This question uses the same regression results as the previous question.

Y = Rent = monthly rent payment measured in dollars

X1 = Family_Size: the number of people living in the apartment

X2 = Income = family income measured in dollars

X3 = Southwest = a dummy variable equal to one if the apartment is in the Southwest region of the United States

X4 = Northwest = a dummy variable equal to one if the apartment is in the Northwest region

X5 = Northeast = a dummy variable equal to one if the apartment is in the Northeast region

***The base category is living in the Southeast region" ***

Questions:

(a)Suppose you added an additional independent variable to the regression model.If the new variable was theaverage price of a homein the surrounding community, do you think that adding this variable would cause the R-square to increase, decrease, or remain constant?Explain.(4 points)

(b)Again, suppose you added an additional independent variable to the regression model.If the new variable was thenumber of flavors at the local ice parlor(or something seemingly unrelated to monthly rent), do you think that adding this variable would cause the R-square to increase, decrease, or remain constant?Explain.(4 points)

Model Summary (Rent) R R Square Adjusted R Square Std. Error of the Estimate .64 41 .41 273.09 ANOVA (Rent) Sum of Squares of Mean Square F Sig. Regression 25947092.50 5 5189418.50 69.58 000 Residual 36842922.05 494 74580.81 Total 62790014.55 499 Coefficients (Rent) Unstandardized Coefficients Standardized Coefficients B Std. Error Beta Sig. (Constant) 581.45 47.97 .00 12.12 .000 Family_Size -13.17 7.85 -.06 -1.68 .094 Income .00 .00 .17 3.58 .000 Southwest 356.63 39.19 .44 9.10 .000 Northwest 492.94 45.90 .60 10.74 .000 Northeast 238.11 35.56 .29 6.70 .000