I know those Equations but I cannot show the standard error of fitted value, please help me out, much appreciated.
$$ SE(\hat{\beta_1})=\hat{\sigma}\sqrt{\frac{1}{(n-1)s_x^2}}\\ SE(\hat{\beta_0})=\hat\sigma\sqrt{\frac{1}{n}+\frac{\bar{x}^2}{(n-1)s_x^2}}\\ \hat\sigma=\sqrt{\frac{\sum_i(Y_i-\hat{Y})}{n-2}} $$
How do I show the $SE(\hat{\beta_0}+\hat{\beta_1}x_0)=\hat{\sigma}\sqrt{\frac{1}{n}+\frac{(x_0-\bar{x})^2}{(n-1)s_x^2}}$
