Guide to Using Minitab For Basic
Statistical Applications
To Accompany
Business Statistics: A Decision Making
Approach, 6th Ed.
Chapter 14:
Multiple Regression Analysis and Model
Building
By
Groebner, Shannon, Fry, & Smith
Prentice-Hall Publishing Company
Copyright, 2005
Chapter 14 Minitab
Examples

Multiple Regression
First City Real Estate
 Multiple Regression – Variance Inflation Factor
First City Real Estate
 Multiple Regression – Dummy Variable
First City Real Estate
 Curvilinear Regression Prediction
Ashley Investment Services
 Interaction Effects
Ashley Investment Services
More Examples
Chapter 14 Minitab
Examples

Standard Stepwise Regression
Motor Fan Magazine
 Best Subsets Regression
Fortune 50 Companies
 Residual Analysis
First City Real Estate
Multiple Regression
First City Real Estate
Issue:
First City management wishes to build a
model that can be used to predict sales prices
for residential property.
Objective:
Use Minitab to build a multiple regression
model relating sales price to a set of measurable
variables. Data file is First City.mtw
Multiple Regression – First City Real Estate
Open File First City.mtw
Multiple Regression – First City Real Estate
First click on
Stat, then
Basic
Statistics and
finally on
Correlation.
Multiple Regression – First City Real Estate
Identify columns for Variables.
Click on O.K.
Multiple Regression – First City Real Estate
The Minitab
output shows
the correlation
and p-value
between Age
and Square
Feet.
Multiple Regression – First City Real Estate
The correlation
between each
predictor and
Price is highly
significant.
Thus, each
predictor will be
inserted into the
regression
model.
Multiple Regression – First City Real Estate
Click on Stat, then
Regression and then
Regression again.
Multiple Regression – First City Real Estate
Define the
columns
containing the
Response and
Predictor
Variables
Multiple Regression – First City Real Estate
The regression
coefficients, R2,
S, and sum of
squares are all
generated by the
regression
command.
Multiple Regression –
Variance Inflation Factor
First City Real Estate
Issue:
First City managers wish to identify any
multicollinearity that exists in the predictor
variables.
Objective:
Use Minitab to calculate the variance inflation
factors (VIF). Data file is First City.mtw
Multiple Regression – VIF - First City
Open file First
City.mtw.
Multiple Regression – VIF - First City
Click on Stat
then
Regression
and then
Regression.
Multiple Regression – VIF - First City
Define the columns
containing the
Response and Predictor
Variables then select
Options to use the VIF.
Multiple Regression – VIF - First City
Click to
determine the
Variance
Inflation Factors
Multiple Regression – VIF - First City
The output shows the
variance inflation factors.
All VIFs are below 5.
Multicollinearity is not
evident.
Multiple Regression –
Dummy Variable
First City Real Estate
Issue:
First City managers wish to improve the
model by adding a location variable.
Objective:
Use Minitab to improve a regression model by
adding a dummy variable. Data file is First City.mtw
Multiple Regression – Dummy Variable - First City
Open file First
City.mtw. Move to
column on the
worksheet containing
the Area data.
Multiple Regression – Dummy Variable - First City
Click on Stat
then
Regression
and then
Regression.
Multiple Regression – Dummy Variable - First City
Define the columns
containing the
Response and Predictor
Variables then select
Options to use the VIF.
Multiple Regression – Dummy Variable - First City
Click to
determine the
Variance
Inflation Factors
Multiple Regression – Dummy Variable - First City
The output shows an
improved regression
model.
Curvilinear Relationships Ashley Investment Services
Issue:
The director of personnel is trying to determine
whether there is a relationship between employee
burnout and time spent socializing with co-workers.
Objective:
Use Minitab to determine whether the
relationship between the two measures is statistically
significant. Data file is Ashley.mtw
Curvilinear Relationships – Ashley Investment Services
Open File Ashley.mtw
File contains values for
20 Investment Advisors.
Curvilinear Relationships – Ashley Investment Services
To develop the
scatter plot
first click on
Graph button
then select
Plot
Curvilinear Relationships – Ashley Investment Services
Identify the columns
containing the variables to
be graphed.
Curvilinear Relationships – Ashley Investment Services
The scatter plot shows
a relationship that
could be either linear or
nonlinear.
Curvilinear Relationships – Ashley Investment Services
To find the
linear model,
return to the
data sheet,
click on Stat,
then
Regression
and finally
Regression
again.
Curvilinear Relationships – Ashley Investment Services
Identify the columns
containing the X and Y
variables. Then click OK.
Curvilinear Relationships – Ashley Investment Services
The output shows the R
Square value and the
Regression Coefficients.
Curvilinear Relationships – Ashley Investment Services
To find a
nonlinear model,
click on Stat then
Regression and
select Fitted Line
Plot.
Curvilinear Relationships – Ashley Investment Services
Minitab
gives the
choice of
three
models,
select
Quadratic.
Curvilinear Relationships – Ashley Investment Services
This gives
the
Quadratic
Regression
Line. The
Regression
Equation
and RSquare value
is given.
Curvilinear Relationships – Ashley Investment Services
This gives
Regression
Equation
and Rsquare
value. The
R-Square
value is
larger than
that for the
linear model.
Interaction Effects Ashley Investment Services
Issue:
The director of personnel is trying to determine
whether the model can be improved by separating
observations between those taken from men and
women.
Objective:
Use Minitab to determine whether the relationship
between the measures can be improved. Data file is
Ashley-2.mtw
Interaction Effects – Ashley Investment Services
Open File Ashley-2.mtw
Interaction Effects – Ashley Investment Services
Click on the
Graph button
then select
Plot
Interaction Effects – Ashley Investment Services
Identify the columns containing
the X and Y variables, and the
column identifying the gender
groups.
Interaction Effects – Ashley Investment Services
The data plot
shows a
different
pattern for
males and
females.
Interaction Effects – Ashley Investment Services
To further
analyze the
data we will
sort it by
gender.
Click on
the Manip
and then
Sort.
Interaction Effects – Ashley Investment Services
Identify the
columns to be
sorted and the
values to
control the
sort.
Interaction Effects – Ashley Investment Services
The data are
now sorted into
groups.
Interaction Effects – Ashley Investment Services
The Burnout and
Socialization values
for males and
females are pasted
into separate
columns.
Interaction Effects – Ashley Investment Services
A Fitted Line Plot
will be
constructed for
both Males and
Females. Click
on Stat, then
Regression and
then Fitted Line
Plot.
Interaction Effects – Ashley Investment Services
The columns
containing
the X and Y
values for
females are
identified.
The same
will be done
for males.
Interaction Effects – Ashley Investment Services
This is the
quadratic
regression
model for
females.
Interaction Effects – Ashley Investment Services
This is the
quadratic
model for
males.
Standard Stepwise Motor Fan Magazine
Issue:
The magazine staff is performing a descriptive
analysis to determine which vehicle characteristics
explain the variation in highway mileage.
Objective:
Use Minitab to perform a standard stepwise
regression analysis using highway mileage as the
dependent variable. Data file is Automobiles.mtw
Standard Stepwise – Motor Fan Magazine
Open file
Automobiles.mtw
Standard Stepwise – Motor Fan Magazine
First click on
Stat, then
Regression and
then on
Stepwise.
Standard Stepwise – Motor Fan Magazine
Identify columns containing the x and y
Variables and Minitab will default on a F
to enter and remove of 4.0. You can
change if desired.
Standard Stepwise – Motor Fan Magazine
This is the final step
in the output. Two
variables have
entered the model.
The last column
shows the
regression
coefficients, their t
values and RSquare.
Best Subsets Regression Fortune 50 Companies
Issue:
We want to understand the variables that lead to
profits for large companies.
Objective:
Use Minitab develop a best subsets regression
model to explain the variation in total profit. Data file is
Fortune 50.mtw
Best Subsets Regression – Fortune 50 Companies
Open file Fortune 50.mtw
Best Subsets Regression – Fortune 50 Companies
First click on
Stat, then
Regression
and then on
Best Subsets.
Best Subsets Regression – Fortune 50 Companies
Identify the columns
containing the X and Y
Variables.
Best Subsets Regression – Fortune 50 Companies
The best
model is the
one with Cp closest to
variables +
1.
Best Subsets Regression – Fortune 50 Companies
Return to the
Regression options.
Best Subsets Regression – Fortune 50 Companies
The Best Subsets model
is is formed using these
variables identified by
the C-p value.
Best Subsets Regression – Fortune 50 Companies
This is the output
for the Best Subsets
model.
Residual Analysis First City Real Estate
Issue:
The company is interested in analyzing the
residuals of the regression model to determine whether
the assumptions are satisfied.
Objective:
Use Minitab to analyze residuals from a
regression model. Data file is First City-3.mtw
Residual Analysis – First City Real Estate
Open file First City-3.mtw
Residual Analysis – First City Real Estate
Click on Stat,
then
Regression
and then
Regression
again.
Residual Analysis – First City Real Estate
Identify the x and y
variables. Minitab
residual options are
found using either
Graphs or Results.
Residual Analysis – First City Real Estate
These are the
options using the
Graphs button.
Residual Analysis – First City Real Estate
These are the
options available
using Results.
Residual Analysis – First City Real Estate
This plot shows the residuals become more
disperse with later observations. This might
be worth investigation.
Residual Analysis – First City Real Estate
The residuals
seem to be
approximately
normally
distributed.
Residual Analysis – First City Real Estate
This is the output if
the Normal
Probability Plot
option is selected.
Residual Analysis – First City Real Estate
Minitab will provide both
Residual and Standardized
Residual values.