Statistical modelling/Multiple regression analysis

In situations where other factors in the analysis of variance model are significant it may be necessary to retain all existing terms in the model whilst fitting the regression terms. The primary aim in this study, however, was to use the parameters for the equation to determine the optimal sucrose concentration. Thus, the precise sizes of the standard errors were not needed here.

A graph showing the linear and quadratic nature of the data is displayed based on the equation m_pgerm=3.17 + 4.417 sucrose – 0.0906 sucrose². One can picture visually the level of sucrose concentration at which the maximum percentage of germination is attained. However, to obtain a precise estimate of the sucrose concentration that yields the maximum percentage germination, the regression equation, can be differentiated with respect to sucrose and the left hand side set to zero.

Thus, d(m_pgerm) / d(sucrose) = 0 = 4.417 − 0.1812 x sucrose.

Therefore, 4.417 = 0.1812 x sucrose.

So the optimal sucrose concentration = 4.417 / 0.1812 = 24.4%.