ch7-1 - Chapter 7 Hypothesis Tests and Confidence Intervals...

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Unformatted text preview: Chapter 7 Hypothesis Tests and Confidence Intervals in Multiple Regression (Part 1) Hypothesis Tests and Confidence Intervals for a Single Coefficient Recall the model we examined in Ch.6. We had a multiple regression model: TestScore = + 1 & STR + 2 & PctEL + u . Applying OLS estimation, the slope , 1 and 2 could be estimated: \ TestScore = 686.0 1.10 & STR 0.650 & PctEL . You may want to test whether the estimated b 1 is statistically significantly different from zero. Hypothesis Tests and Confidence Intervals for a Single Coefficient Testing the hypothesis H : j = j ,0 vs. H 1 : j 6 = j ,0 1. Compute the standard error of b j , SE ( b j ) . 2. Compute the t-statistic, t = b j & j ,0 SE ( b j ) . 3. Compute the p-value = 2 & & t act ,where t act is the value of the t-statistic actually computed. Reject the hypothesis at the 5% significance level if the p-value is less than 0.05 or, equivalently, if t act > 1.96. 95% confidence interval for j : j = [ b j & 1.96 SE ( b j ) , b j + 1.96 SE ( b j )] Confidence Intervals for a Single Coefficient For our example, suppose SE ( b ) = 8.7, SE ( b 1 ) = 0.43 and SE ( b 2 ) = 0.031, \ TestScore = 686.0 & 1.10 STR & 0.650 PctEL ....
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ch7-1 - Chapter 7 Hypothesis Tests and Confidence Intervals...

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