EXERCISE
Show in a simple linear regression model that the variance of $\hat y_{x_0}=\hat b_0+\hat b_1x$ is: $$V(\hat y_{x_0})=σ^2 \dfrac {\sum_{i=1}^{n} x_i^2}{n \cdot \sum_{i=1}^{n} (x_i-\bar x)^2}+ \dfrac{σ^2\cdot x_0}{\sum_{i=1}^{n} (x_i-\bar x)}-\dfrac{2x_0σ^2 \bar x}{\sum_{i=1}^{n} (x_i-\bar x)}=σ^2 [\cdot \dfrac{1}{n}+ \dfrac{(x_0-\bar x)^2}{S_{xx}}]$$
ATTEMPT
Ok, my first option was: We know that $$V(y_{x_0})=V(\hat b_0+ \hat b_1x_0)$$ After i used that: $$\hat b_0=\bar y-\hat b \bar x$$ and $$\hat b_1= \dfrac{S_{xy}}{S_{xx}}$$ but i didn't reach to any conclusion.
Can anyone help me with this exercise? It's the only exercise from a total number of 8 exercises of this type that I don't know how to proceed and I can't find anything that can help me to solve this!
I would really, really appreciate any thorough help or hints/tips.
Thanks in advance!