TABLE 17-2
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 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.
-Referring to Table 17-2,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 17-2
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 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.

-Referring to Table 17-2,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

The partial F test is testing for two different hypotheses. The first hypothesis is that both β₃ and β₄ are equal to zero, which means the degrees of freedom for this hypothesis are 2 numerator degrees of freedom and 15 denominator degrees of freedom (from the residual degrees of freedom). The second hypothesis is that at least one of the coefficients for the number of windows or age of furnace is not equal to zero, which means the degrees of freedom for this hypothesis are 1 numerator degree of freedom and 15 denominator degrees of freedom (from the residual degrees of freedom). Therefore, we have 2 numerator degrees of freedom and 15 denominator degrees of freedom for the partial F test.

TABLE 17-2 One of the Most Common Questions of Prospective House Buyers