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Qualitative Dependent Variables and Dummy Variables in Regression Analysis

Learn about qualitative dependent variables and how to incorporate dummy variables into regression models. Understand how to interpret regression results with dummy variables.

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Qualitative Dependent Variables and Dummy Variables in Regression Analysis

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  1. Chapter 15, part D Qualitative Dependent Variables

  2. VI. Qualitative Dependent Variables For most of our models we have restricted our independent variables to quantitative data, values that can take any value in a range. Past examples include: Salary, G.P.A., # of Customers, Repair Cost $ Qualitative (dummy) variables are those that take two or more values (Gender, Political Party, Region of Country).

  3. A. A Dummy Variable The simplest of dummy variables is one in which there are only two possibilities for a qualitative variable. You arbitrarily assign a value of 1 to one possibility and a value of 0 to the other. Examples: X=1 if Female; X=0 if Male X=1 if Union worker; X=0 if Nonunion X=1 if College Graduate; X=0 if not

  4. B. Inclusion in a Regression Problem #38 builds a model to relate Age (x1), Blood Pressure (x2) and Smoking (x3) to the Risk of Strokes (y). Smoking is a dummy variable, X3 =1 if a smoker; X3=0 if a non smoker.

  5. Output Overall, what do you make of these results?

  6. C. Interpretation The estimated coefficient on the Dummy for smoking is 8.74. Since X3=1 for a smoker, this means the probability a patient has a stroke in the next 10 years rises by 8.74% if they’re a smoker. You can’t do much about your age, but if you lower your blood pressure by 10 points, you lower the risk by 2.5%. Hmmm, what should a person do?

  7. D. Multi-level Dummy Variables There are many wage/salary regression models that wish to examine differences in a wage variable by region of the country. For example, we could divide the country into 4 regions and assign a value of 1 to a worker from that region and 0 for all other regions.

  8. Example Suppose we have 3 workers in a set of data. Franklin is from the North, Elly May is from the South, and Chet is from the West. Our table of data might look like this:

  9. The Model • If you have 4 levels for the qualitative variable “Region”, you can only include 3 in the equation. Including all 4 makes it impossible for least-squares to minimize the sum of squared residuals. • The omission of one region creates a benchmark and allows you to compare all other regions to the one omitted.

  10. Hypothetical Regression Results Let’s say that we leave out “East” and we find the following: Wage(Y) = 100 + 50(North) - 25(South) - 10(West) Remember, “North”=1 only if a worker is from the North and all other regions “South” and “West” are 0 for that worker.

  11. Interpretation Franklin is from the North, so “North”=1 and “South”=“West”=0. His estimated wage is then 100+50=$150. Thus we could say that a worker from the North, all else held constant, would see a $50 increase in his/her wage

  12. Continued... Elly May is from the South, so “South”=1 and “North”=“West”=0. Her estimated wage is then 100-25=$75.

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