I am learning simple linear regression and I was given the following equations to estimate $\beta_0$ and $\beta_1$:
\begin{align*}
\hat{\beta_0}=\bar{y}-\hat{\beta_1}\bar{x}\\
\hat{\beta_1}=\frac{\sum x_iy_i-n\overline{xy}}{\sum x^2_i-n\bar{x}^2}
\end{align*}
I was trying to calculate the values but I do not really know how to treat $\overline{xy}$, things I have considered:
Calculating $\frac{\sum x_i y_i}{n}$, $\bar{x} \times \bar{y}$, and considering them as two dependent random variables, but all seem like they make sense to me so I am confused. If anyone could help it would be appreicated
Best Answer
The ones who typeset this equation were a little lazy. The overline is properly separate for each variable: $$\hat{\beta_1}=\frac{\sum x_iy_i-n\bar x\bar y}{\sum x^2_i-n\bar x^2}$$ So the means of $x$ and $y$ are multiplied.