Linear Regression Cross Validation

Linear Regression and Best Model Selection using Cross Validation:

Ad = read.csv("Advertising.csv") #Seperate dataset to training set and test set trainRows = runif(nrow(Ad))>0.25 #Choose 75% of data as our training data train = Ad[trainRows,] #Make the training dataset test = Ad[!trainRows,] #Put rest of data into test set

#fit two linear regression models fit1 = lm(Sales~Radio+Newspaper,data=train) summary(fit1)

fit2 = lm(Sales~TV+Radio,data=train) summary(fit2)

#method2 set.seed(1) Ad = read.csv("Advertising.csv") train = sample(1:nrow(Ad),0.75*nrow(Ad))

test = -train

attach(Ad)

fit1 = lm(SalesTV+Newspaper,data=Ad[train,]) #first model we run. Sales predicted using TV and Newspaper fit2 = lm(SalesTV+Radio,data=Ad[train,]) #second model we run. Sales predicted using Tv and Radio

#test our models on test dataset ##NOTICE: when we do predict on test data set, we need to write "newdata=" rather than "data="

Sales.test.pred1 = predict(fit1,newdata = Ad[test,]) Sales.test.pred2 = predict(fit2,newdata = Ad[test,])

mse1= mean((Sales[test] - Sales.test.pred1)^2) mse2= mean((Sales[test] - Sales.test.pred2)^2)

#mse2 is much lower. seems that the second model is a better representative of the data.

Important to note that we have not done train validation test. Only train and test.

Doing train, validation and test requires adding another level to the same process.

#Generating New Variables can come in handy in various models . As an example, we will generate an interaction term. Ad$TV_Newspaper = TV*Newspaper fit3 = lm(Sales~TV+Newspaper+TV_Newspaper,data=Ad[train,]) summary(fit3)

#Another way of adding the interaction term to your regression: fit4 = lm(Sales~TV*Newspaper,data=Ad[train,]) summary(fit4)

###################################### #Some more variable manipulation college = read.csv("C:\Users\umair\Documents\Columbia\Business Analytics for OR\course_files_export\Recitations\Recitation 2\College.csv") head(college) attach(college) college$Private = ifelse(Private=="Yes",1,0) college$Private

######################################

#To calculate the confidence intervals of the sample coefficients on Tv and Newspaper, use the confint command. The default level is 0.95 confint(fit4)

#To calculate a prediction interval for a particular point, use the predict command. predict(fit4, data.frame(TV = 60, Newspaper = 1300), interval = "prediction", level = 0.95) predict(fit4, data.frame(TV = 60, Newspaper = 1300), interval = "prediction") # gives the same answer. The default level is 0.95 predict(fit4, data.frame(TV = 60, Newspaper = 1300), interval = "prediction", level = 0.99) #As you can see, predictions for individual points are not that precise. This is expected, because individual points can vary considerably.

####################################### #Regression with non linear independent variables Ad = read.csv("C:\Users\umair\Documents\Columbia\Business Analytics for OR\course_files_export\Recitations\Recitation 2\Advertising.csv")

attach(Ad) l1 = lm(Sales~TV) summary(l1)

l2 = lm(Sales~I(TV^2)) #regresses on the square of TV summary(l2)

library('Hmisc') library(dplyr) require(Hmisc)

#Load data eCarData = read.csv("Car_Data--Extract.csv")

#######

#Generate bins for APR eCarData$RateBin = cut2(eCarData$Rate, c(4,4.5,5, 5.5, 6, 6.5,7, 7.5, 8, 8.5))

#Select Outcomes and the bins for APR, group by the APR bins, and calculate the average for each bin. Conversion_Rate_VS_APR= eCarData %>% select(Outcome, RateBin) %>% group_by(RateBin) %>% summarise(Conversion_Rate = mean(Outcome))

#generate bar chart barplot(Conversion_Rate_VS_APR$Conversion_Rate, ylab = "Conversion Rate", xlab= "APR", main = "Conversion Rate vs APR", names.arg = Conversion_Rate_VS_APR$RateBin)

barplot(Conversion_Rate_VS_APR$Conversion_Rate, ylab = "Conversion Rate", xlab= "APR", main = "Conversion Rate vs APR")

####### #page 6/19 first graph

Generate a variable call count, and sum it up after grouping by APR bins.

Quotes_by_APR = eCarData %>% mutate(count = 1) %>% select(count, RateBin) %>% group_by(RateBin) %>% summarise(Quotes = sum(count))

Generate bar chart

barplot(Quotes_by_APR$Quotes, ylab = "Number of Quotes", xlab = "APR", main = "Number of Quotes by APR", names.arg = Quotes_by_APR$RateBin)

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college_private = college %>% filter(Private == 1)

####### #ADDENDUM

#Correlation between different variables in a dataset can be calculated using the cor() function

rm(list=ls(all=TRUE)) # removes prior data from R

Ad = read.csv("Advertising.csv") cor(Ad)