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)

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)

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)

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)

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)

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)

Illustration (c) 2007 IUPUI SPEA K300 (4392)