3
$\begingroup$

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

$\endgroup$

1 Answer 1

4
$\begingroup$

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.

$\endgroup$
1
  • $\begingroup$ Thank you, it is my first time learning about linear regressions and I was confused... $\endgroup$
    – Sergio
    Oct 1, 2022 at 7:52

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .