Question

For 10 observations on price (X) and supply (Y) the following data were

obtained (in appropriate units):

∑X = 130, ∑Y = 220, ∑X

2 = 2288, ∑Y

2 = 5506 and ∑XY = 3467.

Obtain the line of regression of Y on X and estimate the supply when the price is 16

units, and find out the standard error of the estimate.

Answer 1

The line of regression of Y on X is expressed as:

$Y=a+bX$

Where;

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

$b=\frac{(10\times3467)-(130)(220)}{10 (2288)^2-(130)^2}$

$b=1.02$

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

$a=\frac{220-1.02\times130}{10}$

$a=8.74$

$Y=8.74+1.02X$

If the price (X) is 16 units then supply (Y) is:

$Y=8.74+1.02\times16$

$Y=25.06$

The standard error of the estimate is:

$s=\sqrt{\frac{\Sigma Y^2-a\Sigma Y-b\Sigma XY}{n-2}}$

$s=\sqrt{\frac{5506-(8.74\times220)-(1.02\times3467)}{10-2}}$

$s=2.42$