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 1 ), the amount of insulation in inches (X 2 ), the number of windows in the house (X 3 ), and the age of the furnace in years (X 4 ). Given below are the EXCEL outputs of two regression models. Model 1 Note: 2.96869E-05 = 2.96869×10 -5 Model 2 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 β_j ≠ 0, j = 1, 2, ..., 4 using Model 1? A) Do not reject H₀ and conclude that the 4 independent variables have significant individual linear effects on heating costs. B) Reject H₀ and conclude that the 4 independent variables taken as a group have significant linear effects on heating costs. C) Do not reject H₀ and conclude that the 4 independent variables taken as a group do not have significant linear effects on heating costs. D) Reject H₀ and conclude that the 4 independent variables taken as a group do not have significant linear effects on heating costs.

Question

Quizplus · Accepted Answer

Based on Model 1, the F-statistic is 1105.67 and the p-value is 2.96869E-05, which is less than the significance level of 0.01. Therefore, we reject the null hypothesis H₀ and conclude that at least one of the independent variables has a significant linear effect on heating costs. In other words, the four independent variables taken as a group have significant linear effects on heating costs.

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