Trend lines on scatter plots in Matplotlib - Step-by-Step Execution

Concept Flow - Trend lines on scatter plots

Start with data points

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Plot scatter points

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Calculate trend line coefficients

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Create line points using coefficients

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Plot trend line on scatter plot

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Show plot

We start with data points, plot them as a scatter plot, calculate the trend line, then draw it over the scatter plot.

Execution Sample

Matplotlib

import matplotlib.pyplot as plt
import numpy as np
x = np.array([1,2,3,4,5])
y = np.array([2,3,5,7,11])
plt.scatter(x, y)
coef = np.polyfit(x, y, 1)
plt.plot(x, coef[0]*x + coef[1])
plt.show()

This code plots points and draws a straight trend line fitting those points.

Execution Table

Step	Action	Variable/Expression	Result/Value
1	Create x array	x	[1 2 3 4 5]
2	Create y array	y	[2 3 5 7 11]
3	Plot scatter points	plt.scatter(x, y)	Scatter plot with 5 points
4	Calculate trend line coefficients	np.polyfit(x, y, 1)	coef = [2.2, -1.0]
5	Calculate trend line y values	coef[0]*x + coef[1]	[1.2 3.4 5.6 7.8 10. ]
6	Plot trend line	plt.plot(x, coef[0]*x + coef[1])	Line drawn over scatter
7	Show plot	plt.show()	Scatter plot with trend line displayed

💡 Plot displayed and execution ends

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 4	After Step 5	Final
x	undefined	[1 2 3 4 5]	[1 2 3 4 5]	[1 2 3 4 5]	[1 2 3 4 5]	[1 2 3 4 5]
y	undefined	undefined	[2 3 5 7 11]	[2 3 5 7 11]	[2 3 5 7 11]	[2 3 5 7 11]
coef	undefined	undefined	undefined	[2.2, -1.0]	[2.2, -1.0]	[2.2, -1.0]
trend_y	undefined	undefined	undefined	undefined	[1.2 3.4 5.6 7.8 10. ]	[1.2 3.4 5.6 7.8 10. ]

Key Moments - 3 Insights

Why does the trend line not pass through all scatter points exactly?

The trend line is a best fit line calculated by np.polyfit which minimizes overall distance, not necessarily passing through every point (see Step 4 and 5 in execution_table).

What do the two numbers in coef represent?

coef[0] is the slope (steepness) of the line, coef[1] is the intercept (where line crosses y-axis), shown in Step 4 of execution_table.

Why do we multiply coef[0] by x and add coef[1]?

This calculates y values on the trend line for each x, creating points to draw the line (Step 5 in execution_table).

Visual Quiz - 3 Questions

Look at the execution_table at Step 4, what does coef equal?

A [2.2, -1.0]

B [1, 0]

C [0, 1]

D [5, 11]

💡 Hint

Check the 'Result/Value' column at Step 4 in execution_table.

At which step do we calculate the y values for the trend line?

A Step 3

B Step 5

C Step 2

D Step 6

💡 Hint

Look for when coef[0]*x + coef[1] is computed in execution_table.

If we change the degree in np.polyfit from 1 to 2, what changes in the execution_table?

A Scatter points change

B x array changes

C coef will have 3 values instead of 2

D Plot will not show

💡 Hint

Think about polynomial degree and number of coefficients in Step 4.

Concept Snapshot

Trend lines on scatter plots:
- Use plt.scatter(x, y) to plot points
- Use np.polyfit(x, y, 1) to get line coefficients
- Calculate line y: slope*x + intercept
- Use plt.plot(x, line_y) to draw trend line
- Shows overall data trend visually

Full Transcript

We start with data points x and y. We plot these points as a scatter plot using plt.scatter. Then, we calculate the best fit line coefficients using np.polyfit with degree 1, which returns slope and intercept. Next, we compute y values on the trend line by multiplying slope with x and adding intercept. We plot this line over the scatter plot using plt.plot. Finally, we show the plot with plt.show. The trend line shows the general direction of the data but does not pass through all points exactly.