1.This is related to problem 19 in chapter 12. Dataset "ch12q19.character.txt" includes a categorical variable "location" which has 3 categories: intown, inner suburbs and outer suburbs. The goal of this problem is to practice analyzing a dataset with categorical predictors of more than 2 levels. Taking intown as the reference group, use the dataset "ch12q19.character.txt" and use SAS to fit models and answer the following questions.

(a)Fit the regression model of Y on X1, location and X1*location. Specify how the dummy variables are defined. Write down the model you're fitting (model with notations of beta0, beta1, ...) and the fitted regression model (plug in fitted values of betas').

(b)Based on the fitted model in (a), write down the fitted regression model of Y on X1 for each location.

(c)Test the null hypothesis that the straight lines for the three locations coincide with alpha=0.05. State your null hypothesis in terms of the coefficients. Provide you SAS code and output for conducting the analysis. Figure out your F value and p value based on output, and then draw a conclusion.

(d)Test the null hypothesis that the straight lines for the three locations are parallel with alpha=0.05. State your null hypothesis in terms of the coefficients. Provide you SAS code and output for conducting the analysis. Figure out your F value and p value based on output, and then draw a conclusion.

'HOUSE' 'Y' 'X1' 'X2' 'X3' 'X4' 'Z1' 'Z2' 1 84 13.8 3 7 10 1 0 2 93 19 2 7 22 0 1 3 83.1 10 2 7 15 0 1 4 85.2 15 3 7 12 0 1 5 85.2 12 3 7 8 0 1 6 85.2 15 3 7 12 0 1 7 85.2 12 3 7 8 0 1 8 63.3 9.1 3 6 2 0 1 9 84.3 12.5 3 7 11 0 1 10 84.3 12.5 3 7 11 0 1 11 77.4 12 3 7 5 1 0 12 92.4 17.9 3 7 18 0 0 13 92.4 17.9 3 7 18 0 0 14 61.5 9.5 2 5 8 0 0 15 88.5 16 3 7 11 0 0 16 88.5 16 3 7 11 0 0 17 40.6 8 2 5 5 0 0 18 81.6 11.8 3 7 8 0 1 19 86.7 16 3 7 9 1 0 20 89.7 16.8 2 7 12 0 0 21 86.7 16 3 7 9 1 0 22 89.7 16.8 2 7 12 0 0 23 75.9 9.5 3 6 6 0 1 24 78.9 10 3 6 11 1 0 25 87.9 16.5 3 7 15 1 0 26 91 15.1 3 7 8 0 1 27 92 17.9 3 8 13 0 1 28 87.9 16.5 3 7 15 1 0 29 90.9 15 3 7 8 0 1 30 91.9 17.8 3 8 13 0 1