SCENARIO 18-2 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 ( ), the amount of insulation in inches ( ), the number of windows in the house ( ), and the age of the furnace in years ( ).Given below are the EXCEL outputs of two regression models.
-Referring to Scenario 18-2, what are the degrees of freedom of the partial F test for j =3, 4 ?
A)2 numerator degrees of freedom and 15 denominator degrees of freedom
B)15 numerator degrees of freedom and 2 denominator degrees of freedom
C)2 numerator degrees of freedom and 17 denominator degrees of freedom
D)17 numerator degrees of freedom and 2 denominator degrees of freedom

Question

SCENARIO 18-2 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 (  ), the amount of insulation in inches (  ), the number of windows in the house (  ), and the age of the furnace in years (  ).Given below are the EXCEL outputs of two regression models. 
-Referring to Scenario 18-2, what are the degrees of freedom of the partial F test for  j =3, 4 ?
A)2 numerator degrees of freedom and 15 denominator degrees of freedom 
B)15 numerator degrees of freedom and 2 denominator degrees of freedom 
C)2 numerator degrees of freedom and 17 denominator degrees of freedom 
D)17 numerator degrees of freedom and 2 denominator degrees of freedom

Quizplus · Accepted Answer

In the partial F test for a regression coefficient, the numerator degrees of freedom are always 1 and the denominator degrees of freedom are equal to the residual degrees of freedom, which is the total sample size minus the number of explanatory variables in the model. For j = 3, the model has 3 explanatory variables, so the residual degrees of freedom are 18 - 3 = 15. For j = 4, the model has 4 explanatory variables, so the residual degrees of freedom are 18 - 4 = 14. Therefore, the degrees of freedom for the partial F tests are 2 numerator degrees of freedom and 15 denominator degrees of freedom for j = 3, and 2 numerator degrees of freedom and 14 denominator degrees of freedom for j = 4. The only answer choice that matches the first set of degrees of freedom is A. The degrees of freedom for the partial F test for a regression model with four variables are 2 numerator degrees of freedom and 15 denominator degrees of freedom. Therefore, the partial F test for 11ebc114_12e0_7aed_8acb_b93d85d41849_TB8562_11 j=3,4 would also have 2 numerator degrees of freedom and 15 denominator degrees of freedom.

SCENARIO 18-2 One of the Most Common Questions of Prospective