TABLE 12-6

One of the most common questions of prospective house buyers pertains to the average cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following 4 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the EXCEL outputs of two regression models.

Model 1

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Regression Statistics

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R Square 0.8080

Adjusted R Square 0.7568

Observations 20

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ANOVA

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df SS MS F Significance F

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Regression 4(NNN) NNN-NNNN42375.86 15.7874 2.96869E-05

Residual 15NNN-NN-NNNN 2684.155

Total 19 209765.75

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Coefficients Standard Error t Stat P-value Lower 90% Upper 90%

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Intercept (NNN) NNN-NNNN77.8614 5.4125 7.2E-05(NNN) NNN-NNNN557.9227

X1 (Temperature) -4.5098 0.8129 -5.5476 5.58E-05 -5.9349 -3.0847

X2 (Insulation) -14.9029 5.0508 -2.9505 0.0099 -23.7573 -6.0485

X3 (Windows) 0.2151 4.8675 0.0442 0.9653 -8.3181 8.7484

X4 (Furnace Age) 6.3780 4.1026 1.5546 0.1408 -0.8140 13.5702

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Model 2

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Regression Statistics

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R Square 0.7768

Adjusted R Square 0.7506

Observations 20

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ANOVA

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df SS MS F Significance F

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Regression 2(NNN) NNN-NNNN81479.11 29.5923 2.9036E-06

Residual 17NNN-NN-NNNN 2753.384

Total 19 209765.75

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Coefficients Standard Error t Stat P-value Lower 95% Upper 95%

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Intercept (NNN) NNN-NNNN 43.9826 11.1253 3.17E-09(NNN) NNN-NNNN582.1180

X1 (Temperature) -5.1103 0.6951 -7.3515 1.13E-06 -6.5769 -3.6437

X2 (Insulation) -14.7195 4.8864 -3.0123 0.0078 -25.0290 -4.4099

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19. Referring to Table 12-6, the estimated value of the partial regression parameter B1 in Model 1 means that:

a. all else equal, an estimated expected $1 increase in average heating costs is associated with a decrease in the daily minimum outside temperature by 4.51 degrees.

b. all else equal, a 1 degree increase in the daily minimum outside temperature results in a decrease in average heating costs by $4.51.

c. all else equal, a 1 degree increase in the daily minimum outside temperature results in an estimated expected decrease in average heating costs by $4.51.

d. all else equal, a 1% increase in the daily minimum outside temperature results in an estimated expected decrease in average heating costs by 4.51%.

20. Referring to Table 12-6, what is the 90% confidence interval for the expected change in average heating costs as a result of a 1 degree Fahrenheit change in the daily minimum outside temperature using Model 1?

a. [-6.58, -3.65]

b. [-6.24, -2.78]

c. [-5.94, -3.08]

d. [-2.37, 15.12]