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.

A company that produces and markets video games wants to estimate the predictability of per capita consumer spending on video games in a particular country. For the most recent 7 years, the amount of annual spending per person per year is shown here.

Original Time Series

Year	1	2	3	4	5	6	7
$ per capita	32.25	34.01	37.85	43.39	44.64	49.69	51.88

(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.

x	32.25	34.01	37.85	43.39	44.64	49.69
y

(b) For the

(x, y)

data set of part (a), compute the equation of the sample least-squares line

ŷ = a + bx.

(Use 4 decimal places.)

a
b

If the per capita spending was

x = $42

one year, what do you predict for the spending the next year? (Use 2 decimal places.)

$  per capita

(c) Compute the sample correlation coefficient r and the coefficient of determination

r².

(Use 4 decimal places.)

r
r2

Test

ρ > 0

at the 1% level of significance. (Use 2 decimal places.)

t
critical t

Answer 1