General Linear Regression l Linear regression may have

General Linear Regression l Linear regression may have more than one regressors (multiple regression) l How many regressors are needed? 1, 100, 1000? l Parsimony of a model l The smaller (# regressors), the better as long as having same explanatory power (c) 2007 IUPUI SPEA K 300 (4392)

Good Regression Models l Specification that makes sense l Parsimonious models l Supported by reliable data l Large N l Larger explanatory power (R 2) l Less sensitive to outliers l Less sensitive to including additional regressors (c) 2007 IUPUI SPEA K 300 (4392)

Significant Coefficients Needed? l l l Should all coefficients be significant to be a good model? Not necessarily When # regressors is large (say 100), F test and R 2 are less informative. Not likely that all coefficients are significant Regressors of interest: important Regressors for control; less important (c) 2007 IUPUI SPEA K 300 (4392)

Dummy Variable What if we want to compare male and female using a linear regression model? l A dummy variable is a binary variable that has either 0 or 1. l Of course, this is a nominal scale (categorical) whose values indicate names of categories (no substantive meaning) l Dummy variables can be used in a linear regression and influence the intercept. l (c) 2007 IUPUI SPEA K 300 (4392)

Lease Squares Dummy Variable l Suppose we have a dummy variable x 2 in a linear regression. X 2 is 0 for male and 1 for female l For male (x 2=0), l l For female (x 2=1), l For female, intercept is β 0+β 2 (c) 2007 IUPUI SPEA K 300 (4392)

Coefficient of a Dummy Variable l How do we interpret the coefficient of a dummy variable x 2? l β 2 is the difference of intercepts of groups 0 and 1 l Intercept of group 0: β 0 l Intercept of group 1: β 0+β 2 l Β 2=(β 0+β 2 )-β 0 (c) 2007 IUPUI SPEA K 300 (4392)

Illustration (c) 2007 IUPUI SPEA K 300 (4392)