1 G492 Eric Rasmusen, 29 September 2009 Regressions

2 How would you explain how regressions work? Here is a fun way.

What does it mean for a test to be accurate at the 5% confidence level? 3

4 Consider testing whether a coin is fair by flipping once and rejecting fairness if Heads comes up. That test will falsely reject 50% of the time. You DONT say there is a 50% probability the coin is unfair. The 50% is saying something about the test reliability as well as the estimates. Rice Applet: Confidence Levels

5 KNOW THY DATA! In being persuasive, data management is important. Anyone can understand a data entry mistake. That destroys credibility. Maybe have one member of the team just for data.

6 ETHICS … the problem is not that one is always being asked to step across a well- defined line by unscrupulous lawyers. Rather, it is that one becomes caught up in the adversary proceeding itself and acquires the desire to win. … Continuing to regard oneself as objective, one can slip little by little from true objectivity.

7 The Data (abridged)

8 An Excel file with the data is at

9 Principles of Tables 1. Keep the data-to-ink ratio high. 2. Leave out dividing lines and boxes unless you have a good reason for them. 3. Leave off repetitive, useless numbers. 4. Don't use just capital letters. 5. Circle or otherwise mark important numbers, in particular, ones you mention in the text or talk. 6. Make the table self-contained. Don't require the reader to refer to the text or a previous table. Include the source and the units of measurement. 7. Number and title every table.

10 Uniform Crime Reports: Crime in the United StatesUniform Crime Reports: Crime in the United States, Section IV

11 Back to the Election Data

12 The correlation coefficient is the square root of the R 2 for a regression of one variable on a constant and the other variable.

13 If income rises by $100, how much does the Republican vote rise?

14 Principles of Regression Presentation 1.Only present relevant and meaningful numbers. 2. Do not write when rounding to 1.23 will do just as well. Fewer digits yield greater clarity. 3. Use correlation matrices to show the simple correlations between important variables. 4. Give summary statistics. Think about which are most useful. Think about presenting the mean, median, mode, minimum, maximum, standard deviations, and number of observations. Do not present all of these--think.

15 5. Use words for variable names, not computer codes. 6. Present the coefficients, standard errors or t-statistics (not both), R 2, and number of observations. Do not present other statistics (e.g. an F-test for all coefficients equalling zero) unless you have a reason to. 7. If the left-hand variable (y-variable, dependent variable, endogenous variable) takes only a few values (e.g., 0 and 1) then use a special technique such as logit or tobit. If a right-hand variable (x-variable, independent variable, exogenous variable) takes only a few values, that does not create a need to use anything besides OLS.

16 Consider using nonlinear specifications, as illustrated in the java applet at ormations/index.html