April 22, 2004
Presenting Regression Results
You might include a table much like the Stata output. In the text of a report, there are two standard formats. One has the standard errors in parentheses below the coefficient estimates. The other has the t ratios in parentheses below the coefficient estimates.
R-squared
The R-squared gives the percentage of the variance in the dependent variable that is explained by the regression. While this is not a formal test of anything, it is an interesting descriptive measure of how well the regression explains the variable of interest.
April 20, 2004
Specification Testing
We capped our discussion of regressions with an overview of specification testing. Including variables in a regression "controls for" various effects on the dependent (left-hand side) variable. Leaving out a variable that should be in a regression makes it likely that the estimated coefficients for the variables that are in the equation will "pick up" the left-out influence to some extent.
Let us frame the discussion in terms of whether or not we should include the variable z. The formula for the coefficient for x is pretty complicated under the alternative hypothesis that z belongs in the equation, but we were satisfied just to note that all kinds of covariances are involved. Regression analysis looks at lots of relationships among variables before producing coefficient estimates.
If we leave out z by mistake, we will get "left-out variable bias" in the coefficient for x. We can analyze this by substituting into the formula for that coefficient and applying algebra. The end result is that the magnitude of the left-out variable bias depends on the covariance between x and z and on the true coefficient for z.
Examples where specification testing could be important:
The people who were not in class on Tuesday are required to memorize these equations for the final exam.
April 15, 2004
MT 2 Answers
An answer sheet is available for Midterm 2. This entry gives selected views from the discussion of the exam.
April 13, 2004
Regression Theory
This lecture presents some fundamental notes on regression theory. You are strongly urged to read Chapter 10.
April 12, 2004
Stata 5
Stata 5 will be the take-home part of your final exam. You will need these links for the data and the variable definitions. For those of you who are bandwidth-impaired, there is a truncated 1000 observation dataset.
April 06, 2004
April 01, 2004
Midterm 2 for Fall 2003
After you have worked a couple hundred study guide problems, you might want to try taking MT 2 for Fall 2003. Give yourself 75 minutes.
Once you are done, you can check the answers.
Unified Theory
Once we get the basic concepts down, we can apply them in a variety of contexts.
Binomial Hypothesis Testing
For a change of pace, we considered hypothesis testing within the context of a binomial random variable. This examples helps us to understand the concepts of hypothesis testing.
Moving to a larger sample size allows us to invoke the normal approximation.
The two-tailed test has symmetric rejection regions.
