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 Multiple Regression

## Type III Tests

The Type III Tests table presents the Type III sums of squares associated with the estimated coefficients in the model. Type III sums of squares are commonly called partial sums of squares (for a complete discussion, refer to the chapter titled "The Four Types of Estimable Functions" in the SAS/STAT User's Guide). The Type III sum of squares for a particular variable is the increase in the model sum of squares due to adding the variable to a model that already contains all the other variables in the model. Type III sums of squares, therefore, do not depend on the order in which the explanatory variables are specified in the model. Furthermore, they do not yield an additive partitioning of the Model sum of squares unless the explanatory variables are uncorrelated (which they are not for this example). F tests are formed from this table as explained previously in the "Analysis of Variance" section. Note that when DF = 1, the Type III F statistic for a given parameter estimate is equal to the square of the t statistic for the same parameter estimate. For example, the T Stat value for HSM given in the Parameter Estimates table is 4.7494. The corresponding F Stat value in the Type III Tests table is 22.5569, which is 4.7494 squared.

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