The unrestricted regression will be the one given by equation

(4.30) above. To derive the restricted regression, first impose the restriction:

(4.31)

Replacing β2 and β3 by their values under the null hypothesis

(4.32)

Rearranging

(4.33)

Defining z = y – x2 – x3

, the restricted regression is one of z on a constant and x4

(4.34)

The formula for the F-test statistic is given in equation (4.12) above.

For this application, the following inputs to the formula are available: T

= 144, k = 4, m = 2, RRSS = 436.1, URSS = 397.2. Plugging these into the formula gives an F-test statistic value of 6.86. This statistic should be compared with an F(m, T – k), which in this case is an F(2, 140).

The critical values are 3.07 at the 5% level and 4.79 at the 1% level.

Note that the table does not include a row for 140, so we use the closest, which is 120 rather than ∞. The test statistic clearly exceeds the critical values at both the 5% and 1% levels, and hence the null hypothesis is rejected. It would thus be concluded that the restriction is not supported by the data.