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I want to do a simple linear regression with fixed intercept (a real number which I've defined beforehand). Is there any restriction or condition to use such regression? Or is there any 'helpful' article/journal summarizing it? So I can get in-depth understanding of when to use it.

Thank you.

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You can subtract the intercept from your dependent variable and then simply run the regression as usual, but without the intercept.

More mathematically, let your model be $$y_i = c + \beta x_i'+u_i,$$,where $u_i$ is the error term and $\beta$ are the coefficient parameters. We can estimate this model for fixed $c$ by letting $y_i^*=y_i-c$ for all $i$. We can then estimate $y_i^*=\beta x_i'+u_i$ as usual.

If you want to check whether this is a good idea, I would recommend t-testing whether indeed $H_0: c=c_0$, where $c_0$ is the fixed value of $c$ you have in mind.

Do you know how to perform a t-test for the intercept?

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