Answer Happy

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 Average Monthly Gas Bill for Last Year Age Square Footage Rooms $70.20 16 2,537 6 $76.76 1 2,412 7 $81.33 2 3,457 8 $60.40 26 900 6 $45.86 27 976 6 $44.07 14 1,386 5 $59.21 12 1,713 7 $24.68 20 1,299 4 $117.88 16 3,979 10 $62.70 17 1,441 $59.78 2 1,328 7 $45.37 13 582 4 $47.01 27 1,251 $38.09 10 2,140 4 $52.89 4 827 5 $45.31 22 908 6 $32.90 12 645 4 $52.45 25 1,568 5 $67.04 29 2,849 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.) 61.5358 0.1636 X (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= 6
(c) At the 0.05 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). State the null and alternative hypotheses. O Ho: One or more of the parameters is not equal to zero. Hai By = By = D ⒸH₂: B₂=₂=0 H: One or more of the parameters is not equal to zero. O Ho: B₁ = P₂ = 0 H₂: One or more of the parameters is not equal to zero. O Ho: One or more of the parameters is not equal to zero. Hai P₂-03-1 Find the value of the test statistic. (Round your answer to two decimal places.) 38.0454 x Find the p-value. (Round your answer to four decimal places.) p-value=0.0000 Is the addition of the interaction term and the smoker variable significant? Ⓒ Reject H. We conclude that the addition of the two independent variables are statistically significant. O Reject Ho. We conclude that the addition of the two independent variables are not statistically significant. O Do not reject Ho. We conclude that the addition of the two independent variables are statistically significant. O Do not reject Hg. We conclude that the addition of the two independent variables are not statistically significant.