Lease data 1/Sq Feet Parking/Sq Ft e Lease Cost ($ per Sq Ft) $3,263 $2,908 $28,159 $8,929 $3,501 $7,673 $7,749 $11,479 $387 $514 $1,905 $19,085 $4,437 $674 $888 $451 $929 $16,009 $1,503 $4,912 0.0050009 0.0053116 0.0006497 0.0019094 0.0042877 0.0018838 0.0019452 0.0016121 0.0595516 0.0403073 0.0097621 0.0008135 0.0033657 0.0272963 0.0170784 0.0349534 0.0166451 0.0009814 0.0133115 0.0031291 0.0300054 0.0212464 0.0188413 0.0229128 0.0257262 0.0131866 0.0252876 0.0209573 0 0 0.0390484 0.0219645 0.0437541 0 0 0 0 0.0196280 0.0133115 0.031291 The accompanying data table gives annual costs of 20 commercial leases. The cost of the lease is measured in dollars per square foot, per year. Parking counts the number of parking spots in an adjacent garage that the realtor will build into the cost of the lease. The slope of 1/Sq Ft captures the fixed costs of the lease, those present regardless of the number of square feet. Fit the multiple regression of Cost per Sq Ft on 1/Sq Ft and Parking/Sq Ft, then complete parts (a) through (e) below - Click the icon to view the table of lease data. C Use technology to find the multiple regression model. Assume that x, corresponds to 1/Sq Ft and X, corresponds to Parking/Sq Ft. y = ( ) + ( x + ( D xa (Round to two decimal places as needed.) (a) Thinking marginally for a moment, should there be a correlation between the number of parking spots and the fixed cost of a lease? O A. No, because the parking spots are not being leased. OB. No, because the number of parking spots does not determine the fixed cost of a lease. OC. Yes, because the number of parking spots will attract more buyers for that lease. OD. Yes, because the number of parking spots increases the cost of maintaining the property. (b) Interpret the coefficient of Parking/Sq Ft. Once you figure out the units of the slope, you should be able to get the interpretation. Choose the correct answer below. O A. The coefficient of Parking/Sq Ft represents the number of square feet in the leased property per parking spot available for that property. OB. The coefficient of Parking/Sq Ft represents the number of parking spots available for a lease per square foot of the property leased. O C. The coefficient of Parking/Sq Ft represents the increase in cost of the lease per one parking spot increase in available parking spots. OD. The coefficient of Parking/Sq Ft represents the increase in parking spots available per one dollar increase in the cost of the lease. (c) One of the two explanatory variables explains slightly more than statistically significant variation in the price. Had the two explanatory variables been uncorrelated (and produced these estimates), would the variation have been more clearly statistically significant? Use the VIF to see. Find the VIF between 1/Sq Ft and Parking/Sq Ft. VIF = (Round to three decimal places as needed.) (c) One of the two explanatory variables explains slightly more than statistically significant variation in the price. Had the two explanatory variables been uncorrelated (and produced these estimates), would the variation have been more clearly statistically significant? Use the VIF to see. Find the VIF between 1/Sq Ft and Parking/Sq Ft. VIF = (Round to three decimal places as needed.) Had the two explanatory variables been uncorrelated, would the variation have been more clearly statistically significant? O A. The t-statistic for the slope of Parking/Sq Ft would have been smaller by a factor of /VIF. This is enough to be statistically significant. OB. The t-statistic for the slope of Parking/Sq Ft would have been larger by a factor of /VIF. This is not enough to be statistically significant. OC. The t-statistic for the slope of Parking/Sq Ft would have been smaller by a factor of /VIF. This is not enough to be statistically significant. OD. The t-statistic for the slope of Parking/Sq Ft would have been larger by a factor of /VIF. This is enough to be statistically significant. (d) We can see the effects of collinearity by constructing a plot that shows the slope of the multiple regression. To do this, we have to remove the effect of one of the explanatory variables from the other variables. Here's how to make a so-called partial regression leverage plot for these data. First, regress Cost/Sq Ft on Parking/Sq Ft and save the residuals. Second, regress 1/Sq Ft on Parking/Sq Ft and save these residuals. Now, make a scatterplot of the residuals from the regression of Cost/Sq Ft on Parking/Sq Ft on the residuals from the regression of 1/Sq Ft on Parking/Sq Ft. Fit the simple regression for this scatterplot, and compare the slope in this fit to the partial slope for 1/Sq Ft in the multiple regression. Are they different? Choose the correct partial regression leverage plot. O A. . 0.044 30000 - 15000 30000 . -0.04 (Cost/Sq Ft) 445000- (1/Sq Ft) B Oc. OD 0.04 30000 - 15000 30000 -0.04 115000 Fit the simple regression for this scatterplot. Assume that x, corresponds to the residuals of 1/Sq Ft on Parking/Sq Ft. = (O+( Ox (Round to two decimal places as needed.) Compare the slope in this fit to the partial slope for 1/Sq Ft in the multiple regression. Are they different? O A. No, the two slopes are the same. O B. Yes, the two slopes are not the same. The slope from the partial regression leverage plot is the opposite sign. OC. Yes, the two slopes are not the same. The slope from the partial regression leverage plot is smaller. OD. Yes, the two slopes are not the same. The slope from the partial regression leverage plot is larger. (e) Compare the scatterplot of Cost/Sq Ft on 1/Sq Ft to the partial regression plot constructed in part (d). What has changed? Choose the correct scatterplot for Cost/Sq Ft on 1/Sq Ft. OA. . 10000 129000 Cost/Sq Ft Cost/SqF 0.07 E 1/Sq Ft 1/Sq Ft OC. OD 10000 29000 Cost/Sq Ft Cost/Sq Ft 0.07 0.07 1/Sq Ft 1/Sq Ft What has changed between these two plots? O A. There's more variation and more association in the residuals plot. The residuals scatterplot shows a strong curved pattern and the other scatterplot also shows a strong curved pattern. O C. There's more variation and less association in the residuals plot. The residuals scatterplot shows a weak curved pattern, but the other scatterplot shows strong curved pattern. OB. There's less variation and less association in the residuals plot. The residuals scatterplot shows a weak curved pattern, but the other scatterplot shows a strong curved pattern. OD. There's less variation and more association in the residuals plot. The residuals scatterplot shows a strong curved pattern, but the other scatterplot shows weak curved pattern. Lease data 1/Sq Feet Parking/Sq Ft e Lease Cost ($ per Sq Ft) $3,263 $2,908 $28,159 $8,929 $3,501 $7,673 $7,749 $11,479 $387 $514 $1,905 $19,085 $4,437 $674 $888 $451 $929 $16,009 $1,503 $4,912 0.0050009 0.0053116 0.0006497 0.0019094 0.0042877 0.0018838 0.0019452 0.0016121 0.0595516 0.0403073 0.0097621 0.0008135 0.0033657 0.0272963 0.0170784 0.0349534 0.0166451 0.0009814 0.0133115 0.0031291 0.0300054 0.0212464 0.0188413 0.0229128 0.0257262 0.0131866 0.0252876 0.0209573 0 0 0.0390484 0.0219645 0.0437541 0 0 0 0 0.0196280 0.0133115 0.031291 The accompanying data table gives annual costs of 20 commercial leases. The cost of the lease is measured in dollars per square foot, per year. Parking counts the number of parking spots in an adjacent garage that the realtor will build into the cost of the lease. The slope of 1/Sq Ft captures the fixed costs of the lease, those present regardless of the number of square feet. Fit the multiple regression of Cost per Sq Ft on 1/Sq Ft and Parking/Sq Ft, then complete parts (a) through (e) below - Click the icon to view the table of lease data. C Use technology to find the multiple regression model. Assume that x, corresponds to 1/Sq Ft and X, corresponds to Parking/Sq Ft. y = ( ) + ( x + ( D xa (Round to two decimal places as needed.) (a) Thinking marginally for a moment, should there be a correlation between the number of parking spots and the fixed cost of a lease? O A. No, because the parking spots are not being leased. OB. No, because the number of parking spots does not determine the fixed cost of a lease. OC. Yes, because the number of parking spots will attract more buyers for that lease. OD. Yes, because the number of parking spots increases the cost of maintaining the property. (b) Interpret the coefficient of Parking/Sq Ft. Once you figure out the units of the slope, you should be able to get the interpretation. Choose the correct answer below. O A. The coefficient of Parking/Sq Ft represents the number of square feet in the leased property per parking spot available for that property. OB. The coefficient of Parking/Sq Ft represents the number of parking spots available for a lease per square foot of the property leased. O C. The coefficient of Parking/Sq Ft represents the increase in cost of the lease per one parking spot increase in available parking spots. OD. The coefficient of Parking/Sq Ft represents the increase in parking spots available per one dollar increase in the cost of the lease. (c) One of the two explanatory variables explains slightly more than statistically significant variation in the price. Had the two explanatory variables been uncorrelated (and produced these estimates), would the variation have been more clearly statistically significant? Use the VIF to see. Find the VIF between 1/Sq Ft and Parking/Sq Ft. VIF = (Round to three decimal places as needed.) (c) One of the two explanatory variables explains slightly more than statistically significant variation in the price. Had the two explanatory variables been uncorrelated (and produced these estimates), would the variation have been more clearly statistically significant? Use the VIF to see. Find the VIF between 1/Sq Ft and Parking/Sq Ft. VIF = (Round to three decimal places as needed.) Had the two explanatory variables been uncorrelated, would the variation have been more clearly statistically significant? O A. The t-statistic for the slope of Parking/Sq Ft would have been smaller by a factor of /VIF. This is enough to be statistically significant. OB. The t-statistic for the slope of Parking/Sq Ft would have been larger by a factor of /VIF. This is not enough to be statistically significant. OC. The t-statistic for the slope of Parking/Sq Ft would have been smaller by a factor of /VIF. This is not enough to be statistically significant. OD. The t-statistic for the slope of Parking/Sq Ft would have been larger by a factor of /VIF. This is enough to be statistically significant. (d) We can see the effects of collinearity by constructing a plot that shows the slope of the multiple regression. To do this, we have to remove the effect of one of the explanatory variables from the other variables. Here's how to make a so-called partial regression leverage plot for these data. First, regress Cost/Sq Ft on Parking/Sq Ft and save the residuals. Second, regress 1/Sq Ft on Parking/Sq Ft and save these residuals. Now, make a scatterplot of the residuals from the regression of Cost/Sq Ft on Parking/Sq Ft on the residuals from the regression of 1/Sq Ft on Parking/Sq Ft. Fit the simple regression for this scatterplot, and compare the slope in this fit to the partial slope for 1/Sq Ft in the multiple regression. Are they different? Choose the correct partial regression leverage plot. O A. . 0.044 30000 - 15000 30000 . -0.04 (Cost/Sq Ft) 445000- (1/Sq Ft) B Oc. OD 0.04 30000 - 15000 30000 -0.04 115000 Fit the simple regression for this scatterplot. Assume that x, corresponds to the residuals of 1/Sq Ft on Parking/Sq Ft. = (O+( Ox (Round to two decimal places as needed.) Compare the slope in this fit to the partial slope for 1/Sq Ft in the multiple regression. Are they different? O A. No, the two slopes are the same. O B. Yes, the two slopes are not the same. The slope from the partial regression leverage plot is the opposite sign. OC. Yes, the two slopes are not the same. The slope from the partial regression leverage plot is smaller. OD. Yes, the two slopes are not the same. The slope from the partial regression leverage plot is larger. (e) Compare the scatterplot of Cost/Sq Ft on 1/Sq Ft to the partial regression plot constructed in part (d). What has changed? Choose the correct scatterplot for Cost/Sq Ft on 1/Sq Ft. OA. . 10000 129000 Cost/Sq Ft Cost/SqF 0.07 E 1/Sq Ft 1/Sq Ft OC. OD 10000 29000 Cost/Sq Ft Cost/Sq Ft 0.07 0.07 1/Sq Ft 1/Sq Ft What has changed between these two plots? O A. There's more variation and more association in the residuals plot. The residuals scatterplot shows a strong curved pattern and the other scatterplot also shows a strong curved pattern. O C. There's more variation and less association in the residuals plot. The residuals scatterplot shows a weak curved pattern, but the other scatterplot shows strong curved pattern. OB. There's less variation and less association in the residuals plot. The residuals scatterplot shows a weak curved pattern, but the other scatterplot shows a strong curved pattern. OD. There's less variation and more association in the residuals plot. The residuals scatterplot shows a strong curved pattern, but the other scatterplot shows weak curved pattern