Question

Sales of Body	Price of Lens	Gender	Sales of Lens
155	$700	1	122
101	650	1	120
157	725	0	135
180	575	1	95
150	600	0	100
201	750	0	174
99	560	1	118
137	500	0	130
155	675	1	128
165	550	1	166
152	725	0	131
127	750	1	102
217	565	0	165
186	670	0	154
176	600	1	97
123	585	0	129
109	645	0	98
90	575	1	105
176	660	0	120
129	650	1	105

1. Find the regression coefficients and the regression equation for this data by using the method of least squares analysis.
2. Provide meanings for each of the regression coefficients. Be sure these meanings relate specifically to the context of the problem.
3. Use your regression equation to predict the sales of the lens when sales of the camera body are 200 and the price of the lens is $800. Do the same when the sales of the camera body are 150 and the price of the lens is $700. Do you have any concerns with either of these predictions? State a reason or reasons for any concerns you might have.

Answer 1

using excel>data>data analysis>Regression

we have

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.550144
R Square	0.302659
Adjusted R Square	0.220618
Standard Error	21.41716
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	2	3384.389	1692.195	3.689152	0.046697
Residual	17	7797.811	458.6947
Total	19	11182.2
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	66.39459	46.02609	1.442542	0.167321	-30.712	163.5012
Sales of Body	0.3821	0.142372	2.683803	0.015697	0.08172	0.682479
Price of Lens	0.002009	0.068783	0.029215	0.977033	-0.14311	0.147128

1 ) the regression equation is  

sales =66.395 +0.3821*body+0.002*price

2 ) Interpretation of Body : for every one unit increase in sales of camera body , there is corresponding 0.3821 unit increase in sales of lens .

Interpretation of price of lens: for every one unit increase in price of lensy , there is corresponding 0.002 unit increase in sales of lens

3 ) for the camera body are 200 and the price of the lens is $800

estimated sales =66.395 +0.3821*200+0.002*800 = 144.415

for the camera body are 150 and the price of the lens is $700

estimated sales =66.395 +0.3821*150+0.002*700 = 125.11

yes , as the price got increase, sales of the lens got decreases and as the sales of camera body increases sales of the lens got decreases