I have the following sample :
$$
\begin{array}{c|lr}
X&80&100&120&140&160&180&200&220&240&260\\
\hline
Y & 70 &65&90&95&110&115&120&140&155&150 \\
\end{array}
$$
Now i have to calculate
$\mathbb V(\hat\beta_0)=\sigma^2[\frac{1}{n}+\frac{\bar X^2}{\sum(X_i-\bar X)^2}]$
here,
X is independent and Y response variable.
$\beta_0$ intercept parameter
$\sigma^2$ population variance
But i have my sample data.
Best Answer
You can't calculate the population variance $\sigma^2$, but you can estimate it with $$\widehat{\sigma^2} = \frac{\Sigma (Y_i - \hat Y_i)^2}{n-2}.$$
Here, $\hat Y_i= \beta_0 + \beta_1 X_i$ denotes the predicted value of $Y$ given $X_i$.