= Regression coefficient test power ignores nuisance coefficients
In a fixed full-rank <normal linear model>, the studentized estimator of one coefficient has a <noncentral t-distribution> with noncentrality equal to that coefficient divided by its standard deviation. The fitted and residual <orthogonal projections> of the <Gaussian noise> are <independent>. Therefore the <statistical power> of its exact <Student's t-test> does not depend on the other regression coefficients, with design and variance fixed.
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