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Thus if we reject the null hypothesis we can say that the coefficient β1 is not equal to zero and hence is significant for the model.
Meaning of linear hypothesis. A linear parametric function l admits a unique least squares estimate if and only if l is estimable. The linear hypothesis is that the mean average of a random observation can be written as a linear combination of some observed predictor variables. The null and alternate hypothesis used in the case of linear regression respectively are.
If the intra subject transformation is absent the default the multivariate test concerns all of the corresponding coefficients for the response variables. For example coleman et al. If the linear parametric function l is estimable then the linear estimator l ˆ where ˆ is a solution of x xxy ˆ is the best linear unbiased estimator of l.
Theorem 2 gauss markoff theorem. A linear hypothesis for a multivariate linear model i e an object of class mlm can optionally include an intra subject transformation matrix for a repeated measures design. The linear hypothesis was chosen for regulatory purposes because a it is extremely conservative and b it isn t hard for the nuclear industry to meet standards based on it.
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