计量经济学(英文版)课件

1、计量经济学(英文版),1,Chapter 4 Statistical Properties of the OLS Estimators,XiAn Institute of Post 2= 0.3 means 2 is either greater than or less than 0.3. But suppose prior experience suggests to us that the MPC is expected to be greater than 0.3. In this case we have: H0:2 0.3 and H1:2 0.3. Although H1 is

2、still a composite hypothesis, It is now one-sided.,计量经济学(英文版),54,To test this hypothesis, we use the one-tail test (the right tail), as shown in Figure 5.5. The test procedure is the same as before except that the upper confidence limit or critical value now corresponds to t = t.05, that is, the 5 p

3、ercent level. As Figure 5.5 shows, we need not consider the lower tail of the t distribution in this case. Whether one uses a two- or one-tail test of significance will depend upon how the alternative hypothesis is formulated, which, in turn, may depend upon some a priori considerations or prior emp

4、irical experience.,5.30,计量经济学(英文版),55,5.31,计量经济学(英文版),56,HYPOTHESIS TESTING: 2 THE TEST-OF-SIGNIFICANCE APPROACH Testing the Significance of Regression Coefficients: The t Test An alternative but complementary approach to the confidence-interval method of testing statistical hypotheses is the test-o

5、f-significance approach developed along independent lines by R. A. Fisher and jointly by Neyman and Pearson. Broadly speaking, a test of significance is a procedure by which sample results are used to verify the truth or falsity of a null hypothesis. The key idea behind tests of significance is that

6、 of a test statistic (estimator) and the sampling distribution of such a statistic under the null hypothesis. The decision to accept or reject H0 is made on the basis of the value of the test statistic obtained from the data at hand. As an illustration, recall that under the normality assumption the

7、 variable follows the t distribution with n-2 df. If the value of true 2 is specified under the null hypothesis, the t value can readily be computed from the available sample, and therefore it can serve as a test statistic.,5.32,计量经济学(英文版),57,5.33,计量经济学(英文版),58,5.34,计量经济学(英文版),59,5.35,计量经济学(英文版),60,

8、5.36,计量经济学(英文版),61,APPLICATION OF REGRESSION ANALYSIS: THE PROBLEM OF PREDICTION On the basis of the sample data of Table 3.2 we obtained the following sample regression: Y = 24.4545+0.5091Xi,5.37,计量经济学(英文版),62,5.38,计量经济学(英文版),63,计量经济学(英文版),64,5.39,计量经济学(英文版),65,5.40,计量经济学(英文版),66,SUMMARYAND CONCLUS

9、IONS,1. The basic framework of regression analysis is the CLRM (Classic Linear Regression Model). 2. The CLRM is based on a set of assumptions. 3. Based on these assumptions, the least-squares estimators take on certain properties summarized in the GaussMarkov theorem, which states that in the class

10、 of linear unbiased estimators, the least-squares estimators have minimum variance. In short, they are BLUE,计量经济学(英文版),67,SUMMARYAND CONCLUSIONS,4. The precision of OLS estimators is measured by their standard errors. to draw inferences on the population parameters, the coefficients. 5. The overall

11、goodness of fit of the regression model is measured by the coefficient of determination, r2.It tells what proportion of the variation in the dependent variable, or regressand, is explained by the explanatory variable, or regressor. This lies between 0 and 1; the closer it is to 1, the better is the

12、fit.,计量经济学(英文版),68,SUMMARYAND CONCLUSIONS,6. A concept related to the coefficient of determination is the coefficient of correlation, r. It is a measure of linear association between two variables and it lies between -1 and 1. 7. The CLRM is a theoretical construct or abstraction because it is based on a set of assumptions that may be stringent or “unrealistic.” But such abstraction is often necessary in the initial stages of studying any field of knowledge. Once the CLRM is mastered, one can find out what happens. Note: if one or more of its