Calculation and Testing of the Regression Coefficients

On the basis of the multifactorial plan (Tab. 10-3) the specific model can be formulated 

The coefficients a0 to a7 are calculated by multiplication of the vector xt by the response vector y, and division by the number of solutions (experiments), for example  

The variables x3 and Jt5 represent pseudovariables. The components of the vector x3 can be represented by multiplication of the corresponding components of the vectors jci, x6, and x7 or x2, x4, and x6. By analogy, the components of the vector Jt5 can be obtained by multiplication of the vector components jci, x4, and x6 or x2, x6, and x7. From this the following equivalent model equations result for the investigated system  

The regression coefficients obtained for potassium and sodium have to be proved for significance. Firstly the average measurement error sy is calculated according to  

The test of the regression coefficients is based on the /-test according to STUDENT  

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