Ch. 14. Dummy Variables in Regression
I. Introduction
A. Dummy Variable: Quantification of a categorical
variable (e.g., Male=1 and Female=0, Yes=1 and No=0,
and etc.).
B. If we have a categorical variable related to multiple
regression, we have two options: a separate regression
line for each category and one regression line with a
dummy variable.
C. Since we need numerical variables for multiple
regression, the quantification of a non-numerical
variable is necessary for one regression line with a
dummy variable.
II. Two Separate Regression Lines: Develop two separate lines.
A. Testing for Parallelism (Testing for Two Slopes)
Ho: β1M = β1F H1: β1M ≠ β1F
(or directional)
α: .05 or .01 t(crit): df = nM + nF - 4
TS
b1M - b1F
t(obs) = ────────────
SE(b1M-b1F)
(see the formulas on pp. 322-323)
Decision: If |t(obs)| ≥ t(crit), reject Ho.
*If we reject Ho, it means that we do not have
parallel lines (two slopes are different).
B. Testing Two Intercepts
Ho: β0M = β0F H1: β0M ≠ β0F
(or directional)
α: .05 or .01 t(crit): df = nM + nF - 4
TS
b0M - b0F
t(obs) = ────────────
SE(b0M-b0F)
(see the formulas on p. 325)
Decision: If |t(obs)| ≥ t(crit), reject Ho.
*If we reject Ho, it means that we do not have equal
intercept (two intercepts are different).
C. Testing for Coincidence
1. Testing for identical regression line for two
different categories.
2. If either two β1s or two β0s are different, we
reject Ho for testing coincidence.
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