TABLE 13-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four 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 Microsoft Excel outputs of two regression models.

-Referring to Table 13-6 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?
A) Do not reject H₀ and conclude that the four independent variables have significant individual linear effects on heating costs.
B) Reject H₀ and conclude that the four independent variables taken as a group have significant linear effects on heating costs.
C) Do not reject H₀ and conclude that the four independent variables taken as a group do not have significant linear effects on heating costs.
D) Reject H₀ and conclude that the four independent variables taken as a group do not have significant linear effects on heating costs.

Question

TABLE 13-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following four 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 Microsoft Excel outputs of two regression models.

-Referring to Table 13-6 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?
A) Do not reject H₀ and conclude that the four independent variables have significant individual linear effects on heating costs. 
B) Reject H₀ and conclude that the four independent variables taken as a group have significant linear effects on heating costs. 
C) Do not reject H₀ and conclude that the four independent variables taken as a group do not have significant linear effects on heating costs. 
D) Reject H₀ and conclude that the four independent variables taken as a group do not have significant linear effects on heating costs.

Quizplus · Accepted Answer

In Model 1, the F-test statistic is 148.90 with a p-value of 3.05E-23 which is less than 0.01. This indicates that at least one of the coefficients is not zero, and hence we reject the null hypothesis (H₀) and can conclude that the four independent variables taken as a group have significant linear effects on heating costs.

TABLE 13-6 One of the Most Common Questions of Prospective House Buyers