# Is the intercept fit differently for each regressor in Multiple Linear Regression?

is the intercept B0 in y = B0 + B1X1 + .... fit differently for every feature x1.

Is it different for every feature coefficient or the same for all feature coefficients and why so?

• Because B0 is not multiplied by X1, it is always B0. Oct 21, 2020 at 17:58
• How is B0 multiplied by X1? It is added to B1 times X1 as the formula clearly indicates. Oct 21, 2020 at 19:57

NO, there is only one intercept in the model, with only one value. It is not clear from where your misconception comes, but from the algebra $$y_i=\beta_0 + \beta_1 x_{i1} + \beta_2 x_{i2} +\dotso +\epsilon_i$$ which is the multiple linear regression model, the constant term (intercept) $$\beta_0$$ has only one index $$_0$$, is only one symbol, and can only represent one number.
The different predictor variables $$x$$ have indices $$_{i1}, _{i2}, \dotsc$$ the last number $$1,2,\dotsc$$ indicating which predictor variable it is. This number does not occur with the intercept, so there is no connection.