diff --git a/DAY 2/Jupyter Notebooks/ml-sig-scikit-learn.ipynb b/DAY 2/Jupyter Notebooks/ml-sig-scikit-learn.ipynb new file mode 100644 index 0000000..39f5db1 --- /dev/null +++ b/DAY 2/Jupyter Notebooks/ml-sig-scikit-learn.ipynb @@ -0,0 +1 @@ +{"metadata":{"kernelspec":{"language":"python","display_name":"Python 3","name":"python3"},"language_info":{"name":"python","version":"3.10.12","mimetype":"text/x-python","codemirror_mode":{"name":"ipython","version":3},"pygments_lexer":"ipython3","nbconvert_exporter":"python","file_extension":".py"},"kaggle":{"accelerator":"none","dataSources":[],"dockerImageVersionId":30918,"isInternetEnabled":true,"language":"python","sourceType":"notebook","isGpuEnabled":false}},"nbformat_minor":4,"nbformat":4,"cells":[{"cell_type":"markdown","source":"# Linear Regression with scikit-learn\n\nIn this notebook, we'll explore linear regression using scikit-learn. We'll cover both single-variable (simple) and multivariable (multiple) linear regression, including data generation, model fitting, evaluation, and visualization.","metadata":{"_uuid":"db19bda7-dc86-4042-932e-471c742fbcc1","_cell_guid":"02063fa2-f2fe-4e29-89fa-9e134a98a000","trusted":true,"collapsed":false,"jupyter":{"outputs_hidden":false}}},{"cell_type":"markdown","source":"## 1. Setup and Imports","metadata":{"_uuid":"4339a9f0-adcd-4ab0-8abb-5a02478f158c","_cell_guid":"12f49a67-bce3-4152-8782-8b0dd5aeee80","trusted":true,"collapsed":false,"jupyter":{"outputs_hidden":false}}},{"cell_type":"code","source":"import numpy as np\nimport pandas as pd\nimport matplotlib.pyplot as plt\nimport seaborn as sns\nfrom sklearn.linear_model import LinearRegression\nfrom sklearn.model_selection import train_test_split\nfrom sklearn.metrics import mean_squared_error, r2_score\nfrom sklearn.datasets import make_regression\n\n# Set plotting style\\ sns.set(style=\"whitegrid\")","metadata":{"_uuid":"94f0644f-0cb1-4bfc-91a1-79f9a0e0d337","_cell_guid":"1792b567-daf8-4998-9304-cf78f2e2df69","trusted":true,"collapsed":false,"jupyter":{"outputs_hidden":false},"execution":{"iopub.status.busy":"2025-04-06T05:29:26.474325Z","iopub.execute_input":"2025-04-06T05:29:26.474603Z","iopub.status.idle":"2025-04-06T05:29:29.461010Z","shell.execute_reply.started":"2025-04-06T05:29:26.474570Z","shell.execute_reply":"2025-04-06T05:29:29.459861Z"}},"outputs":[],"execution_count":1},{"cell_type":"markdown","source":"## 2. Single-Variable (Simple) Linear Regression","metadata":{"_uuid":"27eb3fa3-118e-4009-9e7a-2f3c06eddaab","_cell_guid":"b637b39b-425b-4f2d-ba22-f0766c8587b3","trusted":true,"collapsed":false,"jupyter":{"outputs_hidden":false}}},{"cell_type":"markdown","source":"**2.1 Generate Synthetic Data**","metadata":{"_uuid":"25ebf501-7eeb-467d-b118-dfbbeea79c6d","_cell_guid":"4d9199fb-62a0-4bca-8c1a-6fe281df4597","trusted":true,"collapsed":false,"jupyter":{"outputs_hidden":false}}},{"cell_type":"code","source":"# Generate a linear relationship y = 2x + noise\ntheta0 = 1.5 # intercept\ntheta1 = 2.0 # slope\nn_samples = 100\nnp.random.seed(42)\nX_single = 2 * np.random.rand(n_samples, 1)\ny_single = theta0 + theta1 * X_single.flatten() + np.random.randn(n_samples) * 0.5\n\n# Convert to DataFrame for convenience\ndf_single = pd.DataFrame({\"x\": X_single.flatten(), \"y\": y_single})\ndf_single.head()","metadata":{"_uuid":"9b8f4d03-7572-41ab-962f-448f171c660b","_cell_guid":"5888ce7a-9cad-4057-b24d-886fad37d017","trusted":true,"collapsed":false,"jupyter":{"outputs_hidden":false},"execution":{"iopub.status.busy":"2025-04-06T05:29:29.462305Z","iopub.execute_input":"2025-04-06T05:29:29.462840Z","iopub.status.idle":"2025-04-06T05:29:29.501652Z","shell.execute_reply.started":"2025-04-06T05:29:29.462801Z","shell.execute_reply":"2025-04-06T05:29:29.500346Z"}},"outputs":[{"execution_count":2,"output_type":"execute_result","data":{"text/plain":" x y\n0 0.749080 3.041684\n1 1.901429 5.153354\n2 1.463988 4.473856\n3 1.197317 2.900849\n4 0.312037 2.014239","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 \n \n \n \n \n \n \n \n \n \n \n \n \n \n
xy
00.7490803.041684
11.9014295.153354
21.4639884.473856
31.1973172.900849
40.3120372.014239
\n
"},"metadata":{}}],"execution_count":2},{"cell_type":"markdown","source":"**2.2 Visualize Data**","metadata":{"_uuid":"020ab89b-d730-400c-aba9-93fa8af40838","_cell_guid":"e9d548e4-5507-4d74-9795-c93a875cb89f","trusted":true,"collapsed":false,"jupyter":{"outputs_hidden":false}}},{"cell_type":"code","source":"plt.figure(figsize=(8, 5))\nplt.scatter(df_single['x'], df_single['y'], color='blue', alpha=0.6)\nplt.title('Synthetic Data for Simple Linear Regression')\nplt.xlabel('x')\nplt.ylabel('y')\nplt.show()","metadata":{"_uuid":"31ba00df-97c6-44bc-b0f3-5c165e01dd30","_cell_guid":"744f9bef-f655-43b1-84d7-57c053570660","trusted":true,"collapsed":false,"jupyter":{"outputs_hidden":false},"execution":{"iopub.status.busy":"2025-04-06T05:29:29.504021Z","iopub.execute_input":"2025-04-06T05:29:29.504351Z","iopub.status.idle":"2025-04-06T05:29:29.889889Z","shell.execute_reply.started":"2025-04-06T05:29:29.504324Z","shell.execute_reply":"2025-04-06T05:29:29.888677Z"}},"outputs":[{"output_type":"display_data","data":{"text/plain":"
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\n"},"metadata":{}}],"execution_count":3},{"cell_type":"markdown","source":"**2.3 Fit the Model**","metadata":{"_uuid":"5b980ac8-fffe-4245-8939-18604a6795de","_cell_guid":"eea0a510-9519-4aaa-87a7-e9ee78306583","trusted":true,"collapsed":false,"jupyter":{"outputs_hidden":false}}},{"cell_type":"code","source":"# Initialize and fit the linear regression model\nmodel_simple = LinearRegression()\nmodel_simple.fit(X_single, y_single)\n\n# Extract parameters\nintercept_simple = model_simple.intercept_\nslope_simple = model_simple.coef_[0]\nprint(f\"Fitted intercept: {intercept_simple:.3f}\")\nprint(f\"Fitted slope: {slope_simple:.3f}\")","metadata":{"_uuid":"fdbb9a3d-612f-4557-a889-dc524e62ccfe","_cell_guid":"3ac537f0-2d0f-4a9b-9ed6-8c10378746a1","trusted":true,"collapsed":false,"jupyter":{"outputs_hidden":false},"execution":{"iopub.status.busy":"2025-04-06T05:29:29.891782Z","iopub.execute_input":"2025-04-06T05:29:29.892072Z","iopub.status.idle":"2025-04-06T05:29:29.942792Z","shell.execute_reply.started":"2025-04-06T05:29:29.892047Z","shell.execute_reply":"2025-04-06T05:29:29.941792Z"}},"outputs":[{"name":"stdout","text":"Fitted intercept: 1.608\nFitted slope: 1.885\n","output_type":"stream"}],"execution_count":4},{"cell_type":"markdown","source":"**2.4 Plot Regression Line**","metadata":{"_uuid":"c6e5cb37-5f24-44cc-a5a0-57df8bf09b84","_cell_guid":"6d24cd0c-db30-4e66-9a6d-501267fc692d","trusted":true,"collapsed":false,"jupyter":{"outputs_hidden":false}}},{"cell_type":"code","source":"# Generate predictions for plotting\ny_pred_line = model_simple.predict(X_single)\n\nplt.figure(figsize=(8, 5))\nplt.scatter(X_single, y_single, color='blue', alpha=0.6, label='Data')\nplt.plot(X_single, y_pred_line, color='red', linewidth=2, label='Fitted line')\nplt.title('Simple Linear Regression Fit')\nplt.xlabel('x')\nplt.ylabel('y')\nplt.legend()\nplt.show()","metadata":{"_uuid":"ed0bba75-3c9f-4d1b-a15f-60827b868b0c","_cell_guid":"d3bc4347-b3ad-463d-9f5e-13535dfb755d","trusted":true,"collapsed":false,"jupyter":{"outputs_hidden":false},"execution":{"iopub.status.busy":"2025-04-06T05:29:29.943903Z","iopub.execute_input":"2025-04-06T05:29:29.944193Z","iopub.status.idle":"2025-04-06T05:29:30.215917Z","shell.execute_reply.started":"2025-04-06T05:29:29.944169Z","shell.execute_reply":"2025-04-06T05:29:30.214607Z"}},"outputs":[{"output_type":"display_data","data":{"text/plain":"
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\n"},"metadata":{}}],"execution_count":5},{"cell_type":"markdown","source":"**2.5 Model Evaluation**","metadata":{"_uuid":"e8305f74-9f2d-458b-8afa-19331e54fca0","_cell_guid":"a4cf7f2b-701f-4d97-9e7c-858f65227bc7","trusted":true,"collapsed":false,"jupyter":{"outputs_hidden":false}}},{"cell_type":"code","source":"mse_simple = mean_squared_error(y_single, y_pred_line)\nr2_simple = r2_score(y_single, y_pred_line)\nprint(f\"Mean Squared Error: {mse_simple:.3f}\")\nprint(f\"R^2 Score: {r2_simple:.3f}\")","metadata":{"_uuid":"54171561-75dc-4ab9-b386-156cfece97aa","_cell_guid":"8f2104bd-7472-46bb-8a18-4a9d6d5859ba","trusted":true,"collapsed":false,"jupyter":{"outputs_hidden":false},"execution":{"iopub.status.busy":"2025-04-06T05:29:30.217108Z","iopub.execute_input":"2025-04-06T05:29:30.217515Z","iopub.status.idle":"2025-04-06T05:29:30.225331Z","shell.execute_reply.started":"2025-04-06T05:29:30.217477Z","shell.execute_reply":"2025-04-06T05:29:30.224063Z"}},"outputs":[{"name":"stdout","text":"Mean Squared Error: 0.202\nR^2 Score: 0.861\n","output_type":"stream"}],"execution_count":6},{"cell_type":"markdown","source":"## 3. Multivariable (Multiple) Linear Regression","metadata":{"_uuid":"0168d86d-c92c-4600-a89c-3267dbfbb000","_cell_guid":"5dceae4f-03e2-4bb5-b79d-3bea9627c9d5","trusted":true,"collapsed":false,"jupyter":{"outputs_hidden":false}}},{"cell_type":"markdown","source":"**3.1 Generate Synthetic Data**","metadata":{"_uuid":"6d8dd02d-22fe-42ef-932f-ae5240adf0c0","_cell_guid":"c885a5d2-6ed2-4b5f-9696-892add72da84","trusted":true,"collapsed":false,"jupyter":{"outputs_hidden":false}}},{"cell_type":"code","source":"# Create a dataset with 3 features\nd X_multi, y_multi, coef_true = make_regression(\n n_samples=200,\n n_features=3,\n noise=10.0,\n coef=True,\n random_state=42\n)\n\n# Create DataFrame\nfeature_names = [f\"x{i+1}\" for i in range(X_multi.shape[1])]\ndf_multi = pd.DataFrame(X_multi, columns=feature_names)\ndf_multi['y'] = y_multi\n\ndf_multi.head()","metadata":{"_uuid":"02b5d062-3b69-4f22-b490-d50aef160fc7","_cell_guid":"64058309-b140-4112-8ffb-5db0073d1275","trusted":true,"collapsed":false,"jupyter":{"outputs_hidden":false},"execution":{"iopub.status.busy":"2025-04-06T05:29:30.226677Z","iopub.execute_input":"2025-04-06T05:29:30.227054Z","iopub.status.idle":"2025-04-06T05:29:30.247316Z","shell.execute_reply.started":"2025-04-06T05:29:30.227018Z","shell.execute_reply":"2025-04-06T05:29:30.244805Z"}},"outputs":[{"traceback":["\u001b[0;36m File \u001b[0;32m\"\"\u001b[0;36m, line \u001b[0;32m2\u001b[0m\n\u001b[0;31m d X_multi, y_multi, coef_true = make_regression(\u001b[0m\n\u001b[0m ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"],"ename":"SyntaxError","evalue":"invalid syntax (, line 2)","output_type":"error"}],"execution_count":7},{"cell_type":"markdown","source":"**3.2 Explore Feature Relationships**","metadata":{"_uuid":"d3d45173-f5e2-446f-a68b-14a2ead78fac","_cell_guid":"82b75349-1192-4bb0-a545-48e491104a6c","trusted":true,"collapsed":false,"jupyter":{"outputs_hidden":false}}},{"cell_type":"code","source":"sns.pairplot(df_multi.sample(100), x_vars=feature_names, y_vars='y', height=3)\nplt.suptitle('Pairplot of Features vs. Target', y=1.02)\nplt.show()","metadata":{"_uuid":"d0376afb-baf5-4206-ba9c-e001b3887a77","_cell_guid":"b8aa7bc7-04a3-4e5c-903b-9cd027dea6cc","trusted":true,"collapsed":false,"jupyter":{"outputs_hidden":false},"execution":{"iopub.status.busy":"2025-04-06T05:29:30.248352Z","iopub.status.idle":"2025-04-06T05:29:30.248908Z","shell.execute_reply":"2025-04-06T05:29:30.248692Z"}},"outputs":[],"execution_count":null},{"cell_type":"markdown","source":"**3.3 Split into Train and Test Sets**","metadata":{"_uuid":"cfc96b7f-a276-491a-a153-ff9ab4e04564","_cell_guid":"5b4a7e26-4491-4d21-a21e-c30e632ec2b4","trusted":true,"collapsed":false,"jupyter":{"outputs_hidden":false}}},{"cell_type":"code","source":"X_train, X_test, y_train, y_test = train_test_split(\n df_multi[feature_names], df_multi['y'], test_size=0.2, random_state=42\n)\n\nprint(f\"Training samples: {X_train.shape[0]}\")\nprint(f\"Test samples: {X_test.shape[0]}\")","metadata":{"_uuid":"21386997-68dc-4aa6-832a-bcc438782e09","_cell_guid":"cbd46203-ed60-4fec-b956-1e2030f1526f","trusted":true,"collapsed":false,"jupyter":{"outputs_hidden":false},"execution":{"iopub.status.busy":"2025-04-06T05:29:30.249989Z","iopub.status.idle":"2025-04-06T05:29:30.250363Z","shell.execute_reply":"2025-04-06T05:29:30.250215Z"}},"outputs":[],"execution_count":null},{"cell_type":"markdown","source":"**3.4 Fit the Multiple Linear Regression Model**","metadata":{"_uuid":"b3836cc7-8c12-475a-ae3a-28b01473de4b","_cell_guid":"3c7f8ff2-23a4-44c9-8454-794a2dae4af9","trusted":true,"collapsed":false,"jupyter":{"outputs_hidden":false}}},{"cell_type":"code","source":"model_multi = LinearRegression()\nmodel_multi.fit(X_train, y_train)\n\n# Extract coefficients\nintercept_multi = model_multi.intercept_\ncoef_multi = model_multi.coef_\nprint(f\"Fitted intercept: {intercept_multi:.3f}\")\nfor name, coef in zip(feature_names, coef_multi):\n print(f\"Coefficient for {name}: {coef:.3f}\")","metadata":{"_uuid":"1bd9010c-fad5-482a-9966-a21d43f6b4c1","_cell_guid":"33617041-92e5-45b2-a483-2924e9bb74bc","trusted":true,"collapsed":false,"jupyter":{"outputs_hidden":false},"execution":{"iopub.status.busy":"2025-04-06T05:29:30.251447Z","iopub.status.idle":"2025-04-06T05:29:30.251823Z","shell.execute_reply":"2025-04-06T05:29:30.251692Z"}},"outputs":[],"execution_count":null},{"cell_type":"markdown","source":"**3.5 Evaluate on Test Set**","metadata":{"_uuid":"7da409c2-0f5b-4834-b7cf-f2727a5059bb","_cell_guid":"6768962b-41be-4a31-95a6-027aed099aea","trusted":true,"collapsed":false,"jupyter":{"outputs_hidden":false}}},{"cell_type":"code","source":"# Predict\ny_pred_multi = model_multi.predict(X_test)\n\n# Metrics\nmse_multi = mean_squared_error(y_test, y_pred_multi)\nr2_multi = r2_score(y_test, y_pred_multi)\nprint(f\"Test Mean Squared Error: {mse_multi:.3f}\")\nprint(f\"Test R^2 Score: {r2_multi:.3f}\")","metadata":{"_uuid":"f053197f-4d86-4f0f-9f9a-b7045bc306fe","_cell_guid":"f43a8a41-eb73-4234-948c-da9d7d1a41a0","trusted":true,"collapsed":false,"jupyter":{"outputs_hidden":false},"execution":{"iopub.status.busy":"2025-04-06T05:29:30.252569Z","iopub.status.idle":"2025-04-06T05:29:30.252939Z","shell.execute_reply":"2025-04-06T05:29:30.252803Z"}},"outputs":[],"execution_count":null},{"cell_type":"markdown","source":"**3.6 Residual Plot**","metadata":{"_uuid":"f7865ff0-f861-49e0-8a34-5d5b525c6e7e","_cell_guid":"eafa87f0-1ea7-4744-bec2-857e21257299","trusted":true,"collapsed":false,"jupyter":{"outputs_hidden":false}}},{"cell_type":"code","source":"residuals = y_test - y_pred_multi\nplt.figure(figsize=(8, 5))\nplt.scatter(y_pred_multi, residuals, alpha=0.6)\nplt.axhline(0, color='red', linestyle='--')\nplt.title('Residuals vs. Predicted Values')\nplt.xlabel('Predicted Values')\nplt.ylabel('Residuals')\nplt.show()","metadata":{"_uuid":"d567ba0b-2166-4431-a40c-bab986f5eb9c","_cell_guid":"5e81d796-587f-46be-b1cc-10b87f3ab63e","trusted":true,"collapsed":false,"jupyter":{"outputs_hidden":false},"execution":{"iopub.status.busy":"2025-04-06T05:29:30.253867Z","iopub.status.idle":"2025-04-06T05:29:30.254255Z","shell.execute_reply":"2025-04-06T05:29:30.254110Z"}},"outputs":[],"execution_count":null},{"cell_type":"markdown","source":"## 4. Conclusion\n\nIn this notebook, we covered:\n- Generating synthetic data for regression tasks\n- Fitting and visualizing simple linear regression models\n- Evaluating model performance using MSE and R²\n- Extending to multiple features with multiple linear regression\n- Examining model coefficients and residuals\n\nNext steps could include exploring regularized linear models (Ridge, Lasso), polynomial regression, and cross-validation techniques.","metadata":{"_uuid":"b3c99095-1632-49ae-82a3-65cdf9f18bc5","_cell_guid":"7ffc2c29-5ec9-47fb-83c0-4a632b695176","trusted":true,"collapsed":false,"jupyter":{"outputs_hidden":false}}}]} \ No newline at end of file