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

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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
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<sub>1</sub>) , the amount of insulation in inches (X<sub>2</sub>) , the number of windows in the house (X<sub>3</sub>) , and the age of the furnace in years (X<sub>4</sub>) . Given below are the EXCEL outputs of two regression models. Model 1 Note: 2.96869E-05 = 2.96869×10<sup>-5</sup> Model 2 Note: 2.9036E-06 = 2.9036×10<sup>-6</sup> -Referring to Table 14-6, what are the degrees of freedom of the partial F test for H<sub>0</sub> : β<sub>3</sub> = β<sub>4</sub> = 0 vs. H<sub>1</sub> : At least one β<sub>j</sub> ≠ 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 Note: 2.96869E-05 = 2.96869×10-5
Model 2
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<sub>1</sub>) , the amount of insulation in inches (X<sub>2</sub>) , the number of windows in the house (X<sub>3</sub>) , and the age of the furnace in years (X<sub>4</sub>) . Given below are the EXCEL outputs of two regression models. Model 1 Note: 2.96869E-05 = 2.96869×10<sup>-5</sup> Model 2 Note: 2.9036E-06 = 2.9036×10<sup>-6</sup> -Referring to Table 14-6, what are the degrees of freedom of the partial F test for H<sub>0</sub> : β<sub>3</sub> = β<sub>4</sub> = 0 vs. H<sub>1</sub> : At least one β<sub>j</sub> ≠ 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 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 βj ≠ 0, j = 3, 4?

Definitions:

Random Sample

A subset of a population selected in such a manner that every individual has an equal chance of being chosen.

Regression Line

A line of best fit through a scatter plot of data points that shows the linear relationship between two variables.

Linear Regression

A statistical method used to model the relationship between a dependent variable and one or more independent variables by fitting a linear equation to observed data.

Standard Error

A measure of the statistical accuracy of an estimate, indicating the variability of an estimate when different samples are taken from the same population.

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