Sum of squares due to regression

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 matrix may be used to calculate still another useful sum of squares, the sum of squares due to the factors as they appear in the model, sometimes called the sum of squares due to regression,... 

Figure 9.4 emphasizes the relationship among three sums of squares in the ANOVA tree - the sum of squares due to the factors as they appear in the model, SSf (sometimes called the sum of squares due to regression, SS ) the sum of squares of residuals, SS, and the sum of squares corrected for the mean, (or the total sum of squares, SSj, if there is no Pq term in the model). 

U we put the values of the variables in experiment i in the model we can calculate a predicted value of the response, For the series of experiments it is thus possible to compute the sum of squares of the predicted responses. This is called the sum of squares due to regression, SSR, is the vector of predicted responses it is... 

We can also compute the mean square due to regression, MSR, by dividing the sum of squares due to regression by the corresponding degrees of freedom. 

This technique to apportion the total sum of squares over the different sources of contribution and to compare the estimated mean squares thus obtained to estimates of the error variance is called analysis of variance. It is often abbreviated as ANOVA. The analysis of variance is usually presented as a table showing (a) the total sum of squares, the sum of squares due to regression (sometimes divided into the contribution of the individual terms in the model), the error sum of squares, (b) the degrees of freedom associated with the sums of squares, (c) the mean squares,... 

Sum of squares due to regression degression Sum of squares due to residual d-esiduai... 

It can be noted that the sum of squares due to regression can be further partitioned if an orthogonal basis is used to define the regression parameters. This will be explored in greater detail in Chap. 4, including how to define an orthogonal basis for regression. 

The variation which can be attributed to the regression line. This can be calculated as the sum of squares due to regression [in the plot, this would... 

The first two lines represent the regression model and the residual, where the residual can be divided into two parts lack of fit and pure error. We start with the regression and residual used to test if the model is significant. The sum of squares due to regression, SSReg, can be calculated according to... 

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