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

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

2. plot the regression line. State any additional observations about the behavior of the data you can state based upon this scatter diagram.

3. Provide meanings for each of the regression coefficients. Be sure these meanings relate specifically to the problem you are studying

Answer 1

1. The sales of body and sales of lens is collected. The data is summarized in the question and is:

Sales of Body (X)	Sales of Lens (Y)
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

We are to perform a linear regression for this data. The regression model is:

The coefficients of the regression model can be evaluated using least-squares regression. The formulae for calculating these coefficients are:

Calculating the sums required for the formulae:

	Sales of Body (X)	Sales of Lens (Y)
	155	122	24025	18910
	101	120	10201	12120
	157	135	24649	21195
	180	95	32400	17100
	150	100	22500	15000
	201	174	40401	34974
	99	118	9801	11682
	137	130	18769	17810
	155	128	24025	19840
	165	166	27225	27390
	152	131	23104	19912
	127	102	16129	12954
	217	165	47089	35805
	186	154	34596	28644
	176	97	30976	17072
	123	129	15129	15867
	109	98	11881	10682
	90	105	8100	9450
	176	120	30976	21120
	129	105	16641	13545
SUM	2985	2494	468617	381072

Substituting the values in the formulae for calculating the coefficients:

Therefore, the regression model for the data becomes:

2. Plotting the data along with the regression line, we get:

As can be seen from the plot, the regression model does not fit very well with the data. There seems to be large deviations between the regression line and the data points present on the plot. Additionally, these deviations appear to be larger for the large body sales and smaller for smaller body sales. The data and the trendline in general appears to be increasing implying that as the sales of the body increase, the sales of the lens also tends to increase.

3. The slope of the line is

This implies that for increase in 1 unit of body sale, there is an accompanying increase of 0.383 unit increase in lens sale.

Also, the y-intercept of the model is

This implies that the approximate number of sales of lens for 0 sales of body is 67.5.

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