The marketing manager of a large supermarket chain would lik

The marketing manager of a large supermarket chain would like to use shelf space to predict the sales of pet food. A random sample of 12 equal-sized stores is selected. The shelf space (X) and sales for the week in dollars (Y) are observed. a. Is it necessary to compute the Durbin-Watson statistic in this case? Explain. b. Under what circumstances is it necessary to compute the Durbin-Watson statistic before proceeding with the least-squares method of regression analysis? a. Select the correct answer below. A. Yes, because the number of observations is sufficiently small that autocorrelation is a concern. B. No, because the number of observations is sufficiently small that autocorrelation is not a concern. c. Yes, it is always necessary to compute the Durbin-Watson statistic. D. No, because the data were not collected over time. b. Select the correct answer below. A. If a larger number of stores had been selected, it would be necessary to compute the Durbin-Watson statistic. B. It is always necessary to compute the Durbin-Watson statistic. C. If fewer stores had been selected, it would be necessary to compute the Durbin-Watson statistic. D. If a single store had been selected and studied over a period of time, it would be necessary to compute the Durbin-Watson statistic.

Solution

In statistics, the Durbin–Watson statistic is a test statistic used to detect the presence of autocorrelation (a relationship between values separated from each other by a given time lag) in the residuals (prediction errors) from a regression analysis.

a) The correct option is D. No, because the data were not collected over time.

Note that a random sample of 12 equal sized stores is selected and the self space (X) and sales for the week in dollars (Y) are observed.

b) The correct option is D. If a single store is selected and studied over a period of time, it would be necessary to compute the Durbin-Watson statistic.

This is because the Durbin–Watson test is suitable for time series data, i.e. data taken over a period of time.