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TABLE 14-6 One of the Most Common Questions of Prospective House Buyers

question 118

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TABLE 14-6
One of the most common questions of prospective house buyers pertains to the average cost of heating in dollars (Y) . To provide its customers with information on that matter, a large real estate firm used the following 4 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1) , the amount of insulation in inches (X2) , the number of windows in the house (X3) , and the age of the furnace in years (X4) . Given below are the EXCEL outputs of two regression models.
Model 1
TABLE 14-6 One of the most common questions of prospective house buyers pertains to the average cost of heating in dollars (Y) . To provide its customers with information on that matter, a large real estate firm used the following 4 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X<sub>1</sub>) , the amount of insulation in inches (X<sub>2</sub>) , the number of windows in the house (X<sub>3</sub>) , and the age of the furnace in years (X<sub>4</sub>) . Given below are the EXCEL outputs of two regression models. Model 1 Note: 2.96869E-05 = 2.96869×10<sup>-5</sup> Model 2 Note: 2.9036E-06 = 2.9036×10<sup>-6</sup> -Referring to Table 14-6 and allowing for a 1% probability of committing a type I error, what is the decision and conclusion for the test H<sub>0</sub> : β<sub>1</sub> = β<sub>2</sub> = β<sub>3</sub> = β<sub>4</sub> = 0 vs. H<sub>1</sub> : At least one β<sub>j</sub> ≠ 0, j = 1, 2, ..., 4 using Model 1? A) Do not reject H<sub>0</sub> and conclude that the 4 independent variables have significant individual linear effects on heating costs. B) Reject H<sub>0</sub> and conclude that the 4 independent variables taken as a group have significant linear effects on heating costs. C) Do not reject H<sub>0</sub> and conclude that the 4 independent variables taken as a group do not have significant linear effects on heating costs. D) Reject H<sub>0</sub> and conclude that the 4 independent variables taken as a group do not have significant linear effects on heating costs. Note: 2.96869E-05 = 2.96869×10-5
Model 2
TABLE 14-6 One of the most common questions of prospective house buyers pertains to the average cost of heating in dollars (Y) . To provide its customers with information on that matter, a large real estate firm used the following 4 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X<sub>1</sub>) , the amount of insulation in inches (X<sub>2</sub>) , the number of windows in the house (X<sub>3</sub>) , and the age of the furnace in years (X<sub>4</sub>) . Given below are the EXCEL outputs of two regression models. Model 1 Note: 2.96869E-05 = 2.96869×10<sup>-5</sup> Model 2 Note: 2.9036E-06 = 2.9036×10<sup>-6</sup> -Referring to Table 14-6 and allowing for a 1% probability of committing a type I error, what is the decision and conclusion for the test H<sub>0</sub> : β<sub>1</sub> = β<sub>2</sub> = β<sub>3</sub> = β<sub>4</sub> = 0 vs. H<sub>1</sub> : At least one β<sub>j</sub> ≠ 0, j = 1, 2, ..., 4 using Model 1? A) Do not reject H<sub>0</sub> and conclude that the 4 independent variables have significant individual linear effects on heating costs. B) Reject H<sub>0</sub> and conclude that the 4 independent variables taken as a group have significant linear effects on heating costs. C) Do not reject H<sub>0</sub> and conclude that the 4 independent variables taken as a group do not have significant linear effects on heating costs. D) Reject H<sub>0</sub> and conclude that the 4 independent variables taken as a group do not have significant linear effects on heating costs. Note: 2.9036E-06 = 2.9036×10-6
-Referring to Table 14-6 and allowing for a 1% probability of committing a type I error, what is the decision and conclusion for the test H0 : β1 = β2 = β3 = β4 = 0 vs. H1 : At least one βj ≠ 0, j = 1, 2, ..., 4 using Model 1?

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