Understanding Basic Statistics 6th Edition by Charles Henry Brase,Corrinne Pellillo Brase

Exercise 40

Expand Your Knowledge: Time Series and Serial Correlation An Internet advertising agency is studying the number of "hits" on a certain website during an advertising compaign. It is hoped that as the compaign progresses, the number of hits on the website will also increase in a predictable way from one day to the next. For 10 days of the compaign, the number of hits × 10 5 is shown:
Original Time Series

(a) To construct a serial correlation, we use data pairs ( x , y ) where x = original data and y = original 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 Problem15.)

(b) For the ( x , y ) data set of part (a), compute the equation of the sample least-squares line
. If the number of hits was 9.3 (×10 5 ) 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 r 2. Test 0 at the 1% level of significance. Would you say the time series of website hits is relatively predictable from one day to the next Explain.