Caveat Emptor, Inc. is a home inspection service that provides prospective homebuyers with a thorough assessment of the major systems in a house prior to the execution of the purchase contract. Prospective homebuyers often ask the company for an estimate of the average monthly heating cost of the home during the winter. To answer this question, the company wants to build a regression model to help predict the average monthly heating cost (Y) as a function of the average outside temperature in winter 1X1 2, the amount of attic insulation in the house 1X2 2, the age of the furnace in the house 1X3 2, and the size of the house measured in square feet 1X4 2. Data on these variables for a number of homes was collected and may be found in the file CaveatEmptor.xlsx. a. Prepare scatter plots showing the relationship between the average heating cost and each of the potential independent variables. What sort of relationship does each plot suggest? b. If the company wanted to build a regression model using only one independent variable to predict the average heating cost of these houses, what variable should be used? 47412_ch09_ptg01_447-498.indd 493 08/11/16 11:10 AM Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203 494 Chapter 9 Regression Analysis c. If the company wanted to build a regression model using only two independent variables to predict the average heating cost of these houses, what variables should be used?
Caveat Emptor, Inc. is a home inspection service that provides prospective homebuyers with a thorough assessment of the major systems in a house prior to the
execution of the purchase contract. Prospective homebuyers often ask the company
for an estimate of the average monthly heating cost of the home during the winter.
To answer this question, the company wants to build a regression model to help
predict the average monthly heating cost (Y) as a
temperature in winter 1X1 2, the amount of attic insulation in the house 1X2 2, the
age of the furnace in the house 1X3 2, and the size of the house measured in square
feet 1X4 2. Data on these variables for a number of homes was collected and may be
found in the file CaveatEmptor.xlsx.
a. Prepare
and each of the potential independent variables. What sort of relationship does
each plot suggest?
b. If the company wanted to build a regression model using only one independent
variable to predict the average heating cost of these houses, what variable should
be used?
47412_ch09_ptg01_447-498.indd 493 08/11/16 11:10 AM
Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203
494 Chapter 9 Regression Analysis
c. If the company wanted to build a regression model using only two independent
variables to predict the average heating cost of these houses, what variables
should be used?
d. If the company wanted to build a regression model using only three independent variables to predict the average heating cost of these houses, what variables
should be used?
e. Suppose the company chooses to use the regression function with all four independent variables. What is the estimated regression function?
f. Suppose the company decides to use the model with the highest adjusted-R2
statistic. Develop a 95% prediction interval for the average monthly heating cost of a
house with 4 inches of attic insulation, a 5-year-old furnace, 2500 square feet, and
in a location with an average outside winter temperature of 40 degrees. Interpret
this interval.
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