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 ( 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.

-Referring to Scenario 18-2,what are the degrees of freedom of the partial F test for H 0 : $\beta$ 3 =$\beta$ 4 = 0 vs.H 1 : At least one $\beta$j $\neq$ 0,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 ( 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.

-Referring to Scenario 18-2,what are the degrees of freedom of the partial F test for H 0 : $\beta$ 3 =$\beta$ 4 = 0 vs.H 1 : At least one $\beta$j $\neq$ 0,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

For the partial F test of H₀, there are 2 numerator degrees of freedom (one for the variable being tested and one for the residual) and 15 denominator degrees of freedom (total sample size minus number of coefficients being tested minus 1). For the test of H₁, there are 3 numerator degrees of freedom (two for the variables being tested and one for the residual) and 4 denominator degrees of freedom (total sample size minus number of coefficients being tested minus 1).

SCENARIO 18-2 One of the Most Common Questions of Prospective β\betaβ

SCENARIO 18-2
One of the Most Common Questions of Prospective $\beta$