NO.PZ2024120401000071
问题如下：
We want to regress hourly Earnings against years of Education(the regressor) based on the following OLS regression model: Earnings(i) = β0 + β1*Education(i) + u(i), where u(i) is the error term. After we run the regression, which of the following statement MOST NEARLY demonstrates homoskedasticity?
选项：
A.Education(i) is not a linear function of any other regressor
B.Earnings(i) is independent of Education(i)
C.The variance of the error, u(i), is independent of Education(i)
D.解释：
The error term u(i) is homoskedastic if the variance of the conditional distribution of u(i) given X(i) [in this case, Education(i)] is constant for and in particular does not depend on [the regressor; the independent variable] . Otherwise, the error term is heteroskedastic.
Homoskedasticity means that the variance of u(i) is unrelated to the value of the independent variable. Heteroskedasticity means that the variance of u(i) is related to the value of the independent variable.
助教老师好，这里我觉得C选项并不充分啊，C选项只是说Error term跟X1的方差是independent的，只能证明Error Term和X1是没关系的，但并不能证明它就一定是同方差啊，假如存在多重共线性，或者Error Term自相关，说明还有其他没清理干净的信息跟Y有关系，但这个没清理干净的信息不一定跟X1也有关系吧？
D选项的前半句是error term的假设之一，假如E(ui)不等于0，那么虽然不一定是异方差，这Error term垃圾桶的作用就没有发挥完全呀。后半句，我认为意思跟C是一样的呀，就是在说X1和ui的corr=0，不就是相互独立吗，他们相互独立的话，方差不就也相互独立了吗？我理解的不对吗？