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Strange linearity test for ANCOVA

There is an easy way to test the linearity hypothesis for a simple regression model $y \sim {\cal N}(\alpha+\beta x,\sigma^2)$: calling $H_0$ this model, perform a test against the ANOVA model $H_1$ ...
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How to determine if a change in F value when introducing a covariate, is significant?

My question may be very basic but I hope that you can help me. I have got two groups (A and B). I am measuring two continuous biological measures (X and Y) which are significantly positively ...