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# Bayesian multiple regression

I am very new to this topic. I have been working through some examples and I have a question regarding the intercept mean value in the posterior summary. This appears to be the mean value for the dependent variable. Is this a result of centering? How does one calculate (if you can) the intercept for the output model in an analogous fashion to simple frequentist multiple linear regression and hence allow the use of the output for prediction?

Apologies for what must appear a naïve question.

Regard,

Leigh

## Comments

• Hi Leigh,

I'm forwarding this to our expert.

Cheers,

E.J.

• Hi Leigh,

This appears to be the mean value for the dependent variable. Is this a result of centering?

That is correct.

How does one calculate (if you can) the intercept for the output model in an analogous fashion to simple frequentist multiple linear regression and hence allow the use of the output for prediction?

First, compute the means of the predictors used to fit the model. Second, use those means to center the values for prediction. Third, compute the regression as you would in the frequentist case. So if your original predictor matrix is X with means muX and your new predictor matrix is X_pred, you would first center X_pred with respect to muX and then compute the predictions as usual, e.g., y_pred = intercept + (X_pred - muX) * beta.

Hope that helps!

Cheers,

Don

• This helps a lot. Many thanks.

Leigh

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