Despite the downturn in home prices and listings, the manager of 4Sale Realty is trying to understand some of the factors inuencing the selling price of a home. It's well known that house size and location are key factors1 but the manager wants to develop a more refined model and wants to understand the impact on price of 3 additional factors; a pool, home security systems, Canada Post 'at home' mail delivery. She asks you to investigate this and provide some insight. A random sample of 30 homes are selected. For each home, the following information was gathered {all gures are in thousands of dollars): 3/ = House selling price Xi = In ground swimming pools X2 = Security systems and oodlights X3 = Home mail delivery by Canada Post The sample data produced the following results: SUMMARY OUTPUT Regression Statistics Multiple R 0.8050 R Square 0.6480 Adj R Square 0.6074 Standard Error 9.1987 Observations 30 ANOVA df SS MS F Regression UNKOWN 4,050.0000 UNKOWN UNKOWN Residual UNKOWN 2,200.0000 UNKOWN Total 29 6,250.0000 Regression output Coefficients Std Error t Stat Intercept 14.0000 7.0000 2.0000 Pool -1.0000 0.7000 -1.4286 Home Security 30.0000 5.2000 5.7692 Mail Delivery 0.2000 0.0800 2.5000 a. Test to determine at the 5% significance level whether in ground swimming pools is related to the house selling price. b. State the population regression line. c. Test the overall validity of the model at a 5% significance level. d. If you identified variables in the model that are not related to the selling price of a home, and you removed these variables, what will happen to R2? Explain