Standard error of parameters in response surface models

2 Standard errors of parameters in response surface models 

The variance-covariance matrix of the estimated parameters will be as shown on the next page. 

It is seen, that the diagonal elements consist of the variances of the estimated model parameters. The square roots of these variances are the standard errors. 

Let us now go back to the elimination experiment. The estimated error variance with four degrees of freedom determined by the pilot experiment was = 1,34 The variance-covariance matrix (X X)s will therefore be 

The t distribution for four degrees of freedom gives t = 2.78, (at the 95 % probability level). We can therefore determine 95 % confidence limits for the estimated parameters. 

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