How to overplot a line on a scatter plot in python?

I’m partial to scikits.statsmodels. Here an example:

import statsmodels.api as sm
import numpy as np
import matplotlib.pyplot as plt

X = np.random.rand(100)
Y = X + np.random.rand(100)*0.1

results = sm.OLS(Y,sm.add_constant(X)).fit()

print(results.summary())

plt.scatter(X,Y)

X_plot = np.linspace(0,1,100)
plt.plot(X_plot, X_plot * results.params[1] + results.params[0])

plt.show()

The only tricky part is sm.add_constant(X) which adds a columns of ones to X in order to get an intercept term.

     Summary of Regression Results
=======================================
| Dependent Variable:            ['y']|
| Model:                           OLS|
| Method:                Least Squares|
| Date:               Sat, 28 Sep 2013|
| Time:                       09:22:59|
| # obs:                         100.0|
| Df residuals:                   98.0|
| Df model:                        1.0|
==============================================================================
|                   coefficient     std. error    t-statistic          prob. |
------------------------------------------------------------------------------
| x1                      1.007       0.008466       118.9032         0.0000 |
| const                 0.05165       0.005138        10.0515         0.0000 |
==============================================================================
|                          Models stats                      Residual stats  |
------------------------------------------------------------------------------
| R-squared:                     0.9931   Durbin-Watson:              1.484  |
| Adjusted R-squared:            0.9930   Omnibus:                    12.16  |
| F-statistic:                1.414e+04   Prob(Omnibus):           0.002294  |
| Prob (F-statistic):        9.137e-108   JB:                        0.6818  |
| Log likelihood:                 223.8   Prob(JB):                  0.7111  |
| AIC criterion:                 -443.7   Skew:                     -0.2064  |
| BIC criterion:                 -438.5   Kurtosis:                   2.048  |
------------------------------------------------------------------------------

Another way to do it, using axes.get_xlim():

import matplotlib.pyplot as plt
import numpy as np

def scatter_plot_with_correlation_line(x, y, graph_filepath):
    '''
    http://stackoverflow.com/a/34571821/395857
    x does not have to be ordered.
    '''
    # Create scatter plot
    plt.scatter(x, y)

    # Add correlation line
    axes = plt.gca()
    m, b = np.polyfit(x, y, 1)
    X_plot = np.linspace(axes.get_xlim()[0],axes.get_xlim()[1],100)
    plt.plot(X_plot, m*X_plot + b, '-')

    # Save figure
    plt.savefig(graph_filepath, dpi=300, format='png', bbox_inches='tight')

def main():
    # Data
    x = np.random.rand(100)
    y = x + np.random.rand(100)*0.1

    # Plot
    scatter_plot_with_correlation_line(x, y, 'scatter_plot.png')

if __name__ == "__main__":
    main()
    #cProfile.run('main()') # if you want to do some profiling

A one-line version of this excellent answer to plot the line of best fit is:

plt.plot(np.unique(x), np.poly1d(np.polyfit(x, y, 1))(np.unique(x)))

Using np.unique(x) instead of x handles the case where x isn’t sorted or has duplicate values.

The call to poly1d is an alternative to writing out m*x + b like in this other excellent answer.

plt.plot(X_plot, X_plot*results.params[0] + results.params[1])

versus

plt.plot(X_plot, X_plot*results.params[1] + results.params[0])

I like Seaborn’s regplot or lmplot for this:

To achieve this, do:

import numpy as np
import seaborn as sns

N = 100
x = np.random.rand(N)
y = 3 * x + np.random.rand(N)
sns.regplot(x=x, y=y)

You can use this tutorial by Adarsh Menon https://towardsdatascience.com/linear-regression-in-6-lines-of-python-5e1d0cd05b8d

This way is the easiest I found and it basically looks like:

import numpy as np
import matplotlib.pyplot as plt  # To visualize
import pandas as pd  # To read data
from sklearn.linear_model import LinearRegression
data = pd.read_csv('data.csv')  # load data set
X = data.iloc[:, 0].values.reshape(-1, 1)  # values converts it into a numpy array
Y = data.iloc[:, 1].values.reshape(-1, 1)  # -1 means that calculate the dimension of rows, but have 1 column
linear_regressor = LinearRegression()  # create object for the class
linear_regressor.fit(X, Y)  # perform linear regression
Y_pred = linear_regressor.predict(X)  # make predictions
plt.scatter(X, Y)
plt.plot(X, Y_pred, color='red')
plt.show()

New in matplotlib 3.3

Use the new plt.axline to plot y = m*x + b given the slope m and intercept b:

plt.axline(xy1=(0, b), slope=m)

Example of plt.axline with np.polyfit :

import numpy as np
import matplotlib.pyplot as plt

# generate random vectors
rng = np.random.default_rng(0)
x = rng.random(100)
y = 5*x + rng.rayleigh(1, x.shape)
plt.scatter(x, y, alpha=0.5)

# compute slope m and intercept b
m, b = np.polyfit(x, y, deg=1)

# plot fitted y = m*x + b
plt.axline(xy1=(0, b), slope=m, color='r', label=f'$y = {m:.2f}x {b:+.2f}$')

plt.legend()
plt.show()

Here the equation is a legend entry, but see how to rotate annotations to match lines if you want to plot the equation along the line itself.