Chapter 15, part D

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Chapter 15, part D

• Qualitative Independent Variables

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VI. Qualitative Independent 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).

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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 X1 if Female X0 if Male
• X1 if Union worker X0 if Nonunion
• X1 if College Graduate X0 if not

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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 X30 if a non smoker.

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Output

• Overall, what do you make of these results?

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C. Interpretation

• The estimated coefficient on the Dummy for
  smoking is 8.74.
• Since X31 for a smoker, this means the
  probability a patient has a stroke in the next 10
  years rises by 8.74 if theyre a smoker.
• You cant 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?

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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.

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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

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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.

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Hypothetical Regression Results

• Lets say that we leave out East and we find
  the following
• Wage(Y) 100 50(North) - 25(South) - 10(West)
• Remember, North1 only if a worker is from the
  North and all other regions South and West
  are 0 for that worker.

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Interpretation

• Franklin is from the North, so North1 and
  SouthWest0. His estimated wage is then
  10050150. Thus we could say that a worker
  from the North, all else held constant, would see
  a 50 increase in his/her wage

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Continued...

• Elly May is from the South, so South1 and
  NorthWest0. Her estimated wage is then
  100-2575.