
## 4521 4522 4523 4524 4525
## 378061.8100 405667.3250 -493064.0847 -190951.3747 -585597.6493
## 4526 4527 4528 4529 4530
## -440521.4884 -329078.4748 -266939.3953 -251586.8752 -349685.1951
## 4531 4532 4533 4534 4535
## -273417.8102 8660.1300 -100987.3499 473976.6749 1163696.1052
## 4536 4537 4538 4539 4540
## -166339.8700 -60670.8050 684275.2506 599821.9999 173131.3498
## 4541 4542 4543 4544 4545
## -261092.8649 264541.4302 -43803.8948 -211305.1002 -242079.6801
## 4546 4547 4548 4549 4550
## -206586.8752 -276446.5903 135949.1000 -323769.1250 -269614.4500
## 4551 4552 4553 4554 4555
## -41234.3551 30174.5200 292850.7801 -396585.6699 -422499.3293
## 4556 4557 4558 4559 4560
## 433485.0752 -346585.6699 -92571.2798 -237079.6801 -11459.7751
## 4561 4562 4563 4564 4565
## -349826.6853 -365457.3644 -257713.9753 -614078.4748 -10205.5749
## 4566 4567 4568 4569 4570
## -351657.6203 -270299.0187 -500529.3148 -44332.6750 263625.3601
## 4571 4572 4573 4574 4575
## -363487.3499 84892.7450 -31936.9846 -143769.1250 1275810.0205
## 4576 4577 4578 4579 4580
## -311939.3953 277937.1206 -531428.2254 -425832.6750 -882570.0744
## 4581 4582 4583 4584 4585
## -452360.2498 -133248.7452 -69964.5595 -35657.0176 -281207.2624
## 4586 4587 4588 4589 4590
## -148134.8298 -4896.2250 95976.6749 -776231.9444 -456438.1900
## 4591 4592 4593 4594 4595
## -739823.6720 -465851.8495 -374332.6750 -356769.1250 -130094.0702
## 4596 4597 4598 4599 4600
## 75614.5860 579387.9031 -685944.1797 -206374.6399 -1006018.5038
## 4601 4602 4603 4604 4605
## -503389.0300 -404883.0403 -210107.2550 541867.5809 527920.3199
## 4606 4607 4608 4609 4610
## 848512.6501 -443066.4954 -329389.0300 -441725.9547 -557416.6048
## 4611 4612 4613 4614 4615
## -310248.7452 -510036.5099 -237501.7400 100034.2352 134540.2249
## 4616 4617 4618 4619 4620
## 1774259.6552 -340530.5202 -478106.5318 -158678.0001 -117925.0052
## 4621 4622 4623 4624 4625
## -700028.1095 -103628.8401 -574331.4697 -471516.1301 -485387.8247
## 4626 4627 4628 4629 4630
## -235037.7152 -16769.1250 -251586.8752 67525.8348 -419951.3747
## 4631 4632 4633 4634 4635
## -422219.9650 -568978.9495 -447432.2003 -218909.4098 -979260.7246
## 4636 4637 4638 4639 4640
## -424896.2250 -712077.2695 -397572.4851 -104754.7349 -116303.8948
## 4641 4642 4643 4644 4645
## -360318.2849 130527.0402 215879.5603 775668.5303 -277712.7699
## 4646 4647 4648 4649 4650
## 53132.5551 -342219.9650 -257657.6203 -295572.4851 456.2951
## 4651 4652 4653 4654 4655
## -46710.3593 -235318.2849 -748105.3264 1111302.8255 -143769.1250
## 4656 4657 4658 4659 4660
## -254655.3014 -105100.0599 -496302.6895 -131255.9402 -439374.6399
## 4661 4662 4663 4664 4665
## -19403.4201 -786020.9145 -148452.5801 -379332.6750 -574895.0197
## 4666 4667 4668 4669 4670
## -322221.1703 -222150.4252 -284861.4552 -338770.3303 -802077.2695
## 4671 4672 4673 4674 4675
## -488839.8700 1100456.2951 -560303.8948 -666155.2096 -197638.4088
## 4676 4677 4678 4679 4680
## 569613.3807 -260176.7947 -493487.3499 -95389.0300 -464332.6750
## 4681 4682 4683 4684 4685
## -319023.3251 1403836.9927 -161276.3200 983837.5954 1361794.4251
## 4686 4687 4688 4689 4690
## 129753.6655 197993.4756 1401512.6501 -361373.4346 -362642.0249
## 4691 4692 4693 4694 4695
## -261796.6998 502005.4550 -201795.4944 103838.8007 379330.4003
## 4696 4697 4698 4699 4700
## 336584.6005 -202980.1549 -440387.8247 -330909.4098 -283670.8050
## 4701 4702 4703 4704 4705
## 191230.8750 789541.4302 507500.6707 498554.6150 386441.9050
## 4706 4707 4708 4709 4710
## -252219.9650 -20389.0300 -92572.4851 191443.1103 282920.3199
## 4711 4712 4713 4714 4715
## 48230.8750 -755025.7303 4258.4499 349612.1753 243907.1351
## 4716 4717 4718 4719 4720
## 289541.4302 -683486.1446 -312797.9051 -193980.1549 -250952.5801
## 4721 4722 4723 4724 4725
## -370728.0038 -212290.7101 -207234.3551 -167430.9949 -153980.7576
## 4726 4727 4728 4729 4730
## 216794.4251 20033.0299 320174.5200 -250389.0300 422992.2703
## 4731 4732 4733 4734 4735
## -274050.9000 -124402.2148 -687471.7545 -424078.4748 -420318.2849
## 4736 4737 4738 4739 4740
## -493417.8102 -175656.4149 795952.7160 348625.3601 -231652.7989
## 4741 4742 4743 4744 4745
## 366682.9204 -411163.6100 -127290.7101 46441.9050 -286868.6502
## 4746 4747 4748 4749 4750
## -141104.2601 -267995.7503 -114748.7452 -435881.8350 -363769.1250
## 4751 4752 4753 4754 4755
## -100740.3448 221865.1702 820035.4405 -386303.8948 -170417.4486
## 4756 4757 4758 4759 4760
## -291585.6699 -212783.5150 -508107.2550 712992.2703 604541.4302
## 4761 4762 4763 4764 4765
## 171441.9050 -190178.0001 223651.7296 -635035.3046 -563061.6740
## 4766 4767 4768 4769 4770
## -721654.0043 -129163.6100 -431698.3799 -198648.4077 101329.1950
## 4771 4772 4773 4774 4775
## 3816374.7759 1736022.2558 -135883.0403 -36797.9051 808414.3301
## 4776 4777 4778 4779 4780
## 1024682.9204 256443.1103 -361642.0249 -118487.3499 -628909.4098
## 4781 4782 4783 4784 4785
## -491367.4449 -172360.2498 284681.7151 985176.9307 -337430.9949
## 4786 4787 4788 4789 4790
## 62624.9985 1610.9700 -240037.7152 894288.4354 645247.6758
## 4791 4792 4793 4794 4795
## -392571.2798 -183768.1250 -383896.2250 -206023.4457 693696.1052
## 4796 4797 4798 4799 4800
## -280459.7751 -298260.3630 -735247.5398 -770740.3448 -120670.8050
## 4801 4802 4803 4804 4805
## -134261.9299 994681.7151 3795952.7160 -504162.4046 -413627.6348
## 4806 4807 4808 4809 4810
## -400452.3390 538908.3404 -184332.6750 -375007.4284 -190670.8050
## 4811 4812 4813 4814 4815
## -46444.1797 -31923.7999 -175217.5543 199187.7048 -117880.6296
## 4816 4817 4818 4819 4820
## 248540.2249 -125459.7751 -25458.5698 -360672.0104 -309474.1652
## 4821 4822 4823 4824 4825
## 27570.2104 983413.1248 469119.3704 -164966.9701 345245.2651
## 4826 4827 4828 4829 4830
## 33697.3105 -1810100.0230 -83050.9000 -38769.1250 202569.0051
## 4831 4832 4833 4834 4835
## -156234.3551 55772.8400 -40600.0599 624401.1454 -360234.3551
## 4836 4837 4838 4839 4840
## -110294.5450 -420142.0249 -195812.2952 -306444.1797 93977.8802
## 4841 4842 4843 4844 4845
## -641585.6699 1134823.2053 607921.5252 783711.7006 -382008.9351
## 4846 4847 4848 4849 4850
## -349121.6451 345470.4441 180456.2951 -229261.9299 -185601.2653
## 4851 4852 4853 4854 4855
## -1212426.1736 -497514.9248 -670315.8742 1582.1898 1174963.4901
## 4856 4857 4858 4859 4860
## 368907.1351 -223981.3602 -289657.6203 -193769.1250 -652642.0249
## 4861 4862 4863 4864 4865
## -86023.3251 -741513.7194 98063.0154 -281373.4346 -369965.7648
## 4866 4867 4868 4869 4870
## -273868.6502 642230.8750 -212925.0052 -65150.4252 -351866.2395
## 4871 4872 4873 4874 4875
## -183487.3499 -312994.5450 -634022.1198 -583811.0899 -550389.0300
## 4876 4877 4878 4879 4880
## 159399.9401 169864.4470 -451656.4149 17654.1403 162994.6810
## 4881 4882 4883 4884 4885
## -82779.8990 127920.3199 -282925.0052 -32643.2302 -269543.7049
## 4886 4887 4888 4889 4890
## -191374.6399 -187572.4851 -293698.3799 -1848972.9229 1565529.4508
## 4891 4892 4893 4894 4895
## 257500.6707 404401.1454 -104050.9000 121158.9246 773134.9658
## 4896 4897 4898 4899 4900
## 394543.8409 1198628.9761 332668.5303 940034.2352 -290248.7452
## 4901 4902 4903 4904 4905
## -90318.2849 -348050.9000 1574259.6552 509681.7151 66232.0804
## 4906 4907 4908 4909 4910
## -564603.5212 21427.5149 122710.4953 -233832.6750 381963.6134
## 4911 4912 4913 4914 4915
## -555459.7751 -252925.0052 696724.8853 71863.9648 595103.7750
## 4916 4917 4918 4919 4920
## -356277.5253 2569.0051 -394402.2148 -160416.6048 1049908.3404
## 4921 4922 4923 4924 4925
## 250739.2754 -503487.3499 194076.2001 -162205.5749 438794.4251
## 4926 4927 4928 4929 4930
## -683880.5091 -463486.1446 -345175.5894 -179260.7246 -232360.2498
## 4931 4932 4933 4934 4935
## -95387.8247 666443.1103 385949.1000 424963.4901 -232643.2302
## 4936 4937 4938 4939 4940
## -403837.4594 -258662.4046 -43628.8401 -259361.4552 -477571.2798
## 4941 4942 4943 4944 4945
## -691824.2746 -485176.7947 -261797.9051 -100529.3148 203343.5851
## 4946 4947 4948 4949 4950
## -25951.3747 -298134.8298 -257598.8546 -2522067.6268 94739.2754
## 4951 4952 4953 4954 4955
## -451939.3953 -409544.9103 -404332.6750 -691077.2695 1393923.9359
## 4956 4957 4958 4959 4960
## 1670174.5200 -380036.5099 325668.5303 -248214.0040 -255036.5099
## 4961 4962 4963 4964 4965
## -393697.1745 -472853.0548 -571551.4109 69047.4199 6019473.0958
## 4966 4967 4968 4969 4970
## -344544.9103 33132.5551 1263909.5458 1545600.1959 -234642.0249
## 4971 4972 4973 4974 4975
## -215175.5894 -334614.4500 38977.8802 -686044.0953 -135459.7751
## 4976 4977 4978 4979 4980
## -355150.4252 264821.9999 525878.3549 1540529.4508 -385205.5749
## 4981 4982 4983 4984 4985
## 727783.6510 -386995.7503 -216163.6100 -877288.9021 -15585.6699
## 4986 4987 4988 4989 4990
## -1033625.2241 -576231.9444 160485.0752 -223205.5749 538908.3404
## 4991 4992 4993 4994 4995
## -402897.4304 -331783.5150 -125598.8546 249921.5252 235500.6707
## 4996 4997 4998 4999 5000
## -259233.1497 529907.1351 197921.5252 -135881.8350 -531090.4542
## 5001 5002 5003 5004 5005
## -124050.9000 -187936.2746 -221374.6399 -203205.5749 309660.1300
## 5006 5007 5008 5009 5010
## -113079.7404 -51656.4149 197921.5252 35795.0278 301696.1052
## 5011 5012 5013 5014 5015
## -244052.1053 750317.8182 -116163.6100 -394896.2250 -136727.1600
## 5016 5017 5018 5019 5020
## 259399.9401 480525.8348 21865.1702 245667.3250 595033.0299
## 5021 5022 5023 5024 5025
## 132076.2001 -256374.6399 -766698.1240 -554267.7648 293836.3900
## 5026 5027 5028 5029 5030
## -312044.9103 -171692.3902 -559261.9299 -357994.5450 -385178.0001
## 5031 5032 5033 5034 5035
## -226797.9051 -528769.1250 -150107.2550 -159050.9000 -34797.9051
## 5036 5037 5038 5039 5040
## -489107.2550 -1652242.7185 -637570.0744 137921.5252 -160727.1600
## 5041 5042 5043 5044 5045
## -197993.3396 -1700100.0230 -449542.4996 -112994.5450 -54263.1352
## 5046 5047 5048 5049 5050
## -338277.5253 6512.6501 77216.4850 -664288.2994 2026935.9153
## 5051 5052 5053 5054 5055
## -470458.5698 882498.2600 205738.0701 -423909.4098 -64332.6750
## 5056 5057 5058 5059 5060
## 256569.0051 -232361.4552 1422781.2403 831374.7759 485807.6098
## 5061 5062 5063 5064 5065
## 149259.6552 295160.1300 -98302.6895 492780.0350 173976.6749
## 5066 5067 5068 5069 5070
## -1292917.7732 459893.9504 -575148.0146 -187712.7699 -165923.7999
## 5071 5072 5073 5074 5075
## -83769.1250 -136727.1600 -496161.1993 102934.7099 237427.5149
## 5076 5077 5078 5079 5080
## -673176.7947 -736233.1497 -320951.3747 -454880.6296 -158909.4098
## 5081 5082 5083 5084 5085
## -24156.4149 -432922.5945 559893.9504 -364755.9402 -156303.8948
## 5086 5087 5088 5089 5090
## -231234.3551 -66868.6502 -408011.4033 -377121.6451 -136092.8649
## 5091 5092 5093 5094 5095
## -774188.7741 -334824.2746 -702570.0744 -846066.0996 380103.7750
## 5096 5097 5098 5099 5100
## -144966.9701 836.3900 1118063.0154 788934.7099 -611655.2096
## 5101 5102 5103 5104 5105
## -8769.1250 -487289.5047 -601233.1497 -365790.7101 1689474.3012
## 5106 5107 5108 5109 5110
## -208205.5749 -430008.9351 -748345.8597 -492670.8050 -456479.5522
## 5111 5112 5113 5114 5115
## -416854.2601 -390953.5443 -260951.3747 -391374.6399 228061.8100
## 5116 5117 5118 5119 5120
## -142430.9949 695668.5303 234399.9401 303272.8400 -292219.9650
## 5121 5122 5123 5124 5125
## -259966.9701 -226441.7690 -287359.0445 -187936.2746 -238417.8102
## 5126 5127 5128 5129 5130
## 5107.3910 245949.1000 197921.5252 -117572.4851 -26023.3251
## 5131 5132 5133 5134 5135
## 107216.4850 -150248.7452 197104.3776 -212538.4645 -117571.2798
## 5136 5137 5138 5139 5140
## -399091.6596 -227783.5150 -477150.4252 -105100.0599 -767780.6222
## 5141 5142 5143 5144 5145
## -210107.2550 -423486.1446 -602993.3396 340598.9906 -257640.8195
## 5146 5147 5148 5149 5150
## -515317.0796 361585.8058 -243625.2241 107220.1010 -391923.7999
## 5151 5152 5153 5154 5155
## 214963.4901 89541.4302 -403625.2241 -533343.4491 218236.8648
## 5156 5157 5158 5159 5160
## 868288.1943 -208275.8379 -155390.2353 493660.1300 958981.4962
## 5161 5162 5163 5164 5165
## -239121.6451 -490584.4645 564610.9700 -411374.6399 52780.0350
## 5166 5167 5168 5169 5170
## -348981.3602 380597.7852 98230.8750 -85248.7452 -192474.1652
## 5171 5172 5173 5174 5175
## -81837.0402 209752.4602 877357.9751 574681.7151 -361585.6699
## 5176 5177 5178 5179 5180
## 435389.1660 -358699.5852 384808.8152 -287074.8588 142570.2104
## 5181 5182 5183 5184 5185
## -553387.8247 1583.3952 447595.6304 451654.1403 268131.3498
## 5186 5187 5188 5189 5190
## -435389.0300 -356261.9299 -68558.0950 772501.8760 235879.5603
## 5191 5192 5193 5194 5195
## -255601.2653 147357.9751 -287150.4252 -232148.0146 -659823.0693
## 5196 5197 5198 5199 5200
## 680210.4953 -686542.4996 555696.1052 -274754.7349 10077.3330
## 5201 5202 5203 5204 5205
## 950174.5200 1025922.7305 2385955.1267 50343.5851 280879.5603
## 5206 5207 5208 5209 5210
## -663838.6647 500772.8400 -260812.2952 -280234.3551 192780.0350
## 5211 5212 5213 5214 5215
## -474038.9145 16794.4251 614258.4499 -79332.6750 308976.6749
## 5216 5217 5218 5219 5220
## 81863.9648 -634627.6348 -801148.0146 -581374.6399 -780669.5997
## 5221 5222 5223 5224 5225
## -236305.1002 -488740.3448 -307500.5347 -278909.4098 -728697.1745
## 5226 5227 5228 5229 5230
## -347921.3892 -199529.3148 425743.7297 286865.1702 60739.2754
## 5231 5232 5233 5234 5235
## -817705.5379 -245072.4851 -499471.7545 -65670.8050 -534401.0094
## 5236 5237 5238 5239 5240
## 52314.8049 438061.8100 159330.4003 -471938.1900 -430487.3499
## 5241 5242 5243 5244 5245
## -483434.0658 -584683.9898 1055385.5500 -208980.1549 -46501.7400
## 5246 5247 5248 5249 5250
## -315558.8182 -197993.3396 -262642.0249 -95234.3551 -366769.1250
## 5251 5252 5253 5254 5255
## 156089.3849 -394685.1951 -118417.8102 -268205.5749 -115290.7101
## 5256 5257 5258 5259 5260
## 359485.0752 191160.1300 25034.2352 -244965.7648 -443805.1002
## 5261 5262 5263 5264 5265
## -191909.4098 -233225.9547 -330529.3148 -845315.8742 -347853.0548
## 5266 5267 5268 5269 5270
## 1250739.2754 1532288.4354 757667.3250 1807909.5458 -51128.8401
## 5271 5272 5273 5274 5275
## -266713.9753 -294474.1652 -194501.7400 -75318.8876 -248558.0950
## 5276 5277 5278 5279 5280
## -362836.7992 -360389.0300 549188.9101 -606486.1446 -680070.0744
## 5281 5282 5283 5284 5285
## -657007.7297 -565529.3148 -453627.6348 -548525.4317 192125.3601
## 5286 5287 5288 5289 5290
## 514892.7450 506372.3652 -274959.7751 -234683.9898 -331375.8453
## 5291 5292 5293 5294 5295
## -107501.7400 1065217.6903 -463343.4491 -664895.0197 -400695.9692
## 5296 5297 5298 5299 5300
## -387712.7699 -654514.9248 -490642.0249 -333769.1250 633414.3301
## 5301 5302 5303 5304 5305
## 115667.3250 -327572.4851 -427290.7101 -469079.6801 -129685.1951
## 5306 5307 5308 5309 5310
## -700047.9496 -750634.8298 -569825.4800 288274.0453 628203.3002
## 5311 5312 5313 5314 5315
## -170459.7751 -178910.6151 -169332.6750 -124332.6750 -154754.7349
## 5316 5317 5318 5319 5320
## -130445.3850 -713625.2241 244682.9204 -340248.7452 -293205.5749
## 5321 5322 5323 5324 5325
## -284895.9840 -257642.0249 359131.3498 582.1898 194752.4602
## 5326 5327 5328 5329 5330
## 508512.6501 -179163.6100 -174303.8948 447146.9452 286230.8750
## 5331 5332 5333 5334 5335
## -82887.8247 332639.7502 -210303.8948 -231994.5450 -320417.8102
## 5336 5337 5338 5339 5340
## 410385.5500 -164896.2250 -147741.5501 80173.3147 42709.2899
## 5341 5342 5343 5344 5345
## 95738.0701 -73049.6946 -207711.5646 -212466.9701 -337783.5150
## 5346 5347 5348 5349 5350
## -455247.5398 -186867.4449 -234685.1951 -342446.5903 487371.1599
## 5351 5352 5353 5354 5355
## -177586.8752 -246584.4645 -73910.6151 -338627.6348 -39403.4201
## 5356 5357 5358 5359 5360
## 58765.6449 1407782.4457 -280108.4603 -226023.3251 -582680.3738
## 5361 5362 5363 5364 5365
## -282925.0052 -586796.6998 -221373.4346 -206163.6100 -355712.7699
## 5366 5367 5368 5369 5370
## 943368.5739 801230.8750 -82006.5244 -200389.0300 -41586.8752
## 5371 5372 5373 5374 5375
## 359540.2249 -664754.7349 -292712.7699 -236022.1198 -372360.2498
## 5376 5377 5378 5379 5380
## -386163.6100 -386769.1250 -209403.4201 59734.3966 14878.1741
## 5381 5382 5383 5384 5385
## -1374680.3738 -116523.3251 -443909.4098 -224332.6750 -152324.2746
## 5386 5387 5388 5389 5390
## -262643.2302 -375037.7152 -978694.7639 -1102496.9187 -242432.2003
## 5391 5392 5393 5394 5395
## 279625.3601 -252149.2199 -479260.7246 -147332.6750 -212361.4552
## 5396 5397 5398 5399 5400
## -248910.6151 418766.8503 -404530.5202 -547642.0249 239401.1454
## 5401 5402 5403 5404 5405
## 128160.1300 70175.7254 -53867.6859 -382221.1703 -178839.8700
## 5406 5407 5408 5409 5410
## -319825.4800 87357.9751 64120.5757 -81276.8021 -95741.5501
## 5411 5412 5413 5414 5415
## -401995.7503 -214464.1652 -139964.5595 -688799.8309 -646020.9145
## 5416 5417 5418 5419 5420
## -668035.3046 -81374.6399 -164614.4500 -28896.2250 -326939.3953
## 5421 5422 5423 5424 5425
## 246188.9101 -434260.7246 -302642.0249 -199614.4500 -289682.7844
## 5426 5427 5428 5429 5430
## -369260.7246 -537191.1848 -392923.7999 -232980.1549 166557.0257
## 5431 5432 5433 5434 5435
## 10739.2754 388485.0752 -274896.2250 245245.2651 47499.4653
## 5436 5437 5438 5439 5440
## -281445.3850 -249052.1053 -631796.6998 -495283.5150 169724.8853
## 5441 5442 5443 5444 5445
## -390754.7349 -16305.1002 -11797.9051 -255657.6203 -556796.6998
## 5446 5447 5448 5449 5450
## -165881.8350 -392514.9248 -400390.2353 -354052.1053 -313192.3902
## 5451 5452 5453 5454 5455
## 102005.4550 -133910.6151 -386586.8752 -225952.5801 -224247.5398
## 5456 5457 5458 5459 5460
## -1019821.8639 -256656.4149 -353276.3200 -129952.5801 -497008.9351
## 5461 5462 5463 5464 5465
## -248770.3303 -182529.8102 -1372210.3223 345316.0102 713979.0855
## 5466 5467 5468 5469 5470
## 359892.7450 -321508.9351 -419754.7349 -284896.2250 -199613.2447
## 5471 5472 5473 5474 5475
## -323205.5749 -357150.4252 453836.3900 -273269.1250 -160783.5150
## 5476 5477 5478 5479 5480
## -334163.6100 -365318.2849 -454121.6451 218203.3002 -439121.6451
## 5481 5482 5483 5484 5485
## -512219.9650 -725598.8546 -602381.8350 -154474.1652 -193372.0866
## 5486 5487 5488 5489 5490
## -440458.5698 -454049.6946 -318705.5749 -650669.5997 -393656.4149
## 5491 5492 5493 5494 5495
## -423318.2849 -444867.4449 -406514.9248 160034.2352 -360585.9109
## 5496 5497 5498 5499 5500
## -344892.6090 197598.9906 736090.5902 264402.3507 -100178.0001
## 5501 5502 5503 5504 5505
## -165797.9051 -72472.9598 -5951.3747 -203416.6048 -316247.5398
## 5506 5507 5508 5509 5510
## -309728.3654 561302.8255 834471.8905 -191795.4944 -407981.3602
## 5511 5512 5513 5514 5515
## -8061.6740 -252178.0001 125949.1000 -323824.2746 -518133.6245
## 5516 5517 5518 5519 5520
## -950103.6390 -526866.2395 669188.9101 -593486.1446 -944821.8639
## 5521 5522 5523 5524 5525
## -488839.8700 -602042.4996 -155037.7152 -59579.6801 493140.9555
## 5526 5527 5528 5529 5530
## -105262.4120 -502627.6348 -299234.3551 -259432.2003 -215629.5633
## 5531 5532 5533 5534 5535
## -131234.3551 -747289.5047 -546198.3799 -117776.3200 -373614.4500
## 5536 5537 5538 5539 5540
## -470670.8050 276584.6005 -98162.4046 -435783.5150 -355107.2550
## 5541 5542 5543 5544 5545
## -417149.2199 -482642.0249 -249333.8803 103.7750 -587980.1549
## 5546 5547 5548 5549 5550
## -668484.9393 -547627.6348 -256091.6596 -545472.9598 -420896.2250
## 5551 5552 5553 5554 5555
## -195459.7751 -260812.2952 -522501.7400 -301657.6203 -630151.6881
## 5556 5557 5558 5559 5560
## 285456.2951 611794.4251 193907.1351 -264092.8649 -413937.1052
## 5561 5562 5563 5564 5565
## 14694.8998 260175.7254 881929.9256 1005528.2455 219893.9504
## 5566 5567 5568 5569 5570
## -19260.7246 206233.2857 100456.2951 104541.4302 -402218.7597
## 5571 5572 5573 5574 5575
## 1705673.3517 1009330.4003 455668.5303 -38558.0950 -272896.2250
## 5576 5577 5578 5579 5580
## 440596.5799 -20104.8443 -21498.1240 -424965.7648 -298205.5749
## 5581 5582 5583 5584 5585
## -360459.7751 -700905.7938 106513.8554 1129965.9008 -851230.7391
## 5586 5587 5588 5589 5590
## -537747.5398 720386.7553 -32149.2199 -59824.2746 -1734309.8476
## 5591 5592 5593 5594 5595
## 360878.3549 -640746.3345 -187150.4252 -761866.2395 -771020.9145
## 5596 5597 5598 5599 5600
## -636895.0197 -425514.9248 -372078.4748 -249318.2849 491161.3353
## 5601 5602 5603 5604 5605
## -453558.0950 -227923.7999 -897217.5543 -176330.2643 426652.9349
## 5606 5607 5608 5609 5610
## -458387.8247 -119261.9299 1978274.0453 -282361.4552 715880.7656
## 5611 5612 5613 5614 5615
## -112918.9785 405808.8152 -202150.4252 737005.4550 299329.1950
## 5616 5617 5618 5619 5620
## -300037.7152 -308206.1776 -646513.7194 -417867.4449 1343559.4363
## 5621 5622 5623 5624 5625
## -383770.3303 648838.8007 -2628.8401 690046.2146 -359614.4500
## 5626 5627 5628 5629 5630
## -261092.8649 -171178.0001 -358064.0847 317850.7801 -275883.0403
## 5631 5632 5633 5634 5635
## 886442.0858 488554.6150 748766.8503 426301.6201 -210601.2653
## 5636 5637 5638 5639 5640
## -166416.6048 -328699.5852 661230.8750 -616725.9547 389048.6253
## 5641 5642 5643 5644 5645
## -607851.8495 -331234.3551 233343.5851 545949.1000 46892.7450
## 5646 5647 5648 5649 5650
## -76445.3850 -279685.1951 346088.1795 -757078.4748 -242678.0001
## 5651 5652 5653 5654 5655
## -311965.7648 -331346.3419 2427360.3858 678061.8100 657640.9555
## 5656 5657 5658 5659 5660
## 1177077.4055 1555667.3250 -115035.3046 -295531.4214 310878.3549
## 5661 5662 5663 5664 5665
## -738697.1745 433909.5458 -748133.6245 158414.3301 94543.8409
## 5666 5667 5668 5669 5670
## 377637.3395 347757.2815 -280191.5464 -96866.2395 -154037.7152
## 5671 5672 5673 5674 5675
## -353488.5553 -198134.8298 -391059.3004 -391059.3004 -145824.2746
## 5676 5677 5678 5679 5680
## -720106.0496 -54192.3902 1517146.9452 345103.7750 -307713.9753
## 5681 5682 5683 5684 5685
## 2604965.9008 -192136.0352 85357.9751 34047.4199 -469825.4800
## 5686 5687 5688 5689 5690
## -374683.9898 -335879.4243 -235036.5099 -168697.1745 -236022.1198
## 5691 5692 5693 5694 5695
## 922709.2899 -668345.8597 409610.9700 -297713.9753 -231501.7400
## 5696 5697 5698 5699 5700
## 458485.0752 89474.3012 18909.5458 -323205.5749 -266234.3551
## 5701 5702 5703 5704 5705
## 670881.9709 -664120.4397 -577571.2798 35879.5603 -77709.1539
## 5706 5707 5708 5709 5710
## -86442.9743 -317712.7699 655386.7553 314963.4901 -287711.5646
## 5711 5712 5713 5714 5715
## -453839.8700 -548487.3499 252794.4251 7597.7852 -345175.5894
## 5716 5717 5718 5719 5720
## -716444.1797 -62613.2447 -61797.9051 -285387.8247 -208205.5749
## 5721 5722 5723 5724 5725
## -406072.4851 -332289.5047 -408410.6151 298569.0051 396794.4251
## 5726 5727 5728 5729 5730
## -352289.5047 -219345.8597 991302.8255 -332191.1848 180878.3549
## 5731 5732 5733 5734 5735
## -1007343.4491 -269754.7349 -566161.1993 1398204.5056 -358559.3004
## 5736 5737 5738 5739 5740
## -302847.0651 -502627.6348 -398712.2952 113837.5954 -115636.0352
## 5741 5742 5743 5744 5745
## -377502.9454 20807.6098 -360529.3148 655104.9803 -348699.5852
## 5746 5747 5748 5749 5750
## -386234.3551 -505339.8700 -358544.9103 -146022.1198 -12783.5150
## 5751 5752 5753 5754 5755
## -326939.3953 -650107.2550 -321769.1250 -553909.4098 -438106.0496
## 5756 5757 5758 5759 5760
## -302078.4748 -370331.4697 -327993.3396 -63994.5450 472005.4550
## 5761 5762 5763 5764 5765
## -363570.0744 -536233.1497 -521796.6998 -381374.6399 -898525.6988
## 5766 5767 5768 5769 5770
## -379332.6750 -252537.7152 118626.5654 -865864.3242 -244191.1848
## 5771 5772 5773 5774 5775
## -245319.4903 -403417.8102 62441.9050 -330598.8546 50427.9970
## 5776 5777 5778 5779 5780
## -489600.0599 -398345.8597 -490727.1600 -274192.3902 51160.1300
## 5781 5782 5783 5784 5785
## -115127.2129 -237079.6801 -377007.7297 -127205.5749 170174.5200
## 5786 5787 5788 5789 5790
## 157639.1475 -301023.3251 -282501.7400 -226305.1002 -485522.4814
## 5791 5792 5793 5794 5795
## -586373.4346 -519965.7648 -142642.0249 -463484.9393 -214754.7349
## 5796 5797 5798 5799 5800
## -409332.6750 163272.8400 -452149.2199 -37994.5450 -270670.8050
## 5801 5802 5803 5804 5805
## -325149.2199 -437290.7101 -428276.3200 -495318.2849 -476656.4149
## 5806 5807 5808 5809 5810
## -308883.0403 -631994.5450 -644529.3148 -227987.3499 -305092.8649
## 5811 5812 5813 5814 5815
## -285600.0599 -309683.9898 318977.8802 -5389.0300 167897.5664
## 5816 5817 5818 5819 5820
## 163955.3020 -63205.5749 -94811.0899 -382712.7699 -144191.1848
## 5821 5822 5823 5824 5825
## -178544.9103 307956.2951 41879.5603 338344.7904 158343.5851
## 5826 5827 5828 5829 5830
## -2256367.4079 162850.7801 -353822.4851 -1914607.2180 -635824.3952
## 5831 5832 5833 5834 5835
## -561824.2746 -318136.0352 -11050.9000 -361966.9701 -344754.7349
## 5836 5837 5838 5839 5840
## -280643.2302 -61516.1301 -147572.4851 -339472.9598 -457500.5347
## 5841 5842 5843 5844 5845
## -588740.3448 -542558.0950 -476120.1384 -412951.3747 1525426.4931
## 5846 5847 5848 5849 5850
## -682149.2199 -132417.8102 -432923.7999 -473205.5749 -424332.6750
## 5851 5852 5853 5854 5855
## -304755.9402 -147430.9949 -958934.5740 160174.5200 -439171.4077
## 5856 5857 5858 5859 5860
## 230265.6449 -68909.4098 -168530.5202 -216923.7999 -242008.9351
## 5861 5862 5863 5864 5865
## -462994.5450 -621163.6100 -327149.2199 -270529.3148 -390668.3944
## 5866 5867 5868 5869 5870
## 707499.4653 -591796.6998 -9156.4149 151583.3952 -10669.5997
## 5871 5872 5873 5874 5875
## 633132.5551 -312501.7400 -193205.5749 -281303.8948 -394896.2250
## 5876 5877 5878 5879 5880
## -272981.3602 -164261.9299 63061.8100 332146.9452 545524.6295
## 5881 5882 5883 5884 5885
## -147853.0548 -166727.1600 -365176.7947 856233.2857 290458.7057
## 5886 5887 5888 5889 5890
## -802781.1044 538908.3404 -38253.8021 -396305.1002 248063.0154
## 5891 5892 5893 5894 5895
## -42727.1600 -490811.0899 -454896.2250 187498.2600 201160.1300
## 5896 5897 5898 5899 5900
## 340880.7656 -313270.3303 -568428.5842 -53685.1951 14963.4901
## 5901 5902 5903 5904 5905
## -247572.4851 -281670.8050 -127007.7297 -304332.6750 210527.0402
## 5906 5907 5908 5909 5910
## 198765.6449 -632606.0496 -602078.4748 -635458.5698 -659436.9846
## 5911 5912 5913 5914 5915
## -413360.2498 -349049.6946 -423163.7305 171584.6005 -171712.7699
## 5916 5917 5918 5919 5920
## 73908.3404 -329861.4552 147849.5748 -196670.8050 813766.8503
## 5921 5922 5923 5924 5925
## 228061.8100 -168417.8102 425034.2352 -82783.5150 -235881.8350
## 5926 5927 5928 5929 5930
## -514332.6750 -28558.0950 -322922.5945 -20600.4215 50892.7450
## 5931 5932 5933 5934 5935
## -175037.7152 -278917.8102 -327769.1250 72034.2352 456.2951
## 5936 5937 5938 5939 5940
## -810204.3696 -252782.3097 -363417.8102 -392627.6348 -354896.2250
## 5941 5942 5943 5944 5945
## 346301.6201 50112.1753 -268261.9299 -1811012.4771 -741231.9444
## 5946 5947 5948 5949 5950
## -420389.0300 -668978.9495 -314586.8752 -76163.6100 -132853.0548
## 5951 5952 5953 5954 5955
## -345347.0651 -247176.7947 -274459.7751 -367107.3755 -704585.6699
## 5956 5957 5958 5959 5960
## -360670.8050 -465783.5150 -199524.4990 64610.9700 -393516.1301
## 5961 5962 5963 5964 5965
## -391092.8649 -461234.3551 -638050.9000 -294261.9299 67540.9481
## 5966 5967 5968 5969 5970
## -254951.3747 -365432.2003 -367164.8153 -222910.6151 -276092.8649
## 5971 5972 5973 5974 5975
## 339637.3395 -105170.8050 -19036.1483 -23345.8597 -209418.8320
## 5976 5977 5978 5979 5980
## -388910.6151 -373205.5749 -254544.9103 382780.0350 -78837.4594
## 5981 5982 5983 5984 5985
## -1050125.2241 -348755.5786 -278783.8766 -368276.3200 -394615.6554
## 5986 5987 5988 5989 5990
## -280221.1703 -175108.4603 47498.2600 -446868.6502 -342607.2550
## 5991 5992 5993 5994 5995
## -217886.6193 -292657.6203 600914.3301 -129192.3902 -199860.2498
## 5996 5997 5998 5999 6000
## -239402.2148 647512.6501 -69965.7648 -96444.1797 -475881.8350
## 6001 6002 6003 6004 6005
## -260108.4603 -298981.3602 304963.4901 -224614.4500 -343770.3303
## 6006 6007 6008 6009 6010
## -20106.0496 -511374.6399 -451121.6451 -576697.6567 -2010.1404
## 6011 6012 6013 6014 6015
## -385740.3448 -662240.3448 -583909.4098 -703402.2148 -625458.5698
## 6016 6017 6018 6019 6020
## -449825.4800 -810379.4243 -572472.9598 -242006.5244 -233050.9000
## 6021 6022 6023 6024 6025
## -316994.5450 -356712.7699 153836.3900 -106797.9051 -130219.9650
## 6026 6027 6028 6029 6030
## 8174.5200 -436585.6699 -92248.2630 -254050.9000 -502178.0001
## 6031 6032 6033 6034 6035
## -631191.1848 -535712.7699 -638204.3696 -372572.4851 -580247.5398
## 6036 6037 6038 6039 6040
## -98276.3200 259048.6253 -602596.2659 -97571.8824 297034.2352
## 6041 6042 6043 6044 6045
## -487711.5646 -452430.9949 -364332.6750 -285783.5150 221021.0505
## 6046 6047 6048 6049 6050
## 3297524.6295 633203.3002 -275234.3551 226443.1103 205245.2651
## 6051 6052 6053 6054 6055
## -288839.8700 -202361.4552 -230741.5501 255524.6295 -99332.6750
## 6056 6057 6058 6059 6060
## -258050.9000 -799880.6296 -136586.8752 -202079.6801 -186403.4201
## 6061 6062 6063 6064 6065
## -194883.0403 -171586.8752 217498.2600 -239472.9598 -540951.3747
## 6066 6067 6068 6069 6070
## 146372.3652 1102148.1505 86324.6295 186949.1000 -555951.3747
## 6071 6072 6073 6074 6075
## -448558.0950 -87571.2798 -633337.4594 113416.7408 -171925.0052
## 6076 6077 6078 6079 6080
## 238766.8503 102934.7099 -71360.2498 -240529.3148 -327854.2601
## 6081 6082 6083 6084 6085
## -712060.7125 -550389.0300 -598134.8298 396794.4251 488061.8100
## 6086 6087 6088 6089 6090
## -395741.5501 -38847.0651 -414753.5295 103976.6749 -145459.7751
## 6091 6092 6093 6094 6095
## 86723.6800 -111023.3251 -178082.4497 -385318.2849 -284107.2550
## 6096 6097 6098 6099 6100
## -641260.7246 -523205.5749 -530247.5398 -461050.9000 847780.0350
## 6101 6102 6103 6104 6105
## -288402.2148 -318556.8897 -377150.4252 -658697.1745 -350670.8050
## 6106 6107 6108 6109 6110
## -610597.6493 -364192.3902 440524.6295 -222923.7999 -240670.8050
## 6111 6112 6113 6114 6115
## -407007.7297 -359824.2746 -207923.7999 196512.6501 -190387.8247
## 6116 6117 6118 6119 6120
## -32218.7597 245103.7750 -763727.2695 -759260.7246 812712.9059
## 6121 6122 6123 6124 6125
## -636020.9145 -447500.5347 385738.0701 1416022.2558 -191445.3850
## 6126 6127 6128 6129 6130
## -652149.2199 -460896.2250 -475261.9299 -3613396.1511 -345318.2849
## 6131 6132 6133 6134 6135
## -285022.1198 -576445.3850 -398839.8700 -280741.5501 -614543.7049
## 6136 6137 6138 6139 6140
## -595390.0833 -615486.1446 -416585.6699 100739.2754 -287769.1250
## 6141 6142 6143 6144 6145
## 370963.4901 8028061.8100 -172064.0847 -234755.9402 -18558.0950
## 6146 6147 6148 6149 6150
## -392995.7503 -267685.1951 -375529.3148 369541.4302 -225980.1549
## 6151 6152 6153 6154 6155
## -281023.3251 99330.4003 -55035.3046 -389.0300 -829119.2344
## 6156 6157 6158 6159 6160
## 916194.8998 177851.9854 -311769.1250 -352869.0118 506934.7099
## 6161 6162 6163 6164 6165
## -200481.3602 -653909.4098 -584472.9598 222711.7006 73766.8503
## 6166 6167 6168 6169 6170
## -271514.9248 -415317.0796 178131.3498 -312923.7999 27780.0350
## 6171 6172 6173 6174 6175
## -192925.0052 -233910.6151 -592219.9650 -552149.2199 -607078.4748
## 6176 6177 6178 6179 6180
## -263529.7970 -144896.2250 -360832.6750 -840457.3644 202076.2001
## 6181 6182 6183 6184 6185
## 562711.7006 -411136.0352 -171642.0249 -360381.8350 -472074.2616
## 6186 6187 6188 6189 6190
## -206161.1993 -800175.5894 -698451.3747 -656811.0899 -730654.0043
## 6191 6192 6193 6194 6195
## -573556.8897 -497134.8298 85949.1000 -266083.2332 -193460.2572
## 6196
## 407362.1938plot(mhd$Price, res, ylab = 'Residual', xlab = 'Sales Price', pch = 16,
main = "Residuals for Price vs. Building Area")
abline(0, 0, lwd = 2) 
Answers to Question 7
The coefficients are displayed in the output. The intercept is 510,531.73; the slope is 3,943.64. The linear model is thus y = 510531.73 + 3943.64*the building area of a given property.
The model is statistically significant, w/ the same low p-values seen in the ANOVA runs. The F value is high, 2427, and its p-value is very low also. The residuals are random and normal.
Given the R^2 value, the model explains about 28% of the value of the properties. A more informative model would explain more of the value of the properties. 28% does not appear to be particularly informative.
### Analysis of Single-Family Housing sales prices in Melbourne in 2017
res <- model.matrix(~CouncilArea, data = type_h)
head(res[, -1])## CouncilAreaBayside CouncilAreaBoroondara CouncilAreaBrimbank
## 1 0 0 0
## 2 0 0 0
## 3 0 0 0
## 4 0 0 0
## 5 0 0 0
## 6 0 0 0
## CouncilAreaCardinia CouncilAreaCasey CouncilAreaDarebin CouncilAreaFrankston
## 1 0 0 0 0
## 2 0 0 0 0
## 3 0 0 0 0
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## CouncilAreaGlen Eira CouncilAreaGreater Dandenong CouncilAreaHobsons Bay
## 1 0 0 0
## 2 0 0 0
## 3 0 0 0
## 4 0 0 0
## 5 0 0 0
## 6 0 0 0
## CouncilAreaHume CouncilAreaKingston CouncilAreaKnox CouncilAreaMacedon Ranges
## 1 0 0 0 0
## 2 0 0 0 0
## 3 0 0 0 0
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## CouncilAreaManningham CouncilAreaMaribyrnong CouncilAreaMaroondah
## 1 0 0 0
## 2 0 0 0
## 3 0 0 0
## 4 0 0 0
## 5 0 0 0
## 6 0 0 0
## CouncilAreaMelbourne CouncilAreaMelton CouncilAreaMonash
## 1 0 0 0
## 2 0 0 0
## 3 0 0 0
## 4 0 0 0
## 5 0 0 0
## 6 0 0 0
## CouncilAreaMoonee Valley CouncilAreaMoreland CouncilAreaNillumbik
## 1 0 0 0
## 2 0 0 0
## 3 0 0 0
## 4 0 0 0
## 5 0 0 0
## 6 0 0 0
## CouncilAreaPort Phillip CouncilAreaStonnington CouncilAreaWhitehorse
## 1 0 0 0
## 2 0 0 0
## 3 0 0 0
## 4 0 0 0
## 5 0 0 0
## 6 0 0 0
## CouncilAreaWhittlesea CouncilAreaWyndham CouncilAreaYarra
## 1 0 0 1
## 2 0 0 1
## 3 0 0 1
## 4 0 0 1
## 5 0 0 1
## 6 0 0 1
## CouncilAreaYarra Ranges
## 1 0
## 2 0
## 3 0
## 4 0
## 5 0
## 6 0lin_model <- lm(formula = Price ~ BuildingArea+Bathroom+Bedroom2+Distance+Landsize+Car+CouncilArea, data = type_h)
lin_model##
## Call:
## lm(formula = Price ~ BuildingArea + Bathroom + Bedroom2 + Distance +
## Landsize + Car + CouncilArea, data = type_h)
##
## Coefficients:
## (Intercept) BuildingArea
## 640832.6 1216.6
## Bathroom Bedroom2
## 162452.5 98229.2
## Distance Landsize
## -56910.5 361.5
## Car CouncilAreaBayside
## 35348.8 808920.2
## CouncilAreaBoroondara CouncilAreaBrimbank
## 715462.1 -218923.3
## CouncilAreaCardinia CouncilAreaCasey
## 1044635.5 682936.8
## CouncilAreaDarebin CouncilAreaFrankston
## -40716.1 988461.4
## CouncilAreaGlen Eira CouncilAreaGreater Dandenong
## 350140.0 444535.1
## CouncilAreaHobsons Bay CouncilAreaHume
## 11329.0 -41344.0
## CouncilAreaKingston CouncilAreaKnox
## 343871.5 261234.1
## CouncilAreaMacedon Ranges CouncilAreaManningham
## 1361724.2 161673.3
## CouncilAreaMaribyrnong CouncilAreaMaroondah
## -152742.5 391388.8
## CouncilAreaMelbourne CouncilAreaMelton
## 165836.8 62314.9
## CouncilAreaMonash CouncilAreaMoonee Valley
## 379342.7 -26474.4
## CouncilAreaMoreland CouncilAreaNillumbik
## -137881.3 6956.6
## CouncilAreaPort Phillip CouncilAreaStonnington
## 548796.4 830208.9
## CouncilAreaWhitehorse CouncilAreaWhittlesea
## 429494.8 -31225.7
## CouncilAreaWyndham CouncilAreaYarra
## -214204.5 155534.8
## CouncilAreaYarra Ranges
## 508307.1summary(lin_model)##
## Call:
## lm(formula = Price ~ BuildingArea + Bathroom + Bedroom2 + Distance +
## Landsize + Car + CouncilArea, data = type_h)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3948228 -209442 -25898 150811 8145942
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 640832.60 49333.51 12.990 < 0.0000000000000002
## BuildingArea 1216.64 87.35 13.928 < 0.0000000000000002
## Bathroom 162452.53 12144.75 13.376 < 0.0000000000000002
## Bedroom2 98229.20 10879.85 9.029 < 0.0000000000000002
## Distance -56910.55 2756.49 -20.646 < 0.0000000000000002
## Landsize 361.51 25.11 14.394 < 0.0000000000000002
## Car 35348.84 7500.54 4.713 0.00000252487764789
## CouncilAreaBayside 808920.16 46878.80 17.256 < 0.0000000000000002
## CouncilAreaBoroondara 715462.06 38039.82 18.808 < 0.0000000000000002
## CouncilAreaBrimbank -218923.31 45262.13 -4.837 0.00000136856480388
## CouncilAreaCardinia 1044635.52 214594.80 4.868 0.00000117061247196
## CouncilAreaCasey 682936.77 126773.09 5.387 0.00000007567945388
## CouncilAreaDarebin -40716.12 39619.86 -1.028 0.304167
## CouncilAreaFrankston 988461.36 112097.18 8.818 < 0.0000000000000002
## CouncilAreaGlen Eira 350139.97 41389.69 8.460 < 0.0000000000000002
## CouncilAreaGreater Dandenong 444535.07 109768.66 4.050 0.00005223268588951
## CouncilAreaHobsons Bay 11329.00 45965.43 0.246 0.805333
## CouncilAreaHume -41344.03 58916.07 -0.702 0.482879
## CouncilAreaKingston 343871.49 60684.95 5.667 0.00000001558694560
## CouncilAreaKnox 261234.13 86227.15 3.030 0.002464
## CouncilAreaMacedon Ranges 1361724.23 218623.79 6.229 0.00000000051850297
## CouncilAreaManningham 161673.34 49286.62 3.280 0.001046
## CouncilAreaMaribyrnong -152742.53 40915.37 -3.733 0.000192
## CouncilAreaMaroondah 391388.78 87235.93 4.487 0.00000743916562522
## CouncilAreaMelbourne 165836.75 62683.72 2.646 0.008186
## CouncilAreaMelton 62314.91 82428.94 0.756 0.449703
## CouncilAreaMonash 379342.73 50081.11 7.575 0.00000000000004437
## CouncilAreaMoonee Valley -26474.35 38294.48 -0.691 0.489394
## CouncilAreaMoreland -137881.34 36584.27 -3.769 0.000166
## CouncilAreaNillumbik 6956.61 108896.16 0.064 0.949067
## CouncilAreaPort Phillip 548796.43 51362.82 10.685 < 0.0000000000000002
## CouncilAreaStonnington 830208.94 46975.52 17.673 < 0.0000000000000002
## CouncilAreaWhitehorse 429494.78 53648.42 8.006 0.00000000000000154
## CouncilAreaWhittlesea -31225.74 59949.13 -0.521 0.602485
## CouncilAreaWyndham -214204.46 72915.95 -2.938 0.003325
## CouncilAreaYarra 155534.80 48938.43 3.178 0.001493
## CouncilAreaYarra Ranges 508307.13 149326.41 3.404 0.000671
##
## (Intercept) ***
## BuildingArea ***
## Bathroom ***
## Bedroom2 ***
## Distance ***
## Landsize ***
## Car ***
## CouncilAreaBayside ***
## CouncilAreaBoroondara ***
## CouncilAreaBrimbank ***
## CouncilAreaCardinia ***
## CouncilAreaCasey ***
## CouncilAreaDarebin
## CouncilAreaFrankston ***
## CouncilAreaGlen Eira ***
## CouncilAreaGreater Dandenong ***
## CouncilAreaHobsons Bay
## CouncilAreaHume
## CouncilAreaKingston ***
## CouncilAreaKnox **
## CouncilAreaMacedon Ranges ***
## CouncilAreaManningham **
## CouncilAreaMaribyrnong ***
## CouncilAreaMaroondah ***
## CouncilAreaMelbourne **
## CouncilAreaMelton
## CouncilAreaMonash ***
## CouncilAreaMoonee Valley
## CouncilAreaMoreland ***
## CouncilAreaNillumbik
## CouncilAreaPort Phillip ***
## CouncilAreaStonnington ***
## CouncilAreaWhitehorse ***
## CouncilAreaWhittlesea
## CouncilAreaWyndham **
## CouncilAreaYarra **
## CouncilAreaYarra Ranges ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 435600 on 4051 degrees of freedom
## Multiple R-squared: 0.6373, Adjusted R-squared: 0.6341
## F-statistic: 197.7 on 36 and 4051 DF, p-value: < 0.00000000000000022### Analysis of Single-Family Housing sales prices in Melbourne in 2017
res <- model.matrix(~CouncilArea, data = type_t)
head(res[, -1])## CouncilAreaBayside CouncilAreaBoroondara CouncilAreaBrimbank
## 1 0 0 0
## 2 0 0 0
## 3 0 0 0
## 4 0 0 0
## 5 0 0 0
## 6 0 0 0
## CouncilAreaDarebin CouncilAreaFrankston CouncilAreaGlen Eira
## 1 0 0 0
## 2 0 0 0
## 3 0 0 0
## 4 0 0 0
## 5 0 0 0
## 6 0 0 0
## CouncilAreaHobsons Bay CouncilAreaHume CouncilAreaKingston CouncilAreaKnox
## 1 0 0 0 0
## 2 0 0 0 0
## 3 0 0 0 0
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## CouncilAreaManningham CouncilAreaMaribyrnong CouncilAreaMaroondah
## 1 0 0 0
## 2 0 0 0
## 3 0 0 0
## 4 0 0 0
## 5 0 0 0
## 6 0 0 0
## CouncilAreaMelbourne CouncilAreaMelton CouncilAreaMonash
## 1 0 0 0
## 2 0 0 0
## 3 0 0 0
## 4 0 0 0
## 5 0 0 0
## 6 0 0 0
## CouncilAreaMoonee Valley CouncilAreaMoreland CouncilAreaPort Phillip
## 1 1 0 0
## 2 1 0 0
## 3 1 0 0
## 4 1 0 0
## 5 1 0 0
## 6 1 0 0
## CouncilAreaStonnington CouncilAreaWhitehorse CouncilAreaWhittlesea
## 1 0 0 0
## 2 0 0 0
## 3 0 0 0
## 4 0 0 0
## 5 0 0 0
## 6 0 0 0
## CouncilAreaYarra
## 1 0
## 2 0
## 3 0
## 4 0
## 5 0
## 6 0lin_model <- lm(formula = Price ~ BuildingArea+Bathroom+Bedroom2+Distance+Landsize+Car+CouncilArea, data = type_t)
lin_model##
## Call:
## lm(formula = Price ~ BuildingArea + Bathroom + Bedroom2 + Distance +
## Landsize + Car + CouncilArea, data = type_t)
##
## Coefficients:
## (Intercept) BuildingArea Bathroom
## 370653.677 2644.120 76254.300
## Bedroom2 Distance Landsize
## 45492.550 -27122.644 6.947
## Car CouncilAreaBayside CouncilAreaBoroondara
## 44260.915 654982.342 308877.082
## CouncilAreaBrimbank CouncilAreaDarebin CouncilAreaFrankston
## -177221.457 -4478.313 482668.736
## CouncilAreaGlen Eira CouncilAreaHobsons Bay CouncilAreaHume
## 195328.790 -104951.559 -131053.431
## CouncilAreaKingston CouncilAreaKnox CouncilAreaManningham
## 374057.787 172511.840 127671.453
## CouncilAreaMaribyrnong CouncilAreaMaroondah CouncilAreaMelbourne
## -141702.886 159171.822 74878.870
## CouncilAreaMelton CouncilAreaMonash CouncilAreaMoonee Valley
## -227127.369 168777.930 -62416.671
## CouncilAreaMoreland CouncilAreaPort Phillip CouncilAreaStonnington
## -83901.675 271581.607 457009.351
## CouncilAreaWhitehorse CouncilAreaWhittlesea CouncilAreaYarra
## 197207.447 -70009.552 141221.306summary(lin_model)##
## Call:
## lm(formula = Price ~ BuildingArea + Bathroom + Bedroom2 + Distance +
## Landsize + Car + CouncilArea, data = type_t)
##
## Residuals:
## Min 1Q Median 3Q Max
## -530007 -104135 -15291 84707 1035844
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 370653.677 60273.789 6.150 0.00000000146004931
## BuildingArea 2644.120 204.741 12.914 < 0.0000000000000002
## Bathroom 76254.300 16689.226 4.569 0.00000600493569675
## Bedroom2 45492.550 15718.196 2.894 0.00395
## Distance -27122.644 3367.600 -8.054 0.00000000000000468
## Landsize 6.947 10.487 0.662 0.50792
## Car 44260.915 16063.960 2.755 0.00605
## CouncilAreaBayside 654982.342 53447.367 12.255 < 0.0000000000000002
## CouncilAreaBoroondara 308877.082 49365.201 6.257 0.00000000076977233
## CouncilAreaBrimbank -177221.457 64906.394 -2.730 0.00652
## CouncilAreaDarebin -4478.313 49433.385 -0.091 0.92785
## CouncilAreaFrankston 482668.736 211171.655 2.286 0.02264
## CouncilAreaGlen Eira 195328.790 46729.489 4.180 0.00003371857372447
## CouncilAreaHobsons Bay -104951.559 55385.978 -1.895 0.05861
## CouncilAreaHume -131053.431 96348.599 -1.360 0.17430
## CouncilAreaKingston 374057.787 66800.956 5.600 0.00000003339371618
## CouncilAreaKnox 172511.840 109721.596 1.572 0.11644
## CouncilAreaManningham 127671.453 66564.723 1.918 0.05561
## CouncilAreaMaribyrnong -141702.886 46716.856 -3.033 0.00253
## CouncilAreaMaroondah 159171.822 196422.236 0.810 0.41807
## CouncilAreaMelbourne 74878.870 62439.771 1.199 0.23094
## CouncilAreaMelton -227127.369 193662.437 -1.173 0.24136
## CouncilAreaMonash 168777.930 56160.331 3.005 0.00277
## CouncilAreaMoonee Valley -62416.671 47691.727 -1.309 0.19114
## CouncilAreaMoreland -83901.675 43050.804 -1.949 0.05180
## CouncilAreaPort Phillip 271581.607 67643.675 4.015 0.00006739901790296
## CouncilAreaStonnington 457009.351 53475.354 8.546 < 0.0000000000000002
## CouncilAreaWhitehorse 197207.447 62321.041 3.164 0.00164
## CouncilAreaWhittlesea -70009.552 118745.456 -0.590 0.55571
## CouncilAreaYarra 141221.306 58550.016 2.412 0.01618
##
## (Intercept) ***
## BuildingArea ***
## Bathroom ***
## Bedroom2 **
## Distance ***
## Landsize
## Car **
## CouncilAreaBayside ***
## CouncilAreaBoroondara ***
## CouncilAreaBrimbank **
## CouncilAreaDarebin
## CouncilAreaFrankston *
## CouncilAreaGlen Eira ***
## CouncilAreaHobsons Bay .
## CouncilAreaHume
## CouncilAreaKingston ***
## CouncilAreaKnox
## CouncilAreaManningham .
## CouncilAreaMaribyrnong **
## CouncilAreaMaroondah
## CouncilAreaMelbourne
## CouncilAreaMelton
## CouncilAreaMonash **
## CouncilAreaMoonee Valley
## CouncilAreaMoreland .
## CouncilAreaPort Phillip ***
## CouncilAreaStonnington ***
## CouncilAreaWhitehorse **
## CouncilAreaWhittlesea
## CouncilAreaYarra *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 188200 on 572 degrees of freedom
## Multiple R-squared: 0.7447, Adjusted R-squared: 0.7318
## F-statistic: 57.54 on 29 and 572 DF, p-value: < 0.00000000000000022### Analysis of Single-Family Housing sales prices in Melbourne in 2017
res <- model.matrix(~CouncilArea, data = type_u)
head(res[, -1])## CouncilAreaBayside CouncilAreaBoroondara CouncilAreaBrimbank
## 1 0 0 0
## 2 0 0 0
## 3 0 0 0
## 4 0 0 0
## 5 0 0 0
## 6 0 0 0
## CouncilAreaDarebin CouncilAreaFrankston CouncilAreaGlen Eira
## 1 0 0 0
## 2 0 0 0
## 3 0 0 0
## 4 0 0 0
## 5 0 0 0
## 6 0 0 0
## CouncilAreaGreater Dandenong CouncilAreaHobsons Bay CouncilAreaHume
## 1 0 0 0
## 2 0 0 0
## 3 0 0 0
## 4 0 0 0
## 5 0 0 0
## 6 0 0 0
## CouncilAreaKingston CouncilAreaKnox CouncilAreaManningham
## 1 0 0 0
## 2 0 0 0
## 3 0 0 0
## 4 0 0 0
## 5 0 0 0
## 6 0 0 0
## CouncilAreaMaribyrnong CouncilAreaMaroondah CouncilAreaMelbourne
## 1 0 0 0
## 2 0 0 0
## 3 0 0 0
## 4 0 0 0
## 5 0 0 0
## 6 0 0 0
## CouncilAreaMonash CouncilAreaMoonee Valley CouncilAreaMoreland
## 1 0 0 0
## 2 0 0 0
## 3 0 0 0
## 4 0 1 0
## 5 0 1 0
## 6 0 1 0
## CouncilAreaPort Phillip CouncilAreaStonnington CouncilAreaWhitehorse
## 1 0 0 0
## 2 0 0 0
## 3 0 0 0
## 4 0 0 0
## 5 0 0 0
## 6 0 0 0
## CouncilAreaWhittlesea CouncilAreaWyndham CouncilAreaYarra
## 1 0 0 1
## 2 0 0 1
## 3 0 0 1
## 4 0 0 0
## 5 0 0 0
## 6 0 0 0lin_model <- lm(formula = Price ~ BuildingArea+Bathroom+Bedroom2+Distance+Car+CouncilArea, data = type_u)
lin_model##
## Call:
## lm(formula = Price ~ BuildingArea + Bathroom + Bedroom2 + Distance +
## Car + CouncilArea, data = type_u)
##
## Coefficients:
## (Intercept) BuildingArea
## 73533.9 678.5
## Bathroom Bedroom2
## 124177.2 160269.6
## Distance Car
## -11702.2 72339.5
## CouncilAreaBayside CouncilAreaBoroondara
## 215543.4 82790.3
## CouncilAreaBrimbank CouncilAreaDarebin
## -197199.9 -84711.8
## CouncilAreaFrankston CouncilAreaGlen Eira
## -6450.5 29114.7
## CouncilAreaGreater Dandenong CouncilAreaHobsons Bay
## -63170.1 -67795.2
## CouncilAreaHume CouncilAreaKingston
## -122273.1 156388.9
## CouncilAreaKnox CouncilAreaManningham
## 102360.0 26308.1
## CouncilAreaMaribyrnong CouncilAreaMaroondah
## -157115.5 138610.5
## CouncilAreaMelbourne CouncilAreaMonash
## 4991.6 77303.3
## CouncilAreaMoonee Valley CouncilAreaMoreland
## -83075.4 -86780.7
## CouncilAreaPort Phillip CouncilAreaStonnington
## 67167.2 57638.3
## CouncilAreaWhitehorse CouncilAreaWhittlesea
## 76246.9 -53056.1
## CouncilAreaWyndham CouncilAreaYarra
## -491167.0 15867.7summary(lin_model)##
## Call:
## lm(formula = Price ~ BuildingArea + Bathroom + Bedroom2 + Distance +
## Car + CouncilArea, data = type_u)
##
## Residuals:
## Min 1Q Median 3Q Max
## -998631 -91628 -14927 66943 1420719
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 73533.93 38962.23 1.887 0.059314
## BuildingArea 678.49 94.29 7.195 0.0000000000009871
## Bathroom 124177.20 12336.23 10.066 < 0.0000000000000002
## Bedroom2 160269.63 8477.46 18.905 < 0.0000000000000002
## Distance -11702.21 2029.38 -5.766 0.0000000098474458
## Car 72339.50 9413.99 7.684 0.0000000000000279
## CouncilAreaBayside 215543.41 36598.41 5.889 0.0000000047912645
## CouncilAreaBoroondara 82790.32 32417.17 2.554 0.010752
## CouncilAreaBrimbank -197199.88 51687.14 -3.815 0.000142
## CouncilAreaDarebin -84711.77 32702.71 -2.590 0.009682
## CouncilAreaFrankston -6450.52 129469.16 -0.050 0.960270
## CouncilAreaGlen Eira 29114.74 31185.70 0.934 0.350667
## CouncilAreaGreater Dandenong -63170.14 120402.95 -0.525 0.599901
## CouncilAreaHobsons Bay -67795.24 38242.38 -1.773 0.076472
## CouncilAreaHume -122273.10 86818.03 -1.408 0.159228
## CouncilAreaKingston 156388.89 54851.82 2.851 0.004417
## CouncilAreaKnox 102360.04 87895.11 1.165 0.244381
## CouncilAreaManningham 26308.09 54717.52 0.481 0.630731
## CouncilAreaMaribyrnong -157115.48 34906.58 -4.501 0.0000072935369940
## CouncilAreaMaroondah 138610.54 119238.08 1.162 0.245233
## CouncilAreaMelbourne 4991.62 35555.39 0.140 0.888371
## CouncilAreaMonash 77303.33 40433.76 1.912 0.056089
## CouncilAreaMoonee Valley -83075.36 32722.83 -2.539 0.011227
## CouncilAreaMoreland -86780.72 32844.74 -2.642 0.008325
## CouncilAreaPort Phillip 67167.19 32275.57 2.081 0.037601
## CouncilAreaStonnington 57638.30 33079.63 1.742 0.081645
## CouncilAreaWhitehorse 76246.86 42070.36 1.812 0.070133
## CouncilAreaWhittlesea -53056.13 78569.20 -0.675 0.499604
## CouncilAreaWyndham -491167.02 118478.18 -4.146 0.0000358150488725
## CouncilAreaYarra 15867.67 36251.32 0.438 0.661659
##
## (Intercept) .
## BuildingArea ***
## Bathroom ***
## Bedroom2 ***
## Distance ***
## Car ***
## CouncilAreaBayside ***
## CouncilAreaBoroondara *
## CouncilAreaBrimbank ***
## CouncilAreaDarebin **
## CouncilAreaFrankston
## CouncilAreaGlen Eira
## CouncilAreaGreater Dandenong
## CouncilAreaHobsons Bay .
## CouncilAreaHume
## CouncilAreaKingston **
## CouncilAreaKnox
## CouncilAreaManningham
## CouncilAreaMaribyrnong ***
## CouncilAreaMaroondah
## CouncilAreaMelbourne
## CouncilAreaMonash .
## CouncilAreaMoonee Valley *
## CouncilAreaMoreland **
## CouncilAreaPort Phillip *
## CouncilAreaStonnington .
## CouncilAreaWhitehorse .
## CouncilAreaWhittlesea
## CouncilAreaWyndham ***
## CouncilAreaYarra
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 161100 on 1476 degrees of freedom
## Multiple R-squared: 0.5588, Adjusted R-squared: 0.5502
## F-statistic: 64.47 on 29 and 1476 DF, p-value: < 0.00000000000000022Discussion of the multiple regression results
I built a model w/ building area, bathrooms, bedrooms, number of on-site parking places, and distance from the city center. For each of the 3 housing types, I got R^2 values of around .42 or .43. The additional variables explained more of the sales prices than building area alone, but 43% still is not great. There are 33 council areas in Melbourne. Council Area is a categorical variable, which means dummy variables must be created to include this variable in a regression analysis. Fortunately, stats packages today automatically code dummy variables, unlike in the old days when they had to be created by hand. I created the dummy variables for Council Area for each of the three housing types and learned the following: Council Area is really important for single-family housing; the R^2 value was .6373. For townhouses, R^2 was even higher, .7447. For units in multi-unit buildings, Council Area was not nearly so important; the R^2 value was .5588. This somewhat confirms the adage that the 3 most important factors in real estate are location, location, and location, at least for townhomes and single-family properties in Melbourne.
But there are anomalies in the Council Area output. Seven Council Areas in the single-family housing output are not statistically significant; 11 are not statistically significant for the townhomes, yet w/ Council Area as a variable, townhomes have a higher R^2 value than single-family housing. I can’t explain this.
Other interesting results from the regressions include the following: (1) For single-family properties and units in multi-family properties, the number of bedrooms is statistically significant at the .001 level. For townhomes, the significance dropped to the .o1 level; the same was true for the number of parking spaces for townhomes. Why the # of bedrooms in townhomes is not so important I don’t know. Maybe people who buy townhomes have smaller families. (2) Landsize is not statistically significant at all for townhome purchasers. In some ways this is not surprising, but in someways it is; a bit of yard would seem to be important, even for a townhome.
Question 8 Ethical concerns.
In many countries, including the USA, real estate ownership and sales data are public. With a little digging, it’s possible to learn who owns what properties, the characteristics of the properties, the prices paid for the properties, the valuations for property tax purposes, etc. It’s all public information. It’s even easier now b/c most jurisdictions have the data online. In the old days, a title searcher had to go to the records office in the Court House or other county office building and do a manual search. Now you just sit at home and pop queries into https://sdat.dat.maryland.gov/RealProperty/Pages/default.aspx and you can find what you want about any property in Maryland.
I suppose ethical issues could arise in how the data are used. Perhaps someone wanted to find out if a person owned slum properties and wasn’t maintaining them and then broadcast that data. Maybe that would have ethical implications. But if the slumlord were running for political office, letting voters know the person is gouging poor people and not maintaining the properties may be a public service. I guess it would depend on the circumstances. So yes, ethical issues could possibly arise in connection w/ the use of real property data. But the data are publicly available for anyone.