_{Please solve this Problem}

_{Grade point average The director of admissions of a small college selected 120 students at random from the new freshman class in a study to determine whether a student's grade point average (GPA) at the end of the freshman year (Y) can be predicted from the ACT test score (X). The results of the study follow. Assume that rst-order regression model (linear regression model) is appropriate.}

Refer to the Grade point average problem. An assistant to the director of admissions conjectured that the predictive power of the model could be improved by adding information on whether the student had chosen a major field of concentration at the time the application was submitted. Assume that regression model is appropriate, where X] is entrance test score and X2 = 1 if student had indicated a major field of concentration at the time of application and 0 if the major field was undecided. a. Explain how each regression coefficient in the additive regression model with qualitative predictor can be explained here. b. Fit the regression model and state the estimated regression function. c. Test whether the X2 variable can be dropped from the regression model; use a = 0.01. State the alternatives, decision rule, and con- clusion. d. Obtain the residuals for regression model with qualitative predictor and plot them against X1 X2. Is there any evidence in your plot that it would be helpful to include an interaction term in the model