Chapter 3. Multiple regression analysis

1. How do you interpret Table 3.1?
2. What is the shortcut to obtain (3.11) and a similar expression for ?
3. Explain step-by-step the Frisch-Waugh-Lovell theorem.
4. Write down multiple regression with parameters and the system it becomes after substituting observations. List the classical assumptions about multiple regression. Explain the condition of linear independence of regressors.
5. * Derive the OLS estimator for multiple regression (matrix version). Hint: apply orthogonality
6. * Prove unbiasedness and find the variance of the OLS estimator (matrix form)
7. * State the Gauss-Markov theorem
8. Give and interpret the expression of the population variance of for (without proof).
9. Multicollinearity (exact and general)

1. Why it may occur? Give an example for perfect multicollinearity. Give an example, with discussion, of multicollinearity (equation (3.49)).
2. Why the estimates remain unbiased but the standard errors may be large?
3. What are the signs of multicollinearity?

1. What can you do about multicollinearity (4 direct and 4 indirect ways)?
2. Goodness of fit: If you know the coefficient of determination for regression, how do you find the F statistic for testing significance of all regressors?
3. Definition of adjusted . Adjusted increases if and only the absolute value of the t statistic of the new variable is > 1.
4. F test: Testing significance of a group of variables: the null hypothesis, restricted and unrestricted regressions and the F statistics formula
5. Explain how prediction is obtained, show that the expected value of the prediction error is zero. Give (without proof) the expression for the variance of the prediction error and interpret it. What is hedonic pricing?
6. 3.2, 3.4*, 3.7*, 3.10*, 3.13*, 3.14, 3.15, 3.19*, 3.21*, 3.22*, 3.23*

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