Question

Use the following information to answer the questions below: Heat Power is a utility company that would like to predict the monthly heating bill for a household in a particular region during the month of January. A random sample of 18 households in the region were selected and their January heating bill recorded. The data is shown in the table below along with the square footage of the house (SF), the age of the heating system in years (Age), and the type of heating system (Type: heat pump = 1 or natural gas = 0). Household 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Bill $255 $286 $296 $300 $305 $317 $321 $321 $339 $349 $369 $374 $381 $413 $419 $441 $522 $560 SF 2.070 1,909 2.004 2.307 3,021 2.683 1.511 2.836 2.553 2.497 2.103 2.486 2.279 2.477 3.218 3.080 2.507 3.517 Age 7 17 8 22 5 14 8 3 20 11 12 18 19 17 11 8 20 18 Type Natural Gas Natural Gas Natural Gas Natural Gas Natural Gas Natural Gas Natural Gas Natural Gas Natural Gas Natural Gas Heat Pump Heat Pump Heat Pump Heat Pump Heat Pump Heat Pump Heat Pump Heat Pump SUMMARY OUTPUT Regression Statistics Multiple R 0.8655 R Square Adjusted R Square Standard Error 44.8082 Observations 18 ANOVA df MS F Significance F Regression Residual Total 3 14 17 SS 83,948.96 28.108.82 112.057.78 Coefficients Standard Error 144.7200 65.1807 0.0583 0.0237 2.4158 2.0074 95.0806 24.7518 t Stat 2.2203 2.4648 P-value 0.0434 0.0273 Lower 95% Upper 95% 4.921 284.519 0.008 0.109 Intercept SF Age Type 3.8414 0.0018 41.993 148.168

Answer 1

Suppose Heat Power now would like to determine if multicollinearity is present among the independent variables, and if so, which variable should be removed from the model first. The table below shows the variance inflation factor (VIF) for each individual variable. VIF Independent Variable 13.65 Age of the heating system 1.54 Type of heating system 8.67 Square feet of house Question 59 (1 point) In this regard, which of the following statements is correct? Remove variable age of the heating system first- multicollinearity exits. Remove variable type of heating system first- multicollinearity does not exit. Since multicollinearity exits for all variables, this model is not a good model for Heat Power to predict heating bills in the region. Remove variable square feet of the house first- multicollinearity exits. Question 60 (1 point) Heat Power would now like to determine the best subset regression model for the heating bill data using only the independent variables that do not exhibit multicollinearity issues. Based on the best subset output below, what should it be their best subset choice? Cp 10.07 26.37 Model X X2 X3 X X2 X X X2X3 X X X3 161.78 61.36 10.15 5.71 50.94 4 K+1 R-Square Adj. R-Square Std. Error 2 0.87 0.86 2 0.04 -0.02 74.01 2 0.59 0.56 48.08 0.88 0.87 26.15 0.91 23.09 3 0.66 0.61 45.48 4 0.93 0.91 21.00 0.90 = oX2 = Age of the heating system, X3 - Type of heating system X1 = Square feet of house, X2 = Age of the heating system, X3 = Age of heating system o X1 = Square feet of house, X2 = Type of the heating system OX1 = Square feet of house, X2 = Age of the heating system