1. Consider a set of data from 118 applicants that are admitted to a local college, that includes information on the following: (Data from Kutner et al, 2004) GPA: ACT Score: Major: The grade point average (GPA) at the end of the student's freshman year The ACT score of the student at the time of application to the college A categorical variable that indicates whether or not a student did or did not indicate a desired major at the time of application. a) Using the Grade point average.jmp data set, create a scatter plot that shows the ACT score on the horizontal axis, the GPA on the vertical axis, and the data points colored by Major. Does there appear to be any difference in the relationship between GPA and ACT score for students who had indicated a desired major compared to those that did not? b) Fit a regression model to predict freshman GPA by using the independent variables of ACT Score, Major, and the interaction between ACT Score and Major. In your output, make sure to show the parameter estimates obtained using indicator/dummy coding for Major. c) Test for whether there are two separate regression functions according to Major, showing your hypotheses, test statistic, P-value, and decision. d) Given your output in b), what are the fitted regression equations for GPA explained by major that you have for students who did and did not indicate a major at the time of application? e) Using your equations from d), what would be the predicted GPA of a student with an ACT score of 32 and who did not indicate a major at the time of study? 2. A dataset on manpower needs for personnel for residential quarters for US Navy Officers is provided on Blackboard as BOQ data.jmp (Bachelor Officers Quarters). The data, presented by Raymond Myers, relates the monthly man-hours (y) to the following independent variables that describe features of the residential quarters: x1: Average daily occupancy x3: Weekly hours of service desk operations x5: Number of building wings x7: Number of rooms x2: Monthly average number of check-ins x4: Square feet of common use area x6: Operational berthing capacity Use this dataset with an all-possible regression selection technique to fit what you believe is the best regression model (without any variable transformations). Make sure to look at Mallow's Cp, AICC, BIC, and RMSE in making your decision, and print graphs of each of these statistics plotted against the number of variables in the model. 3. In the context of Mallow's Cp statistic, we defined the mean squared error of an estimator as squared bias plus variance, given by E [(0 0)] = [E (0) 0] + Var(6) Use this definition to find the mean squared error of the estimator of the slope of the simple linear regression line: = b + bx