For this problem, we will use the Carseats data set which is part of the ISLR2 package. To access the data set, load the ISLR2 package into your R session: library (ISLR2) #you will need to do this every time you open a new R session. To get a snapshot of the data, run head (Carseats). To find out more about the data set, we can type ?Carseats. We will now try to predict carseat unit sales (in thousands) using the other variables in this data set. a. Fit a multiple linear regression model to predict carseat unit sales (in thousands) using all other variables as your predictors. What are the least-square estimates and their standard errors? Summarize your output in a table. b. Assume that our random errors (e;) are normally distributed. Carry out the F-test at a = 0.05. Write out the null/alternative hypothesis, test statistic, null distribution, p-value, and conclusion. c. Choose one regression coefficient and test whether it is zero or not at a = the null/alternative hypothesis, test statistic, null distribution, p-value, and conclusion. 0.05. Write out d. Obtain an estimate for o2. e. Interpret the R2 from the fitted model. f. Interpret the regression coefficients associated with Shelving Location. g. Use the model to predict carseat unit sales when the price charged by competitor is average (you'll need to find what the average competitor price is), median community income level, advertising is 15, population is 500, price for car seats at each site is 50, shelving location is good, average age of local population is 30, education level is 10, and the store is in an urban location within the US. What is your prediction for Y given these predictors? Construct an appropriate interval to quantify the uncertainty surrounding this prediction. Set a = 0.01. h. Use the model to predict carseat unit sales when the price charged by competitor is average (you'll need to find what the average competitor price is), median community income level, advertising is 15, population is 500, price for car seats at each site is 50, shelving location is good, average age of local population is 30, education level is 10, and the store is in an urban location within the US. What is your estimate for f(X) given these predictors? Construct an appropriate interval to quantify the uncertainty surrounding this estimation. Set a = 0.01.