Final Problem 3 - House Prices
Peter Gatica
2022-12-18
# Load needed libraries
library(tidyverse)
library(knitr)
library(Matrix)
library(matlib)
library(matrixcalc)
library(MASS)filename <- tempfile()
download.file("https://raw.githubusercontent.com/audiorunner13/Masters-Coursework/main/DATA605%20Fall%202022/FinalExam/FinalProblem3/house-prices-advanced-regression-techniques/train.csv",filename)
train_src <- read.csv(filename)train_src_1Fam <- data.frame(filter(train_src,BldgType == '1Fam'))summary(train_src_1Fam)## Id MSSubClass MSZoning LotFrontage
## Min. : 1.0 Min. : 20.00 Length:1220 Min. : 30.00
## 1st Qu.: 361.8 1st Qu.: 20.00 Class :character 1st Qu.: 60.00
## Median : 726.5 Median : 45.00 Mode :character Median : 71.00
## Mean : 727.2 Mean : 41.57 Mean : 74.50
## 3rd Qu.:1101.2 3rd Qu.: 60.00 3rd Qu.: 83.75
## Max. :1460.0 Max. :120.00 Max. :313.00
## NA's :226
## LotArea Street Alley LotShape
## Min. : 2500 Length:1220 Length:1220 Length:1220
## 1st Qu.: 8359 Class :character Class :character Class :character
## Median : 9819 Mode :character Mode :character Mode :character
## Mean : 11241
## 3rd Qu.: 12000
## Max. :215245
##
## LandContour Utilities LotConfig LandSlope
## Length:1220 Length:1220 Length:1220 Length:1220
## Class :character Class :character Class :character Class :character
## Mode :character Mode :character Mode :character Mode :character
##
##
##
##
## Neighborhood Condition1 Condition2 BldgType
## Length:1220 Length:1220 Length:1220 Length:1220
## Class :character Class :character Class :character Class :character
## Mode :character Mode :character Mode :character Mode :character
##
##
##
##
## HouseStyle OverallQual OverallCond YearBuilt
## Length:1220 Min. : 1.000 Min. :1.000 Min. :1872
## Class :character 1st Qu.: 5.000 1st Qu.:5.000 1st Qu.:1950
## Mode :character Median : 6.000 Median :5.000 Median :1970
## Mean : 6.121 Mean :5.652 Mean :1970
## 3rd Qu.: 7.000 3rd Qu.:6.000 3rd Qu.:2000
## Max. :10.000 Max. :9.000 Max. :2010
##
## YearRemodAdd RoofStyle RoofMatl Exterior1st
## Min. :1950 Length:1220 Length:1220 Length:1220
## 1st Qu.:1965 Class :character Class :character Class :character
## Median :1994 Mode :character Mode :character Mode :character
## Mean :1985
## 3rd Qu.:2004
## Max. :2010
##
## Exterior2nd MasVnrType MasVnrArea ExterQual
## Length:1220 Length:1220 Min. : 0.0 Length:1220
## Class :character Class :character 1st Qu.: 0.0 Class :character
## Mode :character Mode :character Median : 0.0 Mode :character
## Mean : 101.9
## 3rd Qu.: 162.0
## Max. :1600.0
## NA's :7
## ExterCond Foundation BsmtQual BsmtCond
## Length:1220 Length:1220 Length:1220 Length:1220
## Class :character Class :character Class :character Class :character
## Mode :character Mode :character Mode :character Mode :character
##
##
##
##
## BsmtExposure BsmtFinType1 BsmtFinSF1 BsmtFinType2
## Length:1220 Length:1220 Min. : 0.0 Length:1220
## Class :character Class :character 1st Qu.: 0.0 Class :character
## Mode :character Mode :character Median : 384.0 Mode :character
## Mean : 444.3
## 3rd Qu.: 706.5
## Max. :5644.0
##
## BsmtFinSF2 BsmtUnfSF TotalBsmtSF Heating
## Min. : 0.00 Min. : 0 Min. : 0.0 Length:1220
## 1st Qu.: 0.00 1st Qu.: 254 1st Qu.: 814.0 Class :character
## Median : 0.00 Median : 502 Median : 998.5 Mode :character
## Mean : 48.76 Mean : 581 Mean :1074.1
## 3rd Qu.: 0.00 3rd Qu.: 813 3rd Qu.:1284.5
## Max. :1474.00 Max. :2336 Max. :6110.0
##
## HeatingQC CentralAir Electrical X1stFlrSF
## Length:1220 Length:1220 Length:1220 Min. : 334
## Class :character Class :character Class :character 1st Qu.: 894
## Mode :character Mode :character Mode :character Median :1092
## Mean :1175
## 3rd Qu.:1392
## Max. :4692
##
## X2ndFlrSF LowQualFinSF GrLivArea BsmtFullBath
## Min. : 0.0 Min. : 0.000 Min. : 334 Min. :0.0000
## 1st Qu.: 0.0 1st Qu.: 0.000 1st Qu.:1134 1st Qu.:0.0000
## Median : 0.0 Median : 0.000 Median :1483 Median :0.0000
## Mean : 358.1 Mean : 6.184 Mean :1539 Mean :0.4123
## 3rd Qu.: 754.2 3rd Qu.: 0.000 3rd Qu.:1820 3rd Qu.:1.0000
## Max. :2065.0 Max. :572.000 Max. :5642 Max. :2.0000
##
## BsmtHalfBath FullBath HalfBath BedroomAbvGr
## Min. :0.0000 Min. :0.000 Min. :0.0000 Min. :0.000
## 1st Qu.:0.0000 1st Qu.:1.000 1st Qu.:0.0000 1st Qu.:3.000
## Median :0.0000 Median :2.000 Median :0.0000 Median :3.000
## Mean :0.0582 Mean :1.546 Mean :0.3902 Mean :2.928
## 3rd Qu.:0.0000 3rd Qu.:2.000 3rd Qu.:1.0000 3rd Qu.:3.000
## Max. :1.0000 Max. :3.000 Max. :2.0000 Max. :5.000
##
## KitchenAbvGr KitchenQual TotRmsAbvGrd Functional
## Min. :1.000 Length:1220 Min. : 2.000 Length:1220
## 1st Qu.:1.000 Class :character 1st Qu.: 6.000 Class :character
## Median :1.000 Mode :character Median : 6.000 Mode :character
## Mean :1.006 Mean : 6.603
## 3rd Qu.:1.000 3rd Qu.: 7.000
## Max. :3.000 Max. :12.000
##
## Fireplaces FireplaceQu GarageType GarageYrBlt
## Min. :0.0000 Length:1220 Length:1220 Min. :1906
## 1st Qu.:0.0000 Class :character Class :character 1st Qu.:1959
## Median :1.0000 Mode :character Mode :character Median :1978
## Mean :0.6508 Mean :1977
## 3rd Qu.:1.0000 3rd Qu.:2001
## Max. :3.0000 Max. :2010
## NA's :54
## GarageFinish GarageCars GarageArea GarageQual
## Length:1220 Min. :0.00 Min. : 0.0 Length:1220
## Class :character 1st Qu.:1.00 1st Qu.: 325.8 Class :character
## Mode :character Median :2.00 Median : 480.0 Mode :character
## Mean :1.78 Mean : 482.1
## 3rd Qu.:2.00 3rd Qu.: 588.0
## Max. :4.00 Max. :1418.0
##
## GarageCond PavedDrive WoodDeckSF OpenPorchSF
## Length:1220 Length:1220 Min. : 0.00 Min. : 0.00
## Class :character Class :character 1st Qu.: 0.00 1st Qu.: 0.00
## Mode :character Mode :character Median : 0.00 Median : 28.00
## Mean : 96.65 Mean : 48.72
## 3rd Qu.:178.00 3rd Qu.: 72.25
## Max. :857.00 Max. :547.00
##
## EnclosedPorch X3SsnPorch ScreenPorch PoolArea
## Min. : 0.00 Min. : 0.000 Min. : 0.00 Min. : 0.000
## 1st Qu.: 0.00 1st Qu.: 0.000 1st Qu.: 0.00 1st Qu.: 0.000
## Median : 0.00 Median : 0.000 Median : 0.00 Median : 0.000
## Mean : 24.54 Mean : 3.817 Mean : 16.13 Mean : 3.302
## 3rd Qu.: 0.00 3rd Qu.: 0.000 3rd Qu.: 0.00 3rd Qu.: 0.000
## Max. :552.00 Max. :508.000 Max. :480.00 Max. :738.000
##
## PoolQC Fence MiscFeature MiscVal
## Length:1220 Length:1220 Length:1220 Min. : 0.0
## Class :character Class :character Class :character 1st Qu.: 0.0
## Mode :character Mode :character Mode :character Median : 0.0
## Mean : 40.9
## 3rd Qu.: 0.0
## Max. :15500.0
##
## MoSold YrSold SaleType SaleCondition
## Min. : 1.000 Min. :2006 Length:1220 Length:1220
## 1st Qu.: 5.000 1st Qu.:2007 Class :character Class :character
## Median : 6.000 Median :2008 Mode :character Mode :character
## Mean : 6.356 Mean :2008
## 3rd Qu.: 8.000 3rd Qu.:2009
## Max. :12.000 Max. :2010
##
## SalePrice
## Min. : 34900
## 1st Qu.:131475
## Median :167900
## Mean :185764
## 3rd Qu.:222000
## Max. :755000
## Descriptive and Inferential Statistics. Provide univariate descriptive statistics and appropriate plots for the training data set. Provide a scatterplot matrix for at least two of the independent variables and the dependent variable.
sqft_liv <- train_src_1Fam$X1stFlrSF + train_src_1Fam$X2ndFlrSF
x_ax <- sqft_liv
y_ax <- train_src_1Fam$SalePrice/1000
plot(x_ax, y_ax, main = "Sale Price by Square Footage",
xlab = "Square Footage", ylab = "Sale Price (Thousands)",
pch = 21, bg='yellow')
train_src_1Fam %>%
ggplot(aes(x=Neighborhood,SalePrice,y=SalePrice/1000)) +
geom_bar(stat = 'identity',fill="#f68060",position=position_dodge(),alpha=.6, width=.4) +
coord_flip() +
labs(y = ("Sale Price (Thousands)"),x = ("Neighborhood"),
title = ("Sale Price by Neighborhood") ) +
theme_minimal()
Derive a correlation matrix for any three quantitative variables in the dataset. Test the hypotheses that the correlations between each pairwise set of variables is 0 and provide an 80% confidence interval. Discuss the meaning of your analysis. Would you be worried about familywise error? Why or why not? 5 points
train_src_1Fam$SqftLiv <- paste(train_src_1Fam$X1stFlrSF+train_src_1Fam$X2ndFlrSF)
train_1Fam_temp <- train_src_1Fam[,c("LotArea","SalePrice","SqftLiv")]
train_1Fam_temp$SqftLiv <- as.integer(train_1Fam_temp$SqftLiv)
head(train_1Fam_temp,10)## LotArea SalePrice SqftLiv
## 1 8450 208500 1710
## 2 9600 181500 1262
## 3 11250 223500 1786
## 4 9550 140000 1717
## 5 14260 250000 2198
## 6 14115 143000 1362
## 7 10084 307000 1694
## 8 10382 200000 2090
## 9 6120 129900 1774
## 10 11200 129500 1040(train_1Fam_corr <- cor(train_1Fam_temp))## LotArea SalePrice SqftLiv
## LotArea 1.0000000 0.2742846 0.2694855
## SalePrice 0.2742846 1.0000000 0.7472224
## SqftLiv 0.2694855 0.7472224 1.0000000Linear Algebra and Correlation. Invert your correlation matrix from above. (This is known as the precision matrix and contains variance inflation factors on the diagonal.) Multiply the correlation matrix by the precision matrix, and then multiply the precision matrix by the correlation matrix. Conduct LU decomposition on the matrix. 5 points
(train_1Fam_corr_inv <- solve(train_1Fam_corr))## LotArea SalePrice SqftLiv
## LotArea 1.0924921 -0.1803732 -0.1596319
## SalePrice -0.1803732 2.2939719 -1.6654992
## SqftLiv -0.1596319 -1.6654992 2.2875168train_1Fam_corr %*% train_1Fam_corr_inv## LotArea SalePrice SqftLiv
## LotArea 1.000000e+00 0 0
## SalePrice -1.387779e-17 1 0
## SqftLiv 0.000000e+00 0 1train_1Fam_corr_inv %*% train_1Fam_corr## LotArea SalePrice SqftLiv
## LotArea 1.000000e+00 -8.326673e-17 -5.551115e-17
## SalePrice 1.110223e-16 1.000000e+00 2.220446e-16
## SqftLiv 0.000000e+00 -2.220446e-16 1.000000e+00lu.decomposition(train_1Fam_corr)## $L
## [,1] [,2] [,3]
## [1,] 1.0000000 0.0000000 0
## [2,] 0.2742846 1.0000000 0
## [3,] 0.2694855 0.7280817 1
##
## $U
## [,1] [,2] [,3]
## [1,] 1 0.2742846 0.2694855
## [2,] 0 0.9247680 0.6733067
## [3,] 0 0.0000000 0.4371553lu.decomposition(train_1Fam_corr_inv)## $L
## [,1] [,2] [,3]
## [1,] 1.0000000 0.0000000 0
## [2,] -0.1651026 1.0000000 0
## [3,] -0.1461172 -0.7472224 1
##
## $U
## [,1] [,2] [,3]
## [1,] 1.092492 -1.803732e-01 -0.1596319
## [2,] 0.000000 2.264192e+00 -1.6918549
## [3,] 0.000000 2.220446e-16 1.0000000Calculus-Based Probability & Statistics. Many times, it makes sense to fit a closed form distribution to data. Select a variable in the Kaggle.com training dataset that is skewed to the right, shift it so that the minimum value is absolutely above zero if necessary. Then load the MASS package and run fitdistr to fit an exponential probability density function. (See https://stat.ethz.ch/R-manual/R- devel/library/MASS/html/fitdistr.html ). Find the optimal value of λ for this distribution, and then take 1000 samples from this exponential distribution using this value (e.g., rexp(1000, λ)).
hist(train_src_1Fam$LotArea, col='steelblue',main="Original")
sqrt_LotArea <- train_src_1Fam$LotArea^(1/3)
hist(sqrt_LotArea, col='coral2', main='Square Root Transformed')
fitdistr(sqrt_LotArea,"exponential")## rate
## 0.045788314
## (0.001310916)sqrt_LotArea_samp <- rexp(1000, rate = 0.045788314)Plot a histogram and compare it with a histogram of your original variable. Using the exponential pdf, find the 5th and 95th percentiles using the cumulative distribution function (CDF). Also generate a 95% confidence interval from the empirical data, assuming normality. Finally, provide the empirical 5th percentile and 95th percentile of the data. Discuss. 10 points
hist(sqrt_LotArea_samp, probability=TRUE, col= gray(.9))
dexp(sqrt_LotArea_samp, # X-axis values (> 0)
rate = 0.045788314) ## [1] 5.230897e-04 1.824241e-02 1.827953e-02 3.456530e-02 3.617138e-02
## [6] 2.837149e-02 3.211005e-02 4.318452e-02 9.049063e-03 1.008403e-02
## [11] 4.301431e-02 4.389249e-02 2.807342e-02 9.267590e-03 3.346309e-02
## [16] 2.681004e-02 4.277282e-02 3.639294e-02 3.155240e-02 2.748687e-02
## [21] 4.095019e-02 1.652983e-03 3.697788e-02 1.983926e-02 4.239553e-02
## [26] 2.797060e-02 3.664426e-02 1.982713e-03 4.460923e-03 2.587514e-02
## [31] 3.566758e-02 1.934241e-02 4.456074e-02 6.095516e-03 4.285907e-02
## [36] 1.525209e-02 3.969734e-02 2.180697e-03 1.608209e-03 4.245600e-02
## [41] 2.437151e-02 2.368382e-02 1.503825e-02 1.701597e-02 5.186987e-03
## [46] 1.960717e-03 2.796747e-03 1.900507e-02 4.058980e-02 5.908559e-03
## [51] 3.475868e-02 3.232511e-02 2.985063e-02 4.247425e-03 2.137176e-02
## [56] 3.209692e-02 2.092034e-02 2.430515e-02 1.806026e-02 8.106613e-03
## [61] 9.726189e-03 3.822920e-02 2.236383e-02 1.031578e-02 1.460095e-02
## [66] 4.256584e-02 2.996476e-02 4.798963e-03 4.343711e-02 2.384253e-02
## [71] 3.372570e-02 3.142719e-02 1.635134e-02 2.836007e-02 2.979171e-04
## [76] 6.638784e-03 2.008961e-02 4.201724e-02 3.173970e-03 1.750644e-02
## [81] 3.908094e-02 3.368891e-02 3.367670e-02 3.834214e-02 1.495146e-02
## [86] 2.285903e-02 2.842321e-03 1.394050e-02 2.942944e-02 1.836682e-02
## [91] 3.880119e-02 4.228568e-02 4.408311e-02 7.285972e-03 2.556704e-02
## [96] 1.894250e-02 1.383113e-03 2.415489e-02 9.668075e-03 2.031255e-02
## [101] 2.870636e-02 3.017008e-02 3.629915e-02 3.463259e-03 2.845096e-02
## [106] 3.507279e-02 2.265881e-02 1.140930e-02 2.292453e-02 2.249360e-02
## [111] 2.428763e-03 4.565268e-03 3.402738e-02 4.070317e-02 3.018300e-02
## [116] 8.040141e-03 1.137549e-02 4.041835e-02 2.961915e-02 2.677086e-02
## [121] 4.200860e-02 2.522141e-02 3.705119e-02 6.697347e-03 3.186712e-02
## [126] 1.034936e-02 2.926780e-02 1.565848e-02 4.032174e-02 3.057834e-02
## [131] 1.013329e-02 7.923884e-03 3.548238e-02 3.886819e-02 1.837598e-02
## [136] 2.735510e-02 3.830109e-02 7.736644e-03 3.708556e-02 3.505205e-02
## [141] 1.975305e-03 2.021743e-03 2.300827e-02 4.058458e-03 4.405314e-02
## [146] 4.571376e-02 1.645894e-02 3.063315e-02 7.116864e-03 1.409601e-02
## [151] 3.988704e-02 1.873907e-02 4.773223e-03 5.100463e-03 3.915126e-02
## [156] 1.340175e-02 6.167318e-05 1.541270e-02 2.393834e-02 4.142077e-02
## [161] 2.417987e-02 4.571102e-02 1.027254e-02 1.409909e-02 2.822738e-02
## [166] 2.605848e-02 7.850854e-04 2.241752e-02 1.408789e-02 3.403797e-03
## [171] 2.161020e-02 3.277538e-02 2.662605e-02 4.265802e-02 1.435216e-02
## [176] 1.304538e-02 3.682443e-02 4.507982e-02 1.120498e-03 8.579623e-03
## [181] 2.244057e-04 2.792097e-02 3.237226e-02 2.522357e-02 1.408161e-02
## [186] 1.950688e-02 7.698019e-03 1.516612e-02 3.232583e-02 3.664705e-02
## [191] 4.410910e-02 3.994953e-02 3.289883e-02 2.378600e-03 2.566938e-02
## [196] 4.088190e-02 3.320971e-03 7.710443e-03 3.682590e-02 2.300473e-02
## [201] 3.883141e-02 1.950979e-02 1.848909e-02 1.823358e-02 1.381357e-02
## [206] 2.293125e-02 4.314674e-02 3.571141e-02 1.248480e-02 8.342837e-03
## [211] 2.786127e-02 3.444297e-02 1.874100e-02 9.220342e-03 2.714121e-02
## [216] 2.231790e-02 2.316058e-03 1.179905e-02 3.110214e-02 2.094002e-02
## [221] 2.465048e-02 3.933574e-02 1.908110e-03 3.820083e-02 4.131496e-02
## [226] 3.319039e-02 3.834344e-02 1.833631e-04 4.095201e-02 4.378895e-02
## [231] 1.918638e-02 1.380741e-02 1.333175e-02 2.113979e-02 1.818439e-02
## [236] 4.329826e-02 7.509413e-03 4.370498e-02 2.580063e-02 3.371480e-02
## [241] 2.755452e-02 2.184145e-02 3.145244e-03 4.131354e-02 3.927263e-02
## [246] 1.308608e-02 1.044904e-02 4.321788e-02 1.041172e-02 1.548642e-02
## [251] 3.279829e-02 3.087229e-02 2.061045e-03 1.468491e-02 1.839450e-02
## [256] 4.061465e-02 4.230226e-02 1.834052e-02 8.198213e-03 6.756754e-03
## [261] 4.258453e-02 9.859869e-03 3.904515e-02 2.311232e-02 1.108665e-02
## [266] 1.619557e-02 3.438108e-02 2.170632e-03 4.078095e-02 1.475430e-02
## [271] 3.271407e-02 3.554755e-02 4.273962e-02 8.606353e-03 2.526836e-02
## [276] 2.626610e-03 2.474467e-02 3.802931e-02 2.690980e-02 3.457867e-02
## [281] 2.648154e-02 2.777011e-02 5.380618e-03 2.151521e-02 7.859687e-03
## [286] 2.978436e-02 9.135899e-03 5.363423e-03 1.276618e-02 4.103276e-02
## [291] 3.234882e-02 2.645793e-02 3.093412e-02 1.369737e-02 3.731309e-02
## [296] 1.271837e-02 3.685883e-02 3.886531e-02 2.719947e-02 3.472466e-02
## [301] 4.205458e-02 1.272140e-02 1.406175e-03 3.701373e-02 1.818003e-02
## [306] 4.058256e-02 1.158018e-02 6.888535e-03 3.580753e-04 2.088078e-02
## [311] 7.373116e-03 3.302581e-02 2.496342e-03 1.936818e-02 3.292679e-04
## [316] 2.978722e-02 1.008036e-02 1.525129e-02 1.166014e-02 4.532908e-02
## [321] 1.031833e-02 3.194496e-02 2.013371e-03 2.355481e-02 1.294223e-02
## [326] 2.966910e-02 2.149667e-02 2.700873e-02 1.958414e-02 3.090479e-02
## [331] 1.250524e-02 3.431684e-02 1.107496e-02 4.236464e-02 8.070724e-03
## [336] 2.906450e-02 4.125017e-02 4.305612e-02 6.638586e-03 3.603024e-02
## [341] 3.051492e-02 4.334313e-02 1.958703e-02 2.357269e-02 4.312786e-02
## [346] 1.670621e-02 3.632999e-02 8.152741e-04 2.306268e-02 9.857315e-03
## [351] 2.901137e-03 7.062069e-03 2.132691e-02 3.053065e-02 3.519169e-02
## [356] 1.938567e-02 7.784131e-03 6.845774e-04 7.736467e-03 1.225574e-02
## [361] 3.509615e-02 3.645673e-02 1.462848e-03 2.222238e-02 2.089079e-02
## [366] 3.483021e-02 1.589283e-02 1.018155e-02 1.865077e-02 1.700222e-02
## [371] 3.210574e-02 1.208581e-02 2.025172e-02 2.884894e-02 2.164405e-02
## [376] 3.377902e-02 4.215325e-02 3.490157e-02 9.923679e-03 2.924496e-02
## [381] 4.706821e-04 3.922623e-02 1.034385e-02 2.315796e-02 4.247386e-02
## [386] 2.130341e-02 4.076977e-02 3.072819e-02 1.244167e-02 2.809452e-02
## [391] 4.154588e-03 2.428266e-02 3.536935e-02 2.647456e-02 3.413209e-02
## [396] 3.160116e-03 5.639382e-03 2.753327e-02 3.939996e-02 1.240744e-02
## [401] 1.002063e-02 3.517620e-02 5.017568e-03 2.390092e-02 1.113854e-02
## [406] 1.170517e-02 3.446189e-02 3.330904e-02 4.788576e-03 3.674031e-03
## [411] 1.728683e-02 1.877628e-02 4.038442e-02 1.052286e-02 1.053029e-02
## [416] 2.339494e-02 1.932659e-02 2.952414e-02 2.888606e-02 8.675596e-03
## [421] 1.741520e-02 4.527936e-02 2.995365e-02 4.276306e-02 9.709044e-03
## [426] 1.016224e-02 1.225061e-02 3.286272e-02 4.055940e-02 3.580593e-02
## [431] 2.632440e-02 3.259799e-02 1.445989e-02 2.610287e-02 3.522255e-02
## [436] 4.318085e-02 1.774932e-02 3.838760e-02 3.942312e-02 3.568817e-03
## [441] 2.036527e-02 9.750783e-04 1.371470e-02 3.189026e-02 4.911983e-03
## [446] 2.758783e-02 2.278873e-02 1.771561e-02 4.735256e-03 1.973194e-03
## [451] 3.327262e-02 1.921394e-02 3.375339e-02 3.291060e-02 1.821652e-02
## [456] 2.440859e-02 2.437106e-02 2.216208e-02 2.283562e-02 1.797040e-02
## [461] 5.028526e-04 2.061196e-02 3.138615e-02 1.273789e-03 3.233897e-02
## [466] 7.009476e-03 3.635550e-02 3.688375e-02 4.115168e-02 8.497266e-03
## [471] 2.370324e-02 2.463886e-02 2.841204e-02 2.517632e-02 1.724741e-02
## [476] 2.201084e-02 4.581835e-03 2.599579e-02 2.330930e-02 8.246597e-03
## [481] 2.901776e-02 1.773819e-02 1.059786e-02 7.168380e-03 4.296358e-02
## [486] 4.441480e-02 4.468152e-02 4.208416e-02 4.469538e-02 3.214314e-02
## [491] 3.432471e-05 2.894597e-02 2.455752e-02 1.753619e-02 3.664457e-02
## [496] 4.107368e-02 4.334040e-03 1.278581e-02 3.180150e-02 5.247064e-03
## [501] 4.070986e-02 4.051900e-02 4.496145e-02 9.416055e-03 2.137908e-02
## [506] 2.894434e-02 1.142816e-02 3.630485e-02 1.866692e-02 4.305573e-02
## [511] 3.923883e-02 1.808173e-03 5.832156e-03 7.147438e-04 2.371691e-02
## [516] 7.086596e-03 6.436649e-03 2.107638e-02 1.147587e-02 3.823299e-02
## [521] 2.340433e-02 4.109038e-02 5.148993e-03 5.809245e-03 3.381859e-02
## [526] 4.954404e-03 8.882881e-03 1.641376e-02 7.050822e-05 1.499933e-02
## [531] 2.421720e-02 3.564453e-02 2.043673e-02 3.092543e-02 4.051162e-02
## [536] 1.061229e-02 4.492695e-02 4.571370e-02 2.947248e-02 1.552300e-02
## [541] 1.785777e-02 3.190026e-02 4.904103e-03 1.828288e-02 4.514112e-02
## [546] 3.898278e-02 4.207198e-02 3.003325e-02 2.504888e-02 1.244050e-02
## [551] 2.580802e-02 2.037247e-02 3.144820e-02 2.908994e-02 3.572292e-02
## [556] 8.241733e-04 3.410481e-03 4.221431e-02 3.803005e-02 2.249426e-02
## [561] 2.990068e-02 1.699087e-02 3.008485e-02 3.192830e-03 1.257736e-02
## [566] 3.715656e-02 1.845805e-02 3.913645e-02 3.427627e-03 3.106614e-02
## [571] 2.246608e-02 3.683489e-02 1.212957e-02 3.617463e-02 2.730302e-02
## [576] 4.211570e-02 3.967763e-02 3.761936e-02 4.172118e-04 7.106769e-03
## [581] 4.101084e-02 3.002670e-02 2.711373e-02 3.579338e-02 4.048286e-02
## [586] 1.025934e-02 1.954258e-02 6.113114e-03 3.012467e-02 3.817288e-02
## [591] 1.484613e-02 4.029347e-02 2.760323e-02 4.147829e-02 3.004827e-02
## [596] 4.186815e-02 1.177274e-03 1.479548e-02 3.092055e-03 6.221035e-03
## [601] 4.703574e-03 3.344789e-03 3.900873e-02 4.224284e-02 3.120702e-02
## [606] 2.807630e-03 2.034393e-02 1.110615e-02 5.563498e-03 2.532366e-02
## [611] 3.072920e-02 2.849631e-02 3.543096e-02 4.839884e-03 2.704825e-02
## [616] 2.447205e-02 2.986538e-02 1.184730e-02 3.105543e-02 3.592034e-02
## [621] 2.393801e-03 4.398596e-02 2.453941e-02 2.831245e-02 2.018698e-02
## [626] 2.622309e-04 7.521975e-03 8.813409e-03 1.986800e-02 1.126647e-02
## [631] 3.413732e-02 3.981988e-02 2.635060e-02 4.069756e-02 4.200880e-02
## [636] 4.317349e-02 4.127825e-02 4.349635e-02 2.402720e-02 3.083079e-02
## [641] 1.998321e-02 5.913020e-03 3.338621e-02 4.047272e-02 9.541329e-03
## [646] 2.513442e-02 9.707317e-03 6.738506e-04 3.190130e-02 1.356138e-02
## [651] 4.168587e-02 4.492243e-02 1.149658e-02 1.578503e-02 2.964201e-02
## [656] 2.683475e-02 2.468725e-02 2.172867e-02 1.473665e-02 3.810304e-02
## [661] 3.111739e-02 3.967904e-03 1.707183e-02 7.378061e-03 1.521873e-02
## [666] 4.229194e-02 2.904860e-02 1.374094e-02 2.424112e-02 2.691047e-03
## [671] 1.582524e-02 3.019657e-02 1.967370e-02 3.717350e-02 8.477793e-03
## [676] 2.800292e-02 3.550213e-02 2.028828e-02 8.663873e-03 1.240558e-02
## [681] 1.518055e-04 3.600323e-02 4.476622e-02 8.882348e-03 3.225778e-02
## [686] 2.622341e-02 3.257355e-02 1.800799e-02 4.507273e-02 2.663667e-02
## [691] 2.813570e-02 4.075252e-02 3.574304e-02 4.134483e-02 1.930805e-02
## [696] 2.866271e-02 1.912813e-02 4.296648e-02 2.143641e-02 1.478622e-02
## [701] 2.284788e-02 3.441072e-02 1.568774e-02 2.867439e-02 4.300174e-02
## [706] 4.267817e-02 9.957785e-03 3.791209e-02 9.216372e-03 1.111326e-02
## [711] 3.570420e-02 3.624585e-02 4.205692e-02 4.332463e-02 5.019939e-03
## [716] 1.770717e-02 2.496854e-02 1.081603e-02 1.880746e-02 3.684184e-02
## [721] 3.308282e-02 3.611276e-02 5.799809e-04 8.931671e-03 1.359433e-02
## [726] 3.161595e-02 3.109843e-02 1.282274e-02 2.132630e-02 2.387204e-02
## [731] 1.006905e-02 4.680985e-04 3.752199e-02 1.375336e-02 4.293491e-02
## [736] 2.965803e-02 2.208311e-04 3.480655e-02 3.567160e-02 2.239024e-02
## [741] 4.017525e-02 8.201058e-03 2.644049e-02 4.482778e-03 3.546454e-03
## [746] 3.316546e-02 3.969054e-02 1.497688e-02 5.581554e-03 1.094346e-02
## [751] 2.507944e-02 2.452227e-02 1.120598e-02 3.998381e-02 2.672964e-02
## [756] 1.509778e-02 1.273471e-02 3.938318e-02 2.281420e-03 2.724054e-02
## [761] 7.863409e-03 2.428605e-02 2.599237e-02 4.465144e-02 3.202547e-02
## [766] 2.628133e-02 3.449371e-02 1.426183e-02 2.327198e-02 4.516885e-02
## [771] 4.274852e-02 2.668694e-02 2.269814e-02 9.059664e-03 3.278662e-02
## [776] 2.400877e-03 4.745040e-03 4.558225e-03 9.410693e-03 2.379332e-02
## [781] 7.836154e-03 1.643825e-02 1.155527e-02 5.483577e-03 1.319906e-02
## [786] 2.897413e-02 3.879203e-02 2.984535e-02 1.421165e-02 3.792219e-02
## [791] 6.439603e-03 2.858892e-02 2.058525e-02 1.558992e-03 2.924037e-02
## [796] 5.511467e-03 1.989862e-02 3.863273e-02 2.999753e-02 2.458263e-02
## [801] 8.619305e-03 2.340411e-02 1.176078e-02 3.969784e-02 1.879102e-02
## [806] 1.780681e-02 3.314012e-02 3.385951e-02 1.467967e-02 8.732139e-03
## [811] 1.894709e-02 1.394982e-02 1.439178e-02 3.336343e-03 6.857966e-04
## [816] 3.737394e-02 3.434971e-03 1.227926e-02 4.328448e-02 1.907512e-02
## [821] 3.574836e-02 1.528798e-02 1.968934e-02 2.325684e-02 3.531334e-02
## [826] 2.725585e-02 2.990307e-03 2.115985e-02 3.815173e-02 2.123259e-02
## [831] 2.050390e-02 4.247981e-02 2.305630e-02 2.490699e-02 2.776499e-02
## [836] 4.528350e-02 3.690563e-02 7.020419e-03 1.226848e-02 3.873631e-02
## [841] 2.311051e-02 4.401690e-02 2.027149e-02 1.753718e-02 4.503697e-02
## [846] 3.146843e-02 4.123481e-02 4.485092e-02 8.560544e-03 4.215464e-02
## [851] 4.003597e-03 1.772113e-02 2.610497e-02 7.131673e-03 2.153609e-02
## [856] 3.817198e-03 3.046045e-02 8.068836e-03 4.497463e-02 2.823737e-02
## [861] 7.830348e-03 4.093235e-02 4.445496e-02 1.056178e-02 4.017639e-02
## [866] 3.780308e-02 9.035599e-03 3.101854e-03 4.113935e-02 1.257523e-02
## [871] 2.631830e-02 3.845719e-02 2.347882e-02 3.138712e-04 1.220615e-02
## [876] 2.262208e-02 2.954907e-02 2.407494e-02 2.420638e-03 6.563327e-03
## [881] 1.577601e-02 4.266677e-02 4.249415e-02 1.414537e-02 1.339426e-02
## [886] 4.167883e-02 2.094022e-02 2.219800e-02 1.011960e-02 1.762601e-02
## [891] 3.613058e-02 2.055867e-03 3.032761e-04 3.504451e-02 3.675562e-02
## [896] 2.415869e-02 1.839303e-02 4.458913e-02 1.868497e-02 1.749397e-02
## [901] 3.940973e-02 4.288929e-02 1.412668e-02 5.253999e-03 6.090144e-03
## [906] 3.958131e-02 1.293308e-02 2.526153e-02 4.296249e-02 4.475916e-02
## [911] 3.562339e-02 2.197616e-02 3.934630e-02 1.897555e-02 1.490746e-02
## [916] 3.641148e-02 2.646678e-02 3.743065e-02 1.722247e-02 9.310793e-04
## [921] 2.091391e-02 2.380775e-02 1.832907e-03 5.678027e-03 2.506565e-02
## [926] 1.531826e-02 2.994159e-03 4.657484e-03 9.101961e-03 3.524810e-03
## [931] 1.702176e-02 3.603233e-02 1.340116e-02 3.574988e-02 3.143267e-02
## [936] 3.903179e-02 2.939816e-02 2.038582e-02 4.160475e-03 1.291112e-02
## [941] 6.289666e-03 2.843574e-02 4.134898e-02 1.600748e-02 3.095385e-02
## [946] 8.146132e-03 2.326760e-02 4.241448e-03 1.819773e-03 2.368686e-04
## [951] 4.278128e-02 2.304398e-02 2.463900e-02 3.865279e-03 4.505418e-02
## [956] 2.031962e-02 2.471117e-02 1.754006e-03 3.021995e-02 4.446453e-03
## [961] 1.298202e-02 2.713160e-02 1.452239e-02 4.160805e-02 2.897585e-02
## [966] 1.947880e-02 2.952078e-02 4.018906e-02 1.966140e-02 1.846426e-03
## [971] 4.488350e-02 1.843231e-02 3.695805e-02 2.431156e-03 6.069857e-03
## [976] 1.391765e-02 2.977582e-02 2.133163e-02 4.136789e-02 2.845469e-02
## [981] 3.280762e-02 8.435481e-03 1.214882e-02 3.280017e-02 3.290361e-02
## [986] 3.757744e-02 2.542544e-02 2.666068e-02 3.132306e-02 1.095761e-02
## [991] 2.586898e-02 8.781245e-03 1.861225e-02 1.793753e-02 8.169260e-03
## [996] 3.136325e-02 8.513183e-03 3.397851e-02 3.323680e-02 3.833107e-02pexp(sqrt_LotArea_samp,
rate = 0.045788314,
lower.tail = TRUE, # If TRUE, probabilities are P(X <= x), or P(X > x) otherwise
log.p = FALSE)## [1] 0.988575912 0.601592348 0.600781685 0.245106498 0.210030321 0.380377075
## [7] 0.298728363 0.056865842 0.802371779 0.779768502 0.060583272 0.041404175
## [13] 0.386886735 0.797599236 0.269178385 0.414478509 0.065857221 0.205191506
## [19] 0.310907047 0.399696925 0.105662764 0.963899462 0.192416644 0.566717919
## [25] 0.074097266 0.389132410 0.199702763 0.956698274 0.902575077 0.434896340
## [31] 0.221033192 0.577568910 0.026809662 0.866876157 0.063973684 0.666899907
## [37] 0.133024683 0.952374381 0.964877305 0.072776605 0.467735172 0.482753955
## [43] 0.671570180 0.628377513 0.886718109 0.957178658 0.938920072 0.584936229
## [49] 0.113533544 0.870959230 0.240883096 0.294031509 0.348073251 0.907237797
## [55] 0.533248647 0.299015116 0.543107450 0.469184446 0.605570645 0.822954536
## [61] 0.787583594 0.165088317 0.511582208 0.774707162 0.681120617 0.070377718
## [67] 0.345580636 0.895192399 0.051349439 0.479287837 0.263443093 0.313641607
## [73] 0.642892731 0.380626540 0.993493600 0.855011381 0.561250380 0.082358805
## [79] 0.930681653 0.617665714 0.146486670 0.264246609 0.264513266 0.162621612
## [85] 0.673465679 0.500767129 0.937924750 0.695544583 0.357271798 0.598875429
## [91] 0.152596309 0.076496140 0.037241083 0.840877036 0.441625184 0.586302694
## [97] 0.969793316 0.472466059 0.788852791 0.556381453 0.373063611 0.341096496
## [103] 0.207239772 0.924363683 0.378641443 0.234023039 0.505139999 0.750825016
## [109] 0.499336662 0.508747910 0.946956716 0.900296219 0.256854436 0.111057775
## [115] 0.340814297 0.824406277 0.751563365 0.117278074 0.353128582 0.415334137
## [121] 0.082547626 0.449173694 0.190815686 0.853732394 0.304033840 0.773973787
## [127] 0.360801893 0.658024479 0.119388044 0.332180292 0.778692634 0.826945276
## [133] 0.225077764 0.151133046 0.598675336 0.402574543 0.163518221 0.831034539
## [139] 0.190064983 0.234476050 0.956860072 0.955845884 0.497507839 0.911364766
## [145] 0.037895548 0.001628185 0.640542782 0.330983290 0.844570291 0.692148243
## [151] 0.128881640 0.590745613 0.895754564 0.888607764 0.144950876 0.707310679
## [157] 0.998653080 0.663392347 0.477195478 0.095385494 0.471920465 0.001688081
## [163] 0.775651425 0.692080994 0.383524283 0.430892403 0.982854022 0.510409627
## [169] 0.692325725 0.925662315 0.528041075 0.284197604 0.418496805 0.068364507
## [175] 0.686554098 0.715093758 0.195767931 0.015473280 0.975528731 0.812624181
## [181] 0.995099062 0.390216203 0.293001638 0.449126384 0.692462750 0.573976931
## [187] 0.831878078 0.668777480 0.294015622 0.199641767 0.036673328 0.127516979
## [193] 0.281501499 0.948052241 0.439390214 0.107154197 0.927471209 0.831606760
## [199] 0.195735740 0.497585212 0.151936247 0.573913437 0.596205090 0.601785248
## [205] 0.698316588 0.499189962 0.057690957 0.220075791 0.727336468 0.817795493
## [211] 0.391520039 0.247778251 0.590703504 0.798631108 0.407245834 0.512585240
## [217] 0.949418148 0.742313084 0.320740733 0.542677629 0.461642558 0.140921861
## [223] 0.958327570 0.165707943 0.097696365 0.275134149 0.162593379 0.995995417
## [229] 0.105623030 0.043665274 0.580976533 0.698451236 0.708839504 0.538314692
## [235] 0.602859550 0.054381860 0.835997179 0.045499318 0.436523591 0.263681118
## [241] 0.398219415 0.522990646 0.931309018 0.097727430 0.142300199 0.714204736
## [247] 0.771796806 0.056137281 0.772611828 0.661782246 0.283697261 0.325760602
## [253] 0.954987529 0.679286841 0.598270820 0.112990879 0.076134036 0.599449808
## [259] 0.820954024 0.852434965 0.069969436 0.784664081 0.147268217 0.495235343
## [265] 0.757871550 0.646294683 0.249129832 0.952594185 0.109358901 0.677771463
## [271] 0.285536664 0.223654513 0.066582335 0.812040415 0.448148372 0.942635793
## [277] 0.459585486 0.169453749 0.412299851 0.244814450 0.421652833 0.393510987
## [283] 0.882489284 0.530115756 0.828347318 0.349520463 0.800475304 0.882864799
## [289] 0.721191243 0.103859520 0.293513558 0.422168590 0.324410188 0.700854423
## [295] 0.185095790 0.722235363 0.195016639 0.151195856 0.405973460 0.241626229
## [301] 0.081543350 0.722169250 0.969289649 0.191633646 0.602954840 0.113691680
## [307] 0.747093197 0.849556919 0.992179767 0.543971356 0.838973855 0.278728514
## [313] 0.945480804 0.577006145 0.992808911 0.349458115 0.779848629 0.666917439
## [319] 0.745346714 0.010029611 0.774651463 0.302333868 0.956028710 0.485571647
## [325] 0.717346388 0.352037656 0.530520519 0.410139151 0.572289647 0.325050641
## [331] 0.726890115 0.250532807 0.758126864 0.074771861 0.823738356 0.365241985
## [337] 0.099111347 0.059670023 0.855015721 0.213112721 0.333565434 0.053401828
## [343] 0.572226371 0.485181176 0.058103272 0.635142578 0.206566374 0.982194712
## [349] 0.496319534 0.784719863 0.936640233 0.845767003 0.534228195 0.333221705
## [355] 0.231426389 0.576624146 0.829997422 0.985049080 0.831038400 0.732339219
## [361] 0.233513039 0.203798439 0.968051942 0.514671266 0.543752870 0.239320876
## [367] 0.652906440 0.777638597 0.592673963 0.628677818 0.298822339 0.736050281
## [373] 0.557709945 0.369949771 0.527301961 0.262278623 0.079388478 0.237762480
## [379] 0.783270498 0.361300691 0.989720475 0.143313599 0.774094188 0.494238572
## [385] 0.072386479 0.534741362 0.109603091 0.328907639 0.728278406 0.386425937
## [391] 0.909265316 0.469675608 0.227546271 0.421805254 0.254567731 0.930984229
## [397] 0.876837966 0.398683367 0.139519265 0.729025956 0.781153139 0.231764700
## [403] 0.890418152 0.478012607 0.756738459 0.744363362 0.247364841 0.272542872
## [409] 0.895419248 0.919760516 0.622461988 0.589932874 0.118019102 0.770184652
## [415] 0.770022359 0.489063190 0.577914404 0.355203659 0.369138978 0.810528167
## [421] 0.619658417 0.011115393 0.345823349 0.066070515 0.787958041 0.778060498
## [427] 0.732451087 0.282290304 0.114197544 0.218011633 0.425084719 0.288071736
## [433] 0.684201363 0.429922780 0.230752425 0.056946116 0.612361413 0.161628799
## [439] 0.139013448 0.922058337 0.555229859 0.978704648 0.700476071 0.303528412
## [445] 0.892724094 0.397491819 0.502302529 0.613097531 0.896583733 0.956906162
## [451] 0.273338261 0.580374689 0.262838359 0.281244520 0.602157947 0.466925352
## [457] 0.467745088 0.515988382 0.501278389 0.607533123 0.989017883 0.549842416
## [463] 0.314537993 0.972180908 0.293728807 0.846915603 0.206009153 0.194472312
## [469] 0.101262353 0.814422814 0.482329956 0.461896402 0.379491493 0.450158319
## [475] 0.623322848 0.519291367 0.899934396 0.432261456 0.490933362 0.819897338
## [481] 0.366262725 0.612604435 0.768546528 0.843445198 0.061691130 0.029996971
## [487] 0.024171958 0.080897298 0.023869339 0.298005496 0.999250361 0.367830536
## [493] 0.463672694 0.617016019 0.199696122 0.102965977 0.905346160 0.720762500
## [499] 0.305466799 0.885406054 0.110911521 0.115079879 0.018058504 0.794356817
## [505] 0.533088625 0.367866126 0.750413244 0.207115402 0.592321409 0.059678636
## [511] 0.143038275 0.960510154 0.872627860 0.984390257 0.482031347 0.845231351
## [517] 0.859425937 0.539699679 0.749371267 0.165005493 0.488857922 0.102601201
## [523] 0.887547875 0.873128228 0.261414303 0.891797631 0.806001128 0.641529482
## [529] 0.998460126 0.672420091 0.471105205 0.221536519 0.553669299 0.324599893
## [535] 0.115241097 0.768231570 0.018811947 0.001629436 0.356331911 0.660983473
## [541] 0.609992900 0.303309948 0.892896187 0.600708682 0.014134423 0.148630383
## [547] 0.081163349 0.344084853 0.452941660 0.728304010 0.436362224 0.555072704
## [553] 0.313182871 0.364686397 0.219824601 0.982000357 0.925516336 0.078055036
## [559] 0.169437651 0.508733515 0.346980073 0.628925537 0.342957895 0.930269760
## [565] 0.725315120 0.188514341 0.596882894 0.145274307 0.925141892 0.321526940
## [571] 0.509348996 0.195539518 0.735094618 0.209959245 0.403711953 0.080208557
## [577] 0.133455009 0.178407059 0.990888248 0.844790772 0.104338356 0.344227977
## [583] 0.407846172 0.218285647 0.115869139 0.775939705 0.573197196 0.866491833
## [589] 0.342088168 0.166318275 0.675765958 0.120005311 0.397155538 0.094129253
## [595] 0.343756856 0.085614901 0.974288777 0.676872179 0.932470661 0.864134883
## [601] 0.897275674 0.926951026 0.148063693 0.077431759 0.318450120 0.938682380
## [607] 0.555695954 0.757445828 0.878495234 0.446940528 0.328885562 0.377651071
## [613] 0.226200801 0.894298713 0.409276224 0.465539428 0.347751064 0.741259235
## [619] 0.321760682 0.215512951 0.947720260 0.039362745 0.464068270 0.381666531
## [625] 0.559123816 0.994272974 0.835722828 0.807518377 0.566090249 0.753944407
## [631] 0.254453491 0.130348381 0.424512580 0.111180187 0.082543196 0.057106809
## [637] 0.098498216 0.050055716 0.475254707 0.326666887 0.563573959 0.870861817
## [643] 0.270857455 0.116090567 0.791620874 0.451073535 0.787995760 0.985283350
## [649] 0.303287403 0.703824477 0.089595768 0.018910687 0.748919007 0.655260754
## [655] 0.352629456 0.413938984 0.460839499 0.525453911 0.678156951 0.167843549
## [661] 0.320407663 0.913342420 0.627157555 0.838865842 0.667628508 0.076359437
## [667] 0.365589226 0.699902848 0.470582750 0.941228512 0.654382632 0.340517952
## [673] 0.570333534 0.188144427 0.814848116 0.388426496 0.224646474 0.556911477
## [679] 0.810784187 0.729066580 0.996684623 0.213702750 0.022322144 0.806012773
## [685] 0.295501844 0.427290440 0.288605650 0.606712177 0.015628036 0.418264795
## [691] 0.385526708 0.109979974 0.219385035 0.097044037 0.578319201 0.374016859
## [697] 0.582248756 0.061627911 0.531836707 0.677074388 0.501010621 0.248482451
## [703] 0.657385442 0.373761891 0.060857804 0.067924368 0.782525614 0.172013910
## [709] 0.798717820 0.757290434 0.220233459 0.208403861 0.081492202 0.053805887
## [715] 0.890366372 0.613281964 0.454696302 0.763781759 0.589252010 0.195387712
## [721] 0.277483228 0.211310662 0.987333431 0.804935586 0.703104864 0.309519316
## [727] 0.320821587 0.719956142 0.534241512 0.478643484 0.780095659 0.989776901
## [733] 0.180533577 0.699631556 0.062317391 0.352279458 0.995177130 0.239837652
## [739] 0.220945327 0.511005272 0.122587292 0.820891897 0.422549317 0.902097764
## [745] 0.922546736 0.275678563 0.133173077 0.672910506 0.878100904 0.760998949
## [751] 0.452274190 0.464442620 0.755265402 0.126768193 0.416234476 0.670269953
## [757] 0.721878579 0.139885807 0.950174628 0.405076530 0.828266029 0.469601475
## [763] 0.432336190 0.024828872 0.300575376 0.426025315 0.246670111 0.688526945
## [769] 0.491748481 0.013528817 0.066387978 0.417166933 0.504280854 0.802140269
## [775] 0.283952149 0.947565719 0.896370076 0.900450043 0.794473912 0.480362520
## [781] 0.828861272 0.640994719 0.747637209 0.880240695 0.711737456 0.367215589
## [787] 0.152796369 0.348188523 0.689622859 0.171793293 0.859361424 0.375628477
## [793] 0.550425747 0.965952176 0.361401038 0.879631582 0.565421368 0.156275404
## [799] 0.344864959 0.463124321 0.811757529 0.488862801 0.743148863 0.133013783
## [805] 0.589611011 0.611105756 0.276231941 0.260520807 0.679401428 0.809293290
## [811] 0.586202603 0.695341088 0.685688768 0.927135491 0.985022454 0.183766786
## [817] 0.924981493 0.731825473 0.054682772 0.583406445 0.219268808 0.666116104
## [823] 0.569991940 0.492079156 0.228769573 0.404742171 0.934692784 0.537876581
## [829] 0.166780214 0.536287940 0.552202410 0.072256522 0.496458780 0.456040369
## [835] 0.393622876 0.011024947 0.193994464 0.846676618 0.732060794 0.154013110
## [841] 0.495274963 0.038687099 0.557278071 0.616994442 0.016409115 0.312740984
## [847] 0.099446812 0.020472362 0.813040866 0.079358052 0.912562903 0.612977098
## [853] 0.429877098 0.844246884 0.529659696 0.916633805 0.334754957 0.823779585
## [859] 0.017770486 0.383306129 0.828988076 0.106052489 0.029119933 0.769334671
## [865] 0.122562324 0.174394663 0.802665826 0.932256648 0.101531677 0.725361658
## [871] 0.425217895 0.160108982 0.487231185 0.993145169 0.733422091 0.505941999
## [877] 0.354659218 0.474212153 0.947134147 0.856659344 0.655457680 0.068173315
## [883] 0.071943425 0.691070290 0.707474268 0.089749587 0.542673255 0.515203790
## [889] 0.778991593 0.615054467 0.210921333 0.955100620 0.993376561 0.234640644
## [895] 0.197270836 0.472383106 0.598302885 0.026189832 0.591927006 0.617938087
## [901] 0.139305883 0.063313645 0.691478449 0.885254584 0.866993489 0.135558783
## [907] 0.717546294 0.448297344 0.061714906 0.022476412 0.221998211 0.520048824
## [913] 0.140691189 0.585580862 0.674426475 0.204786538 0.421975135 0.182528427
## [919] 0.623867529 0.979665570 0.543247781 0.480047517 0.959969984 0.875993973
## [925] 0.452575472 0.665454784 0.934608673 0.898282250 0.801216512 0.923019439
## [931] 0.628250938 0.213067205 0.707323575 0.219235647 0.313522071 0.147559900
## [937] 0.357954981 0.554781088 0.909136755 0.718025924 0.862636004 0.378973814
## [943] 0.096953418 0.650402510 0.323979246 0.822091452 0.491844151 0.907368335
## [949] 0.960256829 0.994826878 0.065672537 0.496727935 0.461893361 0.915583731
## [955] 0.016033113 0.556227020 0.460317148 0.961693148 0.340007442 0.902891099
## [961] 0.716477367 0.407455706 0.682836337 0.091295487 0.367178087 0.574590105
## [967] 0.355277090 0.122285569 0.570602229 0.959674738 0.019760793 0.597445185
## [973] 0.192849663 0.946904438 0.867436541 0.696043562 0.349707019 0.534124918
## [979] 0.096540439 0.378559990 0.283493578 0.815772196 0.734674124 0.283656383
## [985] 0.281397225 0.179322496 0.444717694 0.417740601 0.315915876 0.760689826
## [991] 0.435030985 0.808220835 0.593515207 0.608250864 0.821586357 0.315038193
## [997] 0.814075205 0.257921710 0.274120497 0.162863488(sqrt_LotArea_samp_CDF <- ecdf(sqrt_LotArea_samp))## Empirical CDF
## Call: ecdf(sqrt_LotArea_samp)
## x[1:1000] = 0.035588, 0.035615, 0.036898, ..., 144.36, 157.16Modeling. Build some type of multiple regression model and submit your model to the competition board. Provide your complete model summary and results with analysis. Report your Kaggle.com user name and score. 10 points