Correlation in Multiple Linear Regression

222) is analogous to (1.217). The coefficient r2 as defined by Eq. (1.222) is called the multiple coefficient of determination or the multiple correlation coefficient r. 

The multiple coefficient of determination may be obtained for the data of Example 1.47 as a means of determining the goodness of fit of the regression equation already estimated. Eq. (1.222) is used to give  

Such a high correlation coefficient indicates that the regression model describes the experimental data extremely well. Apart from the mentioned multiple correlation coefficient the following partial coefficient of determination  

It is clear that from the partial coefficient of determination rx, y=0.9956 and multi- 

A study was made on the effect of temperature on the yield of a chemical process. The following data (in coded form) were collected  

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