# Standard error in multiple regression

I want to calculate standard error of y-intercept or constant term in the multiple regression equation $$Y = b_0 + b_1X_1 + b_2X_2$$

I found the formula for standard error estimation of co-efficient $$b_1$$ and $$b_2$$ as given in the link

https://i.stack.imgur.com/Bf2s3.png

But I am not getting any formula for estimating the standard error of b0. Could anyone help me out? Regards Koushik

• For the sake of mathematical convenience one often adds an additional variable: X0 which is equal to 1 in all samples. This allow to re-write your regression equation as: $b0X0 + b1X1 + b2X2$, and use the standard results. – Vadim Dec 9 '19 at 15:13

To follow-up @Vadim's comment, I thought I would add how OLS is represented in matrix form. This provides a visual representation for you, in which you can see that the intercept in the OLS model is indeed represented by a vector of unities (i.e. ones). So essentially, the intercept is calculated much like other $$b$$ parameters, but the vector of 1s is used to calculate the intercept.