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As part of an effort to induce the public to conserve energy, a researcher wanted to analyze the factors that determine home heating costs. In a city known for its long, cold winters the researcher took a random sample of 35 houses and collected data on the following variables: cost of heating during the month of January, house size in hundreds of square feet, number of windows, and number of occupants per house. A multiple regression model for the cost of heating was estimated with the Excel output shown below: SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA Regression Residual Total Intercept Size Windows Occupants 0.554 0.511 34.898 35 Df 3 31 34 Coefficients 11.088 5.632 3.179 15.431 SS 46919 37754 84673 Standard Error 4.532 1.489 1.966 6.850 MS 15639.7 1217.9 t Stat 2.45 3.78 1.62 2.25 F 12.84 P-value 0.0202 0.0006 0.1154 0.0316 Significance F 0.000

As part of an effort to induce the public to conserve energy, a researcher wanted to analyze the factors that determine home heating costs. In a city known for its long, cold winters the researcher took a random sample of 35 houses and collected data on the following variables: cost of heating during the month of January, house size in hundreds of square feet, number of windows, and number of occupants per house. A multiple regression model for the cost of heating was estimated with the Excel output shown below: SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA Regression Residual Total Intercept Size Windows Occupants 0.554 0.511 34.898 35 Df 3 31 34 Coefficients 11.088 5.632 3.179 15.431 SS 46919 37754 84673 Standard Error 4.532 1.489 1.966 6.850 MS 15639.7 1217.9 t Stat 2.45 3.78 1.62 2.25 F 12.84 P-value 0.0202 0.0006 0.1154 0.0316 Significance F 0.000

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 8E
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As part of an effort to induce the public to conserve energy, a researcher wanted to analyze the factors that determine home heating costs. In a city known for its long, cold winters the researcher took a random sample of 35 houses and collected data on the following variables: cost of heating during the month of January, house size in hundreds of square feet, number of windows, and number of occupants per house. A multiple regression model for the cost of heating was estimated with the Excel output shown below: SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA Regression Residual Total Intercept Size Windows Occupants 0.554 0.511 34.898 35 Df 31 34 Coefficients 11.088 5.632 3.179 15.431 SS 46919 37754 84673 Standard Error 4.532 1.489 1.966 6.850 MS 15639.7 1217.9 t Stat 2.45 3.78 1.62 2.25 F 12.84 P-value 0.0202 0.0006 0.1154 0.0316 Significance F 0.000 a. Using a 5% significance level, determine if there exists a significant relationship between the independent variables and the dependent variable. State the hypotheses to be tested, the observed value of the test statistic, the corresponding p-value, and your decision.
Transcribed Image Text:As part of an effort to induce the public to conserve energy, a researcher wanted to analyze the factors that determine home heating costs. In a city known for its long, cold winters the researcher took a random sample of 35 houses and collected data on the following variables: cost of heating during the month of January, house size in hundreds of square feet, number of windows, and number of occupants per house. A multiple regression model for the cost of heating was estimated with the Excel output shown below: SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA Regression Residual Total Intercept Size Windows Occupants 0.554 0.511 34.898 35 Df 31 34 Coefficients 11.088 5.632 3.179 15.431 SS 46919 37754 84673 Standard Error 4.532 1.489 1.966 6.850 MS 15639.7 1217.9 t Stat 2.45 3.78 1.62 2.25 F 12.84 P-value 0.0202 0.0006 0.1154 0.0316 Significance F 0.000 a. Using a 5% significance level, determine if there exists a significant relationship between the independent variables and the dependent variable. State the hypotheses to be tested, the observed value of the test statistic, the corresponding p-value, and your decision.
b. Using a 5% significance level, can we conclude that the cost of heating is related to the number of windows per house? State the hypotheses to be tested, the observed value of the test statistic, the corresponding p-value, and your decision. c. Interpret the value of the coefficient for the house size in the estimated regression equation.
Transcribed Image Text:b. Using a 5% significance level, can we conclude that the cost of heating is related to the number of windows per house? State the hypotheses to be tested, the observed value of the test statistic, the corresponding p-value, and your decision. c. Interpret the value of the coefficient for the house size in the estimated regression equation.
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