Sum of squares due to error

The term on the left-hand side is a constant and depends only on the constituent values provided by the reference laboratory and does not depend in any way upon the calibration. The two terms on the right-hand side of the equation show how this constant value is apportioned between the two quantities that are themselves summations, and are referred to as the sum of squares due to regression and the sum of squares due to error. The latter will be the smallest possible value that it can possibly be for the given data. 

This can best be done by the method of least squares. This method minimizes the sum of squares of the differences between the predicted values and the experimental values for the dependent variable. This method minimizes the sum of square differences between estimates and experimental values of dependent variable-responses. The method is based on the principle that the best estimators of (30 and pE are those that minimize the sum of squares due to error, SSE. 

The sum of squares due to error SSE (or deviation about the regression line) ... 

We have previously introduced the sum of squares due to error as MSE=SSE/(n-2) and said that it is the unbiased estimate of error variance a2 because E(MSe)=o2 no matter whether the null hypothesis H0 Pi=0 is correct or not. It is easy to prove that the expected value of the regression mean square, MSR=SSR/1, is the biased estimate of variance o2 if not Pi=0. This can be written in the form ... 

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