Exercise :
Prove that the variance of $\hat{y}_{x_0} = \hat{b_0} + \hat{b_1}x_0$ is : $$\text{Var}(\hat{y}_{x_0}) = \frac{\sigma^2\sum x_i^2}{n\sum(x_i-\bar{x})^2}+\frac{\sigma^2x_0^2}{\sum(x_i-\bar{x})^2}-\frac{2x_0\sigma^2\bar{x}}{\sum (x_i-\bar{x})^2}=\sigma^2\bigg[\frac{1}{n}+\frac{(x_0-\bar{x})^2}{S_{xx}}\bigg]$$
Question : How would one go on to proving all that stuff ? It seems too much to handle at first sight and I am a total beginner at this course.
