From bd3f959c2eee255aaa9a90eda6297cfeef234951 Mon Sep 17 00:00:00 2001
From: Mirko Birbaumer <mirko.birbaumer@hslu.ch>
Date: Mon, 31 Mar 2025 16:56:57 +0000
Subject: [PATCH] Added Bayesian R^2

---
 notebooks/Linear Regression/LR_7_2.ipynb | 102 ++++++++++++++++++++---
 1 file changed, 91 insertions(+), 11 deletions(-)

diff --git a/notebooks/Linear Regression/LR_7_2.ipynb b/notebooks/Linear Regression/LR_7_2.ipynb
index 3801238..87d766a 100644
--- a/notebooks/Linear Regression/LR_7_2.ipynb	
+++ b/notebooks/Linear Regression/LR_7_2.ipynb	
@@ -10,7 +10,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 16,
    "id": "6645d58f-73f2-4bb4-ae9f-17a0b334a652",
    "metadata": {},
    "outputs": [],
@@ -27,7 +27,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 17,
    "id": "a76946c6-bb24-4032-9b40-35a2303dec27",
    "metadata": {
     "scrolled": true
@@ -65,9 +65,11 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 18,
    "id": "97ef4d21-6ffb-4b9e-a973-94c6815600b3",
-   "metadata": {},
+   "metadata": {
+    "scrolled": true
+   },
    "outputs": [
     {
      "name": "stderr",
@@ -120,7 +122,37 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 19,
+   "id": "da7dd39e-0b36-4742-bc45-cc495b55cac8",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "r2        0.825992\n",
+       "r2_std    0.000000\n",
+       "dtype: float64"
+      ]
+     },
+     "execution_count": 19,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "model_trz.predict(idata_trz, kind=\"response\")\n",
+    "y_pred = az.extract(idata_trz.posterior_predictive).Verkauf.values.T\n",
+    "y_obs = werbung.Verkauf.values\n",
+    "# number of predictor variables\n",
+    "p=3\n",
+    "# number of observations\n",
+    "n = len(y_obs)\n",
+    "pm.r2_score( y_pred, y_obs)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
    "id": "27f1854b-e66e-432e-aa61-66b928e73f16",
    "metadata": {},
    "outputs": [],
@@ -137,9 +169,11 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 10,
    "id": "45172e19-c1df-48ed-a524-cb8408a603e4",
-   "metadata": {},
+   "metadata": {
+    "scrolled": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -162,6 +196,29 @@
     "print(\"R²:\", r2)"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "id": "12b11a54-925b-4c1b-b3a2-4f6b479a11b0",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "r2        0.897365\n",
+       "r2_std    0.000000\n",
+       "dtype: float64"
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pm.r2_score(y_obs, y_pred )"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "67580aab-6f1d-47ac-bace-3212033a0e40",
@@ -172,7 +229,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 11,
    "id": "fd86c259-21a6-4ebc-a2c9-6d7165f6a13a",
    "metadata": {},
    "outputs": [
@@ -227,7 +284,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 12,
    "id": "125cbdce-ae89-456c-945b-b603d8cf3d7d",
    "metadata": {},
    "outputs": [],
@@ -243,7 +300,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 13,
    "id": "4990d7e2-8761-469b-aca8-7dc283fd8c99",
    "metadata": {},
    "outputs": [
@@ -276,10 +333,33 @@
     "Die beiden Modelle haben beinahe den identischen $R^2$-Wert, d.h., wir können auf die Prädiktorvariable `Zeitung` ohne Einbusse an der Güte des Modells verzichten."
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "id": "28c5351e-08dd-420d-8d2b-56ec4c4173e9",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "r2        0.897365\n",
+       "r2_std    0.000000\n",
+       "dtype: float64"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pm.r2_score(y_obs, y_pred )"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d07bbeb8-05d2-4e61-a806-b9dbce147722",
+   "id": "8c724547-2917-4675-b39e-41f42a306a9f",
    "metadata": {},
    "outputs": [],
    "source": []
-- 
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