Time Series and Serial Correlation A company that produces and markets video games wants to estimate the predictability of per capita consumer spending on video games in the United States. For the most recent 7 years, the amount of annual spending per person per year is shown here (Reference: Statistical Abstract of the United States, 128th edition):

Year 1 2 3 4 5 6 7

$ per capita 32.23 34.03 37.84 43.34 44.64 49.61 51.89

(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 32.23 34.03 37.84 43.34 44.64 49.61 y 34.03 37.84 43.34 44.64 49.61 51.89

(b) For the (x, y) data set of part

(a) compute the equation of the sample least-squares line yˆ 5a 1bx. If the per capita spending was x 5$42 one year, what do you predict for the spending the next year?

(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 per capita spending on video games is relatively predictable from one year to the next?

Explain.

AppendixLO1