# Regression with fixed intercept

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.

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.