Regression Models with Interaction Between Variables

1
Regression Models with Interaction Between
Variables
Topics Motivational Example Modeling
Interaction Effect Interpreting Slope Coefficient
for Interaction Variables Interaction with two
quantitative Vars. Implementing Interaction
Variables in StatTools
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Problem Scenario

• The Fifth National Bank is facing a
  gender-discrimination suit. The charge is that
  its female employees receive substantially
  smaller salaries than its male employees.

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Investigating Differences Due to Gender

• It is customary for salaries to be pegged to
  years of experience
• Is there any difference between females and males
  in salary increases with years of experience?

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Salary Variation with Years of Experience Males
vs. Females
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Salary Variation with Gender 4 vs. 8 Years
Experience
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Interaction Effect

• From the graphs we conclude
• gender moderates the effect of years of
  experience on salary
• gender has some effect on salary and this is
  moderated by years of experience
• We say that gender interacts with years of
  experience

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Modeling Interaction Effect

• Introduce an extra variable into the model as
  product of interacting variables
• YrsExperFemale
• When Yrs Exper 4 Gender Male (0)
• YrsExperFemale 0

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Regression Model with Interaction
y 0.28x 34.528 Female
y 1.5278x 30.43 Male
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Interpretation of Interaction Regression Slope
coefficient

• Difference in slopes for Salary vs. YrsEper.
  Simple regression Male Female 1.5278 0.28
  1.248
• Coefficient for YrsExperfemale (-1.248) is the
  salary reduction per extra year of experience for
  females compared to males

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Interaction between Quantitative Variables

• A restaurant chain wants to investigate the
  relationship between shop revenue (000s) and the
  median household income (000s) mean age of
  children in the neighborhood
• Is there interaction between mean age and
  household income?

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Interaction between Quantitative Variables
12
Interaction between Quantitative Variables
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Interpretation of Interaction Slope Coefficient

• For each additional year in mean age of
  neighborhood children, the rate of increase of
  gross revenue per 1,000 increase in median
  household income decreases by 2,151 on average

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Creating Interaction Variables in StatTools

• Name the data set in the usual way
• Place the cursor anywhere in the spreadsheet and
  click on the Data Utilities icon (3rd from left)
• Select Interaction and click on the down arrow at
  top to select the type of Interaction Between
  (e.g. two numeric or two categorical variables)

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Creating Interaction Variables in StatTools

• By clicking, check the box beside the names of
  the variables you want to interact then click
  O.K.
• Click yes when StatTools warns if you wish to
  continue to insert a new column
• StatTools will insert the new column with the
  interaction variable next to your data