Find the value of the test statistic. (Round your answer to two decimal places.) 23.95 Find the p-value. (Round your answer to four decimal places.) p-value = Is the addition of the interaction term and the smoker variable significant? Reject Ho. We conclude that the addition of the two independent variables are statistically significant. Reject Ho. We conclude that the addition of the two independent variables are not statistically significant. Do not reject Ho. We conclude that the addition of the two independent variables are statistically significant. ○ Do not reject Ho. We conclude that the addition of the two independent variables are not statistically significant. 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 (years) Square Footage Rooms Average Monthly Gas Age Bill for Last Year Square Footage Rooms $70.20 16 2,537 6 $76.76 1 2,372 7 $81.33 2 3,457 $60.40 26 900 4 $45.86 27 976 $44.07 14 1,386 5 $59.21 12 1,713 $24.68 20 1.299 4 $117.88 16 3,979 10 $62.70 17 1.441 6 $59.78 2 1,328 $45.37 13 542 4 $47.01 27 1,251 $38.09 10 2,140 4 $52.89 4 827 $45.31 22 908 6 $32.90 12 645 $52.45 23 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 x, for age. Round your numerical values to four decimal places.) ex₁ 61.4413 0.1587x1 (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 = -5.2548 +0.1363x₁ +0.0079x2 +8.2220x3 (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 B1-B2 0 H₂: One or more of the parameters is not equal to zero. H₁: B₂ =B3=0 H₁: One or more of the parameters is not equal to zero. O Ho: One or more of the parameters is not equal to zero. HB₁ =B₂ = 0 O Ho: One or more of the parameters is not equal to zero. H₂ B₂ =B3=0

Find the value of the test statistic. (Round your answer to two decimal places.) 23.95 Find the p-value. (Round your answer to four decimal places.) p-value = Is the addition of the interaction term and the smoker variable significant? Reject Ho. We conclude that the addition of the two independent variables are statistically significant. Reject Ho. We conclude that the addition of the two independent variables are not statistically significant. Do not reject Ho. We conclude that the addition of the two independent variables are statistically significant. ○ Do not reject Ho. We conclude that the addition of the two independent variables are not statistically significant. 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 (years) Square Footage Rooms Average Monthly Gas Age Bill for Last Year Square Footage Rooms $70.20 16 2,537 6 $76.76 1 2,372 7 $81.33 2 3,457 $60.40 26 900 4 $45.86 27 976 $44.07 14 1,386 5 $59.21 12 1,713 $24.68 20 1.299 4 $117.88 16 3,979 10 $62.70 17 1.441 6 $59.78 2 1,328 $45.37 13 542 4 $47.01 27 1,251 $38.09 10 2,140 4 $52.89 4 827 $45.31 22 908 6 $32.90 12 645 $52.45 23 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 x, for age. Round your numerical values to four decimal places.) ex₁ 61.4413 0.1587x1 (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 = -5.2548 +0.1363x₁ +0.0079x2 +8.2220x3 (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 B1-B2 0 H₂: One or more of the parameters is not equal to zero. H₁: B₂ =B3=0 H₁: One or more of the parameters is not equal to zero. O Ho: One or more of the parameters is not equal to zero. HB₁ =B₂ = 0 O Ho: One or more of the parameters is not equal to zero. H₂ B₂ =B3=0

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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