A

FIGURE 10.2 The behavior of var(ft2) as a function of r23.

FIGURE 10.2 The behavior of var(ft2) as a function of r23.

have a dramatic effect on the estimated variances and covariances of the OLS estimators. When r23 = 0.50, the var (ft) is 1.33 times the variance when r23 is zero, but by the time r23 reaches 0.95 it is about 10 times as high as when there is no collinearity. And lo and behold, an increase of r23 from 0.95 to 0.995 makes the estimated variance 100 times that when collinearity is zero. The same dramatic effect is seen on the estimated covariance. All this can be seen in Figure 10.2.

The results just discussed can be easily extended to the k-variable model. In such a model, the variance of the kth coefficient, as noted in (7.5.6), can be expressed as:

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