Raising the bar

Chapter 10. Simple regression

Unit 10.6. Questions for repetition

1. Explain the setup of simple regression: what is observed, what is the assumed relation between variables, why we have to include the error, the assumptions about the error and how we write everything in a vector form.

2. Write down the formal equations from Unit 10.1 and other properties of means, variances and covariances until you get used to that notation.

3. Define the OLS estimators, derive them and prove unbiasedness. When you do this, list all the assumptions you use.

4. With the help of $latex t$ statistics, write down confidence intervals for the coefficients. How do you test their significance?

5. How do you evaluate goodness of fit using the coefficient of determination, sum of squared errors and $latex p$-values of the estimated coefficients? In other words, if you have two models for the same dependent variable with different regressors, how can you tell which one is better?

6. How are the estimators of coefficients obtained used for prediction?

7. Prove that the fitted line passes through the point $latex (\bar x, \bar y)$. Geometrically, if the slope is overestimated, what happens to the intercept estimate? Is it biased downward or upward?

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