5. For question 5, you will use a subset of the cars data. Run the following R codes and use the cars2 data set to answer the questions. Include your R codes and output for the following questions. R. codes: set . seed (20) idx - sample (nrow( cars ) ,40, replace FALSE) cars2 = cars [idx , ] (a) Make a scatterplot that shows the relationship between r and Y. From the plot, do you find any relationship between speed and dist? (1 pt) (b) Assume that there is a linear relationship between r and Y. That is, Y, = Bot BI; te where & ~ N(0, o'). Obtain the LS estimates for Bo, 81 and an unbiased estimate for o?. (1 pt) (c) Using the estimates, calculate the residuals es, ey and e10 (i.e. residuals for the observa- tions at the 4th, 7th and 10th rows of the cars? data). (1 pt) (d) Find the residuals whose absolute values are greater than 20. Indicate those residuals in the scatterplot with different a color and shape. (1 pt) (e) Report the fitted model. Add the fitted regression line to the current scatterplot. Predict the distance taken to stop when the speed of the car is 17. (1 pt) (f) State the goodness of fit for the fitted model. What percentage of the variation in the response variable is explained by the fitted model? (1 pt) (g) Consider the statement: "If someone is driving at 100mph, according to the fitted model, the distance taken to stop will be exactly 389.5114ft." Give two brief (reasonable) criticisms of the statement. (2 pt) (h) Construct a 90% confidence interval for 31. (2 pt) (i) Construct a 95% confidence interval for E(Y|x = 15). (1 pt) (j) Is the linear relationship between Y and a significant? Answer the question by conducting an appropriate statistical test at o = 0.05. (1 pt) (k) Test Ho : B1 =5 vs H1 : B1