第二章 一元线性回归的检验和预测2012 川大 计量经济学 课件.ppt

CHAPTER TWO HYPOTHESIS TESTING AND PREDITION OF TWO-VARIABLE LINEAR REGRESSION MODEL 1. t test and confidence interval 2. prediction: point predictor interval predictor 3. report and analysis 4. case Hypothesis test: Is a given observation or finding sufficiently closed to hypothesized value so that we can’t reject the stated hypothesis? There’re two approaches to proceed the hypothesis test: test of significance and confidence interval 2.1 test of significance and confidence interval 2.1.1 test of significance Constituting standardized normal distribution But to obtain , we need Usually , true is unknown, now we substitute for . Furthermore we substitute for and get a t-statistic 1、Put forward hypothesis: Null hypothesis:H0： Alternative hypothesis:H1： 2、Constitute t-statistic and compute the value of T: 3、Decision rule: If |T| ta/2(n-2)，reject the H0, , it means that the explanatory variable indeed infects dependent variable. The variable X is statistically significant . Otherwise, accept H0，it indicates that there isn’t significant correlation between explanatory and dependent variable supplement：decision rule of t-test H0: H1: reject H0 双尾 β1= β1* β1 ≠ β1* |T|tα/2 右尾 β1 ≤ β1* β1＞ β1* Ttα 左尾 β1≥ β1* β1 ＜ β1* T -tα α: level of significance,fixed (1- α)%: confidence df: degree of freedom Critical value P-value:probability actual probability of obtaining a value of T-TEST as much as or greater than obtained in OLS estimation If fixed αis greater than P, we may reject the null hypothesis. 2.1.2 confidence interval For statistic T follows t distribution： Given αlevel of significance： Is called the confidence interval of the true ? given confidence or the level of significance If zero falls within the confidence interval, we accept the null hypothesis. Othe