Coefficients of multiple determination

The coefficient of multiple determination, / is a measure of how much of SS, is accounted for by the factor effects. 

The coefficient of multiple determination ranges from 0 (indicating that the factors, as they appear in the model, have no effect on the response) to 1 (indicating that the factors, as they appear in the model, explain the data perfectly ). The square root of the coefficient of multiple determination is the coefficient of multiple correlation, R. 

Figure 9.4 Relationships among SS, SS and SS for calculating both the coefficient of multiple determination, R, and the variance-ratio for the significance of the factor effects,...

Calculate the coefficient of determination, /-j. and the coefficient of cdrrelation, r, for the model and data of Problem 9.6. What is the difference between the coefficient of determination and the coefficient of multiple determination ... 

Source Schwarzenbach et al. (10) quoting Abraham et al. (11,12). This material is used by permission of John Wiley Sons, Inc. and reproduced by permission of The Royal Society of Chemistry, n is the number of compounds used in this regression, and is the regression s coefficient of multiple determinations. 

The F statistic can also be useful in recognizing suspected outliers within a calibration sample set if the F value decreases when a sample is deleted, the sample was not an outlier. This situation is the result of the sample not affecting the overall fit of the calibration line to the data while at the same time decreasing the number of samples (N). Conversely, if deleting a single sample increases the overall F for regression, the sample is considered a suspected outlier. F is defined as the mean square for regression divided by the mean square for residual (see statistical terms in this table). Statistic Coefficient of Multiple Determination Abbreviations R or r ... 

Summation Notation See coefficient of multiple determination for summation notation ofF. Computational Formula ... 

Table 1 summarizes the regressed parameters a. and jS both for hydrophihc and hydro-phobic surfaces. It should be pointed out that the adjusted coefficient of multiple determination (/f ) was at least 0.9. Moreover, the standard error associated with each parameter was, on average, about 10% of the magnitude of the parameter itself... 

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