5. For questiim 5, you will use a subset of the cars data. Run the following R codes and use the cara2 data set to answer the questions. Include your R codes and output for the following questions. R codes: set . seed (20] id): samplelznmwfcars) ,4,replaceFAI_SE) cars cars [irix ,] (a) Make a scatterplot that shows the relationship between 1' and Y. From the plot, do you nd any relationship between speed and diet? {1 pt) ('1) Assume that there is a. linear relationship between 1' and Y. That is, 5'; = {in + .611}- + e:- where e.- ~ N (D, 02). Obtain the LS estimates for g, ,61 and an unbiased estimate for 03. (1 pt) {c} Using the estimates, calculate the residuals at, e; and em (Le. residuals for the observa tions at the 4th, 7th and 10th rows of the cars2 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 tted model; Add the tted 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 t for the tted model. 1What percentage of the variation in the response variable is explained by the tted mode]? (1 pt) (g) Consider the statement: \"If someone is driving at lmph, according to the tted model, the distance taken to stop will be exactly 339.5114ft.\" Give two brief (reasonable) criticisms of the statement. [2 pt) {h} Construct a 90% condence interval for ,dl. (2 pt) (i) Construct a 95% condence interval for E(VI2: = 15). (1 pt) (j) Is the linmr relationship bctm Y and 3 signicant? Answer the question by conducting an appropriate statistical test at a: = 0.05. (1 pt) {11) thol| =5VSH| 1'31 {5&t=.05. (21$)