In regression when we standardise the data do we need intercept?

Question

I would like to see when we standradize the data and then apply linear regression or Bayesian regression do we need intercept or no? or it has nothing with standardize?

Answer 1

You don't need it, no. You can see this yourself in R:

Build linear regression on mt cars dataset build into R

lm_unscaled_data <- lm(mpg~.,mtcars)
summary(lm_unscaled_data)

Looking at the summary, the intercept has an estimate of 12.3 with a standard error of 18.7

Now we Z score all the columns so they all have a mean of 0 and standard deviation of 1. For reasons that aren't completely clear to me the mean and sd won't be exactly these numbers, but they'll be incredibly close to 0 and 1. It's probably some R thing.

mtcars_scaled <- lapply(X = mtcars, FUN = scale)
mtcars_scaled <- data.frame(mtcars_scaled)

lm_scaled_data <- lm(mpg~.,mtcars_scaled)
summary(lm_scaled_data)

The intercept is now so small its basically 0, the p value is exactly 1.