# 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 = β + β ClassSize & ClassSize . Applying OLS estimation, the slope β 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 β ClassSize is statistically significantly different from zero. Two-Sided Hypotheses Concerning β 1 The null and the alternative hypothesis we will test is: H : β ClassSize = 0 vs. H 1 : β ClassSize 6 = 0. In general, H : β 1 = β 1,0 vs. H 1 : β 1 6 = β 1,0 . Recall from Ch.4 that if the three least squares assumptions are satisfied, b β 1 is approximately normally distributed in large samples. So, we can use the t-statistic to conduct the hypothesis test: t = b β 1 & β 1,0 SE ( b β 1 ) . t-statistic is approximately distributed as a standard normal. Two-Sided Hypotheses Concerning β 1 The first step is to compute the standard error of b β 1 , SE ( b β 1 ) . SE ( b β 1 ) is an estimator of σ b β 1 : SE ( b β 1 ) = q b σ 2 b β 1 , where b σ 2 b β 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 β 1 ) . Two-Sided Hypotheses Concerning β 1 The last step is to compute the p-value: p-value = Pr & j Z j > ¡ ¡ t act ¡ ¡ ¢ = 2 Φ & & ¡ ¡ t act ¡ ¡ ¢ , and reject the hypothesis if it is less than 0.05....
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## This note was uploaded on 11/20/2011 for the course ECONOMICS 220:322 taught by Professor Otusbo during the Fall '10 term at Rutgers.

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

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