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I am currently testing if an OLS slope is statistically different from a known, expected slope. I think I would need to do a one-sampled t-test but I am not exactly sure how. Specifically, is the degree of freedom also N-1 if I have N data points? Thanks for any insight!

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  • $\begingroup$ If testing a slope an OLS model is appropriate, you can then test a hypothesis against any constant (by default 0, but it doesn't have to be). $\endgroup$ Jul 4, 2023 at 7:34
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    $\begingroup$ Does this answer your question? OLS - Why coefficient Beta has Normal Distribution but not t-Distribution My answer to the question gives all the necessary details to perform such a test. $\endgroup$
    – utobi
    Jul 4, 2023 at 7:42

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The degrees of freedom to use are $n-p$ (where $n$ is the number of data points, and $p$ the number of parameters), it relates to the distribution of the residuals which is used to estimate the distribution of the errors.

There are several questions that deal with this.

Also note that the problem of 'the distribution of the slope' might be more complicated when you consider

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