I ran a lasso. I then used the variables that had non-zero coefficients in a linear regression. I would've expected the variables with the largest coefficients in the lasso to have the smallest P-values in the regression output, but this was not the case. In fact, the variable with the largest coefficient in lasso was not significant at all in my regression.
Can someone provide the intuition and/or mathematical reasoning for why this happens?
My leading guess is that it could be because of correlations between the variables used in the regression, leading to multicollinearity? If so, why doesn't multicollinearity matter for lasso?
The top answer under this question begins to answer my question but doesn't provide much of the mathematical intuition: Lasso regression coefficients values