PART A: You can use STATA when you answer the following questions when it's helpful. 1. (15 points) Consider the response function E{Y} = 25 + 3X 1 + 4X2 + 1.5X1X2. Draw a conditional effects plot of the response function against X 1 when X2=3 and X2=6. How is the interaction effect of X1 and X2 on Y apparent from the plot? Describe the nature of the interaction effect. (15 points) The data set steroids . dta contains the level of a steroid (Y) and age (X) in healthy female subjects (ranging from age 8-25). (a) Fit a quadratic regression model, and state the tted model. Plot the data and the fitted regression function. Does the quadratic regression function appear to be a good fit? What is the R2? (b) Test whether or not there is a regression relation. State the alternatives, decision rule, and conclusion. What is the pvalue of the test? (c) Test whether the quadratic term can be dropped from the model. State the alternatives, 3. decision rule, and conclusion. (15 points) A marketing research firm was engaged by an automobile manufacturer to conduct a pilot study to examine the feasibility of using logistic regression for ascertaining the likelihood that a family will purchase a new car during the next year. Data on the annual family income (X1, in thousand dollars), and the current age of the oldest family automobile (X 2, in years) is included in car pu r'chase . cl ta. A follow-up study conducted 12 months later was used to determine whether the family actually purchased a new car (Y =1) or did not (Y =0). (a) Fit a multiple logich regression model including annual family income and age of oldest automobile. State the tted logistic response function. (b) Obtain and interpret exp([31) and exp([3,). (c) Test whether or not the following three terms should be added simultaneously to the model: square of annual family income, square of age of oldest automobile, and interaction between annual family income and age of oldest automobile. State the alternatives you use, decision rule, and conclusion. (Note: you may have to go back and center variables if collinearity is high between the low-order and high-order terms)