Question

For this problem, you will add another independent variable, the variable “gender” to the data. In this case the variable is set to 0 if the purchaser of the camera body is a male and set to 1 if the purchaser of the camera body is not a male (is a female). Rerun the regression model using three independent variables, sales of the camera body (x₁), price of the lens (x₂) and gender (x₃). The dependent variable is still number of lens sold (y). Answer the following questions about this model. Use the material in section 14.6 to help you answer these questions.

1. Find the regression coefficients and the regression equation for this data by using the method of least squares analysis.

2. Provide the meaning of the regression coefficient of the variable “gender” in the context of the model.

3. Is there evidence of a significant relationship between the variable “gender” and sales of the lens? Be sure to state the criterion you use to answer this 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

Answer 1

Excel > Data > Data Analysis > Regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.585858169
R Square	0.343229794
Adjusted R Square	0.220085381
Standard Error	21.42448336
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	3	3838.064205	1279.354735	2.78721368	0.074349765
Residual	16	7344.135795	459.0084872
Total	19	11182.2
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	81.23977826	48.4026951	1.678414355	0.112687166	-21.36935158	183.8489081	-21.36935158	183.8489081
Sales of Body	0.332505289	0.150904937	2.203408953	0.042564016	0.012601114	0.652409465	0.012601114	0.652409465
Price of Lens	-0.001722379	0.068908562	-0.024995144	0.980367925	-0.147802005	0.144357246	-0.147802005	0.144357246
Gender	-10.14324113	10.20269054	-0.994173163	0.334936933	-31.77197887	11.48549662	-31.77197887	11.48549662

a)

	Coefficients
Intercept	81.23977826
Sales of Body(X1)	0.332505289
Price of Lens(X2)	-0.001722379
Gender(X3)	-10.14324113

Regression equation:

Y^ = 81.23977826+0.332505289*X1-0.001722379*X2-10.14324113*X3

b)

If the purchaser of the camera body is a male, number of lens sold is remains same with all other independent variables held constant

If the purchaser of the camera body is a female, number of lens sold is decreased to 10.1432 units with all other independent variables held constant

c)

Gender significance test

Coeff = -10.14324113, SE = 10.20269054

Hypothesis:

H0: β3 = 0

Ha: β3 not = 0

Test:

t stat = Coeff/SE = -10.14324113/10.20269054 = -0.9942

t critical value = 2.1199 (From t table)

Decision:

|t stat| < tc, Do not reject H0

P value = 0.3349 > 0.05, Do not reject H0

Conclusion:

There is not enough evidence to conclude that there is a significant relationship between the variable “gender” and sales of the lens