Question

For the following data a regression equation is obtained.

[Sales are a function of adverting expenses]

Month	Sales	Advertising Expenses
1	264	2.5
2	116	1.3
3	165	1.4
4	101	1.0
5	209	2.0

The regression equation is

• A. 8.317 + 109.98 X
• B. -8.173 +103.92 X
• C. -8.137 + 109.23 X
• D. -8.373 + 102.93 X

Answer 1

The correct option is C -8.137 + 109.23 X

ADV Expenses (X)	Y (sales)	XY	$X^2$	$Y^2$
2.5	264	660	6.25	69696
1.3	116	150.8	1.69	13456
1.4	165	231	1.96	27225
1.0	101	101	1	10201
2.0	209	418	4	43681

$\sum XY=1560.8,\sum X^2=14.9$

$\sum Y^2=164259,\sum X=8.2,\sum Y=855$

$\overline{X}=\frac{\sum X}{n}=\frac{8.2}{5}=1.64$

$\overline{Y}=\frac{\sum Y}{n}=\frac{855}{5}=171$

$b=\frac{\sum XY-n\overline{X}\overline{Y}}{\sum X^2-n{\overline{X}}^2}=\frac{1560.8-5\times 1.64\times 171}{14.9-5\times {1.64}^2}=\frac{158.6}{1.452}=109.23$

$a=\overline{Y}-b\overline{X}=171-109.23\times 1.64=-8.137$

$Y=a+bX=-8.137+109.23X$