In 2016, the average monthly residential natural gas bill for Black Hills Energy customers in Cheyenne, Wyoming, is $67.95 (Wyoming Public Service Commission website). How is the monthly average gas bill for a Cheyenne home related to the square footage, number of rooms, and age of the home? The following data show the average monthly bill over the past year, square footage, number of rooms, and age for a sample of 20 Cheyenne homes. 

a. Develop an estimated regression equation that can be used to predict a residence’s average monthly gas bill for last year given its age. 

b. Develop an estimated regression equation that can be used to predict a residence’s average monthly gas bill for last year given its age, square footage, and number of rooms. 

c. At the .05 level of significance, test whether the two independent variables added in part (b), the square footage and the number of rooms, contribute significantly to the estimated regression equation developed in part (a).

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Average Monthly Gas Bill for Last Year Numer of Rooms Age Square Footage S70.20 16 2537 6 $81.33 $45.86 $59.21 2 3437 8 27 976 6 11 1713 7 $117.88 16 3979 11 $57.78 $47.01 $52.89 $32.90 $67.04 $76.76 $60.40 $44.07 $26.68 $62.70 $45.37 $38.09 $45.31 $52.45 $96.11 1328 7 27 1251 6 4 827 12 645 4 29 2849 2392 900 1 7 26 14 1386 20 1299 4 17 1441 6 13 562 4 10 2140 4 22 908 6 24 1568 27 1140 10