The values of the SS of the deviations from regression for
error and cultivars + error are calculated as follows:

 SSdy.x(error) = Zy2error
 {[(Exy)error]2 / Zx2 error)
 = 10.26 [(67.78)2 / 1066]
 = 5.95

 SSdy.x(cultivars+error) = 18.73
 [(101.84)2 / 1627.33]
 = 12.36

 d.f. = (t-1) + [(t-l)(b-l)-l]

 SSdy.x(adjusted means) = 12.36 5.95
 = 6.41

 d.f. = (t-l)

The MS values for these sources are estimated by dividing
each SS by its corresponding d.f.:

 MSE = SSE / d.f.
 = 5.95 / 14
 = 0.43 and

 MS adj.means = SS adj. means / d.f.
 = 6.41 / 5
 = 1.28
The F test for adjusted means is performed by dividing
MS adj. means / MS error :
 Fc = 1.28 / 0.43
 = 2.98

 d.f. = 5.14

Step 6. Since there is significance at the 5% level when
testing the adjusted means, the covariance is necessary
and the mean values for cultivars should be adjusted. The
error regression coefficient, byx, is calculated as
follows: