Computing the Main Effects

The next step is the very easy computation of the main effects of each factor, the two-factor interaction, and the model parameters of the possible regression function. 

In the case of 2 this is extremely simple For each column, z, in the computational scheme one has to multiply the signs with the respective response, to sum up these values and to average the sums. The average values are the estimates of the wanted regression coefficients. 

Leaving out the z0 column, these coefficients multiplied by 2 immediately yield the effects in the statistical or variance analytical sense. This difference in the computation of the regression coefficients and the effects comes from the different models used in regression analysis and in analysis of variance. The first refers to the zero or medium level, the second refers to the lowest level. 

Without jumping into regression analysis the main and interaction effects are also easily computed directly from responses. The main effect of each factor is the difference between the mean values of the responses obtained at the highest and lowest levels of the factor. The interaction effect is the mean of the difference between the effects of one factor at the highest level and the other factor at the lowest level. 

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