Time Series and Serial Correlation An Internet advertising agency is studying the number of “hits” on a certain web site during an advertising campaign. It is hoped that as the campaign progresses, the number of hits on the web site will also increase in a predictable way from one day to the next. For 10 days of the campaign, the number of hits 3105 is shown:

Original Time Series Day 1 2 3 4 5 6 7 8 9 10 Hits 3 105 1.2 3.5 4.4 7.2 6.9 8.3 9.0 11.2 13.1 14.6

(a) To construct a serial correlation, we use data pairs (x, y) where x 5original data and y 5original data shifted ahead by one time period.

Verify that the data set (x, y) for serial correlation is shown here. (For discussion of serial correlation, see Problem 15.)

x 1.2 3.5 4.4 7.2 6.9 8.3 9.0 11.2 13.1 y 3.5 4.4 7.2 6.9 8.3 9.0 11.2 13.1 14.6

(b) For the (x, y) data set of part (a), compute the equation of the sample least-squares line yˆ 5a 1bx. If the number of hits was 9.3 (3105 )

one day, what do you predict for the number of hits the next day?

(c) Compute the sample correlation coefficient r and the coefficient of determination r2. Test r . 0 at the 1% level of significance. Would you say the time series of web site hits is relatively predictable from one day to the next? Explain.

AppendixLO1