Multiple Regression
Analysis
Chapter 14
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
,Learning Objectives
LO14-1 Use multiple regression analysis to describe and interpret a
relationship between several independent variables and a
dependent variable.
LO14-2 Evaluate how well a multiple regression equation fits the
data.
LO14-3 Test hypotheses about the relationships inferred by a
multiple regression model.
LO14-4 Evaluate the assumptions of multiple regression.
LO14-5 Use and interpret a qualitative, dummy variable in multiple
regression.
LO14-6 Include and interpret an interaction effect in multiple
regression analysis.
LO14-7 Apply stepwise regression to develop a multiple regression
model.
LO14-8 Apply multiple regression techniques to develop a linear
model.
14-2
, LO14-1 Use multiple regression analysis to describe and interpret a relationship
between several independent variables and a dependent variable.
Multiple Regression Analysis
The general multiple regression equation with k independent variables is given by:
X1 … Xk are the independent variables.
a is the y-intercept
b1 is the net change in Y for each unit change in X1 holding X2 … Xk
constant. It is called a partial regression coefficient or just a
regression coefficient.
Determining b1, b2, etc. is very tedious. A software package such as
Excel or MINITAB is recommended.
The least squares criterion is used to develop this equation.
14-3
, LO14-1
Multiple Regression Analysis- Example
Salsberry Realty sells homes along the east
coast of the United States. One of the
questions most frequently asked by
prospective buyers is: If we purchase this
home, how much can we expect to pay to
heat it during the winter? The research
department at Salsberry has been asked
to develop some guidelines regarding
heating costs for single-family homes.
Three variables are thought to relate to the heating costs: (1) the mean daily outside temperature,
(2) the number of inches of insulation in the attic, and (3) the age in years of the furnace.
The Multiple Linear regression equation is:
Heating Cost = a + b1(Mean Outside Temp) + b2(Inches of Attic Insulation) + b 3(Age of the Furnace)
To investigate, Salsberry’s research department selected a random sample of 20 recently sold
homes and measured all four variables.
14-4
Analysis
Chapter 14
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
,Learning Objectives
LO14-1 Use multiple regression analysis to describe and interpret a
relationship between several independent variables and a
dependent variable.
LO14-2 Evaluate how well a multiple regression equation fits the
data.
LO14-3 Test hypotheses about the relationships inferred by a
multiple regression model.
LO14-4 Evaluate the assumptions of multiple regression.
LO14-5 Use and interpret a qualitative, dummy variable in multiple
regression.
LO14-6 Include and interpret an interaction effect in multiple
regression analysis.
LO14-7 Apply stepwise regression to develop a multiple regression
model.
LO14-8 Apply multiple regression techniques to develop a linear
model.
14-2
, LO14-1 Use multiple regression analysis to describe and interpret a relationship
between several independent variables and a dependent variable.
Multiple Regression Analysis
The general multiple regression equation with k independent variables is given by:
X1 … Xk are the independent variables.
a is the y-intercept
b1 is the net change in Y for each unit change in X1 holding X2 … Xk
constant. It is called a partial regression coefficient or just a
regression coefficient.
Determining b1, b2, etc. is very tedious. A software package such as
Excel or MINITAB is recommended.
The least squares criterion is used to develop this equation.
14-3
, LO14-1
Multiple Regression Analysis- Example
Salsberry Realty sells homes along the east
coast of the United States. One of the
questions most frequently asked by
prospective buyers is: If we purchase this
home, how much can we expect to pay to
heat it during the winter? The research
department at Salsberry has been asked
to develop some guidelines regarding
heating costs for single-family homes.
Three variables are thought to relate to the heating costs: (1) the mean daily outside temperature,
(2) the number of inches of insulation in the attic, and (3) the age in years of the furnace.
The Multiple Linear regression equation is:
Heating Cost = a + b1(Mean Outside Temp) + b2(Inches of Attic Insulation) + b 3(Age of the Furnace)
To investigate, Salsberry’s research department selected a random sample of 20 recently sold
homes and measured all four variables.
14-4
