Lecture 11 2009 Slide #1

OLS Review

Review of Multivariate OLS– Topics

– Data Analysis

– Questions

Exam Particulars

Lecture 11 2009 Slide #2

Regression Diagnostics ExampleProblem 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 <insert randomly selected cost> 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

Lecture 11 2009 Slide #3

Model IV’s• Bid (cost to responding household)

• Ideology

• Perceived GCC risk

• Political Ideology

• Income

• Age

• Gender

• Experimental treatment: nuclear option

Lecture 11 2009 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

Lecture 11 2009 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

Lecture 11 2009 Slide #6

Summary of Assumption Failures and their Implications

Problem Biased b Biased SE Invalid t/F Hi Var

Non-linear Yes Yes Yes ---

Omit relev. X Yes Yes Yes ---

Irrel X No No No Yes

X meas. Error Yes Yes Yes ---

Heterosced. No Yes Yes Yes

Autocorr. No Yes Yes Yes

X corr. error Yes Yes Yes ---

Non-normal err. No No Yes Yes

Multicollinearity No No No Yes

Lecture 11 2009 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

Lecture 11 2009 Slide #8

Autocorrelation

• Types of autocorrelation– First order– N-order

• Seasonality, etc

• Identifying: DW statistics• Methods of correction

– Calculating Rho– AR1– ARIMA

Lecture 11 2009 Slide #9

Exam (Quiz) #2

• Posted by noon Wednesday, April 15th

• Will be due 5pm Monday April 20th

• E-mail with subject line: “Methods Exam 2”

• Questions?

• Coming up: Chapter 11: Logit Regression Analysis