The document provides an overview of performing multiple regression analysis using R, including both backward and forward stepwise regression techniques. It details the process of loading the 'usjudgeratings' dataset and fitting models to predict judge retention based on various factors, along with steps to analyze residuals and coefficients. Additionally, it suggests useful R packages and offers contact information for further inquiries.

1. ## Multiple Regression with R##
#One should have the basic concept in statistics and R to understand this and the different terms associated with
this work sheet.
#Please read my Simple Linear Regression With R (http://www.slideshare.net/jeromerick/simple-linear-regression-with-
r-52336944) to get a better understanding of this lesson.
# We will use R's in-built data - USJudgeRatings
data("USJudgeRatings") # loading the data into R
?USJudgeRatings
reg1<- lm(RTEN ~ CONT+INTG+DILG+DECI+FAMI, data = USJudgeRatings) #regression equation for predicting worthy of
retaining the judges using the variables CONT+INTG+DILG+DECI+FAMI
reg1
help(lm)
summary(reg1)
cor(USJudgeRatings$CONT,USJudgeRatings$INTG, method = "pearson") # calculating the correlation between two variables
using Pearson’s correlation method.
plot(reg1) # checking the regression diagnostic plots for this model
anova(reg1) # ANOVA
coef(reg1) #coefficients of the regression equation
confint(reg1, level = .99) # confidence interval of the coefficients
resid(reg1) # Residuals of case by case basis
hist(residuals(reg1)) # Histogram of the residuals
plot(residuals(reg1)) # Plotting the residuals
# Kindly install these packages and go through them as they provide better estimators for regression model
install.packages("selectiveInference")
install.packages("rms")
require(selectiveInference)
require(rms)
?selectiveInference
#Stepwise Regression - Please go through the concept of backward and forward regression selection model
#1. Backward stepwise regression -
reg2<-lm(RTEN ~ CONT+INTG+DMNR+DILG+CFMG+DECI+PREP+FAMI+ORAL+WRIT+PHYS, data = USJudgeRatings) # We start Backward
stepwise regression with all the variables and then eliminating each
summary(reg2)
regb<-step(reg2, direction = "backward", trace = 0) # Trace = 0 means we dont want to print all the steps
summary(regb)
#2. Forward stepwise regression -
reg0<-lm(RTEN ~ 1, data = USJudgeRatings) # We start Forward stepwise regression with the minimal model.
regf<-step(reg0, direction = "forward",scope = (~CONT+INTG+DMNR+DILG+CFMG+DECI+PREP+FAMI+ORAL+WRIT+PHYS), data =
USJudgeRatings, trace = 0) # Trace = 0 means we dont want to print all the steps
summary(regf)
## By Jerome Gomes ##
## For queries and more information feel free to contact me @ jeromegomes89@gmail.com ##
## If you want this R-Script then mail me at the above mail id ##