求助数学二级 significance问题 absolute, standard, original, included, contrast

bulosehi

原版书Reading12,15B 答案里说 " for the debt-to-equity ratio, the absolute value of the estimated coefficient substantially increases from 0.1043 to 0.1829, while its standard error declines. Consequently, it becomes significant in the new model,in contrast to the original model, in which it is not significant at the 5 percent level. The value of the estimated coefficient of the S&P 500 dummy substantially declines from 1.2222 to 0.4218. These changes imply that size should be included in the model." 怎么知道debt-to-equity ratio是significant 呢？怎么知道原来是not significant呢？ 5%的significant,题目没有给出critical value，怎么判断是否significant呢？ 问题二：dummy substantially declines from 1.2222 to 0.4218. 为什么 These changes imply that size should be included in the model.？是否需要背一些常用的critical value？谢谢

apf陈老师

1. 5%的significant的critical value是要求记忆的，等于(+/-)1.96。原来的model中，他的t-statistic=-1.4649是大于-1.96的，落在接受域，所以不能拒绝原假设，所以it is not significant at the 5 percent level.而新的model中，t-statistic=-3.0082小于-1.96，落在拒绝域，所以拒绝原假设，所以it is significant at the 5 percent level. 2.在加入一个新的变量后，原来变量的系数的估计值有很大的改变，就说明新加入的这个变量与原来模型中的这个变量correlated，它对于回归模型来说一个很重要的变量，书中也写到了if the omitted variable is correlated with an included variable, the estimated values of the regression coefficients would be biased and inconsistent.所以不能遗漏这个新变量。