斯托克、沃森着《计量经济学》第五章.pdf

Chapter 5. Regression with a Single Regressor: Hypothesis Tests and Confidence Intervals 5.1 Testing Hypotheses about One of the Regression Coefficients （对单一系数的假设检验） Suppose a skeptic suggests that reducing the number of students in a class has no effect on learning or, specifically, test scores. The skeptic thus asserts the hypothesis, 1 H : β = 0 0 1 We wish to test this hypothesis using data – reach a tentative conclusion whether it is correct or incorrect. Null hypothesis and two-sided alternative: H : β = 0 vs. H : β ≠ 0 0 1 1 1 or, more generally, 2 H : β = β vs. H : β ≠β 0 1 1,0 1 1 1,0 where β is the hypothesized value under the null （β 是一 1,0 1,0 个具体的数）. Null hypothesis and one-sided alternative: H : β = β vs. H : β β 0 1 1,0 1 1 1,0 In economics, it is almost always possible to come up with stories in which an effect could “go either way,” so it is 3 standard to focus on two-sided alternatives. Recall hypothesis testing for population mean using Y : Y −μY ,0 t =