Regression and Time Series Data: Example

Consider the annual student enrollments (fall and winter semesters combined) at the University of Iowa. Observations for the years 1951/52 through

1979/80 are used in the results below.

A plot of the data is below. In the plot, time represents the year (1 = 1951/52 year, etc.). What type of relationship appears to be present?

Next, we fit a simple linear regression model to the data and examine the results.

Regression Analysis: Enrol versus Time

The regression equation is

Enrol = 11606 + 1257 Time

Predictor Coef SE Coef T P

Constant 11606.1 795.4 14.59 0.000

Time 1257.28 46.31 27.15 0.000

S = 2087 R-Sq = 96.5% R-Sq(adj) = 96.3%

Analysis of Variance

Source DF SS MS F P

Regression 1 3208912494 3208912494 737.06 0.000

Residual Error 27 117548232 4353638

Total 28 3326460726

Durbin-Watson statistic = 0.23

A plot of the standardized residuals vs. time (our x variable) is below. Any pattern in the plot?

Note: The Durbin-Watson statistic is given as one of the choices when we use options under Regression.