Multiple Linear Regression: Open Project Talent data set. Below is data relating to six variables for 25 students randomly selected from the Project Talent data bank. This information was collected from high school seniors as part of a comprehensive survey and follow-up of over 400,000 high school students. A short description of each of the variables is as follows: Gender Coded (0) Males and (1) Females (Categorical variable!) Reading Comprehension Total correct out of 48 items Mechanical Reasoning Total correct out of 20 items Sociability Inventory Total of 12 self-reported items, the higher the score the more sociable the person Socioeconomic Status Based on 9 self-reported items such as income, value of home, books in home, father's occupation, parent's education, Standard score with mean of 100 and SD of 10. The higher the score the higher the status Mathematics Test Total correct out of 54 items covering arithmetic and high school mathematics. 1. Perform a multiple regression analysis regressing Math on Gender, Reading, Mechanical, Social, and SES. a. What is the multiple regression equation? b. What are the standard errors for each of the estimates? 2. From the ANOVA table output: a. What are the null and alternative hypotheses being tested? b. What is the value of the F test statistic? c. What are the degrees of freedom for this test? d. What is the p-value of this F test? e. Using \alpha of 0.01, what would be the decision and conclusion of this test? 3. How much of the variation in Math scores is explained by this combination of the five predictors? 4. What is the coefficient of determination after adjusting for the number of predictors in the model? 5. You want to predict Math scores for 4 individuals with the following variable values: Gender, Reading, Mech, Social, SES 0, 23, 8, 5, 86 0, 31, 11, 7, 97 1, 33, 13, 8, 95 1, 37, 15, 10, 104 a. What are the predicted math scores for each of these individuals? b. What are the 97.5% confidence intervals for these predicted Math scores? 6. Create a probability plot of the residuals. a. What are the appropriate hypotheses for this test? b. What is the conclusion of this test at a 5% level of significance?