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Introduction to Regression Procedures |
The general form of a linear hypothesis for the parameters is
where L is q ×k, is k ×1, and c is q ×1. To test this hypothesis, the linear function is taken with respect to the parameter estimates:
This has variance
where b is the estimate of .
A quadratic form called the sum of squares due to the hypothesis is calculated:
If you assume that this is testable, the SS can be used as a numerator of the F test:
This is compared with an F distribution with q and dfe degrees of freedom, where dfe is the degrees of freedom for residual error.
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