0

In our stats lecture it was stated that the OLS regression line equation: $Y = a + bX$ can also be expressed as:

$$ \frac{y-\bar y}{s_y} = r_{xy} \frac{x-\bar x}{s_x} $$

Where are $\bar{x}$ and $\bar{y}$ are means, $s_x$ and $s_y$ are standard deviations, and $r_{xy}$ is the correlation coefficient.

Can someone explain to me how?

Tim
  • 108,699
  • 20
  • 212
  • 390
  • There might be two questions here. In beginning algebra textbooks these equations are discussed under the topics of writing equations of lines: the first is the "y = mx+b" form while the second is the "point-slope formula." Converting from one to the other is a matter of arithmetic. For why SDs and correlations appear, please search our site for [regression formulas](https://stats.stackexchange.com/search?q=regression+formula+++score%3A5). – whuber Jan 28 '22 at 14:30

0 Answers0