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 18-1,one individual in the sample had an annual income of $40,000,a family size of 1,and an education of 8 years.This individual owned a home with an area of 1,000 square feet (House = 10.00).What is the residual (in hundreds of square feet)for this data point?
A)-6.99
B)-5.35
C)5.40
D)16.99

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 18-1,one individual in the sample had an annual income of $40,000,a family size of 1,and an education of 8 years.This individual owned a home with an area of 1,000 square feet (House = 10.00).What is the residual (in hundreds of square feet)for this data point?
A)-6.99 
B)-5.35 
C)5.40 
D)16.99

Quizplus · Accepted Answer

To find the residual for this data point, we need to use the first regression model (Model 1).
The predicted heating cost for this house is:
Y = 28.45 + 0.32(10.00) - 1.70(40) - 0.59(1) + 0.05(50) = 17.36
The actual heating cost for this house is given as $12,000, which is equivalent to 12.00 in hundreds of dollars.
Therefore, the residual for this data point is:
Residual = Actual value - Predicted value
Residual = 12.00 - 17.36
Residual = -5.36
So, the residual in hundreds of square feet is -5.36, which is closest to option B (-5.35).

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