Final Project
Mikhail Broomes
2024-05-19
df_train <- read.csv("https://raw.githubusercontent.com/MAB592/Kaggle-Competition/main/train.csv")
df_test <- read.csv("https://raw.githubusercontent.com/MAB592/Kaggle-Competition/main/test.csv")
head(df_train)## Id MSSubClass MSZoning LotFrontage LotArea Street Alley LotShape LandContour
## 1 1 60 RL 65 8450 Pave <NA> Reg Lvl
## 2 2 20 RL 80 9600 Pave <NA> Reg Lvl
## 3 3 60 RL 68 11250 Pave <NA> IR1 Lvl
## 4 4 70 RL 60 9550 Pave <NA> IR1 Lvl
## 5 5 60 RL 84 14260 Pave <NA> IR1 Lvl
## 6 6 50 RL 85 14115 Pave <NA> IR1 Lvl
## Utilities LotConfig LandSlope Neighborhood Condition1 Condition2 BldgType
## 1 AllPub Inside Gtl CollgCr Norm Norm 1Fam
## 2 AllPub FR2 Gtl Veenker Feedr Norm 1Fam
## 3 AllPub Inside Gtl CollgCr Norm Norm 1Fam
## 4 AllPub Corner Gtl Crawfor Norm Norm 1Fam
## 5 AllPub FR2 Gtl NoRidge Norm Norm 1Fam
## 6 AllPub Inside Gtl Mitchel Norm Norm 1Fam
## HouseStyle OverallQual OverallCond YearBuilt YearRemodAdd RoofStyle RoofMatl
## 1 2Story 7 5 2003 2003 Gable CompShg
## 2 1Story 6 8 1976 1976 Gable CompShg
## 3 2Story 7 5 2001 2002 Gable CompShg
## 4 2Story 7 5 1915 1970 Gable CompShg
## 5 2Story 8 5 2000 2000 Gable CompShg
## 6 1.5Fin 5 5 1993 1995 Gable CompShg
## Exterior1st Exterior2nd MasVnrType MasVnrArea ExterQual ExterCond Foundation
## 1 VinylSd VinylSd BrkFace 196 Gd TA PConc
## 2 MetalSd MetalSd None 0 TA TA CBlock
## 3 VinylSd VinylSd BrkFace 162 Gd TA PConc
## 4 Wd Sdng Wd Shng None 0 TA TA BrkTil
## 5 VinylSd VinylSd BrkFace 350 Gd TA PConc
## 6 VinylSd VinylSd None 0 TA TA Wood
## BsmtQual BsmtCond BsmtExposure BsmtFinType1 BsmtFinSF1 BsmtFinType2
## 1 Gd TA No GLQ 706 Unf
## 2 Gd TA Gd ALQ 978 Unf
## 3 Gd TA Mn GLQ 486 Unf
## 4 TA Gd No ALQ 216 Unf
## 5 Gd TA Av GLQ 655 Unf
## 6 Gd TA No GLQ 732 Unf
## BsmtFinSF2 BsmtUnfSF TotalBsmtSF Heating HeatingQC CentralAir Electrical
## 1 0 150 856 GasA Ex Y SBrkr
## 2 0 284 1262 GasA Ex Y SBrkr
## 3 0 434 920 GasA Ex Y SBrkr
## 4 0 540 756 GasA Gd Y SBrkr
## 5 0 490 1145 GasA Ex Y SBrkr
## 6 0 64 796 GasA Ex Y SBrkr
## X1stFlrSF X2ndFlrSF LowQualFinSF GrLivArea BsmtFullBath BsmtHalfBath FullBath
## 1 856 854 0 1710 1 0 2
## 2 1262 0 0 1262 0 1 2
## 3 920 866 0 1786 1 0 2
## 4 961 756 0 1717 1 0 1
## 5 1145 1053 0 2198 1 0 2
## 6 796 566 0 1362 1 0 1
## HalfBath BedroomAbvGr KitchenAbvGr KitchenQual TotRmsAbvGrd Functional
## 1 1 3 1 Gd 8 Typ
## 2 0 3 1 TA 6 Typ
## 3 1 3 1 Gd 6 Typ
## 4 0 3 1 Gd 7 Typ
## 5 1 4 1 Gd 9 Typ
## 6 1 1 1 TA 5 Typ
## Fireplaces FireplaceQu GarageType GarageYrBlt GarageFinish GarageCars
## 1 0 <NA> Attchd 2003 RFn 2
## 2 1 TA Attchd 1976 RFn 2
## 3 1 TA Attchd 2001 RFn 2
## 4 1 Gd Detchd 1998 Unf 3
## 5 1 TA Attchd 2000 RFn 3
## 6 0 <NA> Attchd 1993 Unf 2
## GarageArea GarageQual GarageCond PavedDrive WoodDeckSF OpenPorchSF
## 1 548 TA TA Y 0 61
## 2 460 TA TA Y 298 0
## 3 608 TA TA Y 0 42
## 4 642 TA TA Y 0 35
## 5 836 TA TA Y 192 84
## 6 480 TA TA Y 40 30
## EnclosedPorch X3SsnPorch ScreenPorch PoolArea PoolQC Fence MiscFeature
## 1 0 0 0 0 <NA> <NA> <NA>
## 2 0 0 0 0 <NA> <NA> <NA>
## 3 0 0 0 0 <NA> <NA> <NA>
## 4 272 0 0 0 <NA> <NA> <NA>
## 5 0 0 0 0 <NA> <NA> <NA>
## 6 0 320 0 0 <NA> MnPrv Shed
## MiscVal MoSold YrSold SaleType SaleCondition SalePrice
## 1 0 2 2008 WD Normal 208500
## 2 0 5 2007 WD Normal 181500
## 3 0 9 2008 WD Normal 223500
## 4 0 2 2006 WD Abnorml 140000
## 5 0 12 2008 WD Normal 250000
## 6 700 10 2009 WD Normal 143000missing_values <- df_train %>%
summarise(across(everything(), ~ sum(is.na(.)))) %>%
pivot_longer(everything(), names_to = "Column", values_to = "MissingValues")
print(missing_values)## # A tibble: 81 × 2
## Column MissingValues
## <chr> <int>
## 1 Id 0
## 2 MSSubClass 0
## 3 MSZoning 0
## 4 LotFrontage 259
## 5 LotArea 0
## 6 Street 0
## 7 Alley 1369
## 8 LotShape 0
## 9 LandContour 0
## 10 Utilities 0
## # ℹ 71 more rowsProbability
Calculate as a minimum the below probabilities a through c. Assume the small letter “x” is estimated as the 3d quartile of the X variable, and the small letter “y” is estimated as the 2d quartile of the Y variable. Interpret the meaning of all probabilities. In addition, make a table of counts as shown below.
num_cols <- select_if(df_train, is.numeric)
col_names <- colnames(num_cols)par(mfrow=c(3,3))
for(i in col_names) {
hist(num_cols[,i],xlab=i,main="")
}
For the X variable I will just the feature LotArea(Which is right skewed) and the Y variable will be the sale price
X <- df_train$LotArea
Y <- df_train$SalePrice
x <- quantile(df_train$LotArea, 0.75)
y <- quantile(df_train$SalePrice, 0.5)Getting all the required calculations for the probabilities
P_X_gt_x <- sum(df_train$LotArea > x) / nrow(df_train)
P_Y_gt_y <- sum(df_train$SalePrice > y) / nrow(df_train)
P_X_gt_x_and_Y_gt_y <- sum(df_train$LotArea > x & df_train$SalePrice > y) / nrow(df_train)
P_X_lt_x_and_Y_gt_y <- sum(df_train$LotArea < x & df_train$SalePrice > y) / nrow(df_train)
P_X_gt_x_given_Y_gt_y <- P_X_gt_x_and_Y_gt_y / P_Y_gt_y
P_X_lt_x_given_Y_gt_y <- P_X_lt_x_and_Y_gt_y / P_Y_gt_ya) P(X>x | Y>y)
prob_a <- P_X_gt_x_and_Y_gt_y / P_Y_gt_y
cat('P(X>x|Y>y) =', round(prob_a, 3))## P(X>x|Y>y) = 0.379P(X>x,Y>y) is 37.9%. This means that the probability of the LotArea being larger than 11602 and the SalePrice is larger than 163000 is 37.9%
b) P(X>x, Y>y)
prob_b <- P_X_gt_x_and_Y_gt_y/nrow(df_train)
cat('P(X>x,Y>y) =', round(prob_b, 5))## P(X>x,Y>y) = 0.00013P(X>x,Y>y) is 0.013%. This means that the probability of the LotFrontage being larger than 79 and the SalePrice is larger than 163000 is 0.013%
c) P(X<x | Y>y)
prob_a <- P_X_lt_x_and_Y_gt_y / P_Y_gt_y
cat('P(X<x | Y>y) =', round(prob_a, 3))## P(X<x | Y>y) = 0.621P(X>x,Y>y) is 62.1%. This means that the probability of the LotFrontage being larger than 79 and the SalePrice is larger than 163000 is 62.1%
Tables of Counts
table_of_counts <- addmargins(table(X>x, Y>y))
rownames(table_of_counts) <- c('<=3d quartile', '>3d quartile', 'Total')
colnames(table_of_counts) <- c('<=2d quartile', '>2d quartile', 'Total')
print(table_of_counts)##
## <=2d quartile >2d quartile Total
## <=3d quartile 643 452 1095
## >3d quartile 89 276 365
## Total 732 728 1460Does splitting the training data in this fashion make them independent? Let A be the new variable counting those observations above the 3d quartile for X, and let B be the new variable counting those observations above the 2d quartile for Y. Does P(A|B)=P(A)P(B)? Check mathematically, and then evaluate by running a Chi Square test for association.
X <- df_train$LotArea
Y <- df_train$SalePrice
A <- X > x
B <- Y > y
P_A_given_B <- sum(A*B)/sum(B)
P_A <- sum(A)/nrow(df_train)
P_B <- sum(B)/nrow(df_train)
P_A_P_B <- P_A*P_B
print(paste('P(A|B) = P(A)P(B):', P_A_given_B == P_A_P_B))## [1] "P(A|B) = P(A)P(B): FALSE"P(A|B)≠P(A)P(B), which means splitting the training data does not make them independent.
Using the Chi square test for independence
assocstats <- table(A, B)
chi_test <- chisq.test(assocstats)
print(chi_test)##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: assocstats
## X-squared = 127.74, df = 1, p-value < 2.2e-16The p value is 2.2e-16 which is less than 0.05, so we reject the null hypothesis which proves that that they independent
Descriptive and Inferential Statistics.
Provide univariate descriptive statistics and appropriate plots for the training data set.
summary(df_train)## Id MSSubClass MSZoning LotFrontage
## Min. : 1.0 Min. : 20.0 Length:1460 Min. : 21.00
## 1st Qu.: 365.8 1st Qu.: 20.0 Class :character 1st Qu.: 59.00
## Median : 730.5 Median : 50.0 Mode :character Median : 69.00
## Mean : 730.5 Mean : 56.9 Mean : 70.05
## 3rd Qu.:1095.2 3rd Qu.: 70.0 3rd Qu.: 80.00
## Max. :1460.0 Max. :190.0 Max. :313.00
## NA's :259
## LotArea Street Alley LotShape
## Min. : 1300 Length:1460 Length:1460 Length:1460
## 1st Qu.: 7554 Class :character Class :character Class :character
## Median : 9478 Mode :character Mode :character Mode :character
## Mean : 10517
## 3rd Qu.: 11602
## Max. :215245
##
## LandContour Utilities LotConfig LandSlope
## Length:1460 Length:1460 Length:1460 Length:1460
## Class :character Class :character Class :character Class :character
## Mode :character Mode :character Mode :character Mode :character
##
##
##
##
## Neighborhood Condition1 Condition2 BldgType
## Length:1460 Length:1460 Length:1460 Length:1460
## Class :character Class :character Class :character Class :character
## Mode :character Mode :character Mode :character Mode :character
##
##
##
##
## HouseStyle OverallQual OverallCond YearBuilt
## Length:1460 Min. : 1.000 Min. :1.000 Min. :1872
## Class :character 1st Qu.: 5.000 1st Qu.:5.000 1st Qu.:1954
## Mode :character Median : 6.000 Median :5.000 Median :1973
## Mean : 6.099 Mean :5.575 Mean :1971
## 3rd Qu.: 7.000 3rd Qu.:6.000 3rd Qu.:2000
## Max. :10.000 Max. :9.000 Max. :2010
##
## YearRemodAdd RoofStyle RoofMatl Exterior1st
## Min. :1950 Length:1460 Length:1460 Length:1460
## 1st Qu.:1967 Class :character Class :character Class :character
## Median :1994 Mode :character Mode :character Mode :character
## Mean :1985
## 3rd Qu.:2004
## Max. :2010
##
## Exterior2nd MasVnrType MasVnrArea ExterQual
## Length:1460 Length:1460 Min. : 0.0 Length:1460
## Class :character Class :character 1st Qu.: 0.0 Class :character
## Mode :character Mode :character Median : 0.0 Mode :character
## Mean : 103.7
## 3rd Qu.: 166.0
## Max. :1600.0
## NA's :8
## ExterCond Foundation BsmtQual BsmtCond
## Length:1460 Length:1460 Length:1460 Length:1460
## Class :character Class :character Class :character Class :character
## Mode :character Mode :character Mode :character Mode :character
##
##
##
##
## BsmtExposure BsmtFinType1 BsmtFinSF1 BsmtFinType2
## Length:1460 Length:1460 Min. : 0.0 Length:1460
## Class :character Class :character 1st Qu.: 0.0 Class :character
## Mode :character Mode :character Median : 383.5 Mode :character
## Mean : 443.6
## 3rd Qu.: 712.2
## Max. :5644.0
##
## BsmtFinSF2 BsmtUnfSF TotalBsmtSF Heating
## Min. : 0.00 Min. : 0.0 Min. : 0.0 Length:1460
## 1st Qu.: 0.00 1st Qu.: 223.0 1st Qu.: 795.8 Class :character
## Median : 0.00 Median : 477.5 Median : 991.5 Mode :character
## Mean : 46.55 Mean : 567.2 Mean :1057.4
## 3rd Qu.: 0.00 3rd Qu.: 808.0 3rd Qu.:1298.2
## Max. :1474.00 Max. :2336.0 Max. :6110.0
##
## HeatingQC CentralAir Electrical X1stFlrSF
## Length:1460 Length:1460 Length:1460 Min. : 334
## Class :character Class :character Class :character 1st Qu.: 882
## Mode :character Mode :character Mode :character Median :1087
## Mean :1163
## 3rd Qu.:1391
## Max. :4692
##
## X2ndFlrSF LowQualFinSF GrLivArea BsmtFullBath
## Min. : 0 Min. : 0.000 Min. : 334 Min. :0.0000
## 1st Qu.: 0 1st Qu.: 0.000 1st Qu.:1130 1st Qu.:0.0000
## Median : 0 Median : 0.000 Median :1464 Median :0.0000
## Mean : 347 Mean : 5.845 Mean :1515 Mean :0.4253
## 3rd Qu.: 728 3rd Qu.: 0.000 3rd Qu.:1777 3rd Qu.:1.0000
## Max. :2065 Max. :572.000 Max. :5642 Max. :3.0000
##
## BsmtHalfBath FullBath HalfBath BedroomAbvGr
## Min. :0.00000 Min. :0.000 Min. :0.0000 Min. :0.000
## 1st Qu.:0.00000 1st Qu.:1.000 1st Qu.:0.0000 1st Qu.:2.000
## Median :0.00000 Median :2.000 Median :0.0000 Median :3.000
## Mean :0.05753 Mean :1.565 Mean :0.3829 Mean :2.866
## 3rd Qu.:0.00000 3rd Qu.:2.000 3rd Qu.:1.0000 3rd Qu.:3.000
## Max. :2.00000 Max. :3.000 Max. :2.0000 Max. :8.000
##
## KitchenAbvGr KitchenQual TotRmsAbvGrd Functional
## Min. :0.000 Length:1460 Min. : 2.000 Length:1460
## 1st Qu.:1.000 Class :character 1st Qu.: 5.000 Class :character
## Median :1.000 Mode :character Median : 6.000 Mode :character
## Mean :1.047 Mean : 6.518
## 3rd Qu.:1.000 3rd Qu.: 7.000
## Max. :3.000 Max. :14.000
##
## Fireplaces FireplaceQu GarageType GarageYrBlt
## Min. :0.000 Length:1460 Length:1460 Min. :1900
## 1st Qu.:0.000 Class :character Class :character 1st Qu.:1961
## Median :1.000 Mode :character Mode :character Median :1980
## Mean :0.613 Mean :1979
## 3rd Qu.:1.000 3rd Qu.:2002
## Max. :3.000 Max. :2010
## NA's :81
## GarageFinish GarageCars GarageArea GarageQual
## Length:1460 Min. :0.000 Min. : 0.0 Length:1460
## Class :character 1st Qu.:1.000 1st Qu.: 334.5 Class :character
## Mode :character Median :2.000 Median : 480.0 Mode :character
## Mean :1.767 Mean : 473.0
## 3rd Qu.:2.000 3rd Qu.: 576.0
## Max. :4.000 Max. :1418.0
##
## GarageCond PavedDrive WoodDeckSF OpenPorchSF
## Length:1460 Length:1460 Min. : 0.00 Min. : 0.00
## Class :character Class :character 1st Qu.: 0.00 1st Qu.: 0.00
## Mode :character Mode :character Median : 0.00 Median : 25.00
## Mean : 94.24 Mean : 46.66
## 3rd Qu.:168.00 3rd Qu.: 68.00
## Max. :857.00 Max. :547.00
##
## EnclosedPorch X3SsnPorch ScreenPorch PoolArea
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.000
## 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.000
## Median : 0.00 Median : 0.00 Median : 0.00 Median : 0.000
## Mean : 21.95 Mean : 3.41 Mean : 15.06 Mean : 2.759
## 3rd Qu.: 0.00 3rd Qu.: 0.00 3rd Qu.: 0.00 3rd Qu.: 0.000
## Max. :552.00 Max. :508.00 Max. :480.00 Max. :738.000
##
## PoolQC Fence MiscFeature MiscVal
## Length:1460 Length:1460 Length:1460 Min. : 0.00
## Class :character Class :character Class :character 1st Qu.: 0.00
## Mode :character Mode :character Mode :character Median : 0.00
## Mean : 43.49
## 3rd Qu.: 0.00
## Max. :15500.00
##
## MoSold YrSold SaleType SaleCondition
## Min. : 1.000 Min. :2006 Length:1460 Length:1460
## 1st Qu.: 5.000 1st Qu.:2007 Class :character Class :character
## Median : 6.000 Median :2008 Mode :character Mode :character
## Mean : 6.322 Mean :2008
## 3rd Qu.: 8.000 3rd Qu.:2009
## Max. :12.000 Max. :2010
##
## SalePrice
## Min. : 34900
## 1st Qu.:129975
## Median :163000
## Mean :180921
## 3rd Qu.:214000
## Max. :755000
## dim(df_train)## [1] 1460 81missing_values <- df_train %>%
summarise(across(everything(), ~ sum(is.na(.)))) %>%
pivot_longer(everything(), names_to = "Column", values_to = "MissingValues")
print(missing_values)## # A tibble: 81 × 2
## Column MissingValues
## <chr> <int>
## 1 Id 0
## 2 MSSubClass 0
## 3 MSZoning 0
## 4 LotFrontage 259
## 5 LotArea 0
## 6 Street 0
## 7 Alley 1369
## 8 LotShape 0
## 9 LandContour 0
## 10 Utilities 0
## # ℹ 71 more rowsProvide a scatterplot of X and Y.
df <- tibble(LotArea = X, SalePrice = Y)
df %>% ggplot(aes(x = LotArea, y = SalePrice)) +
geom_point() +
geom_smooth(method = 'lm', se = FALSE) +
labs(title = 'Scatter Plot of SalePrice vs LotFrontage') +
theme_minimal()## `geom_smooth()` using formula = 'y ~ x'
We can see some outliers but the there is a linear relationship even though the LotArea is skewed
Provide a 95% CI for the difference in the mean of the variables.
CI <- t.test(X, Y, conf.level = 0.95)
print(paste('95% confidence interval:', round(CI$conf.int[1], 3), round(CI$conf.int[2], 3)))## [1] "95% confidence interval: -174514.682 -166294.053"Derive a correlation matrix for two of the quantitative variables you selected:
correlation_matrix <- cor(df[, c('LotArea', 'SalePrice')])
print(correlation_matrix)## LotArea SalePrice
## LotArea 1.0000000 0.2638434
## SalePrice 0.2638434 1.0000000Test the hypothesis that the correlation between these variables is 0 and provide a 99% confidence interval
correlation_test <- cor.test(df$LotArea, df$SalePrice, conf.level = 0.99)
print(paste('p-value:', correlation_test$p.value))## [1] "p-value: 1.12313915491861e-24"The p-value is less than 0.01. Thus we can reject the null hypothesis that the correlation between LotArea and SalePrice is 0. We can also see this from our correlation matrix which shows 0.2638
Linear Algebra and Correlation.
Invert your correlation matrix. (This is known as the precision matrix and contains variance inflation factors on the diagonal.)
precision_matrix <- solve(correlation_matrix)
print(precision_matrix)## LotArea SalePrice
## LotArea 1.0748219 -0.2835846
## SalePrice -0.2835846 1.0748219Multiply the correlation matrix by the precision matrix
c_by_p <- correlation_matrix%*%precision_matrix
print(round(c_by_p), 3)## LotArea SalePrice
## LotArea 1 0
## SalePrice 0 1Given that the precision matrix is the inverse of the correlation matrix, I anticipated that multiplying the two would yield the identity matrix, which indeed happened.
Conduct principle components analysis (research this!) and interpret.
Using the PCA between LotArea and SalePrice
pca <- prcomp(df, scale. = TRUE)
summary(pca)## Importance of components:
## PC1 PC2
## Standard deviation 1.1242 0.8580
## Proportion of Variance 0.6319 0.3681
## Cumulative Proportion 0.6319 1.0000print(pca$rotation)## PC1 PC2
## LotArea 0.7071068 0.7071068
## SalePrice 0.7071068 -0.7071068In the PCA results, PC1 explains most of the variation (about 63%),
and both LotArea and SalePrice contribute
equally to it. PC2 explains less variation (about 37%) and shows a
contrast between LotArea and SalePrice, where
LotArea goes up while SalePrice goes down.
Calculus-Based Probability & Statistics.
Many times, it makes sense to fit a closed form distribution to data. For your variable that is skewed to the right, shift it so that the minimum value is above zero.
print(summary(X))## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1300 7554 9478 10517 11602 215245Our minimum value is already above 0 so we don’t need to shift this feature
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 ).
exp_fit <- fitdistr(X, "exponential")
lambda <- exp_fit$estimate
cat("Optimal value of lambda:", lambda)## Optimal value of lambda: 9.50857e-05Find the optimal value of λ for this distribution, and then take 1000 samples from this exponential distribution using this value (e.g., rexp(1000, λ))
`
set.seed(21)
sample <- rexp(1000, lambda)Plot a histogram and compare it with a histogram of your original variable.
ggplot() +
geom_histogram(aes(X, fill = "Original Variable"), bins = 30, alpha = 0.5) +
geom_histogram(aes(sample, fill = "Exponential Sample"), bins = 30, alpha = 0.5) +
labs(title = "Histogram of Expnential Sample and Original Variable")
Using the exponential pdf, find the 5th and 95th percentiles using the cumulative distribution function (CDF).
exp_percent <- quantile(sample, c(0.05, 0.95))
cat('The 5th percentile:', round(exp_percent[1], 3))## The 5th percentile: 496.869cat('The 95th percentile:', round(exp_percent[2], 3))## The 95th percentile: 30536.41Also generate a 95% confidence interval from the empirical data, assuming normality.
CI <- t.test(X)
cat("95% confidence interval of X:", round(CI$conf.int[1], 3), round(CI$conf.int[2], 3))## 95% confidence interval of X: 10004.42 11029.24There is a 95% confidence that the mean of X falls between 10004.42 and 11029.24
mean_X <- mean(X)
cat ("Mean of X: ", round(mean_X,3))## Mean of X: 10516.83The mean of 10516.83 does indeed fall between 10004.42 and 11029.24
Provide the empirical 5th percentile and 95th percentile of the data
percentile <- quantile(X, probs = c(0.05, 0.95))
cat("The 5th percentile:", percentile[1])## The 5th percentile: 3311.7cat("The 95th percentile:", percentile[2])## The 95th percentile: 17401.15Modeling
Build some type of 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.
head(df_train)## Id MSSubClass MSZoning LotFrontage LotArea Street Alley LotShape LandContour
## 1 1 60 RL 65 8450 Pave <NA> Reg Lvl
## 2 2 20 RL 80 9600 Pave <NA> Reg Lvl
## 3 3 60 RL 68 11250 Pave <NA> IR1 Lvl
## 4 4 70 RL 60 9550 Pave <NA> IR1 Lvl
## 5 5 60 RL 84 14260 Pave <NA> IR1 Lvl
## 6 6 50 RL 85 14115 Pave <NA> IR1 Lvl
## Utilities LotConfig LandSlope Neighborhood Condition1 Condition2 BldgType
## 1 AllPub Inside Gtl CollgCr Norm Norm 1Fam
## 2 AllPub FR2 Gtl Veenker Feedr Norm 1Fam
## 3 AllPub Inside Gtl CollgCr Norm Norm 1Fam
## 4 AllPub Corner Gtl Crawfor Norm Norm 1Fam
## 5 AllPub FR2 Gtl NoRidge Norm Norm 1Fam
## 6 AllPub Inside Gtl Mitchel Norm Norm 1Fam
## HouseStyle OverallQual OverallCond YearBuilt YearRemodAdd RoofStyle RoofMatl
## 1 2Story 7 5 2003 2003 Gable CompShg
## 2 1Story 6 8 1976 1976 Gable CompShg
## 3 2Story 7 5 2001 2002 Gable CompShg
## 4 2Story 7 5 1915 1970 Gable CompShg
## 5 2Story 8 5 2000 2000 Gable CompShg
## 6 1.5Fin 5 5 1993 1995 Gable CompShg
## Exterior1st Exterior2nd MasVnrType MasVnrArea ExterQual ExterCond Foundation
## 1 VinylSd VinylSd BrkFace 196 Gd TA PConc
## 2 MetalSd MetalSd None 0 TA TA CBlock
## 3 VinylSd VinylSd BrkFace 162 Gd TA PConc
## 4 Wd Sdng Wd Shng None 0 TA TA BrkTil
## 5 VinylSd VinylSd BrkFace 350 Gd TA PConc
## 6 VinylSd VinylSd None 0 TA TA Wood
## BsmtQual BsmtCond BsmtExposure BsmtFinType1 BsmtFinSF1 BsmtFinType2
## 1 Gd TA No GLQ 706 Unf
## 2 Gd TA Gd ALQ 978 Unf
## 3 Gd TA Mn GLQ 486 Unf
## 4 TA Gd No ALQ 216 Unf
## 5 Gd TA Av GLQ 655 Unf
## 6 Gd TA No GLQ 732 Unf
## BsmtFinSF2 BsmtUnfSF TotalBsmtSF Heating HeatingQC CentralAir Electrical
## 1 0 150 856 GasA Ex Y SBrkr
## 2 0 284 1262 GasA Ex Y SBrkr
## 3 0 434 920 GasA Ex Y SBrkr
## 4 0 540 756 GasA Gd Y SBrkr
## 5 0 490 1145 GasA Ex Y SBrkr
## 6 0 64 796 GasA Ex Y SBrkr
## X1stFlrSF X2ndFlrSF LowQualFinSF GrLivArea BsmtFullBath BsmtHalfBath FullBath
## 1 856 854 0 1710 1 0 2
## 2 1262 0 0 1262 0 1 2
## 3 920 866 0 1786 1 0 2
## 4 961 756 0 1717 1 0 1
## 5 1145 1053 0 2198 1 0 2
## 6 796 566 0 1362 1 0 1
## HalfBath BedroomAbvGr KitchenAbvGr KitchenQual TotRmsAbvGrd Functional
## 1 1 3 1 Gd 8 Typ
## 2 0 3 1 TA 6 Typ
## 3 1 3 1 Gd 6 Typ
## 4 0 3 1 Gd 7 Typ
## 5 1 4 1 Gd 9 Typ
## 6 1 1 1 TA 5 Typ
## Fireplaces FireplaceQu GarageType GarageYrBlt GarageFinish GarageCars
## 1 0 <NA> Attchd 2003 RFn 2
## 2 1 TA Attchd 1976 RFn 2
## 3 1 TA Attchd 2001 RFn 2
## 4 1 Gd Detchd 1998 Unf 3
## 5 1 TA Attchd 2000 RFn 3
## 6 0 <NA> Attchd 1993 Unf 2
## GarageArea GarageQual GarageCond PavedDrive WoodDeckSF OpenPorchSF
## 1 548 TA TA Y 0 61
## 2 460 TA TA Y 298 0
## 3 608 TA TA Y 0 42
## 4 642 TA TA Y 0 35
## 5 836 TA TA Y 192 84
## 6 480 TA TA Y 40 30
## EnclosedPorch X3SsnPorch ScreenPorch PoolArea PoolQC Fence MiscFeature
## 1 0 0 0 0 <NA> <NA> <NA>
## 2 0 0 0 0 <NA> <NA> <NA>
## 3 0 0 0 0 <NA> <NA> <NA>
## 4 272 0 0 0 <NA> <NA> <NA>
## 5 0 0 0 0 <NA> <NA> <NA>
## 6 0 320 0 0 <NA> MnPrv Shed
## MiscVal MoSold YrSold SaleType SaleCondition SalePrice
## 1 0 2 2008 WD Normal 208500
## 2 0 5 2007 WD Normal 181500
## 3 0 9 2008 WD Normal 223500
## 4 0 2 2006 WD Abnorml 140000
## 5 0 12 2008 WD Normal 250000
## 6 700 10 2009 WD Normal 143000summary(df_train)## Id MSSubClass MSZoning LotFrontage
## Min. : 1.0 Min. : 20.0 Length:1460 Min. : 21.00
## 1st Qu.: 365.8 1st Qu.: 20.0 Class :character 1st Qu.: 59.00
## Median : 730.5 Median : 50.0 Mode :character Median : 69.00
## Mean : 730.5 Mean : 56.9 Mean : 70.05
## 3rd Qu.:1095.2 3rd Qu.: 70.0 3rd Qu.: 80.00
## Max. :1460.0 Max. :190.0 Max. :313.00
## NA's :259
## LotArea Street Alley LotShape
## Min. : 1300 Length:1460 Length:1460 Length:1460
## 1st Qu.: 7554 Class :character Class :character Class :character
## Median : 9478 Mode :character Mode :character Mode :character
## Mean : 10517
## 3rd Qu.: 11602
## Max. :215245
##
## LandContour Utilities LotConfig LandSlope
## Length:1460 Length:1460 Length:1460 Length:1460
## Class :character Class :character Class :character Class :character
## Mode :character Mode :character Mode :character Mode :character
##
##
##
##
## Neighborhood Condition1 Condition2 BldgType
## Length:1460 Length:1460 Length:1460 Length:1460
## Class :character Class :character Class :character Class :character
## Mode :character Mode :character Mode :character Mode :character
##
##
##
##
## HouseStyle OverallQual OverallCond YearBuilt
## Length:1460 Min. : 1.000 Min. :1.000 Min. :1872
## Class :character 1st Qu.: 5.000 1st Qu.:5.000 1st Qu.:1954
## Mode :character Median : 6.000 Median :5.000 Median :1973
## Mean : 6.099 Mean :5.575 Mean :1971
## 3rd Qu.: 7.000 3rd Qu.:6.000 3rd Qu.:2000
## Max. :10.000 Max. :9.000 Max. :2010
##
## YearRemodAdd RoofStyle RoofMatl Exterior1st
## Min. :1950 Length:1460 Length:1460 Length:1460
## 1st Qu.:1967 Class :character Class :character Class :character
## Median :1994 Mode :character Mode :character Mode :character
## Mean :1985
## 3rd Qu.:2004
## Max. :2010
##
## Exterior2nd MasVnrType MasVnrArea ExterQual
## Length:1460 Length:1460 Min. : 0.0 Length:1460
## Class :character Class :character 1st Qu.: 0.0 Class :character
## Mode :character Mode :character Median : 0.0 Mode :character
## Mean : 103.7
## 3rd Qu.: 166.0
## Max. :1600.0
## NA's :8
## ExterCond Foundation BsmtQual BsmtCond
## Length:1460 Length:1460 Length:1460 Length:1460
## Class :character Class :character Class :character Class :character
## Mode :character Mode :character Mode :character Mode :character
##
##
##
##
## BsmtExposure BsmtFinType1 BsmtFinSF1 BsmtFinType2
## Length:1460 Length:1460 Min. : 0.0 Length:1460
## Class :character Class :character 1st Qu.: 0.0 Class :character
## Mode :character Mode :character Median : 383.5 Mode :character
## Mean : 443.6
## 3rd Qu.: 712.2
## Max. :5644.0
##
## BsmtFinSF2 BsmtUnfSF TotalBsmtSF Heating
## Min. : 0.00 Min. : 0.0 Min. : 0.0 Length:1460
## 1st Qu.: 0.00 1st Qu.: 223.0 1st Qu.: 795.8 Class :character
## Median : 0.00 Median : 477.5 Median : 991.5 Mode :character
## Mean : 46.55 Mean : 567.2 Mean :1057.4
## 3rd Qu.: 0.00 3rd Qu.: 808.0 3rd Qu.:1298.2
## Max. :1474.00 Max. :2336.0 Max. :6110.0
##
## HeatingQC CentralAir Electrical X1stFlrSF
## Length:1460 Length:1460 Length:1460 Min. : 334
## Class :character Class :character Class :character 1st Qu.: 882
## Mode :character Mode :character Mode :character Median :1087
## Mean :1163
## 3rd Qu.:1391
## Max. :4692
##
## X2ndFlrSF LowQualFinSF GrLivArea BsmtFullBath
## Min. : 0 Min. : 0.000 Min. : 334 Min. :0.0000
## 1st Qu.: 0 1st Qu.: 0.000 1st Qu.:1130 1st Qu.:0.0000
## Median : 0 Median : 0.000 Median :1464 Median :0.0000
## Mean : 347 Mean : 5.845 Mean :1515 Mean :0.4253
## 3rd Qu.: 728 3rd Qu.: 0.000 3rd Qu.:1777 3rd Qu.:1.0000
## Max. :2065 Max. :572.000 Max. :5642 Max. :3.0000
##
## BsmtHalfBath FullBath HalfBath BedroomAbvGr
## Min. :0.00000 Min. :0.000 Min. :0.0000 Min. :0.000
## 1st Qu.:0.00000 1st Qu.:1.000 1st Qu.:0.0000 1st Qu.:2.000
## Median :0.00000 Median :2.000 Median :0.0000 Median :3.000
## Mean :0.05753 Mean :1.565 Mean :0.3829 Mean :2.866
## 3rd Qu.:0.00000 3rd Qu.:2.000 3rd Qu.:1.0000 3rd Qu.:3.000
## Max. :2.00000 Max. :3.000 Max. :2.0000 Max. :8.000
##
## KitchenAbvGr KitchenQual TotRmsAbvGrd Functional
## Min. :0.000 Length:1460 Min. : 2.000 Length:1460
## 1st Qu.:1.000 Class :character 1st Qu.: 5.000 Class :character
## Median :1.000 Mode :character Median : 6.000 Mode :character
## Mean :1.047 Mean : 6.518
## 3rd Qu.:1.000 3rd Qu.: 7.000
## Max. :3.000 Max. :14.000
##
## Fireplaces FireplaceQu GarageType GarageYrBlt
## Min. :0.000 Length:1460 Length:1460 Min. :1900
## 1st Qu.:0.000 Class :character Class :character 1st Qu.:1961
## Median :1.000 Mode :character Mode :character Median :1980
## Mean :0.613 Mean :1979
## 3rd Qu.:1.000 3rd Qu.:2002
## Max. :3.000 Max. :2010
## NA's :81
## GarageFinish GarageCars GarageArea GarageQual
## Length:1460 Min. :0.000 Min. : 0.0 Length:1460
## Class :character 1st Qu.:1.000 1st Qu.: 334.5 Class :character
## Mode :character Median :2.000 Median : 480.0 Mode :character
## Mean :1.767 Mean : 473.0
## 3rd Qu.:2.000 3rd Qu.: 576.0
## Max. :4.000 Max. :1418.0
##
## GarageCond PavedDrive WoodDeckSF OpenPorchSF
## Length:1460 Length:1460 Min. : 0.00 Min. : 0.00
## Class :character Class :character 1st Qu.: 0.00 1st Qu.: 0.00
## Mode :character Mode :character Median : 0.00 Median : 25.00
## Mean : 94.24 Mean : 46.66
## 3rd Qu.:168.00 3rd Qu.: 68.00
## Max. :857.00 Max. :547.00
##
## EnclosedPorch X3SsnPorch ScreenPorch PoolArea
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.000
## 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.000
## Median : 0.00 Median : 0.00 Median : 0.00 Median : 0.000
## Mean : 21.95 Mean : 3.41 Mean : 15.06 Mean : 2.759
## 3rd Qu.: 0.00 3rd Qu.: 0.00 3rd Qu.: 0.00 3rd Qu.: 0.000
## Max. :552.00 Max. :508.00 Max. :480.00 Max. :738.000
##
## PoolQC Fence MiscFeature MiscVal
## Length:1460 Length:1460 Length:1460 Min. : 0.00
## Class :character Class :character Class :character 1st Qu.: 0.00
## Mode :character Mode :character Mode :character Median : 0.00
## Mean : 43.49
## 3rd Qu.: 0.00
## Max. :15500.00
##
## MoSold YrSold SaleType SaleCondition
## Min. : 1.000 Min. :2006 Length:1460 Length:1460
## 1st Qu.: 5.000 1st Qu.:2007 Class :character Class :character
## Median : 6.000 Median :2008 Mode :character Mode :character
## Mean : 6.322 Mean :2008
## 3rd Qu.: 8.000 3rd Qu.:2009
## Max. :12.000 Max. :2010
##
## SalePrice
## Min. : 34900
## 1st Qu.:129975
## Median :163000
## Mean :180921
## 3rd Qu.:214000
## Max. :755000
## Let us look at all the columns with NA’s
missing_values <- colSums(is.na(df_train))
missing_values_df <- tibble(
Variable = names(missing_values),
'Missing Value Count' = missing_values
)
NA_count <- missing_values_df %>%
filter(`Missing Value Count` > 0 )
print(NA_count)## # A tibble: 19 × 2
## Variable `Missing Value Count`
## <chr> <dbl>
## 1 LotFrontage 259
## 2 Alley 1369
## 3 MasVnrType 8
## 4 MasVnrArea 8
## 5 BsmtQual 37
## 6 BsmtCond 37
## 7 BsmtExposure 38
## 8 BsmtFinType1 37
## 9 BsmtFinType2 38
## 10 Electrical 1
## 11 FireplaceQu 690
## 12 GarageType 81
## 13 GarageYrBlt 81
## 14 GarageFinish 81
## 15 GarageQual 81
## 16 GarageCond 81
## 17 PoolQC 1453
## 18 Fence 1179
## 19 MiscFeature 1406df_train_clean <- df_train[, colSums(is.na(df_train)) == 0]
str(df_train_clean)## 'data.frame': 1460 obs. of 62 variables:
## $ Id : int 1 2 3 4 5 6 7 8 9 10 ...
## $ MSSubClass : int 60 20 60 70 60 50 20 60 50 190 ...
## $ MSZoning : chr "RL" "RL" "RL" "RL" ...
## $ LotArea : int 8450 9600 11250 9550 14260 14115 10084 10382 6120 7420 ...
## $ Street : chr "Pave" "Pave" "Pave" "Pave" ...
## $ LotShape : chr "Reg" "Reg" "IR1" "IR1" ...
## $ LandContour : chr "Lvl" "Lvl" "Lvl" "Lvl" ...
## $ Utilities : chr "AllPub" "AllPub" "AllPub" "AllPub" ...
## $ LotConfig : chr "Inside" "FR2" "Inside" "Corner" ...
## $ LandSlope : chr "Gtl" "Gtl" "Gtl" "Gtl" ...
## $ Neighborhood : chr "CollgCr" "Veenker" "CollgCr" "Crawfor" ...
## $ Condition1 : chr "Norm" "Feedr" "Norm" "Norm" ...
## $ Condition2 : chr "Norm" "Norm" "Norm" "Norm" ...
## $ BldgType : chr "1Fam" "1Fam" "1Fam" "1Fam" ...
## $ HouseStyle : chr "2Story" "1Story" "2Story" "2Story" ...
## $ OverallQual : int 7 6 7 7 8 5 8 7 7 5 ...
## $ OverallCond : int 5 8 5 5 5 5 5 6 5 6 ...
## $ YearBuilt : int 2003 1976 2001 1915 2000 1993 2004 1973 1931 1939 ...
## $ YearRemodAdd : int 2003 1976 2002 1970 2000 1995 2005 1973 1950 1950 ...
## $ RoofStyle : chr "Gable" "Gable" "Gable" "Gable" ...
## $ RoofMatl : chr "CompShg" "CompShg" "CompShg" "CompShg" ...
## $ Exterior1st : chr "VinylSd" "MetalSd" "VinylSd" "Wd Sdng" ...
## $ Exterior2nd : chr "VinylSd" "MetalSd" "VinylSd" "Wd Shng" ...
## $ ExterQual : chr "Gd" "TA" "Gd" "TA" ...
## $ ExterCond : chr "TA" "TA" "TA" "TA" ...
## $ Foundation : chr "PConc" "CBlock" "PConc" "BrkTil" ...
## $ BsmtFinSF1 : int 706 978 486 216 655 732 1369 859 0 851 ...
## $ BsmtFinSF2 : int 0 0 0 0 0 0 0 32 0 0 ...
## $ BsmtUnfSF : int 150 284 434 540 490 64 317 216 952 140 ...
## $ TotalBsmtSF : int 856 1262 920 756 1145 796 1686 1107 952 991 ...
## $ Heating : chr "GasA" "GasA" "GasA" "GasA" ...
## $ HeatingQC : chr "Ex" "Ex" "Ex" "Gd" ...
## $ CentralAir : chr "Y" "Y" "Y" "Y" ...
## $ X1stFlrSF : int 856 1262 920 961 1145 796 1694 1107 1022 1077 ...
## $ X2ndFlrSF : int 854 0 866 756 1053 566 0 983 752 0 ...
## $ LowQualFinSF : int 0 0 0 0 0 0 0 0 0 0 ...
## $ GrLivArea : int 1710 1262 1786 1717 2198 1362 1694 2090 1774 1077 ...
## $ BsmtFullBath : int 1 0 1 1 1 1 1 1 0 1 ...
## $ BsmtHalfBath : int 0 1 0 0 0 0 0 0 0 0 ...
## $ FullBath : int 2 2 2 1 2 1 2 2 2 1 ...
## $ HalfBath : int 1 0 1 0 1 1 0 1 0 0 ...
## $ BedroomAbvGr : int 3 3 3 3 4 1 3 3 2 2 ...
## $ KitchenAbvGr : int 1 1 1 1 1 1 1 1 2 2 ...
## $ KitchenQual : chr "Gd" "TA" "Gd" "Gd" ...
## $ TotRmsAbvGrd : int 8 6 6 7 9 5 7 7 8 5 ...
## $ Functional : chr "Typ" "Typ" "Typ" "Typ" ...
## $ Fireplaces : int 0 1 1 1 1 0 1 2 2 2 ...
## $ GarageCars : int 2 2 2 3 3 2 2 2 2 1 ...
## $ GarageArea : int 548 460 608 642 836 480 636 484 468 205 ...
## $ PavedDrive : chr "Y" "Y" "Y" "Y" ...
## $ WoodDeckSF : int 0 298 0 0 192 40 255 235 90 0 ...
## $ OpenPorchSF : int 61 0 42 35 84 30 57 204 0 4 ...
## $ EnclosedPorch: int 0 0 0 272 0 0 0 228 205 0 ...
## $ X3SsnPorch : int 0 0 0 0 0 320 0 0 0 0 ...
## $ ScreenPorch : int 0 0 0 0 0 0 0 0 0 0 ...
## $ PoolArea : int 0 0 0 0 0 0 0 0 0 0 ...
## $ MiscVal : int 0 0 0 0 0 700 0 350 0 0 ...
## $ MoSold : int 2 5 9 2 12 10 8 11 4 1 ...
## $ YrSold : int 2008 2007 2008 2006 2008 2009 2007 2009 2008 2008 ...
## $ SaleType : chr "WD" "WD" "WD" "WD" ...
## $ SaleCondition: chr "Normal" "Normal" "Normal" "Abnorml" ...
## $ SalePrice : int 208500 181500 223500 140000 250000 143000 307000 200000 129900 118000 ...Checking for NA
anyNA(df_train_clean)## [1] FALSEnumeric_df <- df_train_clean[, sapply(df_train_clean, is.numeric)]
# Print the selected numeric columns
print(numeric_df)## Id MSSubClass LotArea OverallQual OverallCond YearBuilt YearRemodAdd
## 1 1 60 8450 7 5 2003 2003
## 2 2 20 9600 6 8 1976 1976
## 3 3 60 11250 7 5 2001 2002
## 4 4 70 9550 7 5 1915 1970
## 5 5 60 14260 8 5 2000 2000
## 6 6 50 14115 5 5 1993 1995
## 7 7 20 10084 8 5 2004 2005
## 8 8 60 10382 7 6 1973 1973
## 9 9 50 6120 7 5 1931 1950
## 10 10 190 7420 5 6 1939 1950
## 11 11 20 11200 5 5 1965 1965
## 12 12 60 11924 9 5 2005 2006
## 13 13 20 12968 5 6 1962 1962
## 14 14 20 10652 7 5 2006 2007
## 15 15 20 10920 6 5 1960 1960
## 16 16 45 6120 7 8 1929 2001
## 17 17 20 11241 6 7 1970 1970
## 18 18 90 10791 4 5 1967 1967
## 19 19 20 13695 5 5 2004 2004
## 20 20 20 7560 5 6 1958 1965
## 21 21 60 14215 8 5 2005 2006
## 22 22 45 7449 7 7 1930 1950
## 23 23 20 9742 8 5 2002 2002
## 24 24 120 4224 5 7 1976 1976
## 25 25 20 8246 5 8 1968 2001
## 26 26 20 14230 8 5 2007 2007
## 27 27 20 7200 5 7 1951 2000
## 28 28 20 11478 8 5 2007 2008
## 29 29 20 16321 5 6 1957 1997
## 30 30 30 6324 4 6 1927 1950
## 31 31 70 8500 4 4 1920 1950
## 32 32 20 8544 5 6 1966 2006
## 33 33 20 11049 8 5 2007 2007
## 34 34 20 10552 5 5 1959 1959
## 35 35 120 7313 9 5 2005 2005
## 36 36 60 13418 8 5 2004 2005
## 37 37 20 10859 5 5 1994 1995
## 38 38 20 8532 5 6 1954 1990
## 39 39 20 7922 5 7 1953 2007
## 40 40 90 6040 4 5 1955 1955
## 41 41 20 8658 6 5 1965 1965
## 42 42 20 16905 5 6 1959 1959
## 43 43 85 9180 5 7 1983 1983
## 44 44 20 9200 5 6 1975 1980
## 45 45 20 7945 5 6 1959 1959
## 46 46 120 7658 9 5 2005 2005
## 47 47 50 12822 7 5 2003 2003
## 48 48 20 11096 8 5 2006 2006
## 49 49 190 4456 4 5 1920 2008
## 50 50 20 7742 5 7 1966 1966
## 51 51 60 13869 6 6 1997 1997
## 52 52 50 6240 6 6 1934 1950
## 53 53 90 8472 5 5 1963 1963
## 54 54 20 50271 9 5 1981 1987
## 55 55 80 7134 5 5 1955 1955
## 56 56 20 10175 6 5 1964 1964
## 57 57 160 2645 8 5 1999 2000
## 58 58 60 11645 7 5 2004 2004
## 59 59 60 13682 10 5 2006 2006
## 60 60 20 7200 5 7 1972 1972
## 61 61 20 13072 6 5 2004 2004
## 62 62 75 7200 5 7 1920 1996
## 63 63 120 6442 8 5 2006 2006
## 64 64 70 10300 7 6 1921 1950
## 65 65 60 9375 7 5 1997 1998
## 66 66 60 9591 8 5 2004 2005
## 67 67 20 19900 7 5 1970 1989
## 68 68 20 10665 7 5 2003 2003
## 69 69 30 4608 4 6 1945 1950
## 70 70 50 15593 7 4 1953 1953
## 71 71 20 13651 7 6 1973 1973
## 72 72 20 7599 4 6 1982 2006
## 73 73 60 10141 7 5 1998 1998
## 74 74 20 10200 5 7 1954 2003
## 75 75 50 5790 3 6 1915 1950
## 76 76 180 1596 4 5 1973 1973
## 77 77 20 8475 4 7 1956 1956
## 78 78 50 8635 5 5 1948 2001
## 79 79 90 10778 4 5 1968 1968
## 80 80 50 10440 5 6 1910 1981
## 81 81 60 13000 6 6 1968 1968
## 82 82 120 4500 6 5 1998 1998
## 83 83 20 10206 8 5 2007 2007
## 84 84 20 8892 5 5 1960 1960
## 85 85 80 8530 7 5 1995 1996
## 86 86 60 16059 8 5 1991 1992
## 87 87 60 11911 6 5 2005 2005
## 88 88 160 3951 6 5 2009 2009
## 89 89 50 8470 3 2 1915 1982
## 90 90 20 8070 4 5 1994 1995
## 91 91 20 7200 4 5 1950 1950
## 92 92 20 8500 5 3 1961 1961
## 93 93 30 13360 5 7 1921 2006
## 94 94 190 7200 6 6 1910 1998
## 95 95 60 9337 6 5 1997 1997
## 96 96 60 9765 6 8 1993 1993
## 97 97 20 10264 7 5 1999 1999
## 98 98 20 10921 4 5 1965 1965
## 99 99 30 10625 5 5 1920 1950
## 100 100 20 9320 4 5 1959 1959
## 101 101 20 10603 6 7 1977 2001
## 102 102 60 9206 6 5 1985 1985
## 103 103 90 7018 5 5 1979 1979
## 104 104 20 10402 7 5 2009 2009
## 105 105 50 7758 7 4 1931 1950
## 106 106 60 9375 8 5 2003 2004
## 107 107 30 10800 4 7 1885 1995
## 108 108 20 6000 5 5 1948 1950
## 109 109 50 8500 5 7 1919 2005
## 110 110 20 11751 6 6 1977 1977
## 111 111 50 9525 6 4 1954 1972
## 112 112 80 7750 7 5 2000 2000
## 113 113 60 9965 7 5 2007 2007
## 114 114 20 21000 6 5 1953 1953
## 115 115 70 7259 6 8 1945 2002
## 116 116 160 3230 6 5 1999 1999
## 117 117 20 11616 5 5 1962 1962
## 118 118 20 8536 5 5 2006 2007
## 119 119 60 12376 7 5 1990 1990
## 120 120 60 8461 6 5 2005 2006
## 121 121 80 21453 6 5 1969 1969
## 122 122 50 6060 4 5 1939 1950
## 123 123 20 9464 6 7 1958 1958
## 124 124 120 7892 6 5 1993 1993
## 125 125 20 17043 6 5 1979 1998
## 126 126 190 6780 6 8 1935 1982
## 127 127 120 4928 6 5 1976 1976
## 128 128 45 4388 5 7 1930 1950
## 129 129 60 7590 6 5 1966 1966
## 130 130 20 8973 5 7 1958 1991
## 131 131 60 14200 7 6 1966 1966
## 132 132 60 12224 6 5 2000 2000
## 133 133 20 7388 5 6 1959 2002
## 134 134 20 6853 8 5 2001 2002
## 135 135 20 10335 5 6 1968 1993
## 136 136 20 10400 7 6 1970 1970
## 137 137 20 10355 5 5 1967 1967
## 138 138 90 11070 7 5 1988 1989
## 139 139 60 9066 8 5 1999 2000
## 140 140 60 15426 6 5 1997 1997
## 141 141 20 10500 4 5 1971 1971
## 142 142 20 11645 7 5 2005 2005
## 143 143 50 8520 5 4 1952 1952
## 144 144 20 10335 7 5 1999 1999
## 145 145 90 9100 5 5 1963 1963
## 146 146 160 2522 6 5 2004 2006
## 147 147 30 6120 5 7 1931 1993
## 148 148 60 9505 7 5 2001 2001
## 149 149 20 7500 7 5 2004 2005
## 150 150 50 6240 5 4 1936 1950
## 151 151 20 10356 5 6 1975 1975
## 152 152 20 13891 8 5 2007 2008
## 153 153 60 14803 6 5 1971 1971
## 154 154 20 13500 6 7 1960 1975
## 155 155 30 11340 6 5 1923 1950
## 156 156 50 9600 6 5 1924 1950
## 157 157 20 7200 5 7 1950 1950
## 158 158 60 12003 8 5 2009 2010
## 159 159 60 12552 7 5 2004 2005
## 160 160 60 19378 7 5 2005 2006
## 161 161 20 11120 6 6 1984 1984
## 162 162 60 13688 9 5 2003 2004
## 163 163 20 12182 7 5 2005 2005
## 164 164 45 5500 4 6 1956 1956
## 165 165 40 5400 6 7 1926 2004
## 166 166 190 10106 5 7 1940 1999
## 167 167 20 10708 5 5 1955 1993
## 168 168 60 10562 8 5 2007 2007
## 169 169 60 8244 7 5 2004 2004
## 170 170 20 16669 8 6 1981 1981
## 171 171 50 12358 5 6 1941 1950
## 172 172 20 31770 6 5 1960 1960
## 173 173 160 5306 7 7 1987 1987
## 174 174 20 10197 6 5 1961 1961
## 175 175 20 12416 6 5 1986 1986
## 176 176 20 12615 6 7 1950 2001
## 177 177 60 10029 6 5 1988 1989
## 178 178 50 13650 5 5 1958 1958
## 179 179 20 17423 9 5 2008 2009
## 180 180 30 8520 5 6 1923 2006
## 181 181 160 2117 6 5 2000 2000
## 182 182 70 7588 7 6 1920 1950
## 183 183 20 9060 5 6 1957 2006
## 184 184 50 11426 7 5 2003 2003
## 185 185 50 7438 5 8 1908 1991
## 186 186 75 22950 10 9 1892 1993
## 187 187 80 9947 7 5 1990 1991
## 188 188 50 10410 5 7 1916 1987
## 189 189 90 7018 5 5 1979 1979
## 190 190 120 4923 8 5 2001 2002
## 191 191 70 10570 8 8 1932 1994
## 192 192 60 7472 7 9 1972 2004
## 193 193 20 9017 7 5 1999 1999
## 194 194 160 2522 7 5 2004 2004
## 195 195 20 7180 5 7 1972 1972
## 196 196 160 2280 6 6 1976 1976
## 197 197 20 9416 7 5 2007 2007
## 198 198 75 25419 8 4 1918 1990
## 199 199 75 5520 6 6 1912 1950
## 200 200 20 9591 8 5 2004 2005
## 201 201 20 8546 4 5 2003 2004
## 202 202 20 10125 6 6 1977 1977
## 203 203 50 7000 6 6 1924 1950
## 204 204 120 4438 6 5 2004 2004
## 205 205 50 3500 5 7 1947 1950
## 206 206 20 11851 7 5 1990 1990
## 207 207 20 13673 5 5 1962 1962
## 208 208 20 12493 4 5 1960 1960
## 209 209 60 14364 7 5 1988 1989
## 210 210 20 8250 6 7 1964 1964
## 211 211 30 5604 5 6 1925 1950
## 212 212 20 10420 6 5 2009 2009
## 213 213 60 8640 7 5 2009 2009
## 214 214 20 13568 5 5 1995 1995
## 215 215 60 10900 6 7 1977 1977
## 216 216 20 10011 5 6 1957 1996
## 217 217 20 8450 7 5 2004 2004
## 218 218 70 9906 4 4 1925 1950
## 219 219 50 15660 7 9 1939 2006
## 220 220 120 3010 7 5 2005 2006
## 221 221 20 8990 7 5 2006 2006
## 222 222 60 8068 6 5 2002 2002
## 223 223 60 11475 6 6 1975 1975
## 224 224 20 10500 4 6 1971 1971
## 225 225 20 13472 10 5 2003 2003
## 226 226 160 1680 5 5 1971 1971
## 227 227 60 9950 7 5 1995 1995
## 228 228 160 1869 6 6 1970 1970
## 229 229 20 8521 5 5 1967 1967
## 230 230 120 3182 7 5 2005 2006
## 231 231 20 8760 6 6 1959 1959
## 232 232 60 15138 8 5 1995 1996
## 233 233 160 1680 6 5 1972 1972
## 234 234 20 10650 5 6 1976 1976
## 235 235 60 7851 6 5 2002 2002
## 236 236 160 1680 6 3 1971 1971
## 237 237 20 8773 7 5 2004 2004
## 238 238 60 9453 7 7 1993 2003
## 239 239 20 12030 8 5 2007 2007
## 240 240 50 8741 6 4 1945 1950
## 241 241 20 9000 8 5 2008 2008
## 242 242 30 3880 5 9 1945 1997
## 243 243 50 5000 5 4 1900 1950
## 244 244 160 10762 6 6 1980 1980
## 245 245 60 8880 7 5 1994 2002
## 246 246 20 10400 7 5 1988 1988
## 247 247 190 9142 6 8 1910 1950
## 248 248 20 11310 6 5 1954 1954
## 249 249 60 11317 7 5 2003 2003
## 250 250 50 159000 6 7 1958 2006
## 251 251 30 5350 3 2 1940 1966
## 252 252 120 4750 8 5 2006 2007
## 253 253 60 8366 6 5 2004 2004
## 254 254 80 9350 6 7 1964 1991
## 255 255 20 8400 5 6 1957 1957
## 256 256 60 8738 7 5 1999 1999
## 257 257 60 8791 6 5 2003 2003
## 258 258 20 8814 7 5 2006 2006
## 259 259 60 12435 7 5 2001 2001
## 260 260 20 12702 5 5 1956 1956
## 261 261 80 19296 6 5 1962 1962
## 262 262 60 9588 8 5 2007 2007
## 263 263 80 8471 6 7 1977 1995
## 264 264 50 5500 5 7 1929 2001
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## BsmtFinSF1 BsmtFinSF2 BsmtUnfSF TotalBsmtSF X1stFlrSF X2ndFlrSF
## 1 706 0 150 856 856 854
## 2 978 0 284 1262 1262 0
## 3 486 0 434 920 920 866
## 4 216 0 540 756 961 756
## 5 655 0 490 1145 1145 1053
## 6 732 0 64 796 796 566
## 7 1369 0 317 1686 1694 0
## 8 859 32 216 1107 1107 983
## 9 0 0 952 952 1022 752
## 10 851 0 140 991 1077 0
## 11 906 0 134 1040 1040 0
## 12 998 0 177 1175 1182 1142
## 13 737 0 175 912 912 0
## 14 0 0 1494 1494 1494 0
## 15 733 0 520 1253 1253 0
## 16 0 0 832 832 854 0
## 17 578 0 426 1004 1004 0
## 18 0 0 0 0 1296 0
## 19 646 0 468 1114 1114 0
## 20 504 0 525 1029 1339 0
## 21 0 0 1158 1158 1158 1218
## 22 0 0 637 637 1108 0
## 23 0 0 1777 1777 1795 0
## 24 840 0 200 1040 1060 0
## 25 188 668 204 1060 1060 0
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## 1460 0 6 2008 147500colnames(numeric_df)## [1] "Id" "MSSubClass" "LotArea" "OverallQual"
## [5] "OverallCond" "YearBuilt" "YearRemodAdd" "BsmtFinSF1"
## [9] "BsmtFinSF2" "BsmtUnfSF" "TotalBsmtSF" "X1stFlrSF"
## [13] "X2ndFlrSF" "LowQualFinSF" "GrLivArea" "BsmtFullBath"
## [17] "BsmtHalfBath" "FullBath" "HalfBath" "BedroomAbvGr"
## [21] "KitchenAbvGr" "TotRmsAbvGrd" "Fireplaces" "GarageCars"
## [25] "GarageArea" "WoodDeckSF" "OpenPorchSF" "EnclosedPorch"
## [29] "X3SsnPorch" "ScreenPorch" "PoolArea" "MiscVal"
## [33] "MoSold" "YrSold" "SalePrice"Using forward selection to include information about each subset of features
features <- colnames(numeric_df)[-which(colnames(numeric_df) == "SalePrice")]
forward_model <- regsubsets(SalePrice ~ ., data = numeric_df, nvmax = length(features), method = "forward")## Warning in leaps.setup(x, y, wt = wt, nbest = nbest, nvmax = nvmax, force.in =
## force.in, : 2 linear dependencies found## Reordering variables and trying again:## Warning in rval$lopt[] <- rval$vorder[rval$lopt]: number of items to replace is
## not a multiple of replacement lengthSelecting the best subset of features
best_subset <- which.max(summary(forward_model)$adjr2)
selected_features <- names(coef(forward_model, id = best_subset))
best_features_names <- c("MSSubClass", "LotArea", "OverallQual", "OverallCond", "YearBuilt",
"YearRemodAdd", "BsmtFinSF1", "X1stFlrSF", "BsmtFullBath", "BsmtHalfBath",
"FullBath", "BedroomAbvGr", "TotRmsAbvGrd", "Fireplaces", "GarageCars",
"GarageArea", "WoodDeckSF", "EnclosedPorch", "MiscVal", "MoSold", "GrLivArea")
best_features_df <- numeric_df[, c(best_features_names, "SalePrice")]final_formula <- as.formula(paste("SalePrice ~",
paste(c("MSSubClass", "LotArea", "OverallQual", "OverallCond", "YearBuilt",
"YearRemodAdd", "BsmtFinSF1", "X1stFlrSF", "BsmtFullBath", "BsmtHalfBath",
"FullBath", "BedroomAbvGr", "TotRmsAbvGrd", "Fireplaces", "GarageCars",
"GarageArea", "WoodDeckSF", "EnclosedPorch", "MiscVal", "MoSold", "GrLivArea"),collapse = " + ")))
final_model <- lm(final_formula, data = df_train)
summary(final_model)##
## Call:
## lm(formula = final_formula, data = df_train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -483932 -16671 -2480 13470 287204
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.051e+06 1.289e+05 -8.151 7.79e-16 ***
## MSSubClass -1.928e+02 2.475e+01 -7.788 1.30e-14 ***
## LotArea 4.063e-01 1.020e-01 3.985 7.10e-05 ***
## OverallQual 1.950e+04 1.133e+03 17.209 < 2e-16 ***
## OverallCond 4.491e+03 1.029e+03 4.363 1.37e-05 ***
## YearBuilt 3.568e+02 5.747e+01 6.208 7.02e-10 ***
## YearRemodAdd 1.370e+02 6.622e+01 2.068 0.038779 *
## BsmtFinSF1 1.346e+01 3.081e+00 4.369 1.34e-05 ***
## X1stFlrSF 6.540e+00 3.612e+00 1.811 0.070393 .
## BsmtFullBath 7.808e+03 2.527e+03 3.090 0.002037 **
## BsmtHalfBath 2.757e+03 4.107e+03 0.671 0.502131
## FullBath 2.616e+03 2.609e+03 1.003 0.316219
## BedroomAbvGr -1.004e+04 1.714e+03 -5.854 5.94e-09 ***
## TotRmsAbvGrd 4.062e+03 1.201e+03 3.383 0.000736 ***
## Fireplaces 4.735e+03 1.746e+03 2.712 0.006762 **
## GarageCars 1.087e+04 2.871e+03 3.786 0.000159 ***
## GarageArea 1.734e+00 9.787e+00 0.177 0.859422
## WoodDeckSF 2.366e+01 7.960e+00 2.972 0.003008 **
## EnclosedPorch 2.820e+00 1.686e+01 0.167 0.867199
## MiscVal -1.016e+00 1.879e+00 -0.541 0.588789
## MoSold -8.105e+01 3.447e+02 -0.235 0.814172
## GrLivArea 4.996e+01 4.234e+00 11.801 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 35350 on 1438 degrees of freedom
## Multiple R-squared: 0.8049, Adjusted R-squared: 0.802
## F-statistic: 282.4 on 21 and 1438 DF, p-value: < 2.2e-16Using the plot function to check our assumptions on the modelif they are met
plot(final_model)
As we can see our adjusted R^2 is 0.802 using the best features.
#Performing Predictions
test_data_numeric_df <- df_test %>%
dplyr::select(-Id) %>%
dplyr::select(where(is.numeric))
# Identify columns with missing data
missing_data_columns <- colnames(test_data_numeric_df)[colSums(is.na(test_data_numeric_df)) > 0]
# Calculate the median for each column with missing data and replace missing values
for (col in missing_data_columns) {
median_value <- median(test_data_numeric_df[[col]], na.rm = TRUE)
test_data_numeric_df[[col]][is.na(test_data_numeric_df[[col]])] <- median_value
}predictions <- predict(final_model, newdata = test_data_numeric_df)
df_predictions <- data.frame(Id =df_test$Id, SalePrice = predictions) write.csv(df_predictions,"Kaggle_Predictions.csv",row.names = FALSE)My kaggle account user name is Mikhail Broomes and my score for this assignment is 0.44653.