How to Plot a Line of Best Fit in Python (Matplotlib)

To draw a line of best fit in Python with Matplotlib, calculate the slope and intercept with np.polyfit(x, y, 1), then plot slope * x + intercept on top of a scatter plot of the data. This matplotlib best fit line tutorial shows the full code, how to print the equation and R², how to get statistics with scipy.stats.linregress, how to draw a line from a known slope and intercept, curves of best fit, seaborn’s regplot, and what to do about missing values.

Tested with Python 3.12.5, Matplotlib 3.11.2, NumPy 2.5.3, SciPy 1.18.1 and seaborn 0.13.2. Charts are real Matplotlib windows and the numbers come from real runs in the Windows Command Prompt. References: numpy.polyfit, scipy.stats.linregress and Axes.axline.

Scatter plot with a line of best fit

A line of best fit (linear regression line) is the straight line that keeps the squared vertical distances to all points as small as possible. np.polyfit with degree 1 returns its slope and intercept:

import matplotlib.pyplot as plt
import numpy as np

# advertising spend (thousand USD) and sales (thousand units) for 12 months
ad_spend = np.array([2.1, 3.4, 4.0, 4.8, 5.5, 6.1, 6.9, 7.4, 8.2, 9.0, 9.6, 10.5])
sales = np.array([14.0, 17.9, 18.2, 22.5, 23.1, 26.8, 27.0, 30.9, 31.2, 35.8, 35.1, 39.6])

slope, intercept = np.polyfit(ad_spend, sales, 1)     # degree 1 = straight line

plt.scatter(ad_spend, sales, label="Monthly data")
plt.plot(ad_spend, slope * ad_spend + intercept, color="red", label="Line of best fit")
plt.xlabel("Advertising spend (thousand USD)")
plt.ylabel("Sales (thousand units)")
plt.legend()
plt.show()

Print the slope, intercept, equation and R²

The slope says how much y changes when x grows by 1; R² (0 to 1) says how much of the variation the line explains:

import numpy as np

# advertising spend (thousand USD) and sales (thousand units) for 12 months
ad_spend = np.array([2.1, 3.4, 4.0, 4.8, 5.5, 6.1, 6.9, 7.4, 8.2, 9.0, 9.6, 10.5])
sales = np.array([14.0, 17.9, 18.2, 22.5, 23.1, 26.8, 27.0, 30.9, 31.2, 35.8, 35.1, 39.6])

slope, intercept = np.polyfit(ad_spend, sales, 1)
predicted = slope * ad_spend + intercept
r_squared = 1 - np.sum((sales - predicted) ** 2) / np.sum((sales - sales.mean()) ** 2)

print(f"slope     = {slope:.3f}")
print(f"intercept = {intercept:.3f}")
print(f"equation  : y = {slope:.2f}x + {intercept:.2f}")
print(f"R squared = {r_squared:.4f}")
print(f"forecast for 12k spend: {slope * 12 + intercept:.1f} thousand units")

Output:

slope     = 3.030
intercept = 7.276
equation  : y = 3.03x + 7.28
R squared = 0.9842
forecast for 12k spend: 43.6 thousand units

Line of best fit with scipy.stats.linregress

linregress returns the same line plus the correlation coefficient r, the p-value and standard errors in one call:

import numpy as np
from scipy import stats

# advertising spend (thousand USD) and sales (thousand units) for 12 months
ad_spend = np.array([2.1, 3.4, 4.0, 4.8, 5.5, 6.1, 6.9, 7.4, 8.2, 9.0, 9.6, 10.5])
sales = np.array([14.0, 17.9, 18.2, 22.5, 23.1, 26.8, 27.0, 30.9, 31.2, 35.8, 35.1, 39.6])

result = stats.linregress(ad_spend, sales)

print(f"slope     = {result.slope:.3f}")
print(f"intercept = {result.intercept:.3f}")
print(f"r         = {result.rvalue:.4f}  (R squared = {result.rvalue ** 2:.4f})")
print(f"p-value   = {result.pvalue:.2e}")
print(f"std error = {result.stderr:.3f}")

Output:

slope     = 3.030
intercept = 7.276
r         = 0.9921  (R squared = 0.9842)
p-value   = 2.43e-10
std error = 0.121

Show the equation and R² on the plot

import matplotlib.pyplot as plt
import numpy as np
from scipy import stats

# advertising spend (thousand USD) and sales (thousand units) for 12 months
ad_spend = np.array([2.1, 3.4, 4.0, 4.8, 5.5, 6.1, 6.9, 7.4, 8.2, 9.0, 9.6, 10.5])
sales = np.array([14.0, 17.9, 18.2, 22.5, 23.1, 26.8, 27.0, 30.9, 31.2, 35.8, 35.1, 39.6])

res = stats.linregress(ad_spend, sales)
x_line = np.linspace(0, 11, 100)

fig, ax = plt.subplots(figsize=(7, 4.5))
ax.scatter(ad_spend, sales, color="tab:blue", zorder=3)
ax.plot(x_line, res.slope * x_line + res.intercept, color="tab:red",
        label=f"y = {res.slope:.2f}x + {res.intercept:.2f}   (R² = {res.rvalue ** 2:.3f})")
ax.set_xlabel("Advertising spend (thousand USD)")
ax.set_ylabel("Sales (thousand units)")
ax.legend(loc="upper left")
ax.grid(alpha=0.3)
plt.tight_layout()
plt.show()

Plot a line from a slope and intercept

If you already know the slope and intercept, you do not need x-values: ax.axline() (Matplotlib 3.3+) draws an infinite line through a point with a given slope, and it always reaches the edges of the plot:

import matplotlib.pyplot as plt

slope, intercept = 1.5, 2

fig, ax = plt.subplots(figsize=(6, 4.5))
ax.axline((0, intercept), slope=slope, color="purple", label="y = 1.5x + 2")   # infinite line
ax.axline((0, 0), slope=-0.5, color="gray", linestyle="--", label="y = -0.5x")
ax.set_xlim(-2, 6)
ax.set_ylim(-4, 12)
ax.axhline(0, color="black", linewidth=0.6)
ax.axvline(0, color="black", linewidth=0.6)
ax.legend()
plt.show()

Curve of best fit (polynomial)

When the points bend, fit a polynomial of higher degree. np.poly1d turns the coefficients into a function you can call:

import matplotlib.pyplot as plt
import numpy as np

hours = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8])
temperature = np.array([12.0, 14.8, 18.1, 20.2, 21.9, 22.4, 21.8, 20.1, 17.6])

coeffs = np.polyfit(hours, temperature, 2)        # degree 2 = parabola
curve = np.poly1d(coeffs)                          # callable polynomial
print("coefficients (a, b, c):", np.round(coeffs, 3))   # y = a*x**2 + b*x + c
print("temperature at 4.5 h:", round(curve(4.5), 1))

x = np.linspace(0, 8, 200)
plt.scatter(hours, temperature, label="Measured")
plt.plot(x, curve(x), color="darkorange", label="Curve of best fit (degree 2)")
plt.xlabel("Hours after 6 am")
plt.ylabel("Temperature (°C)")
plt.legend()
plt.show()

Output:

coefficients (a, b, c): [-0.442  4.333 11.449]
temperature at 4.5 h: 22.0

Best fit line with a confidence band in seaborn

seaborn’s regplot fits and draws the line in one call and shades a 95% confidence interval around it:

import matplotlib.pyplot as plt
import numpy as np
import seaborn as sns

# advertising spend (thousand USD) and sales (thousand units) for 12 months
ad_spend = np.array([2.1, 3.4, 4.0, 4.8, 5.5, 6.1, 6.9, 7.4, 8.2, 9.0, 9.6, 10.5])
sales = np.array([14.0, 17.9, 18.2, 22.5, 23.1, 26.8, 27.0, 30.9, 31.2, 35.8, 35.1, 39.6])

ax = sns.regplot(x=ad_spend, y=sales, ci=95, line_kws={"color": "red"})   # line + 95% confidence band
ax.set_xlabel("Advertising spend (thousand USD)")
ax.set_ylabel("Sales (thousand units)")
plt.show()

Missing values: np.polyfit returns nan

If x or y contains NaN, np.polyfit does not raise an error. It returns nan for the slope and intercept, and the line simply does not appear on the chart. Drop incomplete pairs first:

import numpy as np

x = np.array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0])
y = np.array([2.1, 3.9, np.nan, 8.2, 9.8, 12.1])   # one missing value

print("with NaN:   ", np.polyfit(x, y, 1))          # no error, just nan

ok = ~np.isnan(x) & ~np.isnan(y)                   # keep only complete pairs
print("NaN removed:", np.polyfit(x[ok], y[ok], 1))

Output:

with NaN:    [nan nan]
NaN removed: [1.99651163 0.03255814]

With pandas, df.dropna(subset=["x", "y"]) does the same.

Which method should you use?

Need	Use
Just the line on a chart	np.polyfit(x, y, 1)
r, p-value, standard errors	scipy.stats.linregress(x, y)
A line from a known slope and intercept	ax.axline((0, b), slope=m)
A curved trend	np.polyfit(x, y, 2) + np.poly1d
A quick chart with a confidence band	seaborn.regplot()

Related Matplotlib and NumPy tutorials:

• Plot a line in Matplotlib
• Plot multiple lines in Python
• Set the axis range in Matplotlib
• Change the title font size

Frequently asked questions