variance of a linear function of a random variable. In both problems, you have a random pair (X, Y) and Y is the best linear predictor of Y based on X Question 3 and 4 are in Homework 13 Part it. You need to complete both parts and make one single submission consists of all four questions on Gradescope to receive full credit 1. The Average of the Residuals a) In Data 8 we say that the regression line passes through the point of averages. Show this by setting X = /x and finding the corresponding value of b) Find E() ). In Data 8 language, this is the average of the fitted values. c) The difference Y - Y is called a residual. It is the difference between the actual and fitted values of Y. Find the expectation of the residual and confirm that the answer justifies the following statement from Data 8: "No matter what the shape of the scatter diagram, the average of the residuals is 0." 2. An Interpretation of r a) Find Var(Y). b) Show that the answer to Part a justifies the following statement from Data 8: SD of fitted values = Irl SD of y Note: Usually, the result above is stated in terms of variances instead of SDs, and hence r is sometimes called "the proportion of variability explained by the linear model". Submission Instructions Please follow the directions below to properly submit your