Serial correlation, also known as autocorrelation, describes the extent to which the result in one period of a time series is related to the result in the next period. A time series with high serial correlation is said to be very predictable from one period to the next. If the serial correlation is low (or near zero), the time series is considered to be much less predictable. For more information about serial correlation, see the book Ibootson SBBI published by Morningstar. 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 x 105 is shown. Original Time Series Day 1 10 Hits x 105 1.2 3.5 4.4 7.3 6.7 8.2 9.0 11.2 13.2 14.6 8 9 (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. Construct the data set (x, y) for serial correlation by filling in the following table. 3.5 9.0 11.2 13.2 (b) For the (x, y) data set of part (a), compute the equation of the sample least-squares line y = a + bx. (Use 4 decimal places.) If the number of hits was 9.3 (x 105) one day, what do you predict for the number of hits the next day? (Use 1 decimal place.) (x 105) hits c) Compute the sample correlation coefficient r and the coefficient of determination /2. (Use 4 decimal places.) Test p > 0 at the 1% level of significance. (Use 2 decimal places.) critical t Conclusion O Reject the null hypothesis, there is sufficient evidence that p > 0. Reject the null hypothesis, there is insufficient evidence that p > 0. O Fail to reject the null hypothesis, there is insufficient evidence that p 2 0. O Fail to reject the null hypothesis, there is sufficient evidence that p > D. Would you say the time series of website hits is relatively predictable from one day to the next? Explain. Yes, the data support a high negative serial correlation and indicate a predictable original time series from one day to the next, O Yes, the data support a high positive serial correlation and indicate a predictable original time series from one day to the next. 1 US 10:00 A O S Oil O back *