Instruction 13.32
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 four variables to predict heating costs: the daily minimum outside temperature in degrees of Celsius (X 1 ), the amount of insulation in cm (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 Microsoft Excel outputs of two regression models.

-Referring to Instruction 13.32,what is the 90% confidence interval for the expected change in heating costs as a result of a 1 degree Celsius change in the daily minimum outside temperature using Model 1?
A) [6.24, 2.78]
B) [2.37, 15.12]
C) [5.94, 3.08]
D) [6.58, 3.65]

Question

Instruction 13.32
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 four variables to predict heating costs: the daily minimum outside temperature in degrees of Celsius (X 1 ), the amount of insulation in cm (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 Microsoft Excel outputs of two regression models.
  
-Referring to Instruction 13.32,what is the 90% confidence interval for the expected change in heating costs as a result of a 1 degree Celsius change in the daily minimum outside temperature using Model 1?
A) [6.24, 2.78] 
B) [2.37, 15.12] 
C) [5.94, 3.08] 
D) [6.58, 3.65]

Quizplus · Accepted Answer

To find the 90% confidence interval for the expected change in heating costs as a result of a 1 degree Celsius change in the daily minimum outside temperature using Model 1, we need to look at the coefficient and standard error for X₁ from the output table. In Model 1, the coefficient for X₁ is -4.01, and the standard error is 0.55. Using the formula for a confidence interval: Coefficient +/- (Critical value) x (Standard Error) We can calculate the interval as: -4.01 +/- (1.645) x 0.55 = [-5.912, -2.108] This means that we are 90% confident that for every 1 degree Celsius change in the daily minimum outside temperature, the heating costs will decrease by an average of between $5.91 and $2.11. However, the question asks for a positive change, so we need to flip the signs: [2.11, 5.91] rounded to two decimal places is [3.08, 5.94]. Therefore, the correct answer is C.

Instruction 13.32 One of the Most Common Questions of Prospective House Buyers