Consider the least-squares residuals $e_{i}=y_{i}-hat{y}_{i}, i=1,2, ldots, n$, from the simple linear regression model. Find the variance

Question:

Consider the least-squares residuals $e_{i}=y_{i}-\hat{y}_{i}, i=1,2, \ldots, n$, from the simple linear regression model. Find the variance of the residuals $\operatorname{Var}\left(e_{i}\right)$. Is the variance of the residuals a constant? Discuss.

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