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.