Update binary_logistic_regression_manual.ipynb

curves interpretation improved

Author: fs446

binary_logistic_regression_manual.ipynb

@@ -694,12 +694,13 @@
     "# receiver operating characteristic (ROC) curve:\n",
     "plt.subplot(2, 2, 1)\n",
     "plt.plot(FPR, TPR, lw=2)  # TN ok, FP ok, FN ok, TP ok\n",
-    "plt.plot(0.05, 0.95, 'C3x'),\n",
+    "plt.plot(0.05, 0.95, 'C3x', label='5%, 95% target'),\n",
     "plt.plot([0, 1], [0, 1])\n",
     "plt.text(0.05, 0.7, 'ROC curve')\n",
     "plt.xlabel('FPR = type I error')\n",
     "plt.ylabel('TPR = recall = sensitivity = power')\n",
     "plt.grid(True)\n",
+    "plt.legend()\n",
     "plt.axis([0, 1, 0, 1])\n",
     "\n",
     "plt.subplot(2, 2, 2)\n",
@@ -737,11 +738,9 @@
    "source": [
     "We see that the model is highly balanced w.r.t. the {0,1}-class predictions.\n",
     "\n",
-    "The model performs with a type-I error less than 5% and with a type-II error less than 5%.\n",
+    "Using the typical 50% decision boundary, the trained model almost ideally performs with 5% / 95% power on the unseen test data.\n",
     "\n",
-    "The model performs with a true positive rate (TPR) larger than 95% and with a true negative rate (TNR) larger than 95%.\n",
-    "\n",
-    "In medical applications (cf. COVID-19 testing) type-I and type-II percentages are typically even smaller; and thus TPR and TNR percentages are typically even larger."
+    "In medical applications (cf. COVID-19 testing) type-I and type-II errors are typically smaller, and TPR / TNR larger."
    ]
   },
   {