Question

In: Statistics and Probability

A fast-food franchise would like to make decisions about their pricing policy. In order to assess...

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

Regression Statistics

Multiple R

0.625540559

R Square

0.391300991

Adjusted R Square

0.382962648

Standard Error

5.09685747

Observations

75

ANOVA

df

SS

MS

F

Significance F

Regression

1

1219.091184

1219.091184

46.92791

1.97077E-09

Residual

73

1896.390793

25.97795607

Total

74

3115.481978

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.

Solutions

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