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Part II: Making Predictions by Using Regression
Pinpointing Possible Relationships
The third step in doing a multiple regression analysis (see the list in the
“Stepping through the analysis” section) is to find out which (if any) of your
possible x variables are actually related to y. If an x variable has no relationship
with y, including it in the model is pointless. Data analysts use a combination
of scatterplots and correlations to examine relationships between pairs of vari-
ables (as you can see in Chapter 4). While these two techniques can be viewed
under the heading of looking for relationships, I walk you through each one
separately in the following sections to discuss their nuances.
Making scatterplots
You make scatterplots in multiple linear regression to get a handle on whether
your possible x variables are even related to the y variable you’re studying. To
investigate these possible relationships, you make one scatterplot of each x
variable with the response variable y. If you have k different x variables being
considered for the final model, you make k different scatterplots.
To make a scatterplot in Minitab, enter your data in columns, where each
column represents a variable and each row represents all the data from one
individual. Go to Graph>Scatterplots>Simple. Select your y variable on the
left-hand side and click Select. That variable appears in the y-variable box on
the right-hand side. Then select your x variable on the left-hand side and
click Select. That variable appears in the x-variable box on the right-hand
side. Click OK.
Scatterplots of TV ad spending versus TV sales and newspaper spending
versus TV sales are shown in Figure 5-1.
20.0 20.0
Figure 5-1:
Scatterplots 17.5 17.5
of TV and 15.0 15.0
newspaper 12.5 12.5
ad spending Sales (in millions) 10.0 Sales (in millions) 10.0
versus
7.5 7.5
plasma TV
sales. 5.0 0 10 20 30 40 50 5.0 0 5 10 15 20 25
TV Ad Spending (in thousands) Newspaper Spending (in thousands)
a b