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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

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    $\begingroup$ 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. $\endgroup$ – Vadim Dec 9 '19 at 15:13
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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.

enter image description here

Then you use the usual formula to calculate model parameters:

enter image description here

Then remember: the standard error of each parameter is the standard deviation of each parameter's sampling distribution. Hence you may proceed to calculate variance-covariance matrix of your parameters including the intercept. This can be done in the following way. Formulae included per your request.

enter image description here

Final note: Apologies for styling, I did not have much time to use LaTeX for formula styling, so included pictures instead.

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