Please do (a),(b),(c),(d),(e)

4.13. Data on last year's sales (y, in 100,000s of dollars) in 15 sales districts are given in the file sales. This file also contains promotional expenditures (x1, in thousands of dollars), the number of active accounts (x2), the number of competing brands (x3), and the district potential (x4, coded) for each of the districts. a. A model with all four regressors is proposed: y = Bo + B1X1 + B2X2 + B3x3 + B4x4 +, {~ N(0,02) Interpret the parameters Bo, B1, and $4. b. Fit the proposed model in (a) and calculate estimates of Bi, i =0,1,...,4, and o?. c. Test the following hypotheses: (i) B4 =0; (ii) B3 = B4 = 0; (iii) B2 = B3; (iv) B1 = B2 = B3 = B4 = 0 d. Consider the reduced (restricted) model with B4 = 0. Estimate its coefficients and give an expression for the expected sales. e. Using the model in (d), obtain a prediction for the sales in a district where x = 3.0, X2 = 45, and x3 = 10. Obtain the corresponding 95% prediction interval. 4.13. Data on last year's sales (y, in 100,000s of dollars) in 15 sales districts are given in the file sales. This file also contains promotional expenditures (x1, in thousands of dollars), the number of active accounts (x2), the number of competing brands (x3), and the district potential (x4, coded) for each of the districts. a. A model with all four regressors is proposed: y = Bo + B1X1 + B2X2 + B3x3 + B4x4 +, {~ N(0,02) Interpret the parameters Bo, B1, and $4. b. Fit the proposed model in (a) and calculate estimates of Bi, i =0,1,...,4, and o?. c. Test the following hypotheses: (i) B4 =0; (ii) B3 = B4 = 0; (iii) B2 = B3; (iv) B1 = B2 = B3 = B4 = 0 d. Consider the reduced (restricted) model with B4 = 0. Estimate its coefficients and give an expression for the expected sales. e. Using the model in (d), obtain a prediction for the sales in a district where x = 3.0, X2 = 45, and x3 = 10. Obtain the corresponding 95% prediction interval