Question 4: Consider the MLR m4.1: Garage and BasementSize are both Categorical Predictors. > table (Garage, BasementSize) Garage No Yes Large 106 630 > summary(m4.1) BasementSize Medium 904 623 Small 506 231 Call: 1m (formula = logprice ~ Garage * BasementSize, data = Housing) Coefficients: (Intercept) GarageYes Estimate Std. Error t value Pr(>|t|) 0.05768 1 0.06234 BasementSizeSmall BasementSizeMedium GarageYes: BasementSizeMedium 2 0.06097 0.06343 4 0.06959 5 0.07817 GarageYes: BasementSizeSmall Residual standard error: 0.5938 on 2994 degrees of freedom Multiple R-squared: 0.4499 ' Adjusted R-squared: 0.4489 F-statistic: 489.7 on 5 and 2994 DF, p-value: anova (m4.1) Analysis of Variance Table Response: logprice Df Sum Sq Mean Sq F value Pr(>F) Garage 1 688.07 688.07 1951.20 < 2.2e-16 *** Basementsize 2 165.96 82.98 235.31 2.2e-16 *** Garage: BasementSize 2 9.33 4.67 13.23 1.904e-06 *** Residuals 2994 1055.80 0.35 A) What does the Y-intercept in m4.1 represent? B) Fill out the missing {s i = 0,1,2,3,4,5 in MLR m4.1 using the house logprice average per group given in the following table: > aggregate (formula=logprice~Garage+BasementSize, FUN=mean) 123456 Garage BasementSize logprice No Large 11.85023 Yes Large 12.44645 No Medium 11.39023 Yes Medium 12.12247 Small 10.91895 Yes Small 11.88455 C) Create the interaction plot where the Basement is on your x-axis. Label your graph. What did you notice? 14- logprice of a House and Garage Status logprice 12- b 8- 6- Garage No Yes Large Medium BasementSize Small D) Use MLR model m4.1 to calculate the differences in the predicted logprices, t scores and their significance (Just Yes or No) of the following pairs of houses types: House Pair 1: The difference in logprice averages of A "No Garage" house that has a "Large Basement" and the "Yes Garage" house with a "Large Basement" Difference House Pair 2: t-value: -" Significance: The difference in logprice averages of A "No Garage" house that has a Large Basement and the "Yes Garage" house with a "Small Basement" Difference t-value: Significance: