问题如下:
Under what circumstances could the explanatory power of regression analysis be overstated?
选项:
A. The
explanatory variables are not correlated with one another.
B. The
variance of the error term decreases as the value of the dependent variable
increases.
C. The
error term is normally distributed.
D. An
important explanatory variable is omitted that influences the explanatory
variables included and the dependent variable.
解释:
If the true regression includes a third variable z that influences both y and x, the error term will not be conditionally independent of x, which violates one of the assumptions of the OLS model. This will artificially increase the explanatory power of the regression. Intuitively, the variable x will appear to explain more of the variation in y simply because it is correlated with z
D选项中的情形,遗漏变量为什么会使回归的解释力度被夸大?遗漏产量不应该会导致回归效果不好吗?以至于回归解释力度下降?