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

i) At the 1% level of significance, is there evidence of an overall relationship between the combination the sales of the camera body and the price of the lens and sales of the lens? Be sure that you explain in some manner the criterion or criteria you have used to arrive at your conclusion.

j) At the 1% level of significance, is there evidence of a relationship between the sales of the camera body and the sales of the lens? Be sure that you explain in some manner the criterion or criteria you have used to arrive at your conclusion.

k) At the 1% level of significance, is there evidence of a relationship between the price of the lens and the sales of the lens? Be sure that you explain in some manner the criterion or criteria you have used to arrive at your conclusion.

Answer 1

Using Excel, go to Data, select Data Analysis, choose Regression. Put Price of lens and Sales of Lens in X input range and Sales of Body in Y input range. Put Confidence Level as 9% (=1-0.01).

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.559
R Square	0.312
Adjusted R Square	0.231
Standard Error	30.578
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	2	7210.948	3605.474	3.856	0.042
Residual	17	15894.802	934.988
Total	19	23105.750
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 99.0%	Upper 99.0%
Intercept	22.155	69.410	0.319	0.753	-124.288	168.598	-179.012	223.322
Price of Lens	0.047	0.098	0.484	0.635	-0.159	0.253	-0.236	0.330
Sales of Lens	0.779	0.290	2.684	0.016	0.167	1.391	-0.062	1.620

i) H₀: β₁ = β₂ = 0, There is no evidence of an overall relationship between the combination of sales of the camera body and the price of the lens and sales of the lens

H₁: At least one of β_i ≠ 0, There is no evidence of an overall relationship between the combination of sales of the camera body and the price of the lens and sales of the lens

p-value (Significance F) = 0.042

Level of significance = 0.01

Since p-value is more than 0.01, we do not reject the null hypothesis.

So, there is no evidence of an overall relationship between the combination of sales of the camera body and the price of the lens and sales of the lens.

j) H₀: β₂ = 0, There is no evidence of an overall relationship between the sales of the camera body and sales of the lens

H₁: β₂ ≠ 0, There is no evidence of an overall relationship between the sales of the camera body and sales of the lens

p-value (Sales of Lens) = 0.635

Level of significance = 0.01

Since p-value is more than 0.01, we do not reject the null hypothesis.

So, there is no evidence of an overall relationship between the the sales of the camera body and sales of the lens.

k) H₀: β₁ = 0, There is no evidence of an overall relationship between the sales of the camera body and price of the lens

H₁: β₁ ≠ 0, There is no evidence of an overall relationship between the sales of the camera body and price of the lens

p-value (Price of Lens) = 0.167

Level of significance = 0.01

Since p-value is more than 0.01, we do not reject the null hypothesis.

So, there is no evidence of an overall relationship between the the sales of the camera body and price of the lens.