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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?

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

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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.

@user20637 says in a comment The intercept will (often) change if a predictor is removed or added. This may be the source of the OPs misconception. If so, the following post will help you: Why is the intercept in multiple regression changing when including/excluding regressors?

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    $\begingroup$ The intercept will (often) change if a predictor is removed or added. This may be the source of the OPs misconception. $\endgroup$
    – user20637
    Oct 21, 2020 at 19:49
  • $\begingroup$ Can not edit since it only involves one word, but it should be "have" and not "has" in the first sentence of the last paragraph. +1 though. $\endgroup$
    – shenflow
    Oct 21, 2020 at 19:56

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