Question

You have been asked to engage in one final project concerning the sales of the Nikon D5 camera. This time you wish to study the nature of the relationship between sales of the camera body and sales of a certain lens that can be used with this body and other Nikon bodies. Specifically, you wish to study whether and to what extent if the sale of Nikon D5 camera bodies explains and predicts the sale of the lens. Data concerning these two variables of interest is collected over a one-year period from a representative sample of stores in the chain of stores that sell both the body and the lens. This data is shown in appendix one. The questions that need to be answered about the results you generate are also shown below. Provide business implications concerning the overall results of the study concentrating on the results of the inferential portions of the problem as you state and develop your implications. Submit your work to the drop box for assignment five that has been created for this purpose. Reference the usual places in your textbook should you need help using PHStat to accomplish this assignment.

Sales of Body                       Sales of Lens                       

                                                155                                         122

                                                101                                         120

                                                157                                         135

                                                180                                         95

                                                150                                         100

                                                201                                         174

                                                99                                         118

                                                137                                         130

                                                155                                         128

                                                165                                         166

                                                152                                         131

                                                127                                         102

                                                217                                         165

                                                186                                         154

                                                176                                         97

                                                123                                         129

                                                109                                         98

                                                90                                         105

                                                176                                         120

                                                129                                         105

f. Find the sample coefficient of determination for the above data. Explain its meaning relative to the problem.

g. Find the adjusted sample coefficient of determination for the above data. Explain its meaning relative to the problem. Why does it differ, if it does, from the coefficient of determination that you found in the previous part of the problem?

h. Find the sample standard error of the estimate for the above data. Explain its meaning relative to the problem

i. Find the sample coefficient of correlation for the above data. Explain its meaning relative to the problem.

Answer 1

Now for the computation of regression equation we use excel, to do this follow the given steps:

1. Firstly you have to install Data analysis toolpak in excel, for this do the following steps:
2. Go to 'file' and click on 'Options'.
3. Then a dialog box will appear, click on add-ins
4. Then in the 'manage' option, select 'excel add-ins' and then click on go.
5. Then a dialog box will appear, tick on 'Analysis ToolPak' and press ok.

Now for regression line:

1. Firstly enter the data in the excel spreadsheet
2. Then go to 'Data' option in the tool bar.
3. Click on 'Data Analysis', then a dialog box will appear.
4. In the dialog box, select regression and click on OK.
5. Then in 'Input Y range:' drag Sale of lens data and in 'Input X range:' drag Sales of body data and finally click on OK.

OUTPUT:

(f). Sample coefficient of determination (R-squared) for the above data is 0.3026. This means that the 30.26% of variation in the response variable (Sales of lens) is explained by the predictor variable (Sale of body).

(g). Adjusted sample coefficient of determination (Adjusted R-squared) for the above data is 0.2639. Adjusted R-squared is the enhance version of R-squared and its value adjusted for the numbers of independent variables. Its differ from R-squared value because the value of Adjusted R-squared only increase if predicted variables are adding statistically significance to the model whereas the value of R-squared always increase by addition of a predicted variable.

(h). The sample standard error of the estimate for the above data is 20.8143. Standard error of estimates gives us the measure accuracy of predictions this means is gives us the difference between the observed values of sales of lens and the predicted values of sales of lens and how accurately our line of regression is fitted.

(i). Sample correlation coefficient (r) = Square root (R-squared) = square root( .3026) = 0.5501. This means there is a positive linear relationship between the sales of body and the sales of lens.