One question for potential home purchasers pertains to teh cost of heating in do
ID: 3217322 • Letter: O
Question
One question for potential home purchasers pertains to teh cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following two variables to predict heating costs: (1) the daily minimum outside temperature in Fahrenheit degress (X1); and 2) the amount of insulation in inches (X2). Please answer the questions below based on the regression model.
1) At the 0.05 level of significance, which explanatory variables are significant in this regression?
2) Interpret the coefficient on Insulation.
3) What is the 95% confidence interval for the expected change in heating costs as a result of a 1 degree Fahrenheit change in the daily minimum outside temperature?
4) Based on the interval found in (3), explain why temperature is significant at the 0.05 significance level.
Regression Statistics Multiple R 0.527 R Square 0.2778 Adjusted R Square 0.1928 Standard Error 40.9107 Observations 20 ANOVA df SS MS F Significance F Regression 2 10943.019 5471.5095 3.2691 0.0629 Residual 17 28452.6027 1673.6825 Total 19 39395.6218 Coefficients Standard Error t Stat P-Value Lower 95% Upper 95% Intercept 448.2925 90.7853 4.9379 0.0001 256.7522 639.8328 Temperature -2.7621 1.2371 -2.2327 0.0393 -5.3721 -0.152 Insulation -15.9408 10.0638 -1.584 0.1316 -37.1736 5.2919Explanation / Answer
Answer
1) At the 0.05 level of significance, which explanatory variables are significant in this regression?
At the 0.05 level of significance, Temperature is significant ( calculated t= -2.237, P=0.0393 which is < 0.05 level.)
2) Interpret the coefficient on Insulation.
When amount of insulation increases by one inches, cost of heating decreases by $15.9408.
3) What is the 95% confidence interval for the expected change in heating costs as a result of a 1 degree Fahrenheit change in the daily minimum outside temperature?
95% confidence interval for the expected change in heating costs = (-5.3721, -0.152).
4) Based on the interval found in (3), explain why temperature is significant at the 0.05 significance level.
95% confidence interval (-5.3721, -0.152) does not contain 0 value. Therefore the regression coefficient is significantly differ from 0.
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