Question

You have been asked to engage in an additional project concerning sales of the Nikon D5 camera etc. Specifically, this time you wish to study the sales of a certain camera lens by first using two independent variables, sales of camera bodies and the price of the lens. These are the independent variables for problem one. For problem two, you will add the gender of the purchaser of the equipment to the model. In the third question, you will examine the non-linear effect of one of the variables

.

Gender 1 1 0 1 0 Sales of lens 122 120 135 95 100 174 118 0 1 0 130 1 Camera Body Sales Lens Pricing 155 700 101 650 157 725 180 575 150 600 201 750 99 560 137 500 155 675 165 550 152 725 127 750 217 565 186 670 176 600 123 585 109 645 901 575 176 660 129 650 1 0 128 166 131 102 165 1 0 154 O 1 97 O 129 O 98 1 105 120 O 1 105

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.

a) Find the regression coefficients and the regression equation for this data by using the method of least squares analysis in PH Stat

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

c)   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.

Answer 1

using excel>addin>phstat>Regression

we have

Regression Analysis
Regression Statistics
Multiple R	0.5859
R Square	0.3432
Adjusted R Square	0.2201
Standard Error	21.4245
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	3	3838.0642	1279.3547	2.7872	0.0743
Residual	16	7344.1358	459.0085
Total	19	11182.2000
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	81.2398	48.4027	1.6784	0.1127	-21.3694	183.8489
Sales of Body	0.3325	0.1509	2.2034	0.0426	0.0126	0.6524
Price of Lens	-0.0017	0.0689	-0.0250	0.9804	-0.1478	0.1444
Gender	-10.1432	10.2027	-0.9942	0.3349	-31.7720	11.4855

a) the regression coefficients and the regression equation for this data by using the method of least squares analysis is

y = 81.2398+0.3325*x1 -0.0017*x2-10.1432*x3

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

if the purchaser of the camera body is male then the number of lenses sold will decrease by 10.1432

c)   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.

No beacsue p value is greater than 0.05