I was working on a project where I had to analyze sales data for a retail chain in the USA. The challenge was to find a way to represent the trend in the data clearly.
While plotting the raw data points was easy, what I really needed was a smooth curve that best represented the overall trend. This is where the concept of a best fit curve in Matplotlib came into play.
In this tutorial, I’ll show you multiple ways to create a best-fit curve in Python using Matplotlib. I’ll explain each method step by step, with full code examples, so you can easily follow along.
What is a Best Fit Curve?
A best-fit curve is a line or curve that approximates the trend of data points in a dataset. It doesn’t pass through every point but tries to minimize the overall error.
In Python, we can generate best-fit curves using libraries like NumPy, SciPy, and Matplotlib. These tools make it simple to fit linear, polynomial, or even non-linear curves.
Method 1 – Best Fit Line Using Python NumPy Polyfit
The simplest way to create a best-fit curve is by using Python numpy.polyfit(). This method works great when you want a straight line or a polynomial curve.
Here’s a step-by-step example.
import numpy as np
import matplotlib.pyplot as plt
# Example dataset: Monthly sales numbers for a US retail store
months = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12])
sales = np.array([120, 150, 170, 200, 210, 250, 300, 280, 320, 330, 360, 400])
# Fit a linear trend line (degree = 1)
coefficients = np.polyfit(months, sales, 1)
polynomial = np.poly1d(coefficients)
# Generate y-values for the best fit line
best_fit_line = polynomial(months)
# Plotting
plt.scatter(months, sales, color='blue', label='Actual Sales')
plt.plot(months, best_fit_line, color='red', label='Best Fit Line')
plt.xlabel("Month")
plt.ylabel("Sales (in $1000s)")
plt.title("Monthly Sales Trend - Best Fit Line")
plt.legend()
plt.show()You can see the output in the screenshot below.
In this example, I used polyfit with degree 1 to create a straight line. The red line shows the best fit curve, while the blue points represent the actual sales data.
Method 2 – Polynomial Best Fit Curve
Sometimes, the data doesn’t follow a straight line. In that case, we can fit a polynomial curve of a higher degree.
Here’s how you can do it.
import numpy as np
import matplotlib.pyplot as plt
# Example dataset: Average temperature over 12 months in New York
months = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12])
temperature = np.array([30, 32, 40, 55, 65, 75, 80, 78, 70, 58, 48, 35])
# Fit a polynomial curve (degree = 3)
coefficients = np.polyfit(months, temperature, 3)
polynomial = np.poly1d(coefficients)
# Generate smooth x values for curve
x_smooth = np.linspace(1, 12, 100)
y_smooth = polynomial(x_smooth)
# Plotting
plt.scatter(months, temperature, color='blue', label='Actual Temperature')
plt.plot(x_smooth, y_smooth, color='green', label='Best Fit Curve (Polynomial)')
plt.xlabel("Month")
plt.ylabel("Temperature (°F)")
plt.title("Average Monthly Temperature in New York")
plt.legend()
plt.show()You can see the output in the screenshot below.
Here, I used a degree 3 polynomial to fit the temperature data. The curve follows the seasonal pattern much more closely than a straight line would.
Method 3 – Nonlinear Curve Fitting with Python SciPy
If your data follows a nonlinear pattern, you can use Python scipy.optimize.curve_fit() to define a custom function and fit it.
Let me show you with an example.
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
# Example dataset: Population growth in a US city
years = np.array([2000, 2005, 2010, 2015, 2020])
population = np.array([2.5, 2.9, 3.6, 4.5, 5.2]) # in millions
# Define an exponential growth function
def growth(x, a, b):
return a * np.exp(b * (x - 2000))
# Fit the curve
params, _ = curve_fit(growth, years, population)
# Generate smooth curve
x_smooth = np.linspace(2000, 2020, 100)
y_smooth = growth(x_smooth, *params)
# Plotting
plt.scatter(years, population, color='blue', label='Actual Population')
plt.plot(x_smooth, y_smooth, color='orange', label='Best Fit Curve (Exponential)')
plt.xlabel("Year")
plt.ylabel("Population (millions)")
plt.title("Population Growth in US City")
plt.legend()
plt.show()You can see the output in the screenshot below.
In this case, I defined an exponential growth function to fit the population data. The resulting curve matches the growth trend very well.
Method 4 – Best Fit Curve with Python Seaborn
Another quick way to plot a best-fit curve is by using Python Seaborn, which is built on top of Matplotlib.
Here’s an example.
import seaborn as sns
import matplotlib.pyplot as plt
# Example dataset: Advertising budget vs sales revenue
budget = [10, 15, 20, 25, 30, 35, 40, 45]
revenue = [25, 28, 35, 40, 42, 50, 52, 60]
# Seaborn regression plot
sns.regplot(x=budget, y=revenue, ci=None, scatter_kws={"color": "blue"}, line_kws={"color": "red"})
plt.xlabel("Advertising Budget ($1000s)")
plt.ylabel("Revenue ($1000s)")
plt.title("Advertising Budget vs Revenue")
plt.show()With just one line of code (sns.regplot), Seaborn automatically fits a regression line. This is the fastest method when you need a quick visualization without much customization.
Choose the Right Method
- Use NumPy polyfit for linear or polynomial trends.
- Use SciPy curve_fit when you need custom nonlinear models.
- Use Seaborn regplot for quick regression visualizations.
Each method has its strengths, and the right choice depends on your dataset and the type of relationship you expect.
Key Takeaways
- A best-fit curve helps reveal trends in your data.
- Matplotlib works seamlessly with NumPy, SciPy, and Seaborn to create these curves.
- Always choose the curve type that best matches your dataset’s behavior.
Creating a best-fit curve in Matplotlib is one of those tasks I find myself doing often. Whether it’s sales forecasting, analyzing temperature data, or modeling population growth, the ability to visualize trends makes decision-making much easier.
While there are multiple methods to achieve this, I recommend starting with numpy.polyfit for simple cases and moving to curve_fit for more complex models.
You may also read other matplotlib articles:
- Plot Multiple Lines in Subplots Using Matplotlib
- Plot Multiple Lines of Different Lengths in Matplotlib
- Make a Multiline Plot from CSV File in Matplotlib
- Plot a Histogram in Python using Matplotlib
Bijay Kumar is an experienced Python and AI professional who enjoys helping developers learn modern technologies through practical tutorials and examples. His expertise includes Python development, Machine Learning, Artificial Intelligence, automation, and data analysis using libraries like Pandas, NumPy, TensorFlow, Matplotlib, SciPy, and Scikit-Learn. At PythonGuides.com, he shares in-depth guides designed for both beginners and experienced developers. More about us.
