1. Lecture 112009 Slide #1 OLS Review Review of Multivariate OLS –Topics –Data Analysis –Questions Exam Particulars

2. Lecture 112009 Slide #2 Regression Diagnostics Example Problem Setup Suppose that a national advisory vote or referendum was held today, and you could vote to advise the federal government on whether to create a National Energy Research and Development Fund, but the fund would cost your household per year in increased energy prices. Where would you place yourself on a scale from zero to 100, where zero means you are absolutely certain that you would vote against the creation of the Fund and 100 means you are absolutely certain that you would vote for it? “Bid” inserted into question bid | Freq. Percent ------------+-------------------------- 6 | 164 7.13 12 | 162 7.05 24 | 132 5.74 48 | 156 6.79 72 | 155 6.74 96 | 165 7.18 120 | 152 6.61 240 | 151 6.57 360 | 150 6.52 480 | 146 6.35 600 | 167 7.26 960 | 142 6.18 1200 | 134 5.83 1800 | 157 6.83 2400 | 166 7.22 ------------+-------------------------- Total | 2,299 100.00

3. Lecture 112009 Slide #3 Model IV’s Bid (cost to responding household) Ideology Perceived GCC risk Political Ideology Income Age Gender Experimental treatment: nuclear option

4. Lecture 112009 Slide #4 Review of Multivariate OLS Matrix algebra E.g., transpose, identity, addition & multiplication –Regression in Matrix Notation –Understanding the Matrix Calculation When X matrix has no unique X -1 Partial Effects –Calculating partial effects; interpretation (!) Variable selection and model building –Risks in model building

5. Lecture 112009 Slide #5 More review... T-tests, hypotheses, etc. F-tests & nested models The evils of stepwise regression –Why is it a problem? Critical OLS Assumptions –Fixed X’s –Errors cancel out –Constant variance of the errors –Errors are uncorrelated –Errors are normally distributed Correctly specified models: –Linear, correct X’s included and omitted Estimating dummy and interactive terms

6. Lecture 112009 Slide #6 Summary of Assumption Failures and their Implications ProblemBiased bBiased SEInvalid t/FHi Var Non-linear YesYesYes--- Omit relev. X YesYesYes--- Irrel X NoNoNoYes X meas. Error YesYesYes--- Heterosced. NoYes YesYes Autocorr. NoYes YesYes X corr. error YesYes Yes--- Non-normal err. NoNoYesYes Multicollinearity NoNoNoYes

7. Lecture 112009 Slide #7 Testing for OLS Failures Can’t check some assumptions –which ones? Can check for: –Linearity –Whether an X should be included –Homoscedasticity –Autocorrelation –Non-normality Method –Univariate and bivariate analyses –Plots –Tolerances –Influence analyses

8. Lecture 112009 Slide #8 Autocorrelation Types of autocorrelation –First order –N-order Seasonality, etc Identifying: DW statistics Methods of correction –Calculating Rho –AR1 –ARIMA

9. Lecture 112009 Slide #9 Exam (Quiz) #2 Posted by noon Wednesday, April 15th Will be due 5pm Monday April 20 th E-mail with subject line: “Methods Exam 2” Questions? Coming up: Chapter 11: Logit Regression Analysis