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USING DUMMY VARIABLES IN REGRESSION MODELS

USING DUMMY VARIABLES IN REGRESSION MODELS. Qualitative Variables. Qualitative variables can be introduced into regression models using dummy variables Dummy variables can take on only two values – 0 or 1 Suppose you feel a person’s income may be affected by his/her gender

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USING DUMMY VARIABLES IN REGRESSION MODELS

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  1. USING DUMMY VARIABLES IN REGRESSION MODELS

  2. Qualitative Variables • Qualitative variables can be introduced into regression models using dummy variables • Dummy variables can take on only two values – 0 or 1 • Suppose you feel a person’s income may be affected by his/her gender • X = 1 (male) X = 0 (female) or vice versa • Add a column of gender to the model • Column of 1’s and 0’s

  3. Multiple Values • It is felt that the starting salary for a business school graduate is affected by whether the graduate majored in MIS, accounting, finance, or another business discipline (“Other”). • Use 3 dummy variables to represent business disciplines. • x1 = MIS • x2 = Accounting • x3 = Finance • Use k-1 dummy variables if there are k choices for the qualitative variable. • If the entries for x1, x2, and x3 were all 0, this indicates “Other” • Never have more than one “1” for x1, x2, x3

  4. Example • Suppose Bill is a business graduate who majored in accounting and received a staring salary of $27,000. • Ellen is a second business graduate who majored in marketing (“Other”) and received a starting salary of $29,000. • The corresponding values for y and x1, x2, and x3 for these graduate would be: Bill: y = 27000 x1 = 0 x2 = 1 x3 = 0 Ellen: y = 29000 x1 = 0 x2 = 0 x3= 0

  5. Models with both Quantitative and Qualitative Variables • Many models include both quantitative and qualitative variables. • Interpretation of coefficient of dummy variable (x) – how y is affected if x goes from 0 to 1. • There is no “in-between” interpretation for the dummy variable x

  6. Excel Example • It is conjectured that starting salaries for business school graduates are a function of the major (MIS, Accounting, Finance, Other), gender (Male, Female), and college grade point average. A sample of 20 students is taken. • Use 3 dummy variables for the 4 choices of major. • Use 1 dummy variable for the 2 choices of gender. • GPA is a quantitative variable. • Use Excel’s IF statement to translate the qualitative responses into 0’s and 1’s.

  7. =IF(I2=“MIS”,1,0) =IF(I2=“Accounting”,1,0) =IF(I2=“Finance”,1,0) =IF(J2=“Male”,1,0) X Range is contiguous Drag cells B2:E2 to B21:E21

  8. Regression Equation Salary = 28124.18 + 2932.57MIS - 260.60Accounting + 2135.38Finance – 270.07Male + 142.38GPA

  9. Review • Dummy variables are regression variables that can only take on the values of 0 or 1. • Multiple dummy variables can be used to represent different values of a qualitative variable. • Use one less dummy variable than the number of possible values the qualitative variable – all 0’s represent the last value. • Dummy variables can be used with other quantitative variables in regression models. • Excel – Use of IF statement

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