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Chapter 7 - linear regression with multiple regressors

# Chapter 7 - linear regression with multiple regressors -...

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7-1 Hypothesis Tests and Confidence Intervals in Multiple Regression (SW Chapter 7) Outline 1. Hypothesis tests and confidence intervals for a single coefficient 2. Joint hypothesis tests on multiple coefficients 3. Other types of hypotheses involving multiple coefficients 4. How to decide what variables to include in a regression model?

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Hypothesis Tests and Confidence Intervals for a Single Coefficient in Multiple Regression (SW Section 7.1) 1 1 1 ˆ ˆ ( ) ˆ var( ) E β β β is approximately distributed N (0,1) (CLT). Thus hypotheses on β 1 can be tested using the usual t - statistic, and confidence intervals are constructed as { 1 ˆ β ± 1.96 × SE ( 1 ˆ β )}. So too for β 2 ,…, β k . 1 ˆ β and 2 ˆ β are generally not independently distributed – so neither are their t -statistics (more on this later). 7-2