Reliability of fitted polynomial parameters

The method of finding uncertainty limits for linear equations can be generalized to higher-order polynomials. The matrix method for finding the minimization 

The quadr atic curve fit leads to a number of residuals equal to the number of points in the data set. The sum of squares of residuals gives SSE by Eqs. (3-23) and MSE by Eq. (3-30), except that now the number of degrees of freedom for n points is 

The uncertainties of the minimization parameters are calculated just as they were for the linear case except that now there are three of them 

In contr ast to the linear case, there are three degrees of freedom, but there is still only one standard deviation of the regression, s. The reader has the opportunity to try out these ideas in Computer Project 3-4. 

COMPUTER PROJECT 3-4 The Partial Molal Volume of ZnCl2 

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