The title says it all: How can I see that OLS estimators (linear regression) do not depend on the scale of the predictor data? I am reading my lecture notes about lasso estimators, where it is mentioned that lasso estimators do depend on the scale of the predictor data, whereas OLS estimators don't. I can somehow see why this would be true for lasso estimators (we need to constrain the L1-norm of the coefficient estimators) and reason why it would be true for OLS estimators (the constraint disappears), but how can I understand this without considering lasso estimators and their properties first?

Thanks in advance!