{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Explained variance demonstration\n", "\n", "This notebook contains a visual demo of explained variance and shows it's relationship to R-squared.\n", "\n", "## Notebook set-up" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "'''Explained variance and R-squared score'''\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from sklearn.linear_model import LinearRegression\n", "from sklearn.metrics import r2_score" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Data" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Some linear data with noise\n", "N=1000\n", "NOISE_WIDTH=50\n", "x=np.array(list(range(N))) + np.random.normal(-NOISE_WIDTH,NOISE_WIDTH,N)\n", "y=np.array(list(range(N))) + np.random.normal(-NOISE_WIDTH,NOISE_WIDTH,N)\n", "\n", "# Linear fit\n", "linear_model=LinearRegression()\n", "linear_model.fit(x.reshape(-1, 1), y)\n", "\n", "# Predict across uniform range for plotting\n", "x_range=np.linspace(0,N)\n", "y_linear=linear_model.predict(x_range.reshape(-1, 1))\n", "\n", "# Make predictions for x\n", "y_predicted=linear_model.predict(x.reshape(-1, 1))\n", "\n", "# Get fit residuals\n", "y_residual=y - y_predicted\n", "\n", "fig, axs=plt.subplots(2,2, figsize=(6,6))\n", "axs=axs.flatten()\n", "\n", "axs[0].set_title('Linear regression')\n", "axs[0].scatter(x, y, s=0.2, color='black', label='Data')\n", "axs[0].plot(x_range, y_linear, color='red', label='Linear model')\n", "axs[0].set_xlabel('x')\n", "axs[0].set_ylabel('y')\n", "axs[0].set_ylim(-200, 1100)\n", "axs[0].legend(loc='upper left', markerscale=10)\n", "\n", "axs[1].set_title('Fit residuals')\n", "axs[1].scatter(x, y_residual, s=0.2, color='black')\n", "axs[1].set_xlabel('x')\n", "axs[1].set_ylabel(r'Residual ($y_i - f_i$)')\n", "axs[1].set_ylim(-650, 650)\n", "\n", "bins=np.linspace(-200, 1100, 30)\n", "axs[2].set_title('Original y distribution')\n", "axs[2].hist(y, color='black', bins=bins, orientation='horizontal')\n", "axs[2].set_xlabel('Count')\n", "axs[2].set_ylabel('y')\n", "\n", "bins=np.linspace(-650, 650, 30)\n", "axs[3].set_title('Fit residual distribution')\n", "axs[3].hist(y_residual, color='black', bins=bins, orientation='horizontal')\n", "axs[3].set_xlabel('Count')\n", "axs[3].set_ylabel(r'Residual ($y_i - f_i$)')\n", "\n", "fig.tight_layout()\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Residual variance and R-squared\n", "\n", "After fitting a model, the **residuals** are the differences between the observed values $y_i$ and the model's predictions $f_i$. The variance of those residuals tells us how much variation the model *failed* to explain.\n", "\n", "We can quantify how well the model did by comparing the residual variance to the original variance of $y$:\n", "\n", "$$R^2 = 1 - \\frac{\\text{Var}(y_i - f_i)}{\\text{Var}(y_i)}$$\n", "\n", "- If the model explains everything, the residuals are zero and $R^2 = 1$.\n", "- If the model explains nothing (no better than predicting the mean), the residual variance equals the original variance and $R^2 = 0$.\n", "\n", "The two histograms above make this visual: the residual distribution (right) is narrower than the original $y$ distribution (left). The reduction in spread is the variance the model captured.\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Data variance: 87995, residual variance: 4796\n", "Fraction of variance explained: 0.945\n" ] } ], "source": [ "y_var=np.var(y)\n", "y_residual_var=np.var(y_residual)\n", "\n", "print(f'Data variance: {y_var:.0f}, residual variance: {y_residual_var:.0f}')\n", "print(f'Fraction of variance explained: {1-(y_residual_var/y_var):.3f}')" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scikit-learn R-squared: 0.945\n" ] } ], "source": [ "sk_r2=r2_score(y, y_predicted)\n", "print(f'Scikit-learn R-squared: {sk_r2:.3f}')" ] } ], "metadata": { "kernelspec": { "display_name": ".venv (3.12.3)", "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": "3.12.3" } }, "nbformat": 4, "nbformat_minor": 2 }