Question 2. [24 Marks] To study car price, following variables of 45 cars are collected: Y : price, in thousand dollars X1 : horsepower X2 : peak-rpm, in thousand X3 : city-mpg X : highway-mpg The fitted regression equation is Y = 13.827637 + 0.151127X1 - 2.072357 X2 + 0.358139X3 - 0.684193X4. The total sum of squares based upon n = 45 observations is SSTO = 181.9391. And, the error sum of squares(SSE) are listed for 15 different models as follows(Table 1). (1) [3 Marks] Based on the criterion of the adjusted coefficient of determination, which of models is the best? (2) [2 Marks] Which predictor variable would enter the model first if you apply 'Forward Stepwise Regression' and Center = 0.05? Explain why. (3) [2 Marks] Which predictor variable would be removed from the model XV first if you apply 'backward Stepwise Regression' and O stay = 0.05? Explain why. (4) [2 Marks] Compute the coefficient of partial correlation between Y and X, given that X1, X2 and X3 are already in the model. (5) [5 Marks] Assuming Model IX is the full model, test at a = 0.05 Ho : By = 8, = 0.Table 1: Adjusted R-Square Selection Method Model Variables SSE Number in Model I 102.7655 x1 II 89.8939 x2 III 146.7121 x3 TV 135.9831 x4 16.8434 x1 x2 VI 102.7388 x1 x3 VII 102.702 xl x4 VIII 46.8965 x2 x3 IX 28.8243 x2 x4 X 134.3641 x3 x4 XI 15.2892 x1 x2 x3 XII 13.7766 x1 x2 x4 XIII 101.828 x1 x3 x4 XIV 23.4674 x2 x3 x4 XV 13.0778 x1 x2 x3 x4