Fit a straight line with NumPy, calculate its y-values across the observed x-range, then draw it over the data using Matplotlib’s scatter and plot methods. The example below shows the complete workflow.
Plot the data and its line of best fit
Replace the example arrays with your paired observations. Each x value must correspond to the y value at the same position.
import numpy as np
import matplotlib.pyplot as plt
# Replace these example arrays with paired observations.
x = np.array([1, 2, 3, 4, 5], dtype=float)
y = np.array([2.1, 2.9, 3.7, 4.2, 5.1], dtype=float)
# Fit a first-degree polynomial: slope first, intercept second.
slope, intercept = np.polyfit(x, y, 1)
# Evaluate the fitted line across the observed x range.
x_fit = np.linspace(x.min(), x.max(), 100)
y_fit = slope * x_fit + intercept
fig, ax = plt.subplots()
ax.scatter(x, y, label="Observed data")
ax.plot(x_fit, y_fit, color="crimson", label="Line of best fit")
ax.set_xlabel("x")
ax.set_ylabel("y")
ax.legend()
ax.grid(True, alpha=0.3)
plt.show()np.polyfit(x, y, 1) performs a degree-one polynomial least-squares fit. The returned values are the slope and intercept, so the fitted equation is y = slope * x + intercept. NumPy documents the fitting function in its numpy.polyfit reference.
The calculation and drawing are separate steps: first estimate the coefficients, then evaluate the equation at x-coordinates and plot those results. np.linspace supplies evenly spaced positions for a clean line segment; it does not change the fit.
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Why use scatter for the observations and plot for the fit?
ax.scatter(x, y) displays the individual observed pairs as markers. ax.plot(x_fit, y_fit) draws the fitted values as a line. Plotting the fitted values against the original observations in their input order can create an awkward zigzag if the x-values are unsorted. Using coordinates from x.min() through x.max() draws the line across the data’s observed interval.
Matplotlib’s documentation covers scatter plots and the plot function. The example labels each artist and adds axis labels and a legend so readers can distinguish observations from the estimated line. These presentation choices do not validate the statistical model.
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Use the Axes interface for explicit plots
The example creates a figure and axes with fig, ax = plt.subplots(), then calls plotting methods on ax. This object-oriented interface makes it clear which axes receive the points and line, and is easier to extend when a figure has multiple plots. Matplotlib describes the Axes interface and pyplot interface; state-based calls such as plt.scatter(...) and plt.plot(...) can be convenient for short interactive snippets.
Check the fit and handle common problems
- Unequal array lengths: Confirm that
xandycontain the same number of corresponding observations. - Non-numeric or unusable values: Check the input arrays before fitting; the least-squares calculation needs usable numerical data.
- No variation in x: If every x-value is the same, the data do not identify a meaningful slope. Review the inputs rather than interpreting the result as a useful fitted line.
- Numerically difficult inputs: NumPy’s
polyfitreference discusses conditioning and points readers toPolynomial.fitas an alternative to consider for new code. The concisepolyfitexample is suitable for ordinary, well-scaled educational data, but difficult numerical cases call for a deliberate choice of fitting method. - Outliers or a non-linear pattern: Ordinary least squares minimizes squared residuals in the response variable; it is not automatically robust to outliers, nor does a straight-line fit suit every relationship.
Style the line and interpret it carefully
Change the line’s appearance with options such as color, linestyle, and linewidth in ax.plot. Marker appearance is controlled separately by ax.scatter. Keep the line within the observed x-range unless there is a specific reason to display extrapolated values: a visual overlay alone does not show that the relationship is linear, establish causation, or demonstrate that predictions beyond the data are reliable.
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