Question 1 [30 points] A local real estate company wants to better understand the housing market in the Seattle area. The company hires you to do some analysis. Suppose that you have collected information on the selling price of 138 houses that have recently sold. Now suppose that in addition to the selling prices you also have data on some other characteristics of these 138 houses. The information available on each house is as follows: PRICE SIZE AGE BDRM DOWNTOWN selling price (in $1,000). gross living space (in square feet). age of the house in years). number of bedrooms. 1 if the house is in downtown Seattle, 0 if outside downtown. You run a multiple regression analysis on this data using SIZE, AGE, BDRM and DOWNTOWN to predict PRICE, which produces the following report: Adj-R Square Standard Error 0.776 86.772 Intercept SIZE AGE BDRM DOWNTOWN Coefficients 180.833 0.307 -3.571 45.421 175.341 Lower 95% -871.169 0.144 -7.650 -51.183 28.634 Upper 95% 1232.834 0.470 0.508 142.024 322.048 a) [5 points] What evidence, if any, suggests that there might be problems with the model? What might you do to improve the current model if you think such improvement is necessary and possible? One of your colleagues runs a different regression on these 138 houses, using only SIZE and DOWNTOWN as the independent variables to predict PRICE. The regressions results are as follows: Adj-R Square Standard Error 0.783 82.26 Intercept SIZE DOWNTOWN Coefficients 185.833 0.320 178.134 Lower 95% -866.9 0.157 31.434 Upper 95% 1237.4 0.483 325.865 b) [5 points] Suppose you are talking to Jaime, a marketing manager in the real estate company, about this new 2-variable regression model. You tell Jaime that the confidence interval for SIZE does not contain zero, applying your knowledge from QMETH450. Jaime then asks you what your statement means. Give a precise explanation of the significance of the 95% confidence interval not containing zero. Question 1 [30 points] A local real estate company wants to better understand the housing market in the Seattle area. The company hires you to do some analysis. Suppose that you have collected information on the selling price of 138 houses that have recently sold. Now suppose that in addition to the selling prices you also have data on some other characteristics of these 138 houses. The information available on each house is as follows: PRICE SIZE AGE BDRM DOWNTOWN selling price (in $1,000). gross living space (in square feet). age of the house in years). number of bedrooms. 1 if the house is in downtown Seattle, 0 if outside downtown. You run a multiple regression analysis on this data using SIZE, AGE, BDRM and DOWNTOWN to predict PRICE, which produces the following report: Adj-R Square Standard Error 0.776 86.772 Intercept SIZE AGE BDRM DOWNTOWN Coefficients 180.833 0.307 -3.571 45.421 175.341 Lower 95% -871.169 0.144 -7.650 -51.183 28.634 Upper 95% 1232.834 0.470 0.508 142.024 322.048 a) [5 points] What evidence, if any, suggests that there might be problems with the model? What might you do to improve the current model if you think such improvement is necessary and possible? One of your colleagues runs a different regression on these 138 houses, using only SIZE and DOWNTOWN as the independent variables to predict PRICE. The regressions results are as follows: Adj-R Square Standard Error 0.783 82.26 Intercept SIZE DOWNTOWN Coefficients 185.833 0.320 178.134 Lower 95% -866.9 0.157 31.434 Upper 95% 1237.4 0.483 325.865 b) [5 points] Suppose you are talking to Jaime, a marketing manager in the real estate company, about this new 2-variable regression model. You tell Jaime that the confidence interval for SIZE does not contain zero, applying your knowledge from QMETH450. Jaime then asks you what your statement means. Give a precise explanation of the significance of the 95% confidence interval not containing zero