NO.PZ2016062402000026
问题如下:
Under what circumstances could the explanatory power of regression analysis be overstated?
选项: The
explanatory variables are not correlated with one another.
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
看了之前的解答还是不明白
“假设X为自变量,Y为因变量。如果存在第三个变量Z能够同时影响Y与X,并且这个变量Z没有纳入我们的模型方程中,那么X对于Y的解释力度就会被高估。这是因为,变量X其实本身是无法具有现在这么高的解释力度的,它之所以现在解释力度高,是因为它包含了一个被我们所遗漏掉的、和X相关的、对Y有解释作用的变量Z。所以,如果这种情况下是高估的”
1.解释力度的评价是不是看R平方或者adjusted R平方?R平方越高说明解释力度越高?
2.遗漏变量的时候,说明模型的回归效果不好,R平方应该会更低才对,为什么这个时候是overstate?当这个被遗漏的变量加入模型后,拟合效果更好,R平方应该上升