Question

5. A company has recorded data on the weekly sales for its product (y) and the unit price of the competitor's product (x). The data resulting from a random sample of 7 weeks is on the data sheet. Use Excel to develop a scatter diagram and to compute the least squares estimated regression equation and the coefficient of determination (R2).

Answer 1

Let X = Price

Y = Sales

SCATTER DIAGRAM 25 22 20 21 19 . 20 16 15 15 Sales 10 5 0 0 0.1 0.2 0.3 0.4 0.5 Price

	X	Y
	0.33	20
	0.25	14
	0.44	22
	0.4	21
	0.35	16
	0.39	19
	0.29	15
MEAN (X&Y)	0.35	18.1429
S.D (0, & oy)	0.0612	2.8997
r	0.8778

The Regression Equation of Y on X is

(Y - Y)=r*°°*(X – X) 0

2.8997 (Y – 18.1429) = 0.8778 * 0.0612 * (X -0.35)

$\Rightarrow (Y - 18.1429) =(41.5908)(X- 0.35)$

$\Rightarrow (Y - 18.1429) =(41.5908)X- 14.5568$

$\Rightarrow Y =(41.5908)X- 14.5568 + 18.1429$

$\Rightarrow Y =(41.5908)X + 3.5861$

The Regression Equation of X on Y is

$(X - \bar{X}) = r*\frac{\sigma _{x}}{\sigma _{y}}*(Y - \bar{Y})$

$\Rightarrow (X - 0.35 ) = 0.8778*\frac{0.0612}{2.8997}*(Y-18.1429)$

$\Rightarrow (X - 0.35 ) = 0.0185*(Y-18.1429)$

$\Rightarrow (X - 0.35 ) =( 0.0185)Y-0.3356$

$\Rightarrow X =( 0.0185)Y-0.3356+ 0.35$

$\Rightarrow X =( 0.0185)Y + 0.0144$

The Correlation Coefficeint "r" = 0.8778

The Coefficient of Determination = $r^{2}$ = 0.7705

Also we can get $r^{2}$ as the Product of two regression coefficients

$r^{2}$ = 41.5908x0.0185

$r^{2}$ = 0.7694

Both are Same; no need to get Confusion. While Calculating Continuously withour break we get such difference.