# Can be λ in lasso exceed one?

let's consider the lasso problem as: $$\frac{1}{2}\|y-X\beta\|_2^2 + \lambda\|\beta\|_1$$ and referring to The lasso by Patrick Breheny

he says the correlation between a predictor and residuals, must exceed a certain minimum threshold λ before it is included in the model.

what if we chose λ equals 2 or any value larger than 1. how that statement could be true? as we know the correlation (Pearson correlation) lies between -1,1. or let's say by that statement if the correlation between a predictor and residuals =0.99 and λ = 2 (arbitrary example) then none of the predictors of my model won't be included in the model

• That's not a correlation, that's a covariance. I wonder if he just experienced a brief mental lapse while typing in his slides? Dec 27, 2022 at 18:29
• I think it's a correlation, not a covariance as all variables are standardized. Dec 28, 2022 at 4:30
• @Nidal a residual is not standardized. Dec 28, 2022 at 6:01
• @AdamO "the variables that have equal (and maximal) absolute correlation with the residual" Dec 28, 2022 at 16:16
• stats.stackexchange.com/questions/351552/… read this also Dec 28, 2022 at 16:22