题目
We want to regress hourly Earnings against years of Education (the regressor) based on the following OLS regression model: Earnings(i) = B(0) + B(1)×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.The error term has a conditional mean of zero, E[u(i)
Education(i)] = 0
答案
C
解析
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] .In regard to (A), there are no other regressors; but, if there were, this would refer tomulticollinearity.In regard to (B), this is contrary to the model itself.In regard to (D), this is an OLS assumption! 如果给定X（i）[在这种情况下，Education（i）]的u（i）的条件分布的方差是恒定的，并且特别地不依赖于[回归变量； 自变量]。 关于（A），没有其他回归变量； 但是，如果有的话，这是指多重共线性。 关于（B），这与模型本身相反。 关于（D），这是一个OLS假设！