Chapter 2. Properties of regression coefficients and hypothesis testing

1. Illustrate cross-sectional, time series and panel data using a table and write down an example of a linear model for each case.
2. Explain the difference between models A, B and C.
3. List the six classical assumptions for model A (verbal and mathematical formulations). Where in the proofs you studied they were used (give one example for each)?
4. Give short derivations for the random components of the regression coefficients (what I call working formulas, see equations (2.18) and (2.20)). Prove unbiasedness of the OLS estimators.
5. Conduct a Monte Carlo experiment in Excel for simple regression generating a normally distributed error. How do you check that the theoretical predictions are true? Summarize the procedure in a few sentences.
6. Derive and interpret the formula for the variance of . Interpret the formula for the variance of .
7. What is the OLS estimator of the error variance (without proof)? How is it used to find standard errors of the coefficient estimators?
8. State the Gauss-Markov theorem. In what sense is the OLS estimator linear? Unbiased? Best? Ex. 2.10.
9. How would you test the hypothesis that the marginal propensity to consume is equal to 1? Less than 1? Give all the required formulas.
10. Give the verbal definition and formula for the F statistic in case of multiple regression (with parameters). How can you calculate it in case of simple regression using ?
11. 2.7*, 2.8*, 2.12*, 2.13*, 2.14, 2.15, 2.16, 2.17, 2.19, 2.23, 2.29*, 2.30*

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