{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "First I am loading the data. I have to import the required libraries.\n", "\n", "\n", "1. **`numpy`** – Numerical computing, array operations. \n", "2. **`pandas`** – Data manipulation, handling tables (DataFrames). \n", "3. **`statsmodels.api`** – Statistical modeling, hypothesis testing, logistic regression. \n", "4. **`matplotlib.pyplot`** – Basic plotting and visualization. \n", "5. **`seaborn`** – Advanced statistical data visualization. \n", "6. **`StandardScaler` (from `sklearn.preprocessing`)** – Feature scaling (standardization). \n", "7. **`VarianceThreshold` (from `sklearn.feature_selection`)** – Removes low-variance features. \n", "8. **`LogisticRegression` (from `sklearn.linear_model`)** – Implements logistic regression for classification. \n" ] }, { "cell_type": "code", "execution_count": 111, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "from sklearn.preprocessing import StandardScaler\n", "from sklearn.feature_selection import VarianceThreshold\n", "from sklearn.linear_model import LogisticRegression" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, I am loading the dataset..." ] }, { "cell_type": "code", "execution_count": 112, "metadata": {}, "outputs": [], "source": [ "# Load Breast Cancer dataset\n", "url = \"https://archive.ics.uci.edu/ml/machine-learning-databases/breast-cancer-wisconsin/wdbc.data\"\n", "\n", "# Define column names\n", "columns = [\"ID\", \"Diagnosis\", \"Radius_mean\", \"Texture_mean\", \"Perimeter_mean\", \"Area_mean\",\n", " \"Smoothness_mean\", \"Compactness_mean\", \"Concavity_mean\", \"Concave_points_mean\",\n", " \"Symmetry_mean\", \"Fractal_dimension_mean\", \"Radius_se\", \"Texture_se\", \n", " \"Perimeter_se\", \"Area_se\", \"Smoothness_se\", \"Compactness_se\", \"Concavity_se\", \n", " \"Concave_points_se\", \"Symmetry_se\", \"Fractal_dimension_se\", \"Radius_worst\",\n", " \"Texture_worst\", \"Perimeter_worst\", \"Area_worst\", \"Smoothness_worst\", \n", " \"Compactness_worst\", \"Concavity_worst\", \"Concave_points_worst\", \n", " \"Symmetry_worst\", \"Fractal_dimension_worst\"]\n", "\n", "# Load data\n", "df = pd.read_csv(url, names=columns)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "drop(columns=[\"ID\"]): The drop method is used to remove a specified column or row. In this case, it's removing the column with the name \"ID\"." ] }, { "cell_type": "code", "execution_count": 113, "metadata": {}, "outputs": [], "source": [ "# Convert Diagnosis (M = Malignant, B = Benign) to numeric (1 = Malignant, 0 = Benign)\n", "df[\"Diagnosis\"] = df[\"Diagnosis\"].map({\"M\": 1, \"B\": 0})" ] }, { "cell_type": "code", "execution_count": 114, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Removed Highly Correlated Features: ['Perimeter_mean', 'Area_mean', 'Concavity_mean', 'Concave_points_mean', 'Perimeter_se', 'Area_se', 'Concavity_se', 'Fractal_dimension_se', 'Radius_worst', 'Texture_worst', 'Perimeter_worst', 'Area_worst', 'Smoothness_worst', 'Compactness_worst', 'Concavity_worst', 'Concave_points_worst', 'Fractal_dimension_worst']\n" ] } ], "source": [ "# Remove Highly Correlated Features to improve CI.\n", "# Compute correlation matrix\n", "corr_matrix = df.corr().abs()\n", "\n", "# Select upper triangle of correlation matrix\n", "upper = corr_matrix.where(np.triu(np.ones(corr_matrix.shape), k=1).astype(bool))\n", "\n", "# Drop highly correlated features (threshold: 0.8)\n", "high_corr_features = [column for column in upper.columns if any(upper[column] > 0.8)]\n", "df_reduced = df.drop(columns=high_corr_features)\n", "\n", "print(\"Removed Highly Correlated Features:\", high_corr_features)\n" ] }, { "cell_type": "code", "execution_count": 115, "metadata": {}, "outputs": [], "source": [ "# Select one feature for visualization\n", "feature = \"Radius_mean\" # Change this if needed\n", "X = df[[feature]]\n", "y = df[\"Diagnosis\"]" ] }, { "cell_type": "code", "execution_count": 116, "metadata": {}, "outputs": [], "source": [ "# Standardize the feature: \n", "scaler = StandardScaler()\n", "X_scaled = scaler.fit_transform(X)" ] }, { "cell_type": "code", "execution_count": 117, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 0.289992\n", " Iterations 8\n" ] } ], "source": [ "# Fit Logistic Regression\n", "logreg = sm.Logit(y, sm.add_constant(X_scaled)).fit()" ] }, { "cell_type": "code", "execution_count": 118, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Logit Regression Results
Dep. Variable: Diagnosis No. Observations: 569
Model: Logit Df Residuals: 567
Method: MLE Df Model: 1
Date: Tue, 25 Mar 2025 Pseudo R-squ.: 0.5608
Time: 13:19:58 Log-Likelihood: -165.01
converged: True LL-Null: -375.72
Covariance Type: nonrobust LLR p-value: 1.192e-93
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
coef std err z P>|z| [0.025 0.975]
const -0.6441 0.140 -4.601 0.000 -0.918 -0.370
x1 3.6392 0.328 11.100 0.000 2.997 4.282
" ], "text/latex": [ "\\begin{center}\n", "\\begin{tabular}{lclc}\n", "\\toprule\n", "\\textbf{Dep. Variable:} & Diagnosis & \\textbf{ No. Observations: } & 569 \\\\\n", "\\textbf{Model:} & Logit & \\textbf{ Df Residuals: } & 567 \\\\\n", "\\textbf{Method:} & MLE & \\textbf{ Df Model: } & 1 \\\\\n", "\\textbf{Date:} & Tue, 25 Mar 2025 & \\textbf{ Pseudo R-squ.: } & 0.5608 \\\\\n", "\\textbf{Time:} & 13:19:58 & \\textbf{ Log-Likelihood: } & -165.01 \\\\\n", "\\textbf{converged:} & True & \\textbf{ LL-Null: } & -375.72 \\\\\n", "\\textbf{Covariance Type:} & nonrobust & \\textbf{ LLR p-value: } & 1.192e-93 \\\\\n", "\\bottomrule\n", "\\end{tabular}\n", "\\begin{tabular}{lcccccc}\n", " & \\textbf{coef} & \\textbf{std err} & \\textbf{z} & \\textbf{P$> |$z$|$} & \\textbf{[0.025} & \\textbf{0.975]} \\\\\n", "\\midrule\n", "\\textbf{const} & -0.6441 & 0.140 & -4.601 & 0.000 & -0.918 & -0.370 \\\\\n", "\\textbf{x1} & 3.6392 & 0.328 & 11.100 & 0.000 & 2.997 & 4.282 \\\\\n", "\\bottomrule\n", "\\end{tabular}\n", "%\\caption{Logit Regression Results}\n", "\\end{center}" ], "text/plain": [ "\n", "\"\"\"\n", " Logit Regression Results \n", "==============================================================================\n", "Dep. Variable: Diagnosis No. Observations: 569\n", "Model: Logit Df Residuals: 567\n", "Method: MLE Df Model: 1\n", "Date: Tue, 25 Mar 2025 Pseudo R-squ.: 0.5608\n", "Time: 13:19:58 Log-Likelihood: -165.01\n", "converged: True LL-Null: -375.72\n", "Covariance Type: nonrobust LLR p-value: 1.192e-93\n", "==============================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "const -0.6441 0.140 -4.601 0.000 -0.918 -0.370\n", "x1 3.6392 0.328 11.100 0.000 2.997 4.282\n", "==============================================================================\n", "\"\"\"" ] }, "execution_count": 118, "metadata": {}, "output_type": "execute_result" } ], "source": [ "logreg.summary()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Check for perfect separation\n", "print(df.groupby(\"Diagnosis\").mean())\n" ] }, { "cell_type": "code", "execution_count": 119, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Confidence Intervals for the Coefficients:\n", " 0 1\n", "const NaN NaN\n", "x1 -2.082353e+12 2.082353e+12\n", "x2 NaN NaN\n", "x3 -2.196362e+12 2.196362e+12\n", "x4 NaN NaN\n", "x5 NaN NaN\n", "x6 -4.917824e+11 4.917824e+11\n", "x7 -1.607140e+12 1.607140e+12\n", "x8 -1.174798e+12 1.174798e+12\n", "x9 NaN NaN\n", "x10 -7.762617e+11 7.762617e+11\n", "x11 -1.125550e+12 1.125550e+12\n", "x12 -1.266793e+10 1.266793e+10\n", "x13 -1.466468e+12 1.466468e+12\n", "x14 -1.662006e+12 1.662006e+12\n", "x15 NaN NaN\n", "x16 NaN NaN\n", "x17 NaN NaN\n", "x18 NaN NaN\n", "x19 NaN NaN\n", "x20 -1.919826e+12 1.919826e+12\n", "x21 NaN NaN\n", "x22 NaN NaN\n", "x23 -1.936092e+12 1.936092e+12\n", "x24 NaN NaN\n", "x25 NaN NaN\n", "x26 -2.296411e+12 2.296411e+12\n", "x27 NaN NaN\n", "x28 NaN NaN\n", "x29 NaN NaN\n", "x30 -2.079799e+12 2.079799e+12\n" ] } ], "source": [ "# Print CI for the coefficients\n", "print(\"Confidence Intervals for the Coefficients:\")\n", "print(conf_int)\n" ] }, { "cell_type": "code", "execution_count": 120, "metadata": {}, "outputs": [], "source": [ "# Visualizing the logistic curve (sigmoid) with confidence intervals\n", "# Select one feature for visualization\n", "feature = \"Radius_mean\"\n", "X_feature = df[[feature]]\n", "X_scaled_feature = scaler.transform(X_feature) # Standardize the feature\n", "X_scaled_feature_const = sm.add_constant(X_scaled_feature) # Add intercept\n" ] }, { "cell_type": "code", "execution_count": 121, "metadata": {}, "outputs": [], "source": [ "# Generate values for the sigmoid curve\n", "X_range = np.linspace(X_scaled.min(), X_scaled.max(), 300) # Create smooth range of X values\n", "X_range_const = sm.add_constant(X_range) # Add intercept\n", "y_prob = logreg.predict(X_range_const) # Compute probabilities" ] }, { "cell_type": "code", "execution_count": 122, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# 🔹 Plot data points and fitted sigmoid curve\n", "plt.figure(figsize=(8, 6))\n", "sns.scatterplot(x=X_scaled.ravel(), y=y, alpha=0.5, label=\"Actual Data\", color=\"blue\")\n", "plt.plot(X_range, y_prob, color=\"red\", linewidth=2, label=\"Logistic Regression Fit\")\n", "plt.xlabel(f\"Standardized {feature}\")\n", "plt.ylabel(\"Probability of Malignant (1)\")\n", "plt.title(\"Logistic Regression Fit\")\n", "plt.legend()\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "base", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.7" } }, "nbformat": 4, "nbformat_minor": 2 }