Analysis of Variance for Regression Models

An excellent paper on the subject of variance tests in regression modeling has been written by DEMING and MORGAN [1979], 

we want to emphasize that one is able to calculate the fraction of the experimental error only if replicate measurements (at least at one point x ) have been taken. It is then possible to compare model and experimental errors and to test the sources of residual errors. Then, in addition to the GOF test one can perform the test of lack of fit, LOF, and the test of adequacy, ADE, (commonly used in experimental design). In the lack of fit test the model error is tested against the experimental error and in the adequacy test the residual error is compared with the experimental error. 

This value can be tested against Fcrit (m-np n-m q=l - a) and should normally lead to the decision that the model error is greater than the experimental error. 

We extend Example 2-4 by simulating n,- = 3 replicates at each of the m = 7 calibration points in such a way that the means of each 3 replicates are equal to the original values given in Example 2-4. The n = 3-7 = 21 y values are given below  

As with single measurements in the calibration range, the GOF test indicates that the regression model is appropriate for description of variation in the data. The LOF confirms that highly precise measurements are at hand and that the model error exceeds the experimental error. The analyst testing calibration performance will be satisfied with this level of agree- 

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