This thesis provides some extensions to the existing method of determining the precision of the path of steepest ascent in response surface methodology to cover situations with correlated and heteroscedastic responses, including the important class of generalised linear models. It is shown how the eigenvalues of a certain matrix can be used to express the proportion of included directions in the confidence cone for the path of steepest ascent as an integral, which can then be computed using numerical integration. In addition, some tight inequalities for
the proportion of included directions are derived for the two, three, and four dimensional cases. For generalised linear models, methods are developed using the Wald approach and profile likelihood confidence regions approach, and bootstrap methods are used to improve the accuracy of the calculations.