Please help me with question 3 and 4

3. Tablel shows the scores in the final examination F and the scores in two preliminary examinations P1 and P2 for 22 students in a statistics course. The data can be found in the book's Web site. (a) Fit each of the following models to the data: Model 1 : F = Bo + B1P1 + Model 2 : F = Bo + B2P2 + 8 Model 3 : F = Bo + B1P1 + B2P2 + 8 (b) Test whether Bo = 0 in each of the three models. (c) Which variable individually, P, or P2, is a better predictor of F? (d) Which of the three models would you use to predict the final examination scores for a student who scored 78 and 85 on the first and second preliminary examinations, respectively? What is your prediction in this case? Table1. Examination Data : Score in the Final (F), First Preliminary(P1), and Second Preliminary(P2) Examinations Row F PI P2 Row F Pi P2 68 78 73 75 79 75 75 74 76 81 89 84 85 82 79 91 94 90 96 4. The relationship between the simple and the multiple regression coefficients can be seen when we compare the following regression equations: ? = Bot BIX1+ $2X2 P = B'ot B'iX1 P = B" o + B'2 X2 X 1 = do + a2X2 X2 = d'o + ax , Using the Examination Data in Table 1 with Y = F, X1 = P1, and X2 = P2, verify that: (a) B'1 = B1 + B2d1, that is, the simple regression coefficient of Y on X, is the multiple regression coefficient of X, plus the multiple regression coefficient of X2 times the coefficient from the regression of X2 on X1- (b) B'2 = B2 + Bid2, that is, the simple regression coefficient of Y on X2 is the multiple regression coefficient of X2 plus the multiple regression coefficient of X, times the coefficient from the regression of X1 on X2