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Say I'm doing 1D linear regression. How can I test the hypothesis that the slope is positive?

I have mostly been doing Bayesian analysis where this could be done easily by computing the proportion of marginal posterior density larger than 0. However, I'm not even sure where to start if using frequentist framework.

Ville
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    This is a standard test: look up threads about "two-tailed" or "two-sided" tests versus one-tailed tests. – whuber Mar 06 '20 at 18:54

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Thank you whuber for the tip!

So the answer is that if the null hypothesis $H_0: \theta = 0,$ where $\theta$ is the parameter of interest and $H_1:\theta \neq 0$ then you would use a two-tailed test. If $H_1: \theta > 0$, then a one-tailed test.

See e.g. Two-sided permutation test vs. two one-sided and https://www.khanacademy.org/math/ap-statistics/inference-slope-linear-regression/inference-slope/v/making-conclusions-for-regression-slope-hypothesis-test

Ville
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