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. Data concerning all variables of interest is collected from a random sample of stores that sell the equipment over a one-year period. This data is shown both below and on the next page. Various questions need to be answered about the results you generate. These questions are within the problems and follow the presentation of the data. You should answer these questions using the outputs you generate using PHStat in excel.

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

Problem ONE:

a) Find the regression coefficients and the regression equation for this data by using the method of least squares analysis. USE ONLY PH STAT IN EXCEL.

b) Provide meanings for each of the regression coefficients. Be sure these meanings relate specifically to the context of the problem.

c) 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

A) Regression coefficient : Intercept 1153.6527 and Coeffifient of sales of Body is -7.0590, Coefficient of Price of lens 0.6838 (Note coeff are rounded upto decimal 4 digit)

Regression equation is given by,

Sale of Lens (Y) = 1153.6527 -7.0590*Sale of Body +0.6838*Price of Lens

B) Regression coefficient Meaning:

Minimum value of Sale of Lens is 1153.6527 unit( i.e for zero value of  all independent variable)

Increasing Sale of Camera Body by one unit decrese Sale of Lens by 7.0590 unit.

Increasing Price of Lens by one unit increases Sale of Lens by 0.6838 unit.

C)

(i) Sale of Lens when sale of camera body 200 and price of lens $800

Sale of Lens=1153.6527-7.0590*200+0.6838*800= 288.8927 (rounded decimal upto 4 digits)

(ii) Sale of Lens when sale of camera body 150 and price of lens $700

Sale of Lens=1153.6527-7.0590*150+0.6838*700= 573.4627 (rounded decimal upto 4 digits)

Above shows that Value of Sale of Lens is more in (ii) becuase sale of camera body decreased.