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
Note: 2.96869E-05 = 2.96869×10^-5
Model 2
Note: 2.9036E-06 = 2.9036×10^-6
-Referring to Table 14-6, what are the degrees of freedom of the partial F test for H₀ : β₃ = β₄ = 0 vs. H₁ : At least one β_j ≠ 0, j = 3, 4?

Question

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

Note: 2.96869E-05 = 2.96869×10^-5
Model 2

Note: 2.9036E-06 = 2.9036×10^-6
-Referring to Table 14-6, what are the degrees of freedom of the partial F test for H₀ : β₃ = β₄ = 0 vs. H₁ : At least one β_j ≠ 0, j = 3, 4?

Quizplus · Accepted Answer

From the output, we can see that the model has 4 predictor variables. Therefore, the denominator degrees of freedom is 15 (sample size - number of predictor variables - 1 = 18 - 4 - 1 = 15). For the partial F test of H₀ : β₃ = β₄ = 0 vs. H₁ : At least one β_j ≠ 0, j = 3, 4, we are testing two restrictions (β₃ = β₄ = 0) and are therefore estimating two fewer coefficients than in the unrestricted model. Hence the numerator degrees of freedom is 2. Therefore, the degrees of freedom for the partial F test are 2 and 15.

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