# here’s a few statistics questions i’m looking to get some answers

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
______________________________________
Regression Statistics
_______________________________________
R Square 0.8080
Observations 20
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ANOVA
__________________________________________________________________________
df SS MS F Significance F
__________________________________________________________________________
Regression 4(NNN) NNN-NNNN42375.86 15.7874 2.96869E-05
Residual 15NNN-NN-NNNN 2684.155
Total 19 209765.75

__________________________________________________________________________

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

__________________________________________________________________________

Model 2
___________________________________
Regression Statistics
___________________________________
R Square 0.7768
Observations 20

___________________________________
ANOVA
__________________________________________________________________________
df SS MS F Significance F
__________________________________________________________________________
Regression 2(NNN) NNN-NNNN81479.11 29.5923 2.9036E-06
Residual 17NNN-NN-NNNN 2753.384
Total 19 209765.75

__________________________________________________________________________

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

__________________________________________________________________________

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]

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