{ "cells": [ { "cell_type": "markdown", "id": "b6767d19", "metadata": {}, "source": [ "# R-Squared\n", "\n", "R-squared is a regression metric. It has the following formula:\n", "\n", "$$\n", " R^2 = 1 - \\frac{RSS}{TSS}.\n", "$$\n", "\n", "Where $RSS$ is the sum of squared residuals and $TSS$ is the total sum of squares.\n", "\n", "In other words, $RSS$ is the total squared difference between the target values\n", "$y$ and the predictions $y_i$. Mathematically, this is:\n", "\n", "$$\n", " RSS = \\sum_{i = 0}^{n} (y_i - \\hat{y}_i) ^ 2.\n", "$$\n", "\n", "$TSS$ is the total difference between $y$ and the mean of $y$ which we denote as $\\bar{y}$. Mathematically, this is:\n", "\n", "$$\n", " TSS = \\sum_{i = 0}^{n} (y - \\bar{y}) ^ 2.\n", "$$\n", "\n", "The quotient in the $R^2$ formula compares our model with a baseline that is\n", "just the mean of $y$. If our model is better at predicting $y$ than the mean\n", "$\\bar{y}$, then $RSS$ will be smaller than $TSS$ and therefore the quotient\n", "$\\frac{RSS}{TSS}$ will be less than 1.\n", "\n", "If the model is not better at predicting $y$ than the mean $\\bar{y}$, then $TSS$\n", "will be smaller than $RSS$ and $\\frac{RSS}{TSS}$ will be greater than 1.\n", "\n", "Why in the $R^2$ formula do we take $\\frac{RSS}{TSS}$ from 1? It makes it easier\n", "to interpret. If our model outperforms the mean $\\bar{y}$ then $R^2$ will be\n", "between 0 and 1. The closer the 1 the better. If our model is not better than\n", "the mean $\\bar{y}$ then $R^2$ will be less than 0.\n", "\n", "# Example 1: Linear Target\n", "\n", "Suppose we have data that is generated from the following underlying process:\n", "\n", "$$\n", " y = 0.5 x + 1 + \\epsilon\n", "$$\n", "\n", "Where $\\epsilon$ is a noise term. Let us model it with a simple linear\n", "regression model. Create the data and fit the model." ] }, { "cell_type": "code", "execution_count": 2, "id": "562dd89e", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from sklearn.linear_model import LinearRegression\n", "\n", "n = 100\n", "x = np.random.normal(0, 1, n).reshape(-1, 1)\n", "epsilon = np.random.normal(0, 0.1, n).reshape(-1, 1)\n", "y = 0.5 * x + 1 + epsilon\n", "\n", "model = LinearRegression()\n", "model.fit(x, y)\n", "y_hat = model.predict(x)\n", "\n", "fig, ax = plt.subplots()\n", "ax.scatter(x[:, 0], y, label=\"Original data\", color=\"tab:blue\")\n", "ax.plot(x[:, 0], y_hat, label=\"Predictions\", color=\"tab:orange\")\n", "ax.legend();" ] }, { "cell_type": "markdown", "id": "18181fef", "metadata": {}, "source": [ "Create a function for computing $R^2$." ] }, { "cell_type": "code", "execution_count": 3, "id": "c5a97ec2", "metadata": {}, "outputs": [], "source": [ "def r_squared(y_true, y_pred):\n", " rss = ((y_true - y_pred) ** 2).sum()\n", " tss = ((y_true - y_true.mean()) ** 2).sum()\n", " return 1 - rss / tss" ] }, { "cell_type": "markdown", "id": "d83dc470", "metadata": {}, "source": [ "Compute the $R^2$ score for our model's predictions." ] }, { "cell_type": "code", "execution_count": 4, "id": "d48ef65b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.9661874237889019" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r_squared(y, y_hat)" ] }, { "cell_type": "markdown", "id": "cab53ed6", "metadata": {}, "source": [ "The $R^2$ is close to 1 to our model is very good.\n", "\n", "## R Squared On Small Datasets Can Give Strange Results\n", "\n", "$R^2$ compares the model predictions with the mean of the target variable. For\n", "small datasets, this mean may not reflect that of the underlying probability\n", "distribution.\n", "\n", "For example suppose we model a cubic function." ] }, { "cell_type": "code", "execution_count": 51, "id": "87bb30be", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 100\n", "x = np.linspace(-1.5, 1.5, 100).reshape(-1, 1)\n", "x = np.sort(x)\n", "epsilon = np.random.normal(0, 0.1, n).reshape(-1, 1)\n", "y = x ** 3 + epsilon\n", "\n", "model = LinearRegression()\n", "model.fit(x, y)\n", "y_hat = model.predict(x)\n", "\n", "fig, ax = plt.subplots()\n", "ax.scatter(x[:, 0], y, label=\"Original data\", color=\"tab:blue\", alpha=0.5)\n", "ax.plot(x[:, 0], y_hat, label=\"Predictions\", color=\"tab:orange\")\n", "ax.legend()\n", "ax.grid(linestyle=\":\")" ] }, { "cell_type": "markdown", "id": "5419b71e", "metadata": {}, "source": [ "Even though we have modelled our cubic function with a straight line, it is not\n", "a bad approximation. Calculate the $R^2$ for our predictions." ] }, { "cell_type": "code", "execution_count": 77, "id": "273f009d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.827909114372573" ] }, "execution_count": 77, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r_squared(y, y_hat)" ] }, { "cell_type": "markdown", "id": "d78d517c", "metadata": {}, "source": [ "The model fit is quite good. However, if we choose a very small specific subset\n", "of the training data, we can get an extrememly negative $R^2$ value." ] }, { "cell_type": "code", "execution_count": 79, "id": "344c5021", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-214.9338556085192" ] }, "execution_count": 79, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mask = (x > 0.5) & (x < 0.7)\n", "x_test = x[mask].reshape((-1, 1))\n", "y_test = y[mask]\n", "y_test_pred = model.predict(x_test)\n", "\n", "r_squared(y_test, y_test_pred)" ] }, { "cell_type": "markdown", "id": "76e7a620", "metadata": {}, "source": [ "Plot these data points and their mean." ] }, { "cell_type": "code", "execution_count": 80, "id": "9ac19758", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "y_test_mean = y_test.mean()\n", "\n", "fig, ax = plt.subplots()\n", "ax.scatter(x[:, 0], y, label=\"Original data\", color=\"tab:blue\", alpha=0.5)\n", "ax.plot(x[:, 0], y_hat, label=\"Predictions\", color=\"tab:orange\")\n", "ax.scatter(x_test[:, 0], y_test, label=\"Test set\", color=\"black\")\n", "ax.axhline(y_test_mean, color=\"gray\", linestyle=\"--\", label=\"Mean of test set\")\n", "\n", "ax.legend()\n", "ax.grid(linestyle=\":\")" ] }, { "cell_type": "markdown", "id": "0b09b32c", "metadata": {}, "source": [ "For this small subset of data points, the mean is a better approximation than\n", "our model. So, according to $R^2$, our model is terrible.\n", "\n", "This is an unrealistic example but suppose you are predicting house\n", "prices in the UK. Suppose you want to see how well your model performs in a\n", "certain post code which contains 30 houses. The mean house price for that post\n", "code is probably going to be a good approximate and maybe better than a model\n", "trained on prices from the whole of the UK which will lead to negative $R^2$.\n", "\n", "If you are using $R^2$ on a small subset of your entire population you should be\n", "aware that your $R^2$ may be extremely negative if your subset is not\n", "representative of your whole population." ] } ], "metadata": { "kernelspec": { "display_name": ".venv", "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": "3.10.12" } }, "nbformat": 4, "nbformat_minor": 5 }