(f) A real estate agent relates a story about two almost identical real estate properties with the only difference being that one has 40% of the area devoted to the office space and the other has no office space at all. The agent claims that the property without any office space has a higher monthly rental rate than the one with 40% of square footage devoted to the office space. Based on three regression models provided, should you be surprised? Explain your reasoning. (5 points) (g) Vince is thinking about buying a 15,000 square feet building which has 5,000 square feet of office space and which has 50 parking spaces. Use model B to find the probability he will make a profit on this investment if his mortgage payments are equal to $7,548.74 per month. (3 points) Regression Outputs for Question 5 Variables: DumOffice: dummy variable that is equal to 1 if more than 25% of the area (measured in square feet) is devoted to office space and is equal to 0 otherwise. InvDist: 1/(1+ distance in minutes from the building to the nearest freeway entrance), InvYrs: 1/(1+ the age of the building in years), Park: the number of on-site parking spaces, Park_ft: Park/Square Feet, Rent_ft: the monthly rent expressed in dollars per square foot, Square Feet: the building size in square feet, TotalRent the monthly rent expressed in dollars (i.e., Square Feet* Rent_ft). MODEL A TotalRent, 5 Variables TotalRent DumOffice InvDist Inv Yrs Dependent Variable: Independent Variables: Park Square Feet Regression Statistics R Square 0.937 Adj.RSqr 0.930 Std.Err. 1604.871 # Cases 52 #Missing 0 Std.Err. Summary Table Variable Coeff. Intercept -1371.318 DumOffice 1846.324 InvDist 5419.868 InvYrs 1709.634 Park 27.572 Square Feet 0.429 682.963 498.168 3320.793 988.355 13.504 0.024 t Stat -2.008 3.706 1.632 1.730 2.042 17.890 P-value 0.051 0.001 0.109 0.090 0.047 0.000 MODEL B TotalRent, 3 Variables Dependent Variable: TotalRent Independent Variables: DumOffice Park MODEL C Rent/ft?, 2 Variables Dependent Variable: Rent_Ft Independent Variables: DumOffice Park_ft Square Feet Regression Statistics R Square 0.930 Adj.RS ar 0.926 Std.Err 1649.756 # Cases 52 #Missing 0 Regression Statistics R Square 0.420 Adj.RSqr 0.396 Std.Err. 0.080 # Cases 52 #Missing 0 t Stat Summary Table Variable Coeff. Intercept -356.401 DumOffice 1788.868 Park 31.125 Square Feet 0.417 Std.Err. 500.907 490.178 13.728 0.024 -0.712 3.649 2.267 17.387 P-value 0.480 0.001 0.028 0.000 Summary Table Variable Intercept DumOffice Park_ft Coeff 0.406 0.089 32.627 Std.Err. 0.024 0.023 9.659 t Stat. 17.262 3.827 3.378 P-value 0.000 0.000 0.001 Forecasted: TotalRent DumOffice Fcst#1 Forecasted: Rent Ft DumOffice Fcst#1 Fcst#2 Park Square Feet TotalRent 50 15000 9248.846 StErrfst 1693.437 Park_ft 1 0.00333333 0 0 Rent Ft 0.604 0.406 StErrFst 0.082 0.083 (f) A real estate agent relates a story about two almost identical real estate properties with the only difference being that one has 40% of the area devoted to the office space and the other has no office space at all. The agent claims that the property without any office space has a higher monthly rental rate than the one with 40% of square footage devoted to the office space. Based on three regression models provided, should you be surprised? Explain your reasoning. (5 points) (g) Vince is thinking about buying a 15,000 square feet building which has 5,000 square feet of office space and which has 50 parking spaces. Use model B to find the probability he will make a profit on this investment if his mortgage payments are equal to $7,548.74 per month. (3 points) Regression Outputs for Question 5 Variables: DumOffice: dummy variable that is equal to 1 if more than 25% of the area (measured in square feet) is devoted to office space and is equal to 0 otherwise. InvDist: 1/(1+ distance in minutes from the building to the nearest freeway entrance), InvYrs: 1/(1+ the age of the building in years), Park: the number of on-site parking spaces, Park_ft: Park/Square Feet, Rent_ft: the monthly rent expressed in dollars per square foot, Square Feet: the building size in square feet, TotalRent the monthly rent expressed in dollars (i.e., Square Feet* Rent_ft). MODEL A TotalRent, 5 Variables TotalRent DumOffice InvDist Inv Yrs Dependent Variable: Independent Variables: Park Square Feet Regression Statistics R Square 0.937 Adj.RSqr 0.930 Std.Err. 1604.871 # Cases 52 #Missing 0 Std.Err. Summary Table Variable Coeff. Intercept -1371.318 DumOffice 1846.324 InvDist 5419.868 InvYrs 1709.634 Park 27.572 Square Feet 0.429 682.963 498.168 3320.793 988.355 13.504 0.024 t Stat -2.008 3.706 1.632 1.730 2.042 17.890 P-value 0.051 0.001 0.109 0.090 0.047 0.000 MODEL B TotalRent, 3 Variables Dependent Variable: TotalRent Independent Variables: DumOffice Park MODEL C Rent/ft?, 2 Variables Dependent Variable: Rent_Ft Independent Variables: DumOffice Park_ft Square Feet Regression Statistics R Square 0.930 Adj.RS ar 0.926 Std.Err 1649.756 # Cases 52 #Missing 0 Regression Statistics R Square 0.420 Adj.RSqr 0.396 Std.Err. 0.080 # Cases 52 #Missing 0 t Stat Summary Table Variable Coeff. Intercept -356.401 DumOffice 1788.868 Park 31.125 Square Feet 0.417 Std.Err. 500.907 490.178 13.728 0.024 -0.712 3.649 2.267 17.387 P-value 0.480 0.001 0.028 0.000 Summary Table Variable Intercept DumOffice Park_ft Coeff 0.406 0.089 32.627 Std.Err. 0.024 0.023 9.659 t Stat. 17.262 3.827 3.378 P-value 0.000 0.000 0.001 Forecasted: TotalRent DumOffice Fcst#1 Forecasted: Rent Ft DumOffice Fcst#1 Fcst#2 Park Square Feet TotalRent 50 15000 9248.846 StErrfst 1693.437 Park_ft 1 0.00333333 0 0 Rent Ft 0.604 0.406 StErrFst 0.082 0.083