= Solution
An intercept-unpenalized <Lasso> estimator solves the constrained optimization
$$
\boxed{\min_{\alpha,\beta}\ \|Y-\alpha\mathbf1-X\beta\|_2^2
\quad\text{subject to}\quad\sum_{j=1}^6|\beta_j|\leq t.}
$$
For centered predictors, eliminate the intercept as in <ridge regression> and minimize $\|Y_c-X\beta\|_2^2$ under the same constraint. Equivalently, with a suitable tuning parameter $\lambda\geq0$, use $\|Y-\alpha\mathbf1-X\beta\|_2^2+\lambda\sum_j|\beta_j|$. The constraint radius and penalty parameter are different parametrizations; larger radius permits less shrinkage.
The <Lasso> plot parametrizes the <Lasso regularization path> by the fraction of the maximum $l_1$ norm of the standardized slopes. Unlike the ridge quadratic penalty, the corners of the $l_1$ constraint can place some slopes exactly at zero, providing <variable selection>. The maximum norm refers to the path's unpenalized endpoint; centering and scaling conventions must match those used to construct that path.
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