Chapter 1. Simple regression analysis

Review Chapter

1. Read the chapter as necessary, to refresh your knowledge of statistics.

Chapter 1. Simple regression analysis

1. Explain mathematically 5 reasons for inclusion of the error term in the regression model
2. Write down the normal equations and derive the OLS estimators (the general case).
3. Explain the difference between the regression model and fitted line, true and estimated coefficients, error term and residual and between the two decompositions of the dependent variable.
4. How do changes in the units of measurement affect the estimated coefficients? What is meant by demeaning and why may it be desirable?
5. Do Exercise 1.4. In the table of Ex. 1.4 find TSS, RSS, ESS, and interpret p-value of the F statistics, , and adjusted . Find the estimates of the coefficients, their standard errors, t statistics, indicate the corresponding formulas. Find and interpret p-values and confidence intervals. Answer the same questions using Eviews output.
6. Explain geometrically why the mean value of residuals is zero and the sample correlation between the observations of X and the residuals is zero.
7. What happens to the slope estimator if the intercept is underestimated?
8. Assuming orthogonality relations known, derive the decomposition of TSS. Give two equivalent definitions of . Why is maximizing the same thing as minimizing RSS? What happens to when a new explanatory variable is added?
9. Prove the alternative interpretation of .
10. 1.6, 1.7, 1.16*, 1.17*, 1.18*, 1.23* (starred exercises to be presented at the board, the others to be solved but presented only as needed)

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