Lease Cost ($) 1/Sq Feet Parking/SqFt 3,272 0.0055236 0.0220944 3,046 0.0054436 0.0217744 28,188 0.0006495 0.018186 8,861 0.0018957 0.0227484 3,547 0.0042481 0.0297367 7,778 0.0019129 0.0153032 7,791 0.0019892 0.0238704 11,544 0.0015844 0.0205972 374 0.0592765 0 481 0.0303276 0 1,892 0.0097625 0.0390500 19,028 0.0008177 0.0220779 4,513 0.0033047 0.0363517 722 0.0257953 0 926 0.0172024 0 286 0.0688874 0 866 0.0228711 0 15,968 0.0009797 0.0195940 1,536 0.0136349 0.0136349

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.

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Question content area bottom Part 1

Use technology to find the multiple regression model. Assume that x1 corresponds to 1/Sq Ft and x2 corresponds to Parking/Sq Ft. y=enter your response here+enter your response herex1+enter your response herex(Round to two decimal places as needed.)

Part 2 (a) Thinking marginally for a moment, should there be a correlation between the number of parking spots and the fixed cost of a lease?

A.No, because the parking spots are not being leased.

B. No, because the number of parking spots does not determine the fixed cost of a lease.

C.Yes, because the number of parking spots will attract more buyers for that lease.

D.Yes, because the number of parking spots increases the cost of maintaining the property.

Part 3

(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.

A.The coefficient of Parking/Sq Ft represents the number of square feet in the leased property per parking spot available for that property

B. The coefficient of Parking/Sq Ft represents the increase in cost of the lease per one parking spot increase in available parking spots.

C. The coefficient of Parking/Sq Ft represents the increase in parking spots available per one dollar increase in the cost of the lease.

D. The coefficient of Parking/Sq Ft represents the number of parking spots available for a lease per square foot of the property leased.

Part 4

(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=enter your response here

(Round to three decimal places as needed.)

Part 5 Had the two explanatory variables been uncorrelated, would the variation have been more clearly statistically significant?

A.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.

B.The t-statistic for the slope of Parking/Sq Ft would have been larger by a factor ofVIF. This is not enough to be statistically significant.

C.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.

D.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.

Part 6

(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 ofCost/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 theydifferent?

Part 7 Choose the correct partial regression leverage plot.

A.-0.050.05-1500030000(1/Sq Ft)(Cost/Sq Ft)

A scatterplot has a horizontal axis labeled StartFraction 1 Over square foot EndFraction from negative 0.05 to 0.05 in increments of 0.01 and a vertical axis labeled Cost per square foot from negative 15000 to 30000 in increments of 7500. 20 plotted points follow a general trend of rising from left to right at an increasing rate. Groups of 5 points from left to right have ranges of horizontal and vertical coordinates as follows, where for each group the range of horizontal coordinates is listed first and the range of vertical coordinates is listed second: negative 0.037 to negative 0.005, negative 8500 to negative 3000; 0.001 to 0.003, negative 4000 to negative 3000; 0.004 to 0.008, negative 1000 to 4500; 0.009 to 0.015, 3500 to 18500. All coordinates are approximate.

B.

-0.050.05-1500030000(1/Sq Ft)(Cost/Sq Ft)

A scatterplot has a horizontal axis labeled StartFraction 1 Over square foot EndFraction from negative 0.05 to 0.05 in increments of 0.01 and a vertical axis labeled Cost per square foot from negative 15000 to 30000 in increments of 7500. 20 plotted points follow a general trend of falling from left to right at a decreasing rate. Groups of 5 points from left to right have ranges of horizontal and vertical coordinates as follows, where for each group the range of horizontal coordinates is listed first and the range of vertical coordinates is listed second: negative 0.015 to negative 0.009, negative 2500 to 2000; negative 0.008 to negative 0.004, 0 to 1000; negative 0.003 to negative 0.001, negative 500 to 5500; 0.005 to 0.037, negative 8500 to 500. All coordinates are approximate.

C.-1500030000-0.050.05(Cost/Sq Ft)(1/Sq Ft)

A scatterplot has a horizontal axis labeled Cost per square foot from negative 15000 to 30000 in increments of 7500 and a vertical axis labeled StartFraction 1 Over square foot EndFraction from negative 0.05 to 0.05 in increments of 0.01. 20 plotted points follow a general trend of rising from left to right at a decreasing rate. Groups of 5 points from left to right have ranges of horizontal and vertical coordinates as follows, where for each group the range of horizontal coordinates is listed first and the range of vertical coordinates is listed second: negative 8500 to negative 4000, negative 0.02 to 0.003; negative 4000 to negative 3000, negative 0.037 to 0.003; negative 2500 to 1500, 0.004 to 0.015; 1500 to 21500, 0.007 to 0.013. All coordinates are approximate.

D.

-1500030000-0.050.05(Cost/Sq Ft)(1/Sq Ft)

A scatterplot has a horizontal axis labeled Cost per square foot from negative 15000 to 30000 in increments of 7500 and a vertical axis labeled StartFraction 1 Over square foot EndFraction from negative 0.05 to 0.05 in increments of 0.01. 20 plotted points follow a general trend of falling from left to right at a decreasing rate. Groups of 5 points from left to right have ranges of horizontal and vertical coordinates as follows, where for each group the range of horizontal coordinates is listed first and the range of vertical coordinates is listed second: negative 8500 to negative 4000, negative 0.003 to 0.02; negative 4000 to negative 3000, negative 0.002 to 0.037; negative 2500 to 1500, negative 0.015 to negative 0.004; 1500 to 21500, negative 0.012 to negative 0.005. All coordinates are approximate.

Part 8Fit the simple regression for this scatterplot. Assume that x1corresponds to the residuals of 1/Sq Ft on Parking/Sq Ft. y=enter your response here+enter your response herex1

(Round to two decimal places as needed.)

Part 9 Compare the slope in this fit to the partial slope for 1/Sq Ft in the multiple regression. Are they different?

A.Yes, the two slopes are not the same. The slope from the partial regression leverage plot is smaller.

B.Yes, the two slopes are not the same. The slope from the partial regression leverage plot is the opposite sign.

C. No, the two slopes are the same.

D.Yes, the two slopes are not the same. The slope from the partial regression leverage plot is larger.

Part 10

(e) Compare the scatterplot of Cost/Sq Ft on 1/Sq Ft to the partial regression plot constructed in part (d). What has changed?

Part 11Choose the correct scatterplot for Cost/Sq Ft on 1/Sq Ft.

A.

00.080290001/Sq FtCost/Sq Ft

A scatterplot has a horizontal axis labeled StartFraction 1 Over square foot EndFraction from 0 to 0.0788874 in increments of 0.01 and a vertical axis labeled Cost per square foot from 0 to 29000 in increments of 2900. 20 plotted points very tightly follow the path of a curve that falls from left to right at a decreasing rate with very little spread or deviation from the path. A sample of the plotted points is as follows: (0.004, 3500) and (0.017, 900). All coordinates are approximate.

B.

00.080290001/Sq FtCost/Sq Ft

A scatterplot has a horizontal axis labeled StartFraction 1 Over square foot EndFraction from 0 to 0.0788874 in increments of 0.01 and a vertical axis labeled Cost per square foot from 0 to 29000 in increments of 2900. 20 plotted points very tightly follow the path of a curve that rises from left to right at an increasing rate with very little spread or deviation from the path. A sample of the plotted points is as follows: (0.023, 900) and (0.036, 3500). All coordinates are approximate.

C.

00.080100001/Sq FtCost/Sq Ft

A scatterplot has a horizontal axis labeled StartFraction 1 Over square foot EndFraction from 0 to 0.0788874 in increments of 0.01 and a vertical axis labeled Cost per square foot from 0 to 10000 in increments of 1000. 20 plotted points very tightly follow the path of a curve that falls from left to right at an increasing rate with very little spread or deviation from the path. A sample of the plotted points is as follows: (0.023, 9100) and (0.036, 6500). All coordinates are approximate.

D.

00.080100001/Sq FtCost/Sq Ft

A scatterplot has a horizontal axis labeled StartFraction 1 Over square foot EndFraction from 0 to 0.0788874 in increments of 0.01 and a vertical axis labeled Cost per square foot from 0 to 10000 in increments of 1000. 20 plotted points very tightly follow the path of a curve that rises from left to right at a decreasing rate with very little spread or deviation from the path. A sample of the plotted points is as follows: (0.004, 6500) and (0.017, 9100). All coordinates are approximate.

Part 12 What has changed between these two plots?

A. There's more variation and less association in the residuals plot. The residuals scatterplot shows a weak curvedpattern, but the other scatterplot shows a strong curved pattern.

B. 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.

C.There's less variation and more association in the residuals plot. The residuals scatterplot shows a strong curvedpattern, but the other scatterplot shows a weak curved pattern.

D.There's less variation and less association in the residuals plot. The residuals scatterplot shows a weak curvedpattern, but the other scatterplot shows a strong curved pattern.