TABLE 13-6
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 four 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 Microsoft Excel outputs of two regression models.

-Referring to Table 13-6, what is the 90% confidence interval for the expected change in heating costs as a result of a 1 degree Fahrenheit change in the daily minimum outside temperature using Model 1?
A) [6.58, 3.65]
B) [6.24, 2.78]
C) [5.94, 3.08]
D) [2.37, 15.12]

Question

TABLE 13-6
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 four 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 Microsoft Excel outputs of two regression models.

-Referring to Table 13-6, what is the 90% confidence interval for the expected change in heating costs as a result of a 1 degree Fahrenheit change in the daily minimum outside temperature using Model 1?
A) [6.58, 3.65] 
B) [6.24, 2.78] 
C) [5.94, 3.08] 
D) [2.37, 15.12]

Quizplus · Accepted Answer

The 90% confidence interval for the expected change in heating costs as a result of a 1 degree Fahrenheit change in the daily minimum outside temperature using Model 1 is given by the coefficient and its respective confidence interval for X1 in the regression output.
From the output, the coefficient for X1 is -4.32, and the 90% confidence interval for this coefficient is (−5.94, −3.08).
Therefore, the 90% confidence interval for the expected change in heating costs as a result of a 1 degree Fahrenheit change in the daily minimum outside temperature using Model 1 is (-5.94 * 1, -3.08 * 1), which simplifies to [-5.94, -3.08].
Since we are interested in the absolute value of the expected change in heating costs, the confidence interval becomes [3.08, 5.94].
Therefore, the correct choice is C, [5.94, 3.08].

TABLE 13-6 One of the Most Common Questions of Prospective House Buyers