Question

Obtain the two regression equation

X:10,12,14,16,18,20,22,24

Y:14,18,16,22,26,28,27,30 in mathematical foundations of computer science

Answer 1

1) Regression equation ( Y on X):

Regression equation is written as:

$Y=a+bX$

Where;

$b=\frac{n\Sigma XY-\Sigma X \Sigma Y}{n\Sigma X^2-(\Sigma X)^2}$

$a=\frac{\Sigma Y-b\Sigma X}{n}$

Following table shows the calculation:

$b=\frac{(8\times3274)-(136\times181)}{(8\times2480)-(136)^2}=1.173$

$a=\frac{181-(1.173\times136)}{8}=2.690$

Then, regression equation is:

$Y=2.690+1.173X---------(1)$

2) Regression equation ( X on Y):

Regression equation is written as:

$X=a+bY$

Where;

$b=\frac{n\Sigma XY-\Sigma X \Sigma Y}{n\Sigma Y^2-(\Sigma Y)^2}$

$b=\frac{(8\times3274)-(136\times181)}{(8\times4349)-(181)^2}=0.776$

$a=\frac{\Sigma X-b\Sigma Y}{n}$

$a=\frac{136-(0.776\times181)}{8}=-0.556$

Then, regression equation is:

$X=-0.556+0.776Y---------(2)$