How to compute Simple Linear Regression equation not using Least Squares Estimators?

Question

I know how to compute the Simple Linear Regression (SLR) equation using Least Squares Estimators, $b_0$ and $b_1$.

But I was given the following table:

$$ \begin{array}{c|lcr} & \text{mean} & \text{stdev} & \text{correlation} \\ \hline x & 163.5 & 16.2 & -0.774\\ y & 874.1 & 54.2 & \\ \end{array} $$

How to compute the SLR equation using the above table?

(The answer is $\widehat y = 1297.49-2.59x$)

Answer 1

It's simple. Here you are $$b_1=r_{xy}\frac{S_y}{S_x}= (-0.774)( \frac{54.2}{16.2})=-2.59$$ $$b_0=\bar Y-b_1\bar X=874.1-(-2.59)(163.5)=1297.565$$ $$So, \hat y=1297.565−2.59x$$