2. Consider a multiple regression model of the price of houses in thousands of dollars) on three explanatory variables: taxes paid in hundreds of dollars), number of bathrooms, and square feet. The selected and edited) SAS output from the regression on 28 houses is given as follows: DF Analysis of Variance Sum of Squares Mean Square F Value 504541 Pr > F Source Model Error Corrected Total 27 541119 DF t Value Pr > It! 1 Variable Intercept taxes bath sqft Parameter Estimates Parameter Estimate Standard Error -10.65 24.02 0.18966 0.05623 81.87 47.82 0.10063 0.03125 1 1 1 (a) Calculate the adjusted coefficient of multiple determination. (b) Predict the price of a 1.5 bath house of 800 square feet and 1,000 dollars tax paid. (c) Obtain a 95% confidence interval of the regression coefficient for "bath." Based on the interval you calcu- lated, can you simplify the model by dropping "bath"? Briefly explain. (d) Conduct an F test for the significance of regression, using the rejection region approach at a level of significance 5%. Make sure you include (i) the null and alternative hypotheses, (ii) the F statistic value, (iii) the rejection region, and (iv) the conclusion. (e) Conduct a 1 test to determine whether you can omit the variable "taxes" from the regression model, using the rejection region approach at a = 5%. Make sure you include (i) the null and alternative hypotheses, (ii) the appropriate test statistic value, (iii) the rejection region, and (iv) the conclusion