Answer to Question #209033 in Statistics and Probability for hatdog

Question

Compute the estimate of the y−intercept b0 of the regression equation.

Answer 1

The regression equation on y on x is-

$y-\bar{y}=b_{yx}(x-\bar{x})$

Where, $\bar{y}$ = Mean of y

$\bar{x}$ =mean of x

$b_{yx}$ =Regression coefficient of y on x

So, $y=x.b_{yx}-b_{yx}\bar{x} +\bar{y}$

$y=b_{xy} x +\bar{y}-b_{yx}\bar{x}$

On Comparing Above equation with Linear regression equation-

$y=ax+b_o$

The estimate of y-intercept i.e. $b_o=\bar{y}-b_{yx}\bar{x}$