Logistic Regression Decision Boundaries

Palmer penguins dataset (bill length, bill depth, flipper length; NA rows dropped). The model is fit by gradient ascent on the log-likelihood. Drag the 3D view to rotate.

\( p(\mathbf{x}) = \dfrac{e^{\beta_0 + \boldsymbol\beta^\top \mathbf{x}}}{1 + e^{\beta_0 + \boldsymbol\beta^\top \mathbf{x}}} \qquad \text{boundary: } p(\mathbf{x}) = \tfrac12 \iff \beta_0 + \boldsymbol\beta^\top \mathbf{x} = 0 \) \( p_k(\mathbf{x}) = \dfrac{e^{s_k(\mathbf{x})}}{\sum_j e^{s_j(\mathbf{x})}},\quad s_k(\mathbf{x}) = \beta_{0k} + \boldsymbol\beta_k^\top \mathbf{x} \qquad \text{boundary: the top two } p_k \text{ tie} \)
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