Refer to Practical 6, Conch carphones. The company can afford to buy one, but on
ID: 2934379 • Letter: R
Question
Refer to Practical 6, Conch carphones. The company can afford to buy one, but only one, of two new shops A and B. The pedestrians/h and areas are known for both prospective purchases, but there are no relevant sales figures. Assume the sum of fixed and operating costs are about the same for the two shops.
Pedestrians/h
Floor area
Shop A
475
1000
Shop B
880
550
Fit a regression model of Sales on Pedestrians (M1)
Fit a regression model of Sales on Pedestrians and Floor (M2)
(a) Consider the null hypothesis and alternative hypothesis
H0: The coefficient of Floor in the regression of Sales on Pedestrians and Floor = 0
H1: The coefficient is not 0.
One of the following statements is false which is it? Both the other statements are reasonable, but which do you consider is more appropriate?
Statement A There is no evidence against H0 at the 5% level of significance, so Area has no effect on sales.
Statement B There is no evidence against H0 at the 5% level of significance, so we have not determined the coefficient of Area, in the regression of Sales on Pedest and Area, with sufficient precision to be useful. It is preferable to use M1 as it is simpler.
Statement C There is no evidence against H0 at the 5% level of significance, but there is at the 10% level and the sample size is small so the test is not pwerful. It is physically reasonable that a larger Area for given Pedest would increase sales, and the estimate of the coefficient of Area is positive. Moreover, the estimated standard deviation of the errors is smaller with M2. It is preferable to use M2.
(b) Predict sales for Shop A and Shop B using both M1 and M2.
(c) One of the predictions in (b) is dubious. Without calculating prediction intervals, state which of the predictions is dubious and explain why it is dubious.
(d) Which shop would you advise the company to buy?
Pedestrians/h
Floor area
Shop A
475
1000
Shop B
880
550
Explanation / Answer
The most appropriate statement is -
Statement C : There is no evidence against H0 at the 5% level of significance but there is at the 10% level of significance and the sample size is small so the test is not powerful. It is physically reasonable that a larger area for given pedest would increase sales, and the estimate of the coefficient of area is positive. Moreover, the estimated standard deviation of the errors is smaller with M2. It is preferable to use M2.
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