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.


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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