diff --git a/Q2.ipynb b/Q2.ipynb
index 8697e43..c5e6b95 100644
--- a/Q2.ipynb
+++ b/Q2.ipynb
@@ -15,8 +15,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-04-25T20:51:48.510748800Z",
-     "start_time": "2026-04-25T20:51:48.489901400Z"
+     "end_time": "2026-04-25T21:15:54.826174300Z",
+     "start_time": "2026-04-25T21:15:54.817214200Z"
     }
    },
    "cell_type": "code",
@@ -32,20 +32,20 @@
    ],
    "id": "76e70b2ed9af0b56",
    "outputs": [],
-   "execution_count": 5
+   "execution_count": 19
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-04-25T20:51:48.526865400Z",
-     "start_time": "2026-04-25T20:51:48.511753700Z"
+     "end_time": "2026-04-25T21:15:54.842931600Z",
+     "start_time": "2026-04-25T21:15:54.827174Z"
     }
    },
    "cell_type": "code",
    "source": "df = pd.read_csv('data/googleplaystore_new_new.csv')",
    "id": "f44380615d3aba25",
    "outputs": [],
-   "execution_count": 6
+   "execution_count": 20
   },
   {
    "metadata": {},
@@ -63,8 +63,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-04-25T20:51:48.534574700Z",
-     "start_time": "2026-04-25T20:51:48.527865900Z"
+     "end_time": "2026-04-25T21:15:54.857539500Z",
+     "start_time": "2026-04-25T21:15:54.844931800Z"
     }
    },
    "cell_type": "code",
@@ -74,13 +74,13 @@
    ],
    "id": "f6fd7137bf91f31e",
    "outputs": [],
-   "execution_count": 7
+   "execution_count": 21
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-04-25T20:51:48.542093600Z",
-     "start_time": "2026-04-25T20:51:48.535570300Z"
+     "end_time": "2026-04-25T21:15:54.877630200Z",
+     "start_time": "2026-04-25T21:15:54.857539500Z"
     }
    },
    "cell_type": "code",
@@ -90,52 +90,52 @@
    ],
    "id": "b5daf475a5d5ca15",
    "outputs": [],
-   "execution_count": 8
+   "execution_count": 22
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-04-25T20:51:48.568373500Z",
-     "start_time": "2026-04-25T20:51:48.542093600Z"
+     "end_time": "2026-04-25T21:15:54.890619Z",
+     "start_time": "2026-04-25T21:15:54.878630300Z"
     }
    },
    "cell_type": "code",
    "source": "X = pd.get_dummies(X_raw, columns=['Content Rating'])",
    "id": "99a441c665dcc19b",
    "outputs": [],
-   "execution_count": 9
+   "execution_count": 23
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-04-25T20:51:48.586290600Z",
-     "start_time": "2026-04-25T20:51:48.569378200Z"
+     "end_time": "2026-04-25T21:15:54.896884800Z",
+     "start_time": "2026-04-25T21:15:54.891625500Z"
     }
    },
    "cell_type": "code",
    "source": "X_temp, X_test, y_temp, y_test = train_test_split(X, y, test_size=0.2, random_state=101)",
    "id": "c6eb622c0f7ec63c",
    "outputs": [],
-   "execution_count": 10
+   "execution_count": 24
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-04-25T20:51:48.593412500Z",
-     "start_time": "2026-04-25T20:51:48.588327300Z"
+     "end_time": "2026-04-25T21:15:54.904746500Z",
+     "start_time": "2026-04-25T21:15:54.897883400Z"
     }
    },
    "cell_type": "code",
    "source": "X_train, X_val, y_train, y_val = train_test_split(X_temp, y_temp, test_size=0.25, random_state=101)",
    "id": "89e8f117f057e0e2",
    "outputs": [],
-   "execution_count": 11
+   "execution_count": 25
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-04-25T20:51:48.605804800Z",
-     "start_time": "2026-04-25T20:51:48.593412500Z"
+     "end_time": "2026-04-25T21:15:54.914005600Z",
+     "start_time": "2026-04-25T21:15:54.905746300Z"
     }
    },
    "cell_type": "code",
@@ -147,7 +147,7 @@
    ],
    "id": "d529991171fafb3e",
    "outputs": [],
-   "execution_count": 12
+   "execution_count": 26
   },
   {
    "metadata": {},
@@ -158,8 +158,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-04-25T20:51:48.668048800Z",
-     "start_time": "2026-04-25T20:51:48.607804Z"
+     "end_time": "2026-04-25T21:15:54.935689400Z",
+     "start_time": "2026-04-25T21:15:54.915006600Z"
     }
    },
    "cell_type": "code",
@@ -175,7 +175,7 @@
        "LogisticRegression(max_iter=1000)"
       ],
       "text/html": [
-       "<style>#sk-container-id-1 {\n",
+       "<style>#sk-container-id-3 {\n",
        "  /* Definition of color scheme common for light and dark mode */\n",
        "  --sklearn-color-text: #000;\n",
        "  --sklearn-color-text-muted: #666;\n",
@@ -192,7 +192,7 @@
        "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
        "}\n",
        "\n",
-       "#sk-container-id-1.light {\n",
+       "#sk-container-id-3.light {\n",
        "  /* Specific color for light theme */\n",
        "  --sklearn-color-text-on-default-background: black;\n",
        "  --sklearn-color-background: white;\n",
@@ -200,22 +200,22 @@
        "  --sklearn-color-icon: #696969;\n",
        "}\n",
        "\n",
-       "#sk-container-id-1.dark {\n",
+       "#sk-container-id-3.dark {\n",
        "  --sklearn-color-text-on-default-background: white;\n",
        "  --sklearn-color-background: #111;\n",
        "  --sklearn-color-border-box: white;\n",
        "  --sklearn-color-icon: #878787;\n",
        "}\n",
        "\n",
-       "#sk-container-id-1 {\n",
+       "#sk-container-id-3 {\n",
        "  color: var(--sklearn-color-text);\n",
        "}\n",
        "\n",
-       "#sk-container-id-1 pre {\n",
+       "#sk-container-id-3 pre {\n",
        "  padding: 0;\n",
        "}\n",
        "\n",
-       "#sk-container-id-1 input.sk-hidden--visually {\n",
+       "#sk-container-id-3 input.sk-hidden--visually {\n",
        "  border: 0;\n",
        "  clip: rect(1px 1px 1px 1px);\n",
        "  clip: rect(1px, 1px, 1px, 1px);\n",
@@ -227,7 +227,7 @@
        "  width: 1px;\n",
        "}\n",
        "\n",
-       "#sk-container-id-1 div.sk-dashed-wrapped {\n",
+       "#sk-container-id-3 div.sk-dashed-wrapped {\n",
        "  border: 1px dashed var(--sklearn-color-line);\n",
        "  margin: 0 0.4em 0.5em 0.4em;\n",
        "  box-sizing: border-box;\n",
@@ -235,7 +235,7 @@
        "  background-color: var(--sklearn-color-background);\n",
        "}\n",
        "\n",
-       "#sk-container-id-1 div.sk-container {\n",
+       "#sk-container-id-3 div.sk-container {\n",
        "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
        "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
        "     so we also need the `!important` here to be able to override the\n",
@@ -245,7 +245,7 @@
        "  position: relative;\n",
        "}\n",
        "\n",
-       "#sk-container-id-1 div.sk-text-repr-fallback {\n",
+       "#sk-container-id-3 div.sk-text-repr-fallback {\n",
        "  display: none;\n",
        "}\n",
        "\n",
@@ -261,14 +261,14 @@
        "\n",
        "/* Parallel-specific style estimator block */\n",
        "\n",
-       "#sk-container-id-1 div.sk-parallel-item::after {\n",
+       "#sk-container-id-3 div.sk-parallel-item::after {\n",
        "  content: \"\";\n",
        "  width: 100%;\n",
        "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
        "  flex-grow: 1;\n",
        "}\n",
        "\n",
-       "#sk-container-id-1 div.sk-parallel {\n",
+       "#sk-container-id-3 div.sk-parallel {\n",
        "  display: flex;\n",
        "  align-items: stretch;\n",
        "  justify-content: center;\n",
@@ -276,28 +276,28 @@
        "  position: relative;\n",
        "}\n",
        "\n",
-       "#sk-container-id-1 div.sk-parallel-item {\n",
+       "#sk-container-id-3 div.sk-parallel-item {\n",
        "  display: flex;\n",
        "  flex-direction: column;\n",
        "}\n",
        "\n",
-       "#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
+       "#sk-container-id-3 div.sk-parallel-item:first-child::after {\n",
        "  align-self: flex-end;\n",
        "  width: 50%;\n",
        "}\n",
        "\n",
-       "#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
+       "#sk-container-id-3 div.sk-parallel-item:last-child::after {\n",
        "  align-self: flex-start;\n",
        "  width: 50%;\n",
        "}\n",
        "\n",
-       "#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
+       "#sk-container-id-3 div.sk-parallel-item:only-child::after {\n",
        "  width: 0;\n",
        "}\n",
        "\n",
        "/* Serial-specific style estimator block */\n",
        "\n",
-       "#sk-container-id-1 div.sk-serial {\n",
+       "#sk-container-id-3 div.sk-serial {\n",
        "  display: flex;\n",
        "  flex-direction: column;\n",
        "  align-items: center;\n",
@@ -315,14 +315,14 @@
        "\n",
        "/* Pipeline and ColumnTransformer style (default) */\n",
        "\n",
-       "#sk-container-id-1 div.sk-toggleable {\n",
+       "#sk-container-id-3 div.sk-toggleable {\n",
        "  /* Default theme specific background. It is overwritten whether we have a\n",
        "  specific estimator or a Pipeline/ColumnTransformer */\n",
        "  background-color: var(--sklearn-color-background);\n",
        "}\n",
        "\n",
        "/* Toggleable label */\n",
-       "#sk-container-id-1 label.sk-toggleable__label {\n",
+       "#sk-container-id-3 label.sk-toggleable__label {\n",
        "  cursor: pointer;\n",
        "  display: flex;\n",
        "  width: 100%;\n",
@@ -335,13 +335,13 @@
        "  gap: 0.5em;\n",
        "}\n",
        "\n",
-       "#sk-container-id-1 label.sk-toggleable__label .caption {\n",
+       "#sk-container-id-3 label.sk-toggleable__label .caption {\n",
        "  font-size: 0.6rem;\n",
        "  font-weight: lighter;\n",
        "  color: var(--sklearn-color-text-muted);\n",
        "}\n",
        "\n",
-       "#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
+       "#sk-container-id-3 label.sk-toggleable__label-arrow:before {\n",
        "  /* Arrow on the left of the label */\n",
        "  content: \"▸\";\n",
        "  float: left;\n",
@@ -349,25 +349,25 @@
        "  color: var(--sklearn-color-icon);\n",
        "}\n",
        "\n",
-       "#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {\n",
+       "#sk-container-id-3 label.sk-toggleable__label-arrow:hover:before {\n",
        "  color: var(--sklearn-color-text);\n",
        "}\n",
        "\n",
        "/* Toggleable content - dropdown */\n",
        "\n",
-       "#sk-container-id-1 div.sk-toggleable__content {\n",
+       "#sk-container-id-3 div.sk-toggleable__content {\n",
        "  display: none;\n",
        "  text-align: left;\n",
        "  /* unfitted */\n",
        "  background-color: var(--sklearn-color-unfitted-level-0);\n",
        "}\n",
        "\n",
-       "#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
+       "#sk-container-id-3 div.sk-toggleable__content.fitted {\n",
        "  /* fitted */\n",
        "  background-color: var(--sklearn-color-fitted-level-0);\n",
        "}\n",
        "\n",
-       "#sk-container-id-1 div.sk-toggleable__content pre {\n",
+       "#sk-container-id-3 div.sk-toggleable__content pre {\n",
        "  margin: 0.2em;\n",
        "  border-radius: 0.25em;\n",
        "  color: var(--sklearn-color-text);\n",
@@ -375,78 +375,78 @@
        "  background-color: var(--sklearn-color-unfitted-level-0);\n",
        "}\n",
        "\n",
-       "#sk-container-id-1 div.sk-toggleable__content.fitted pre {\n",
+       "#sk-container-id-3 div.sk-toggleable__content.fitted pre {\n",
        "  /* unfitted */\n",
        "  background-color: var(--sklearn-color-fitted-level-0);\n",
        "}\n",
        "\n",
-       "#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
+       "#sk-container-id-3 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
        "  /* Expand drop-down */\n",
        "  display: block;\n",
        "  width: 100%;\n",
        "  overflow: visible;\n",
        "}\n",
        "\n",
-       "#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
+       "#sk-container-id-3 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
        "  content: \"▾\";\n",
        "}\n",
        "\n",
        "/* Pipeline/ColumnTransformer-specific style */\n",
        "\n",
-       "#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
+       "#sk-container-id-3 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
        "  color: var(--sklearn-color-text);\n",
        "  background-color: var(--sklearn-color-unfitted-level-2);\n",
        "}\n",
        "\n",
-       "#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
+       "#sk-container-id-3 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
        "  background-color: var(--sklearn-color-fitted-level-2);\n",
        "}\n",
        "\n",
        "/* Estimator-specific style */\n",
        "\n",
        "/* Colorize estimator box */\n",
-       "#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
+       "#sk-container-id-3 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
        "  /* unfitted */\n",
        "  background-color: var(--sklearn-color-unfitted-level-2);\n",
        "}\n",
        "\n",
-       "#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
+       "#sk-container-id-3 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
        "  /* fitted */\n",
        "  background-color: var(--sklearn-color-fitted-level-2);\n",
        "}\n",
        "\n",
-       "#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
-       "#sk-container-id-1 div.sk-label label {\n",
+       "#sk-container-id-3 div.sk-label label.sk-toggleable__label,\n",
+       "#sk-container-id-3 div.sk-label label {\n",
        "  /* The background is the default theme color */\n",
        "  color: var(--sklearn-color-text-on-default-background);\n",
        "}\n",
        "\n",
        "/* On hover, darken the color of the background */\n",
-       "#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
+       "#sk-container-id-3 div.sk-label:hover label.sk-toggleable__label {\n",
        "  color: var(--sklearn-color-text);\n",
        "  background-color: var(--sklearn-color-unfitted-level-2);\n",
        "}\n",
        "\n",
        "/* Label box, darken color on hover, fitted */\n",
-       "#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
+       "#sk-container-id-3 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
        "  color: var(--sklearn-color-text);\n",
        "  background-color: var(--sklearn-color-fitted-level-2);\n",
        "}\n",
        "\n",
        "/* Estimator label */\n",
        "\n",
-       "#sk-container-id-1 div.sk-label label {\n",
+       "#sk-container-id-3 div.sk-label label {\n",
        "  font-family: monospace;\n",
        "  font-weight: bold;\n",
        "  line-height: 1.2em;\n",
        "}\n",
        "\n",
-       "#sk-container-id-1 div.sk-label-container {\n",
+       "#sk-container-id-3 div.sk-label-container {\n",
        "  text-align: center;\n",
        "}\n",
        "\n",
        "/* Estimator-specific */\n",
-       "#sk-container-id-1 div.sk-estimator {\n",
+       "#sk-container-id-3 div.sk-estimator {\n",
        "  font-family: monospace;\n",
        "  border: 1px dotted var(--sklearn-color-border-box);\n",
        "  border-radius: 0.25em;\n",
@@ -456,18 +456,18 @@
        "  background-color: var(--sklearn-color-unfitted-level-0);\n",
        "}\n",
        "\n",
-       "#sk-container-id-1 div.sk-estimator.fitted {\n",
+       "#sk-container-id-3 div.sk-estimator.fitted {\n",
        "  /* fitted */\n",
        "  background-color: var(--sklearn-color-fitted-level-0);\n",
        "}\n",
        "\n",
        "/* on hover */\n",
-       "#sk-container-id-1 div.sk-estimator:hover {\n",
+       "#sk-container-id-3 div.sk-estimator:hover {\n",
        "  /* unfitted */\n",
        "  background-color: var(--sklearn-color-unfitted-level-2);\n",
        "}\n",
        "\n",
-       "#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
+       "#sk-container-id-3 div.sk-estimator.fitted:hover {\n",
        "  /* fitted */\n",
        "  background-color: var(--sklearn-color-fitted-level-2);\n",
        "}\n",
@@ -558,7 +558,7 @@
        "\n",
        "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
        "\n",
-       "#sk-container-id-1 a.estimator_doc_link {\n",
+       "#sk-container-id-3 a.estimator_doc_link {\n",
        "  float: right;\n",
        "  font-size: 1rem;\n",
        "  line-height: 1em;\n",
@@ -573,7 +573,7 @@
        "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
        "}\n",
        "\n",
-       "#sk-container-id-1 a.estimator_doc_link.fitted {\n",
+       "#sk-container-id-3 a.estimator_doc_link.fitted {\n",
        "  /* fitted */\n",
        "  background-color: var(--sklearn-color-fitted-level-0);\n",
        "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
@@ -581,14 +581,14 @@
        "}\n",
        "\n",
        "/* On hover */\n",
-       "#sk-container-id-1 a.estimator_doc_link:hover {\n",
+       "#sk-container-id-3 a.estimator_doc_link:hover {\n",
        "  /* unfitted */\n",
        "  background-color: var(--sklearn-color-unfitted-level-3);\n",
        "  color: var(--sklearn-color-background);\n",
        "  text-decoration: none;\n",
        "}\n",
        "\n",
-       "#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
+       "#sk-container-id-3 a.estimator_doc_link.fitted:hover {\n",
        "  /* fitted */\n",
        "  background-color: var(--sklearn-color-fitted-level-3);\n",
        "}\n",
@@ -725,7 +725,7 @@
        "    height: 14px;\n",
        "    cursor: pointer;\n",
        "}\n",
-       "</style><body><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LogisticRegression(max_iter=1000)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow\"><div><div>LogisticRegression</div></div><div><a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.8/modules/generated/sklearn.linear_model.LogisticRegression.html\">?<span>Documentation for LogisticRegression</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></div></label><div class=\"sk-toggleable__content fitted\" data-param-prefix=\"\">\n",
+       "</style><body><div id=\"sk-container-id-3\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LogisticRegression(max_iter=1000)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-3\" type=\"checkbox\" checked><label for=\"sk-estimator-id-3\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow\"><div><div>LogisticRegression</div></div><div><a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.8/modules/generated/sklearn.linear_model.LogisticRegression.html\">?<span>Documentation for LogisticRegression</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></div></label><div class=\"sk-toggleable__content fitted\" data-param-prefix=\"\">\n",
        "        <div class=\"estimator-table\">\n",
        "            <details>\n",
        "                <summary>Parameters</summary>\n",
@@ -1074,34 +1074,34 @@
        "    }\n",
        "}\n",
        "\n",
-       "forceTheme('sk-container-id-1');</script></body>"
+       "forceTheme('sk-container-id-3');</script></body>"
       ]
      },
-     "execution_count": 13,
+     "execution_count": 27,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
-   "execution_count": 13
+   "execution_count": 27
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-04-25T20:51:48.694210900Z",
-     "start_time": "2026-04-25T20:51:48.680578900Z"
+     "end_time": "2026-04-25T21:15:54.948876Z",
+     "start_time": "2026-04-25T21:15:54.937689300Z"
     }
    },
    "cell_type": "code",
    "source": "y_val_pred_log = log_model.predict(scaled_X_val)",
    "id": "965e16ce48443c97",
    "outputs": [],
-   "execution_count": 14
+   "execution_count": 28
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-04-25T20:51:48.714470600Z",
-     "start_time": "2026-04-25T20:51:48.695211200Z"
+     "end_time": "2026-04-25T21:15:54.976908500Z",
+     "start_time": "2026-04-25T21:15:54.948876Z"
     }
    },
    "cell_type": "code",
@@ -1121,7 +1121,7 @@
      ]
     }
    ],
-   "execution_count": 15
+   "execution_count": 29
   },
   {
    "metadata": {},
@@ -1132,8 +1132,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-04-25T20:51:48.736063Z",
-     "start_time": "2026-04-25T20:51:48.715973100Z"
+     "end_time": "2026-04-25T21:15:54.988744700Z",
+     "start_time": "2026-04-25T21:15:54.977907500Z"
     }
    },
    "cell_type": "code",
@@ -1143,13 +1143,13 @@
    ],
    "id": "8c4835d7a413a6e6",
    "outputs": [],
-   "execution_count": 16
+   "execution_count": 30
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-04-25T20:51:48.791235200Z",
-     "start_time": "2026-04-25T20:51:48.736063Z"
+     "end_time": "2026-04-25T21:15:55.029426700Z",
+     "start_time": "2026-04-25T21:15:54.989744500Z"
     }
    },
    "cell_type": "code",
@@ -1182,13 +1182,13 @@
      ]
     }
    ],
-   "execution_count": 17
+   "execution_count": 31
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-04-25T20:51:48.823877400Z",
-     "start_time": "2026-04-25T20:51:48.792239400Z"
+     "end_time": "2026-04-25T21:15:55.045639100Z",
+     "start_time": "2026-04-25T21:15:55.030432300Z"
     }
    },
    "cell_type": "code",
@@ -1196,7 +1196,7 @@
     "knn_final = KNeighborsClassifier(n_neighbors=best_k)\n",
     "knn_final.fit(scaled_X_train, y_train)"
    ],
-   "id": "96026b80f506bf93",
+   "id": "9644f7a78b4ff687",
    "outputs": [
     {
      "data": {
@@ -1204,7 +1204,7 @@
        "KNeighborsClassifier(n_neighbors=3)"
       ],
       "text/html": [
-       "<style>#sk-container-id-2 {\n",
+       "<style>#sk-container-id-4 {\n",
        "  /* Definition of color scheme common for light and dark mode */\n",
        "  --sklearn-color-text: #000;\n",
        "  --sklearn-color-text-muted: #666;\n",
@@ -1221,7 +1221,7 @@
        "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
        "}\n",
        "\n",
-       "#sk-container-id-2.light {\n",
+       "#sk-container-id-4.light {\n",
        "  /* Specific color for light theme */\n",
        "  --sklearn-color-text-on-default-background: black;\n",
        "  --sklearn-color-background: white;\n",
@@ -1229,22 +1229,22 @@
        "  --sklearn-color-icon: #696969;\n",
        "}\n",
        "\n",
-       "#sk-container-id-2.dark {\n",
+       "#sk-container-id-4.dark {\n",
        "  --sklearn-color-text-on-default-background: white;\n",
        "  --sklearn-color-background: #111;\n",
        "  --sklearn-color-border-box: white;\n",
        "  --sklearn-color-icon: #878787;\n",
        "}\n",
        "\n",
-       "#sk-container-id-2 {\n",
+       "#sk-container-id-4 {\n",
        "  color: var(--sklearn-color-text);\n",
        "}\n",
        "\n",
-       "#sk-container-id-2 pre {\n",
+       "#sk-container-id-4 pre {\n",
        "  padding: 0;\n",
        "}\n",
        "\n",
-       "#sk-container-id-2 input.sk-hidden--visually {\n",
+       "#sk-container-id-4 input.sk-hidden--visually {\n",
        "  border: 0;\n",
        "  clip: rect(1px 1px 1px 1px);\n",
        "  clip: rect(1px, 1px, 1px, 1px);\n",
@@ -1256,7 +1256,7 @@
        "  width: 1px;\n",
        "}\n",
        "\n",
-       "#sk-container-id-2 div.sk-dashed-wrapped {\n",
+       "#sk-container-id-4 div.sk-dashed-wrapped {\n",
        "  border: 1px dashed var(--sklearn-color-line);\n",
        "  margin: 0 0.4em 0.5em 0.4em;\n",
        "  box-sizing: border-box;\n",
@@ -1264,7 +1264,7 @@
        "  background-color: var(--sklearn-color-background);\n",
        "}\n",
        "\n",
-       "#sk-container-id-2 div.sk-container {\n",
+       "#sk-container-id-4 div.sk-container {\n",
        "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
        "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
        "     so we also need the `!important` here to be able to override the\n",
@@ -1274,7 +1274,7 @@
        "  position: relative;\n",
        "}\n",
        "\n",
-       "#sk-container-id-2 div.sk-text-repr-fallback {\n",
+       "#sk-container-id-4 div.sk-text-repr-fallback {\n",
        "  display: none;\n",
        "}\n",
        "\n",
@@ -1290,14 +1290,14 @@
        "\n",
        "/* Parallel-specific style estimator block */\n",
        "\n",
-       "#sk-container-id-2 div.sk-parallel-item::after {\n",
+       "#sk-container-id-4 div.sk-parallel-item::after {\n",
        "  content: \"\";\n",
        "  width: 100%;\n",
        "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
        "  flex-grow: 1;\n",
        "}\n",
        "\n",
-       "#sk-container-id-2 div.sk-parallel {\n",
+       "#sk-container-id-4 div.sk-parallel {\n",
        "  display: flex;\n",
        "  align-items: stretch;\n",
        "  justify-content: center;\n",
@@ -1305,28 +1305,28 @@
        "  position: relative;\n",
        "}\n",
        "\n",
-       "#sk-container-id-2 div.sk-parallel-item {\n",
+       "#sk-container-id-4 div.sk-parallel-item {\n",
        "  display: flex;\n",
        "  flex-direction: column;\n",
        "}\n",
        "\n",
-       "#sk-container-id-2 div.sk-parallel-item:first-child::after {\n",
+       "#sk-container-id-4 div.sk-parallel-item:first-child::after {\n",
        "  align-self: flex-end;\n",
        "  width: 50%;\n",
        "}\n",
        "\n",
-       "#sk-container-id-2 div.sk-parallel-item:last-child::after {\n",
+       "#sk-container-id-4 div.sk-parallel-item:last-child::after {\n",
        "  align-self: flex-start;\n",
        "  width: 50%;\n",
        "}\n",
        "\n",
-       "#sk-container-id-2 div.sk-parallel-item:only-child::after {\n",
+       "#sk-container-id-4 div.sk-parallel-item:only-child::after {\n",
        "  width: 0;\n",
        "}\n",
        "\n",
        "/* Serial-specific style estimator block */\n",
        "\n",
-       "#sk-container-id-2 div.sk-serial {\n",
+       "#sk-container-id-4 div.sk-serial {\n",
        "  display: flex;\n",
        "  flex-direction: column;\n",
        "  align-items: center;\n",
@@ -1344,14 +1344,14 @@
        "\n",
        "/* Pipeline and ColumnTransformer style (default) */\n",
        "\n",
-       "#sk-container-id-2 div.sk-toggleable {\n",
+       "#sk-container-id-4 div.sk-toggleable {\n",
        "  /* Default theme specific background. It is overwritten whether we have a\n",
        "  specific estimator or a Pipeline/ColumnTransformer */\n",
        "  background-color: var(--sklearn-color-background);\n",
        "}\n",
        "\n",
        "/* Toggleable label */\n",
-       "#sk-container-id-2 label.sk-toggleable__label {\n",
+       "#sk-container-id-4 label.sk-toggleable__label {\n",
        "  cursor: pointer;\n",
        "  display: flex;\n",
        "  width: 100%;\n",
@@ -1364,13 +1364,13 @@
        "  gap: 0.5em;\n",
        "}\n",
        "\n",
-       "#sk-container-id-2 label.sk-toggleable__label .caption {\n",
+       "#sk-container-id-4 label.sk-toggleable__label .caption {\n",
        "  font-size: 0.6rem;\n",
        "  font-weight: lighter;\n",
        "  color: var(--sklearn-color-text-muted);\n",
        "}\n",
        "\n",
-       "#sk-container-id-2 label.sk-toggleable__label-arrow:before {\n",
+       "#sk-container-id-4 label.sk-toggleable__label-arrow:before {\n",
        "  /* Arrow on the left of the label */\n",
        "  content: \"▸\";\n",
        "  float: left;\n",
@@ -1378,25 +1378,25 @@
        "  color: var(--sklearn-color-icon);\n",
        "}\n",
        "\n",
-       "#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {\n",
+       "#sk-container-id-4 label.sk-toggleable__label-arrow:hover:before {\n",
        "  color: var(--sklearn-color-text);\n",
        "}\n",
        "\n",
        "/* Toggleable content - dropdown */\n",
        "\n",
-       "#sk-container-id-2 div.sk-toggleable__content {\n",
+       "#sk-container-id-4 div.sk-toggleable__content {\n",
        "  display: none;\n",
        "  text-align: left;\n",
        "  /* unfitted */\n",
        "  background-color: var(--sklearn-color-unfitted-level-0);\n",
        "}\n",
        "\n",
-       "#sk-container-id-2 div.sk-toggleable__content.fitted {\n",
+       "#sk-container-id-4 div.sk-toggleable__content.fitted {\n",
        "  /* fitted */\n",
        "  background-color: var(--sklearn-color-fitted-level-0);\n",
        "}\n",
        "\n",
-       "#sk-container-id-2 div.sk-toggleable__content pre {\n",
+       "#sk-container-id-4 div.sk-toggleable__content pre {\n",
        "  margin: 0.2em;\n",
        "  border-radius: 0.25em;\n",
        "  color: var(--sklearn-color-text);\n",
@@ -1404,78 +1404,78 @@
        "  background-color: var(--sklearn-color-unfitted-level-0);\n",
        "}\n",
        "\n",
-       "#sk-container-id-2 div.sk-toggleable__content.fitted pre {\n",
+       "#sk-container-id-4 div.sk-toggleable__content.fitted pre {\n",
        "  /* unfitted */\n",
        "  background-color: var(--sklearn-color-fitted-level-0);\n",
        "}\n",
        "\n",
-       "#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
+       "#sk-container-id-4 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
        "  /* Expand drop-down */\n",
        "  display: block;\n",
        "  width: 100%;\n",
        "  overflow: visible;\n",
        "}\n",
        "\n",
-       "#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
+       "#sk-container-id-4 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
        "  content: \"▾\";\n",
        "}\n",
        "\n",
        "/* Pipeline/ColumnTransformer-specific style */\n",
        "\n",
-       "#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
+       "#sk-container-id-4 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
        "  color: var(--sklearn-color-text);\n",
        "  background-color: var(--sklearn-color-unfitted-level-2);\n",
        "}\n",
        "\n",
-       "#sk-container-id-2 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
+       "#sk-container-id-4 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
        "  background-color: var(--sklearn-color-fitted-level-2);\n",
        "}\n",
        "\n",
        "/* Estimator-specific style */\n",
        "\n",
        "/* Colorize estimator box */\n",
-       "#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
+       "#sk-container-id-4 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
        "  /* unfitted */\n",
        "  background-color: var(--sklearn-color-unfitted-level-2);\n",
        "}\n",
        "\n",
-       "#sk-container-id-2 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
+       "#sk-container-id-4 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
        "  /* fitted */\n",
        "  background-color: var(--sklearn-color-fitted-level-2);\n",
        "}\n",
        "\n",
-       "#sk-container-id-2 div.sk-label label.sk-toggleable__label,\n",
-       "#sk-container-id-2 div.sk-label label {\n",
+       "#sk-container-id-4 div.sk-label label.sk-toggleable__label,\n",
+       "#sk-container-id-4 div.sk-label label {\n",
        "  /* The background is the default theme color */\n",
        "  color: var(--sklearn-color-text-on-default-background);\n",
        "}\n",
        "\n",
        "/* On hover, darken the color of the background */\n",
-       "#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {\n",
+       "#sk-container-id-4 div.sk-label:hover label.sk-toggleable__label {\n",
        "  color: var(--sklearn-color-text);\n",
        "  background-color: var(--sklearn-color-unfitted-level-2);\n",
        "}\n",
        "\n",
        "/* Label box, darken color on hover, fitted */\n",
-       "#sk-container-id-2 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
+       "#sk-container-id-4 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
        "  color: var(--sklearn-color-text);\n",
        "  background-color: var(--sklearn-color-fitted-level-2);\n",
        "}\n",
        "\n",
        "/* Estimator label */\n",
        "\n",
-       "#sk-container-id-2 div.sk-label label {\n",
+       "#sk-container-id-4 div.sk-label label {\n",
        "  font-family: monospace;\n",
        "  font-weight: bold;\n",
        "  line-height: 1.2em;\n",
        "}\n",
        "\n",
-       "#sk-container-id-2 div.sk-label-container {\n",
+       "#sk-container-id-4 div.sk-label-container {\n",
        "  text-align: center;\n",
        "}\n",
        "\n",
        "/* Estimator-specific */\n",
-       "#sk-container-id-2 div.sk-estimator {\n",
+       "#sk-container-id-4 div.sk-estimator {\n",
        "  font-family: monospace;\n",
        "  border: 1px dotted var(--sklearn-color-border-box);\n",
        "  border-radius: 0.25em;\n",
@@ -1485,18 +1485,18 @@
        "  background-color: var(--sklearn-color-unfitted-level-0);\n",
        "}\n",
        "\n",
-       "#sk-container-id-2 div.sk-estimator.fitted {\n",
+       "#sk-container-id-4 div.sk-estimator.fitted {\n",
        "  /* fitted */\n",
        "  background-color: var(--sklearn-color-fitted-level-0);\n",
        "}\n",
        "\n",
        "/* on hover */\n",
-       "#sk-container-id-2 div.sk-estimator:hover {\n",
+       "#sk-container-id-4 div.sk-estimator:hover {\n",
        "  /* unfitted */\n",
        "  background-color: var(--sklearn-color-unfitted-level-2);\n",
        "}\n",
        "\n",
-       "#sk-container-id-2 div.sk-estimator.fitted:hover {\n",
+       "#sk-container-id-4 div.sk-estimator.fitted:hover {\n",
        "  /* fitted */\n",
        "  background-color: var(--sklearn-color-fitted-level-2);\n",
        "}\n",
@@ -1587,7 +1587,7 @@
        "\n",
        "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
        "\n",
-       "#sk-container-id-2 a.estimator_doc_link {\n",
+       "#sk-container-id-4 a.estimator_doc_link {\n",
        "  float: right;\n",
        "  font-size: 1rem;\n",
        "  line-height: 1em;\n",
@@ -1602,7 +1602,7 @@
        "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
        "}\n",
        "\n",
-       "#sk-container-id-2 a.estimator_doc_link.fitted {\n",
+       "#sk-container-id-4 a.estimator_doc_link.fitted {\n",
        "  /* fitted */\n",
        "  background-color: var(--sklearn-color-fitted-level-0);\n",
        "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
@@ -1610,14 +1610,14 @@
        "}\n",
        "\n",
        "/* On hover */\n",
-       "#sk-container-id-2 a.estimator_doc_link:hover {\n",
+       "#sk-container-id-4 a.estimator_doc_link:hover {\n",
        "  /* unfitted */\n",
        "  background-color: var(--sklearn-color-unfitted-level-3);\n",
        "  color: var(--sklearn-color-background);\n",
        "  text-decoration: none;\n",
        "}\n",
        "\n",
-       "#sk-container-id-2 a.estimator_doc_link.fitted:hover {\n",
+       "#sk-container-id-4 a.estimator_doc_link.fitted:hover {\n",
        "  /* fitted */\n",
        "  background-color: var(--sklearn-color-fitted-level-3);\n",
        "}\n",
@@ -1754,7 +1754,7 @@
        "    height: 14px;\n",
        "    cursor: pointer;\n",
        "}\n",
-       "</style><body><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>KNeighborsClassifier(n_neighbors=3)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" checked><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow\"><div><div>KNeighborsClassifier</div></div><div><a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.8/modules/generated/sklearn.neighbors.KNeighborsClassifier.html\">?<span>Documentation for KNeighborsClassifier</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></div></label><div class=\"sk-toggleable__content fitted\" data-param-prefix=\"\">\n",
+       "</style><body><div id=\"sk-container-id-4\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>KNeighborsClassifier(n_neighbors=3)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-4\" type=\"checkbox\" checked><label for=\"sk-estimator-id-4\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow\"><div><div>KNeighborsClassifier</div></div><div><a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.8/modules/generated/sklearn.neighbors.KNeighborsClassifier.html\">?<span>Documentation for KNeighborsClassifier</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></div></label><div class=\"sk-toggleable__content fitted\" data-param-prefix=\"\">\n",
        "        <div class=\"estimator-table\">\n",
        "            <details>\n",
        "                <summary>Parameters</summary>\n",
@@ -2007,15 +2007,15 @@
        "    }\n",
        "}\n",
        "\n",
-       "forceTheme('sk-container-id-2');</script></body>"
+       "forceTheme('sk-container-id-4');</script></body>"
       ]
      },
-     "execution_count": 18,
+     "execution_count": 32,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
-   "execution_count": 18
+   "execution_count": 32
   },
   {
    "metadata": {},
@@ -2033,15 +2033,15 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-04-25T20:51:48.841953400Z",
-     "start_time": "2026-04-25T20:51:48.825877800Z"
+     "end_time": "2026-04-25T21:15:55.065809200Z",
+     "start_time": "2026-04-25T21:15:55.059661900Z"
     }
    },
    "cell_type": "code",
    "source": "",
    "id": "65e55b70ad44b2dc",
    "outputs": [],
-   "execution_count": 18
+   "execution_count": 32
   },
   {
    "metadata": {},
@@ -2059,15 +2059,15 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2026-04-25T20:51:48.861351100Z",
-     "start_time": "2026-04-25T20:51:48.842953500Z"
+     "end_time": "2026-04-25T21:15:55.070341Z",
+     "start_time": "2026-04-25T21:15:55.066313200Z"
     }
    },
    "cell_type": "code",
    "source": "",
    "id": "f3535461938f94f5",
    "outputs": [],
-   "execution_count": 18
+   "execution_count": 32
   }
  ],
  "metadata": {