**Problem Formulation:** How to plot the confidence interval in Python?

To plot a filled interval with the width `ci`

and interval boundaries from `y-ci`

to `y+ci`

around function values `y`

, use the `plt.fill_between(x, (y-ci), (y+ci), color='blue', alpha=0.1)`

function call on the Matplotlib `plt`

module.

- The first argument
`x`

defines the`x`

values of the filled curve. You can use the same values as for the original plot. - The second argument
`y-ci`

defines the lower interval boundary. - The third argument
`y+ci`

defines the upper interval boundary. - The fourth argument
`color='blue'`

defines the color of the shaded interval. - The fifth argument
`alpha=0.1`

defines the transparency to allow for layered intervals.

from matplotlib import pyplot as plt import numpy as np # Create the data set x = np.arange(0, 10, 0.05) y = np.sin(x) Define the confidence interval ci = 0.1 * np.std(y) / np.mean(y) # Plot the sinus function plt.plot(x, y) # Plot the confidence interval plt.fill_between(x, (y-ci), (y+ci), color='blue', alpha=0.1) plt.show()

You can also plot two layered confidence intervals by calling the `plt.fill_between()`

function twice with different interval boundaries:

from matplotlib import pyplot as plt import numpy as np # Create the data set x = np.arange(0, 10, 0.05) y = np.sin(x) # Define the confidence interval ci = 0.1 * np.std(y) / np.mean(y) # Plot the sinus function plt.plot(x, y) # Plot the confidence interval plt.fill_between(x, (y-ci), (y+ci), color='blue', alpha=0.1) plt.fill_between(x, (y-2*ci), (y+2*ci), color='yellow', alpha=.1) plt.show()

The resulting plot shows two confidence intervals in blue and yellow:

You can run this in our interactive Jupyter Notebook:

You can also use Seaborn’s regplot() function that does it for you, given a scattered data set of (x,y) tuples.

import numpy as np import seaborn as sns import matplotlib.pyplot as plt #create some random data x = np.random.randint(1, 10, 20) y = x + np.random.normal(0, 1, 20) #create regplot ax = sns.regplot(x, y)

This results in the convenient output:

Note that the 95% confidence interval is calculated automatically. An alternative third ci argument in the `sns.regplot(x, y, ci=80)`

allows you to define another confidence interval (e.g., 80%).

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**Resources**:

- https://matplotlib.org/3.1.1/api/_as_gen/matplotlib.pyplot.fill_between.html
- https://stackoverflow.com/questions/59747313/how-to-plot-confidence-interval-in-python
- https://www.statology.org/plot-confidence-interval-python/

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