Fit a multiple regression model to predict Balance using Age, Education, and Income.

Learning Goal: I’m working on a economics multi-part question and need an explanation and answer to help me learn.

This question should be answered using the Credit data set from ISLR libray below. Please go to ISLR package in R to learn more about the Credit dataset.

library(tidymodels)

library(ISLR)
head(Credit)
model_1=lm(Balance∼Income+Education,data=Credit)
summary(model_1)
AIC(model_1)
BIC(model_1)
Credit$predictions=predict(model_1)
head(Credit)
Credit$residuals=Credit$Balance-Credit$predictions
head(Credit)

res=model_1$residuals
head(res)

plot(Credit$Balance,res)

(balance_mean=mean(Credit$Balance))
(tss=sum((Credit$Balance-balance_mean)^2))
(rss=sum(res^2))

(rsq=1-rss/tss)

(rsq_glance=glance(model_1)$r.squared)

(rho=cor(Credit$predictions, Credit$Balance))
(rho2=rho^2)

library(ggplot2)
ggplot(Credit, aes(x=predictions, y=residuals))+
geom_pointrange(aes(ymin=res, ymax=res))+
geom_line(linetype=3)+
ggtitle(“residuals vs. Linear model Predictions“)

sample_rows<-sample(nrow(Credit), 0.75*nrow(Credit))
sample_rows
Credit_train<-Credit[sample_rows,]
Credit_test<-Credit[-sample_rows,]
head(Credit_train)
head(Credit_test)

model_train=lm(Balance∼Income+Education+I(Income^2)+Student,data=Credit_train)
Credit_train$pred<-predict(model_train, Credit_train)
Credit_test$pred<-predict(model_train, Credit_test)
mean(Credit_test$pred==Credit_test$Balance)

library(Metrics)

(rmse_train=rmse(Credit_train$pred, Credit_train$Balance))
(rmse_test=rmse(Credit_test$pred,Credit_test$Balance))

ggplot(Credit_test, aes(x=predictions, y=Balance))+
geom_point()+
geom_abline()+
ggtitle(“Actual vs. Linear model Predictions”)

newrates=data.frame(Income=20, Education=20)
pred=predict(model_1, newdata=newrates)
pred

(a) Fit a multiple regression model to predict Balance using Age,
Education, and Income.
(b) Provide an interpretation of each coefficient in the model. Be
careful.
(c) For which of the predictors can you reject the null hypothesis
H0 : βj = 0?
(e) Fit a larger model that includes Rating, in addition to Age,
Education, and Income..
(f) How well do the models in (a) and (e) fit the data? (Explain based on adj R2 and AIC or BIC)
(g) Evaluate forecast accuracy of each model. Does Rating improve the forecast accuracy?

(Please upload all the Rcode and R results)!!