Suppose the average monthly residential natural gas bill in a certain town is $67.95. How is the average monthly gas bill for a home in this town related to the square footage, number of rooms, and age of the home? The following tables shows the average monthly gas bill over the past year, square footage, number of rooms, and age for a sample of 20 homes. Average Monthly Gas Bill for Last Year Age Square Footage Rooms $70.20 16 2,537 6 $81.33 2 3,457 8 $45.86 27 976 6 $59.21 12 1,713 7 $117.88 16 3,979 10 $55.78 2 1,328 7 $47.01 27 1,251 6 $52.89 4 827 5 $32.90 12 645 4 $67.04 29 2,849 5 $76.76 1 2,372 7 $60.40 26 900 6 $44.07 14 1,386 5 $28.68 20 1,299 4 $62.70 17 1,441 6 $45.37 13 542 4 $38.09 10 2,140 4 $45.31 22 908 6 $52.45 25 1,568 5 $94.11 27 1,140 10 (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. (Use x1 for age. Round your numerical values to four decimal places.) ŷ = (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. (Use x2 for square footage and x3 for number of rooms. Round your numerical values to four decimal places.) ŷ = (c) At the 0.05 level of significance, test whether the model developed in part (b) is overall significant. State the null and alternative hypotheses.Find the value of the test statistic. (Round your answer to two decimal places. Find the p-value. (Round your answer to four decimal places.) Is the model developed in part (b) statistically significant?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 1GP

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Question

Suppose the average monthly residential natural gas bill in a certain town is $67.95. How is the average monthly gas bill for a home in this town related to the square footage, number of rooms, and age of the home? The following tables shows the average monthly gas bill over the past year, square footage, number of rooms, and age for a sample of 20 homes.

Average Monthly Gas Bill for Last Year	Age	Square Footage	Rooms
$70.20	16	2,537	6
$81.33	2	3,457	8
$45.86	27	976	6
$59.21	12	1,713	7
$117.88	16	3,979	10
$55.78	2	1,328	7
$47.01	27	1,251	6
$52.89	4	827	5
$32.90	12	645	4
$67.04	29	2,849	5
$76.76	1	2,372	7
$60.40	26	900	6
$44.07	14	1,386	5
$28.68	20	1,299	4
$62.70	17	1,441	6
$45.37	13	542	4
$38.09	10	2,140	4
$45.31	22	908	6
$52.45	25	1,568	5
$94.11	27	1,140	10

(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. (Use x₁ for age. Round your numerical values to four decimal places.)

ŷ =

(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. (Use x₂ for square footage and x₃ for number of rooms. Round your numerical values to four decimal places.)

ŷ =

(c)

At the 0.05 level of significance, test whether the model developed in part (b) is overall significant.

State the null and alternative hypotheses.Find the value of the test statistic. (Round your answer to two decimal places.

Find the p-value. (Round your answer to four decimal places.)

Is the model developed in part (b) statistically significant?

(d)

Backward elimination is a variable selection technique used in multiple regression analysis that removes one variable at a time until the adjusted coefficient of determination stops increasing or all slope coefficients in the model have p-values that do not exceed a given threshold value.

Consider the model you developed in part (b), and use backward elimination with a p-value threshold of 0.2 to develop an improved estimated regression equation that can be used to predict a residence's average monthly gas bill for last year. Which variable, if at all, did you remove?

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