EXERCISE 3 Answer the following questions: a. b. Consider the simple regression model yi : g + lm + 64;. Suppose we want to regress the residuals (ei) against the tted values (391). Find the estimates of the intercept and slope of this regression. Use one of the data we used in previous labs to verify your answer in question (a) using R. Consider the simple regression model yi 2 g + [31:121- + 61'. One of the goals of regression is to make predictions on 3; given a new 1: value. Is it always true that when a: = 3': + 1 the predicted value of y will be g + 31? Explain your answer mathematically and use a numerical example in R. Refer to question (c). If a new value of :t: is below a? is it true that the predicted value of y will be always below 37'? Please explain your