Regression Models with Categorical Variables

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Regression Models with Categorical Variables
Topics Motivational Example Dummy
Variables Interpreting Dummy Variable Slope
Coefficients Implementing Dummy 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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Categorical Variables

• The banks employee database contains categorical
  variables for Level of Education and Gender
• Gender Female and Male
• How best to represent with numbers?

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Categorical Variables

• Female 1 and Male 2?
• Use of this numerical scale will bias model in
  favor of males
• Better to use Dummy (binary) variables.

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Dummy Variables for 2 Categories

• Female 1 and Male 0
• Reference category assigned 0
• Selection of reference arbitrary
• Depends on final interpretation
• How different is a females salary compared to
  males?

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Rules for forming Dummy Variables

• We should use one less dummy than the number of
  categories for any categorical variable.
• We shouldnt use any of the original categorical
  variables that the dummies are based on.

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Rules for forming Dummy Variables

• Since gender has only 2 categories, male/female,
  we need just one dummy variable
• Name the dummy variable Female to indicate impact
  on Salary of being female (compared to male)

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Dummy Variables for More than 2 Categories

• EducLev 1 (finished high school), 2 (finished
  some college courses), 3 (obtained a bachelors
  degree), 4 (took some graduate courses) and 5
  (obtained a graduate degree)
• We need four dummy variables

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Categorical Variables for Education Level

• Any four of Ed_1-Ed_5 can be used
• Select the lowest level as reference category to
  model the impact of higher levels of education on
  salary
• Should lead to positive coefficients for the
  dummies easier to interpret.
• Use Ed_2 to Ed_5.

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Quantitative Variables in the Regression Model

• YrsPrior number years worked at another bank
  prior to hire at Fifth National
• YrsExper years of experience working at Fifth
  National

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Regression Model with Dummy Variables Included

• Predicated Salary 26.613
• 0.362YrsPrior - 4.501Female
• 1.033YrsExper 0.160Ed_2
• 4.765Ed_3 7.320Ed_4 11.770Ed_5

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Interpretation of Regression Slope Coefficients
YrsPrior

• Slope coeff. 0.362
• For either gender, any education level, and a
  given number of years experience with Fifth
  National, the expected increase in salary for one
  extra year of prior experience with another bank
  is 362

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Interpretation of Regression Slope Coefficients
YrsExper

• Slope coeff. 1.033
• For either gender, any education level, and a
  given number of years prior experience, the
  expected increase in salary for one extra year of
  experience with Fifth National is 1033

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Interpretation of Regression Slope Coefficients
Female

• Slope coeff. -4.501
• For any education level, a given number of years
  prior experience, and experience with Fifth
  National, a female employee can expect to earn
  4,501 less per year than their male counterparts

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Interpretation of Regression Slope Coefficients
Ed_2

• Slope coeff. 0.160
• Any employee with a given number of years prior
  experience, experience with Fifth National, and
  some completed college courses, can expect to
  earn 160 more per year than employees with just
  a high school education

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Interpretation of Regression Slope Coefficients
Ed_3

• Slope coeff. 4.765
• Any employee with a given number of years prior
  experience, experience with Fifth National, and a
  bachelors degree, can expect to earn 4,765 more
  per year than employees with just a high school
  education

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Interpretation of Regression Slope Coefficients
Ed_4

• Slope coeff. 7.320
• Any employee with a given number of years prior
  experience, experience with Fifth National, and
  some graduate courses completed, can expect to
  earn 7,320 more per year than employees with
  just a high school education

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Interpretation of Regression Slope Coefficients
Ed_5

• Slope coeff. 11.770
• Any employee with a given number of years prior
  experience, experience with Fifth National, and a
  graduate degree, can expect to earn 11,770 more
  per year than employees with just a high school
  education

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Interpretation of Regression Intercept Term
constant

• constant 26.613
• A freshly hired male employee with no prior work
  experience and just a high school education can
  expect to earn 26,613 per year.
• Assumption data includes at least one such
  observation.

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Effect of Changing Dummy Variable Reference
Category

• Regression coefficients for each category will be
  different but interpretation relative to other
  categories will remain the same

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Effect of Changing Dummy Variable Reference
Category
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Conclusion from Regression Analysis

• One explanation for gender differences in salary
  might be job grade. Perhaps females tend to be in
  lower job grades
• Why are females predominantly in the low job
  grades?
• Is management not advancing females as quickly as
  it should?

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Creating Dummy 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 Dummy and by clicking insert a check mark
  in the box next to the variable (s) for which
  you want dummies

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Creating Dummy Variables in StatTools

• Accept the default radio button Create one dummy
  variables for each distinct category 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
  dummy variable (s) next to your data