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• ## Take for instance the race of the respondent in a study of voter preferences

• Race coded white(0) or black(1)
• There are a whole set of factors that are possibly different, or even likely to be different, between voters of different races
• Income, socialization, experience of racial discrimination, attitudes toward a variety of social issues, feelings of political efficacy, etc
• Since we cannot measure all of those differences within the confines of the study we are doing, we use a dummy variable to capture these effects.

• ## The simple case of race is already coded correctly

• Race: coded 0 for white and 1 for black
• Note the coding can be reversed and leads only to changes in sign and direction of interpretation.
• ## The complex nominal version turns into 5 variables:

• White; coded 1 for whites and 0 for non-whites
• Black; coded 1 for blacks and 0 for non-blacks
• Hispanic; coded 1 for Hispanics and 0 for non- Hispanics
• Asian; coded 1 for Asians and 0 for non- Asians
• AmInd; coded 1 for native Americans and 0 for non-native Americans

• ## Interpretation of the dummy variable is usually quite straightforward.

• The intercept term represents the intercept for the omitted category
• The slope coefficient for the dummy variable represents the change in the intercept for the category coded 1 (blacks)

• ## This omitted category is called the reference category

• In the dichotomous case, the reference category is simply the category coded 0
• When we have a series of dummies, you can see that the reference category is both the omitted variable.

• ## To create an interaction term is easy

• Multiply the category * the independent variable
• The full model is thus:
• a is the intercept for Whites;
• (a + B1) is the intercept for Blacks;
• B2 is the slope for Whites; and
• (B2 + B3) is the slope for Blacks
• t-tests for B1 and B3 are whether they are different than a and B2

• ## Tractable non-linearity

• Equation may be transformed to a linear model.
• ## Intractable non-linearity

• No linear transform exists

• ## Several general Types

• Polynomial
• Power Functions
• Exponential Functions
• Logarithmic Functions
• Trigonometric Functions

• ## For instance a logit model

• Or an equilibrium system model

• ## They differ in how they modify and search for those values that minimize the SSE.

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