ch5 - Chapter 5 Regression with a Single Regressor:...

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Unformatted text preview: Chapter 5 Regression with a Single Regressor: Hypothesis Tests and Confidence Intervals Testing Hypotheses About One of the Regression Coefficients Recall the problem we addressed in Ch.4. A linear relationship between class size and test score was assumed: TestScore = + ClassSize & ClassSize . Applying OLS estimation, the slope ClassSize could be estimated: \ TestScore = 698.9 2.28 & STR . Suppose an angry tax payer claims that cutting class size will not help boost test scores. To examine this claim, we are going to test whether the estimated b ClassSize is statistically significantly different from zero. Two-Sided Hypotheses Concerning 1 The null and the alternative hypothesis we will test is: H : ClassSize = 0 vs. H 1 : ClassSize 6 = 0. In general, H : 1 = 1,0 vs. H 1 : 1 6 = 1,0 . Recall from Ch.4 that if the three least squares assumptions are satisfied, b 1 is approximately normally distributed in large samples. So, we can use the t-statistic to conduct the hypothesis test: t = b 1 & 1,0 SE ( b 1 ) . t-statistic is approximately distributed as a standard normal. Two-Sided Hypotheses Concerning 1 The first step is to compute the standard error of b 1 , SE ( b 1 ) . SE ( b 1 ) is an estimator of b 1 : SE ( b 1 ) = q b 2 b 1 , where b 2 b 1 = 1 n & 1 n 2 n i = 1 & X i X 2 b u 2 i h 1 n n i = 1 & X i X 2 i 2 . The second step is computing the t-statistic using this SE ( b 1 ) . Two-Sided Hypotheses Concerning 1 The last step is to compute the p-value: p-value = Pr & j Z j > t act = 2 & & t act , and reject the hypothesis if it is less than 0.05....
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ch5 - Chapter 5 Regression with a Single Regressor:...

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