Help calculating standard error of intercept

#1
Hi all,
I'm running an equally weighted moving average multiple regression with 10 explanatory variables, and I'm looking at the change in alpha (intercept) and betas over time, including change in statistical significance. Since I need to run many regressions (1000+), i'm using Excel and the Linest function. This gives me the alpha and betas, and I've calculated the standard error of the betas, and thus the confidence intervals. However, I cannot find a formula for calculating the standard error of the intercept in a multiple regression.

I've been told there is a way to find SE(intercept) using the other standard errors that I already have. I've been trying to expand the simple regression formula (image attached) for SE(intercept), but I can't get it quite right (close, but no cigar). Can anyone help me figure this out?

This is the last piece of my model, so all help is greatly appreciated! :)
 

Dragan

Super Moderator
#2
The standard error for the intercept can be computed as follows:

\( S_{b_{0}}=S_{y.x}\sqrt{\frac{1}{N}+\frac{\bar{x}^{2}}{SS_{x}}{}} \)

where the term to the left of the square root sign is the standard error of the regression model.
 
#3
Thank you for replying,
That formula works with only one x in the model. In a model with X1 and X2 in the regression it does not work. Perhaps it is possible to extended it to include X2, however, I've failed in my attempts.

I've attached an attempt to extend the formula to include X2, and a .xlsx with a regression and comparison of the results. The solution may well be easy, however, I can't see it.
 
#5
The matrix approach seems to be the best approach to this problem. However, I have no experience working with a matrix in Excel. And since I already have the SSR, all the standard errors of the coefficients, and the SSx, is there not a way to use these to find the standard error of the intercept (avoiding the matrix approach)?

I'm hoping there exists a relationship between all the different standard errors.
 
#6
Ok, using the matrix approach in Excel was really easy, and your link made it quite clear. It leaves me with a problem in Excel: I want to repeat the function for 220 rows but the matrix uses 11 rows (and not just one). However, this is a problem for another forum.

Thank you so much for your help :)