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Answer the following questions: a. Suppose that each value CC; of the predictor variable in a simple least squares problem (with intercept) is duplicated. Therefore we have two independent observations y; and yg. The data will look like below: 3; :1: 91 $1 yi ? 1 ya 372 9'2 3? 2 yn 37\" y; a?\" . . . . . -+ f . . Consider the regression of yj on an; us1ng 2n observations and the regressron of 3\"" 2!" on CC; using so observations. Are the least squares estimates of the intercept and slope the same for both models? b. Refer to question (a). Compare the regression sum of squares of the two models. Please explain your answer mathematically. c. Refer to question (a). Will the two models have the same t and F statistics? How about R2? Please explain your answer. d. Consider the model 1;; 2 g + 1313:; + 1}. The Gauss-Markov conditions hold and also E; N N (0, a). Let 50 and ,8] be the least squares estimates of ,BD and ,81. Suppose that co and c1 are also estimates of ,80 and ,8]. Show that the error sum of squares computed using the least squares estimates is smaller than the error sum os squares computed using on and c1