HousingData
Yatharth Malik
January 10, 2017
Loading libraries
library(caTools)
library(randomForest)Loading data
housing = read.table("http://archive.ics.uci.edu/ml/machine-learning-databases/housing/housing.data")
names = c("CRIM","ZN","INDUS","CHAS","NOX","RM","AGE","DIS","RAD","TAX","PTRATIO","B","LSTAT","MEDV")
names(housing) = names
housing$CHAS = as.factor(housing$CHAS)Creating testing and training set
set.seed(121)
split = sample.split(housing$MEDV,SplitRatio = 0.70)
train = subset(housing,split==T)
test = subset(housing,split==F)Checking for multicollinearity
cor(housing[,-4])## CRIM ZN INDUS NOX RM AGE
## CRIM 1.0000000 -0.2004692 0.4065834 0.4209717 -0.2192467 0.3527343
## ZN -0.2004692 1.0000000 -0.5338282 -0.5166037 0.3119906 -0.5695373
## INDUS 0.4065834 -0.5338282 1.0000000 0.7636514 -0.3916759 0.6447785
## NOX 0.4209717 -0.5166037 0.7636514 1.0000000 -0.3021882 0.7314701
## RM -0.2192467 0.3119906 -0.3916759 -0.3021882 1.0000000 -0.2402649
## AGE 0.3527343 -0.5695373 0.6447785 0.7314701 -0.2402649 1.0000000
## DIS -0.3796701 0.6644082 -0.7080270 -0.7692301 0.2052462 -0.7478805
## RAD 0.6255051 -0.3119478 0.5951293 0.6114406 -0.2098467 0.4560225
## TAX 0.5827643 -0.3145633 0.7207602 0.6680232 -0.2920478 0.5064556
## PTRATIO 0.2899456 -0.3916785 0.3832476 0.1889327 -0.3555015 0.2615150
## B -0.3850639 0.1755203 -0.3569765 -0.3800506 0.1280686 -0.2735340
## LSTAT 0.4556215 -0.4129946 0.6037997 0.5908789 -0.6138083 0.6023385
## MEDV -0.3883046 0.3604453 -0.4837252 -0.4273208 0.6953599 -0.3769546
## DIS RAD TAX PTRATIO B LSTAT
## CRIM -0.3796701 0.6255051 0.5827643 0.2899456 -0.3850639 0.4556215
## ZN 0.6644082 -0.3119478 -0.3145633 -0.3916785 0.1755203 -0.4129946
## INDUS -0.7080270 0.5951293 0.7207602 0.3832476 -0.3569765 0.6037997
## NOX -0.7692301 0.6114406 0.6680232 0.1889327 -0.3800506 0.5908789
## RM 0.2052462 -0.2098467 -0.2920478 -0.3555015 0.1280686 -0.6138083
## AGE -0.7478805 0.4560225 0.5064556 0.2615150 -0.2735340 0.6023385
## DIS 1.0000000 -0.4945879 -0.5344316 -0.2324705 0.2915117 -0.4969958
## RAD -0.4945879 1.0000000 0.9102282 0.4647412 -0.4444128 0.4886763
## TAX -0.5344316 0.9102282 1.0000000 0.4608530 -0.4418080 0.5439934
## PTRATIO -0.2324705 0.4647412 0.4608530 1.0000000 -0.1773833 0.3740443
## B 0.2915117 -0.4444128 -0.4418080 -0.1773833 1.0000000 -0.3660869
## LSTAT -0.4969958 0.4886763 0.5439934 0.3740443 -0.3660869 1.0000000
## MEDV 0.2499287 -0.3816262 -0.4685359 -0.5077867 0.3334608 -0.7376627
## MEDV
## CRIM -0.3883046
## ZN 0.3604453
## INDUS -0.4837252
## NOX -0.4273208
## RM 0.6953599
## AGE -0.3769546
## DIS 0.2499287
## RAD -0.3816262
## TAX -0.4685359
## PTRATIO -0.5077867
## B 0.3334608
## LSTAT -0.7376627
## MEDV 1.0000000Since RAD and TAX are highly correlated, we will consider only one of them for building our model.
Linear Regression
fit.linear = lm(MEDV ~ . -RAD -TAX - AGE -CRIM - INDUS,data = train)
summary(fit.linear)##
## Call:
## lm(formula = MEDV ~ . - RAD - TAX - AGE - CRIM - INDUS, data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.7416 -2.9791 -0.6319 1.8156 27.1933
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 30.975782 5.848664 5.296 2.07e-07 ***
## ZN 0.039667 0.015826 2.506 0.0126 *
## CHAS1 2.293942 1.038846 2.208 0.0279 *
## NOX -19.795182 3.855972 -5.134 4.67e-07 ***
## RM 4.331848 0.490358 8.834 < 2e-16 ***
## DIS -1.600056 0.231814 -6.902 2.34e-11 ***
## PTRATIO -0.799392 0.142535 -5.608 4.09e-08 ***
## B 0.007823 0.003061 2.556 0.0110 *
## LSTAT -0.572201 0.060222 -9.502 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.983 on 358 degrees of freedom
## Multiple R-squared: 0.7297, Adjusted R-squared: 0.7237
## F-statistic: 120.8 on 8 and 358 DF, p-value: < 2.2e-16par(mfrow = c(2,2))
plot(fit.linear)
preds = predict(fit.linear,newdata = test)Calculation of error
RMSE=sqrt(mean((test$MEDV-preds)^2))
RMSE## [1] 4.56878Logistic Regression
fit.log = glm(MEDV ~ . -RAD -TAX - AGE -CRIM - INDUS,data = train)
summary(fit.log)##
## Call:
## glm(formula = MEDV ~ . - RAD - TAX - AGE - CRIM - INDUS, data = train)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -15.7416 -2.9791 -0.6319 1.8156 27.1933
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 30.975782 5.848664 5.296 2.07e-07 ***
## ZN 0.039667 0.015826 2.506 0.0126 *
## CHAS1 2.293942 1.038846 2.208 0.0279 *
## NOX -19.795182 3.855972 -5.134 4.67e-07 ***
## RM 4.331848 0.490358 8.834 < 2e-16 ***
## DIS -1.600056 0.231814 -6.902 2.34e-11 ***
## PTRATIO -0.799392 0.142535 -5.608 4.09e-08 ***
## B 0.007823 0.003061 2.556 0.0110 *
## LSTAT -0.572201 0.060222 -9.502 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 24.83273)
##
## Null deviance: 32888.8 on 366 degrees of freedom
## Residual deviance: 8890.1 on 358 degrees of freedom
## AIC: 2231.3
##
## Number of Fisher Scoring iterations: 2preds.log = predict(fit.log,newdata = test)Calculation of error
RMSE = sqrt(mean((test$MEDV-preds.log)^2))
RMSE## [1] 4.56878Random Forest
trees = 500
fit.RF = randomForest(MEDV ~ .,data = train,ntree = trees,importance = T)
varImpPlot(fit.RF)
preds.RF = predict(fit.RF,newdata = test)Calculation of error
RMSE=sqrt(mean((test$MEDV-preds.RF)^2))
RMSE## [1] 3.104016