Serial correlation, also known as autocorrelation, describes the extent to which

Question

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 Ibbotson 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 10 is shown Original Time Series Da Hits 105 | 6 7 8 9 10 5 1.3 3.5 4.4 7.2 6.8 8. 9.0 11.2 13.2 14.7 (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 1.3 3.5 4.4 7.2 6.8 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 9.1 (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 r2. (Use 4 decimal places.)

Explanation / Answer

a) Ans:

b)

Regression Analysis: Y versus X

The regression equation is
Y = 1.6646 + 0.9756 X

Predictor Coef SE Coef T P
Constant 1.6646 0.7670 2.17 0.067
X 0.9756 0.0957 10.19 0.000

S = 1.01571 R-Sq = 93.7% R-Sq(adj) = 92.8%

Here , a=1.6646 and b= 0.9756

If the number of hits was 9.1 (*10^5) one day, the predicted the number of hits the next day is

Y = 1.6646 + 0.9756 *9.1= 10.5.

c)

r=0.9679

r^2=0.9368

X 1.3 3.5 4.4 7.2 6.8 8.1 9.0 11.2 13.2 Y 3.5 4.4 7.2 6.8 8.1 9.0 11.2 13.2 14.7

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