1. General Linear Regression
Linear regression may have more than one regressors (multiple regression)
How many regressors are needed? 1, 10, 100, 1000?
Parsimony of a model
The smaller (# regressors), the better as long as having same explanatory power
(c) 2007 IUPUI SPEA K300 (4392)

2. Good Regression Models
Specification that makes sense
Parsimonious models
Supported by reliable data
Large N
Larger explanatory power (R2)
Less sensitive to outliers
Less sensitive to including additional regressors
(c) 2007 IUPUI SPEA K300 (4392)

3. Significant Coefficients Needed?
Should all coefficients be significant to be a good model?
Not necessarily
When # regressors is large (say 100), F test and R2 are less informative.
Not likely that all coefficients are significant
Regressors of interest: important
Regressors for control; less important
(c) 2007 IUPUI SPEA K300 (4392)

4. Dummy Variable
What if we want to compare male and female using a linear regression model?
A dummy variable is a binary variable that has either 0 or 1.
Of course, this is a nominal scale (categorical) whose values indicate names of categories (no substantive meaning)
Dummy variables can be used in a linear regression and influence the intercept.
(c) 2007 IUPUI SPEA K300 (4392)

5. Lease Squares Dummy Variable
Suppose we have a dummy variable x2 in a linear regression.
X2 is 0 for male and 1 for female
For male (x2=0),
For female (x2=1),
For female, intercept is β0+β2
(c) 2007 IUPUI SPEA K300 (4392)

6. Coefficient of a Dummy Variable
How do we interpret the coefficient of a dummy variable x2?
β2 is the difference of intercepts of groups 0 and 1
Intercept of group 0: β0
Intercept of group 1: β0+β2
Β2=(β0+β2 )-β0
(c) 2007 IUPUI SPEA K300 (4392)

7. Illustration
(c) 2007 IUPUI SPEA K300 (4392)