{
"cells": [
{
"cell_type": "markdown",
"id": "fcf08efc",
"metadata": {},
"source": [
"# Visual Diagnostics\n",
"Suppose a data scientist has decided to use linear regression to estimate values of one variable (called the **response** variable) based on another variable (called the **predictor**). To see how well this method of estimation performs, the data scientist must measure how far off the estimates are from the actual values. These differences are called ***residuals*** (\"errors\").\n",
"\n",
"$$\n",
"\\mbox{residual} ~=~ \\mbox{observed value} ~-~ \\mbox{regression estimate}\n",
"$$\n",
"\n",
"A residual is what's left over – the residue – after estimation. \n",
"\n",
"Residuals are the vertical distances of the points from the regression line. There is one residual for each point in the scatter plot. The residual is the difference between the observed value of $y$ and the fitted value of $y$, so for the point $(x, y)$,\n",
"\n",
"$$\n",
"\\mbox{residual} ~~ = ~~ y ~-~\n",
"\\mbox{fitted value of }y\n",
"~~ = ~~ y ~-~\n",
"\\mbox{height of regression line at }x\n",
"$$\n",
"\n",
"The function `residual` calculates the residuals. The calculation assumes all the relevant functions we have already defined: `standard_units`, `correlation`, `slope`, `intercept`, and `fit`."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "3019334a",
"metadata": {
"execution": {
"iopub.execute_input": "2026-08-31T06:02:10.439368Z",
"iopub.status.busy": "2026-08-31T06:02:10.438989Z",
"iopub.status.idle": "2026-08-31T06:02:11.226178Z",
"shell.execute_reply": "2026-08-31T06:02:11.225939Z"
},
"tags": [
"hide-input",
"thebe-init",
"runnable"
]
},
"outputs": [],
"source": [
"path_data = '../../data/'\n",
"\n",
"import numpy as np\n",
"import pandas as pd\n",
"from scipy import stats\n",
"\n",
"import matplotlib\n",
"matplotlib.use('Agg')\n",
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"plt.style.use('fivethirtyeight')"
]
},
{
"cell_type": "markdown",
"id": "fda73b24",
"metadata": {},
"source": [
"```{contents}\n",
":local:\n",
":depth: 2\n",
"```\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "eae51cf1",
"metadata": {
"execution": {
"iopub.execute_input": "2026-08-31T06:02:11.227569Z",
"iopub.status.busy": "2026-08-31T06:02:11.227474Z",
"iopub.status.idle": "2026-08-31T06:02:11.235825Z",
"shell.execute_reply": "2026-08-31T06:02:11.235547Z"
},
"tags": []
},
"outputs": [],
"source": [
"family_heights = pd.read_csv(path_data + 'family_heights.csv')\n",
"heights = family_heights[['midparentHeight', 'childHeight']]\n",
"heights = heights.rename(columns={'midparentHeight':'MidParent', 'childHeight':'Child'})\n",
"\n",
"hybrid = pd.read_csv(path_data + 'hybrid.csv')"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "c9fe533a",
"metadata": {
"execution": {
"iopub.execute_input": "2026-08-31T06:02:11.237171Z",
"iopub.status.busy": "2026-08-31T06:02:11.237103Z",
"iopub.status.idle": "2026-08-31T06:02:11.239195Z",
"shell.execute_reply": "2026-08-31T06:02:11.239003Z"
},
"tags": []
},
"outputs": [],
"source": [
"def standard_units(x):\n",
" return (x - np.mean(x))/np.std(x)\n",
"\n",
"def standard_units(any_numbers):\n",
" \"Convert any array of numbers to standard units.\"\n",
" return (any_numbers - np.mean(any_numbers))/np.std(any_numbers) \n",
"\n",
"def correlation(t, x, y):\n",
" return np.mean(standard_units(t[x])*standard_units(t[y]))\n",
"\n",
"def slope(table, x, y):\n",
" r = correlation(table, x, y)\n",
" return r * np.std(table[y])/np.std(table[x])\n",
"\n",
"def intercept(table, x, y):\n",
" a = slope(table, x, y)\n",
" return np.mean(table[y]) - a * np.mean(table[x])\n",
"\n",
"def fit(table, x, y):\n",
" \"\"\"Return the height of the regression line at each x value.\"\"\"\n",
" a = slope(table, x, y)\n",
" b = intercept(table, x, y)\n",
" return a * table[x] + b"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "1015f251",
"metadata": {
"execution": {
"iopub.execute_input": "2026-08-31T06:02:11.240267Z",
"iopub.status.busy": "2026-08-31T06:02:11.240202Z",
"iopub.status.idle": "2026-08-31T06:02:11.241548Z",
"shell.execute_reply": "2026-08-31T06:02:11.241339Z"
},
"tags": []
},
"outputs": [],
"source": [
"def residual(table, x, y):\n",
" return table[y] - fit(table, x, y)"
]
},
{
"cell_type": "markdown",
"id": "2b8a92f9",
"metadata": {},
"source": [
"Continuing our example of estimating the heights of adult children (the response) based on the midparent height (the predictor), let us calculate the fitted values and the residuals."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "27c105ab",
"metadata": {
"execution": {
"iopub.execute_input": "2026-08-31T06:02:11.242700Z",
"iopub.status.busy": "2026-08-31T06:02:11.242641Z",
"iopub.status.idle": "2026-08-31T06:02:11.248354Z",
"shell.execute_reply": "2026-08-31T06:02:11.248149Z"
},
"tags": []
},
"outputs": [
{
"data": {
"text/html": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"residual_plot(heights, 'MidParent', 'Child')"
]
},
{
"cell_type": "markdown",
"id": "49c4ea0c",
"metadata": {},
"source": [
"The midparent heights are on the horizontal axis, as in the original scatter plot. But now the vertical axis shows the residuals. Notice that the plot appears to be centered around the horizontal line at the level 0 (shown in dark blue). Notice also that the plot shows no upward or downward trend. We will observe later that this lack of trend is true of all regressions."
]
},
{
"cell_type": "markdown",
"id": "2cfa406d",
"metadata": {},
"source": [
"## Regression Diagnostics\n",
"Residual plots help us make visual **assessments of the quality of a linear regression** analysis. Such assessments are called *diagnostics*. The function ``regression_diagnostic_plots`` draws the original scatter plot as well as the residual plot for ease of comparison."
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "12a53abc",
"metadata": {
"execution": {
"iopub.execute_input": "2026-08-31T06:02:11.334141Z",
"iopub.status.busy": "2026-08-31T06:02:11.334058Z",
"iopub.status.idle": "2026-08-31T06:02:11.335677Z",
"shell.execute_reply": "2026-08-31T06:02:11.335467Z"
},
"tags": []
},
"outputs": [],
"source": [
"def regression_diagnostic_plots(table, x, y):\n",
" plt.figure(figsize=(4,4))\n",
" scatter_fit(table, x, y)\n",
" residual_plot(table, x, y)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "5b526725",
"metadata": {
"execution": {
"iopub.execute_input": "2026-08-31T06:02:11.336608Z",
"iopub.status.busy": "2026-08-31T06:02:11.336547Z",
"iopub.status.idle": "2026-08-31T06:02:11.388346Z",
"shell.execute_reply": "2026-08-31T06:02:11.388131Z"
},
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"regression_diagnostic_plots(heights, 'MidParent', 'Child')"
]
},
{
"cell_type": "markdown",
"id": "05b76fe2",
"metadata": {},
"source": [
"This residual plot indicates that linear regression was a reasonable method of estimation. Notice how the residuals are distributed fairly symmetrically above and below the horizontal line at 0, corresponding to the original scatter plot being roughly symmetrical above and below. Notice also that the vertical spread of the plot is fairly even across the most common values of the children's heights. In other words, apart from a few outlying points, the plot isn't narrower in some places and wider in others.\n",
"\n",
"In other words, the accuracy of the regression appears to be about the same across the observed range of the predictor variable. \n",
"\n",
"**The residual plot of a good regression shows no pattern. The residuals look about the same, above and below the horizontal line at 0, across the range of the predictor variable.**"
]
},
{
"cell_type": "markdown",
"id": "4087ab83",
"metadata": {},
"source": [
"## Detecting Nonlinearity\n",
"Drawing the scatter plot of the data usually gives an indication of whether the relation between the two variables is non-linear. Often, however, it is easier to spot non-linearity in a residual plot than in the original scatter plot. This is usually because of the scales of the two plots: the residual plot allows us to zoom in on the errors and hence makes it easier to spot patterns."
]
},
{
"cell_type": "markdown",
"id": "4545066c",
"metadata": {},
"source": [
"\n",
"\n",
"Our data are a [dataset](http://www.statsci.org/data/oz/dugongs.html) on the age and length of dugongs, which are marine mammals related to manatees and sea cows (image from [Wikimedia Commons](https://commons.wikimedia.org/wiki/File:Dugong_dugon.jpg)). The data are in a table called `dugong`. Age is measured in years and length in meters. Because dugongs tend not to keep track of their birthdays, ages are estimated based on variables such as the condition of their teeth."
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "fe657097",
"metadata": {
"execution": {
"iopub.execute_input": "2026-08-31T06:02:11.389526Z",
"iopub.status.busy": "2026-08-31T06:02:11.389456Z",
"iopub.status.idle": "2026-08-31T06:02:11.393768Z",
"shell.execute_reply": "2026-08-31T06:02:11.393574Z"
},
"scrolled": true,
"tags": []
},
"outputs": [
{
"data": {
"text/html": [
"
\n",
"\n",
"
\n",
" \n",
"
\n",
"
\n",
"
Length
\n",
"
Age
\n",
"
\n",
" \n",
" \n",
"
\n",
"
0
\n",
"
1.80
\n",
"
1.0
\n",
"
\n",
"
\n",
"
1
\n",
"
1.85
\n",
"
1.5
\n",
"
\n",
"
\n",
"
2
\n",
"
1.87
\n",
"
1.5
\n",
"
\n",
"
\n",
"
3
\n",
"
1.77
\n",
"
1.5
\n",
"
\n",
"
\n",
"
4
\n",
"
2.02
\n",
"
2.5
\n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" Length Age\n",
"0 1.80 1.0\n",
"1 1.85 1.5\n",
"2 1.87 1.5\n",
"3 1.77 1.5\n",
"4 2.02 2.5"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"def move_to_front(df, col_name):\n",
" return df[[col_name] + [c for c in df.columns if c != col_name]]\n",
"\n",
"dugong = pd.read_csv(path_data + 'dugongs.csv')\n",
"dugong = move_to_front(dugong, 'Length')\n",
"dugong.head()"
]
},
{
"cell_type": "markdown",
"id": "7baef319",
"metadata": {},
"source": [
"If we could measure the length of a dugong, what could we say about its age? Let's examine what our data say. Here is a regression of age (the response) on length (the predictor). The correlation between the two variables is substantial, at 0.83."
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "a11e493b",
"metadata": {
"execution": {
"iopub.execute_input": "2026-08-31T06:02:11.394738Z",
"iopub.status.busy": "2026-08-31T06:02:11.394680Z",
"iopub.status.idle": "2026-08-31T06:02:11.396642Z",
"shell.execute_reply": "2026-08-31T06:02:11.396456Z"
},
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
"0.8296474554905714"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"correlation(dugong, 'Length', 'Age').item()"
]
},
{
"cell_type": "markdown",
"id": "ba3dc089",
"metadata": {},
"source": [
"High correlation notwithstanding, the plot shows a curved pattern that is much more visible in the residual plot."
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "c62c5769",
"metadata": {
"execution": {
"iopub.execute_input": "2026-08-31T06:02:11.397636Z",
"iopub.status.busy": "2026-08-31T06:02:11.397580Z",
"iopub.status.idle": "2026-08-31T06:02:11.451295Z",
"shell.execute_reply": "2026-08-31T06:02:11.451072Z"
},
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": "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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": "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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"regression_diagnostic_plots(dugong, 'Length', 'Age')"
]
},
{
"cell_type": "markdown",
"id": "fdd2f9a8",
"metadata": {},
"source": [
"While you can spot the non-linearity in the original scatter, it is more clearly evident in the residual plot.\n",
"\n",
"At the low end of the lengths, the residuals are almost all positive; then they are almost all negative; then positive again at the high end of lengths. In other words the regression estimates have a pattern of being too low, then too high, then too low. That means it would have been better to use a curve instead of a straight line to estimate the ages.\n",
"\n",
"**When a residual plot shows a pattern, there may be a non-linear relation between the variables.**"
]
},
{
"cell_type": "markdown",
"id": "e7312731",
"metadata": {},
"source": [
"## Detecting Heteroscedasticity\n",
"\n",
"*Heteroscedasticity* is a word that will surely be of interest to those who are preparing for Spelling Bees. For data scientists, its interest lies in its meaning, which is \"uneven spread\". \n",
"\n",
"Recall the table `hybrid` that contains data on hybrid cars in the U.S. Here is a regression of fuel efficiency on the rate of acceleration. The association is negative: cars that accelearate quickly tend to be less efficient."
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "93b36413",
"metadata": {
"execution": {
"iopub.execute_input": "2026-08-31T06:02:11.452397Z",
"iopub.status.busy": "2026-08-31T06:02:11.452324Z",
"iopub.status.idle": "2026-08-31T06:02:11.503272Z",
"shell.execute_reply": "2026-08-31T06:02:11.503031Z"
},
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": "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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": "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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"regression_diagnostic_plots(hybrid, 'acceleration', 'mpg')"
]
},
{
"cell_type": "markdown",
"id": "7cf3a143",
"metadata": {},
"source": [
"Notice how the residual plot flares out towards the low end of the accelerations. In other words, the variability in the size of the errors is greater for low values of acceleration than for high values. Uneven variation is often more easily noticed in a residual plot than in the original scatter plot.\n",
"\n",
"**If the residual plot shows uneven variation about the horizontal line at 0, the regression estimates are not equally accurate across the range of the predictor variable.**"
]
},
{
"cell_type": "markdown",
"id": "cell-600eb59a",
"metadata": {},
"source": [
"\n",
"## Section Practice\n",
"\n",
"Use this short exercise to check the main workflow from this section.\n"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "cell-4e72cd65",
"metadata": {
"execution": {
"iopub.execute_input": "2026-08-31T06:02:11.504484Z",
"iopub.status.busy": "2026-08-31T06:02:11.504412Z",
"iopub.status.idle": "2026-08-31T06:02:11.505896Z",
"shell.execute_reply": "2026-08-31T06:02:11.505709Z"
},
"tags": [
"thebe-interactive"
]
},
"outputs": [],
"source": [
"### Exercise: Practice Visual Diagnostics\n",
"# A delivery company fits a regression line of delivery cost on distance.\n",
"# 1. Fit the line (slope and intercept from r and the SDs) and compute the residuals.\n",
"# 2. Draw a residual plot: distance on the x-axis, residual on the y-axis, with a\n",
"# horizontal line at 0.\n",
"# 3. Describe the pattern: is it curved, or does the spread change?\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"distance = np.array([2, 4, 6, 8, 10, 12, 14, 16, 18, 20])\n",
"cost = np.array([9, 11, 12, 16, 15, 22, 18, 30, 21, 36])\n",
"### Your code starts here\n",
"\n",
"\n",
"\n",
"\n",
"### Your code ends here\n"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "cell-03fdcc7c",
"metadata": {
"execution": {
"iopub.execute_input": "2026-08-31T06:02:11.506843Z",
"iopub.status.busy": "2026-08-31T06:02:11.506783Z",
"iopub.status.idle": "2026-08-31T06:02:11.508372Z",
"shell.execute_reply": "2026-08-31T06:02:11.508140Z"
},
"tags": [
"hide-input"
]
},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "",
"image/png": "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"
}
},
{
"output_type": "stream",
"name": "stdout",
"text": "Residuals: [ 1.3 0.8 -0.7 0.8 -2.7 1.7 -4.8 4.7 -6.8 5.7]\n"
}
],
"source": [
"### Solution\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"distance = np.array([2, 4, 6, 8, 10, 12, 14, 16, 18, 20])\n",
"cost = np.array([9, 11, 12, 16, 15, 22, 18, 30, 21, 36])\n",
"\n",
"r = np.corrcoef(distance, cost)[0, 1]\n",
"slope = r * np.std(cost) / np.std(distance)\n",
"intercept = np.mean(cost) - slope * np.mean(distance)\n",
"residuals = cost - (slope * distance + intercept)\n",
"\n",
"fig, ax = plt.subplots(figsize=(5, 3))\n",
"ax.scatter(distance, residuals)\n",
"ax.axhline(0, color='gray')\n",
"ax.set_xlabel('Distance (km)')\n",
"ax.set_ylabel('Residual ($)')\n",
"plt.show()\n",
"\n",
"print('Residuals:', residuals.round(1))\n",
"# The residuals fan out as distance grows (heteroscedasticity): predictions for\n",
"# long deliveries are much less precise than for short ones.\n"
]
}
],
"metadata": {
"celltoolbar": "Tags",
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"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": "3.13.13"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
![](\"https://upload.wikimedia.org/wikipedia/commons/7/75/Dugong_dugon.jpg\"/)
\n",
"\n",
"Our data are a [dataset](http://www.statsci.org/data/oz/dugongs.html) on the age and length of dugongs, which are marine mammals related to manatees and sea cows (image from [Wikimedia Commons](https://commons.wikimedia.org/wiki/File:Dugong_dugon.jpg)). The data are in a table called `dugong`. Age is measured in years and length in meters. Because dugongs tend not to keep track of their birthdays, ages are estimated based on variables such as the condition of their teeth."
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "fe657097",
"metadata": {
"execution": {
"iopub.execute_input": "2026-08-31T06:02:11.389526Z",
"iopub.status.busy": "2026-08-31T06:02:11.389456Z",
"iopub.status.idle": "2026-08-31T06:02:11.393768Z",
"shell.execute_reply": "2026-08-31T06:02:11.393574Z"
},
"scrolled": true,
"tags": []
},
"outputs": [
{
"data": {
"text/html": [
"