Since $\hat{Y}$ is an estimator and given as a linear combination of estimators $\hat{\beta_0}$ and $\hat{\beta_1}$ and X can be treated as a constant in simple linear regression, is it correct that: $Var(\hat{Y}) = Var(\hat{\beta_0}+\hat{\beta_1}X)= Var(\hat{\beta_0})+X^2Var(\hat{\beta_1})+2XCov(\hat{\beta_0},\hat{\beta_1})$
-I see many books on Linear Regression talk of the variance of $\hat{Y}$ in the bias-variance discussion, but few texts describe the calculations of these terms.