A chain of photography and electronics stores created a Web site to promote its photography lessons. The number of weekly visitors grew steadily, at a rate of about 300 new visitors each week. This...

A chain of photography and electronics stores created a Web site to promote its photography lessons. The number of weekly visitors grew steadily, at a rate of about 300 new visitors each week. This timeplot shows the counts of unique visitors over the last 33 weeks.

To describe the growth, an analyst used a linear time trend and estimated the equation to be

with
 denoting the first week,
 the second, and so forth. The company hired a summer employee who had taken some statistics courses, and she suggested using a first-order autoregression [i.e., an AR(1) Model] instead of this time trend.

(a) What do you think the intercept and slope of the AR (1) equations are going to be?

(b) Do you think it’s a good idea to use an autoregression in place of the linear time trend in this situation?