In: Statistics and Probability
A fast-food franchise would like to make decisions about their pricing policy. In order to assess the effect of different price structures on sales a sample of 75 observations is collected. The company collects data on monthly sales revenues (in $1,000 units) and price (in $1 units).
| 
 SUMMARY OUTPUT  | 
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| 
 Regression Statistics  | 
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| 
 Multiple R  | 
 0.625540559  | 
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| 
 R Square  | 
 0.391300991  | 
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| 
 Adjusted R Square  | 
 0.382962648  | 
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| 
 Standard Error  | 
 5.09685747  | 
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| 
 Observations  | 
 75  | 
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| 
 ANOVA  | 
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| 
 df  | 
 SS  | 
 MS  | 
 F  | 
 Significance F  | 
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| 
 Regression  | 
 1  | 
 1219.091184  | 
 1219.091184  | 
 46.92791  | 
 1.97077E-09  | 
|
| 
 Residual  | 
 73  | 
 1896.390793  | 
 25.97795607  | 
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| 
 Total  | 
 74  | 
 3115.481978  | 
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| 
 Coefficients  | 
 Standard Error  | 
 t Stat  | 
 P-value  | 
 Lower 95%  | 
 Upper 95%  | 
|
| 
 Intercept  | 
 121.9001755  | 
 6.526290622  | 
 18.67832473  | 
 0.000000  | 
 108.8932971  | 
 134.907054  | 
| 
 PRICE  | 
 -7.829074013  | 
 1.142864631  | 
 -6.850394879  | 
 0.000000  | 
 -10.10679994  | 
 -5.551348089  | 
a). (10) Test the hypothesis that price has a significant relationship with monthly sales revenues. Choose a significance level of 5%. Show all your work.
b). (10) Calculate the p-value for the test from a). Show a sketch of the p-value. Perform the test using the p-value approach.
c). (5) Interpret the slope coefficient.
d). (5) Based on your answer from c), do you think a strategy of price reduction is a good idea ? Motivate your answer.
d). (5) Comment on the goodness of fit of the model. In particular, interpret the coefficient of determination. Do you think that we have a good fit? Explain your answer.