Algebra
Data and statistics
Line of best fit
20 practice questions
2 video lessons
Theory + worked examples
Theory
The line of best fit (trend line) is the straight line that stays as close as possible to the data points.
Use it to predict \(y\) from \(x\); its slope is the rate of change.
A line modeling the trend.
The line of best fit.
A best-fit model:
\[y=mx+b\]
Predict by substituting an \(x\)-value.
How to use a line of best fit
- Draw or compute the trend line.
- Read its equation \(y=mx+b\).
- Substitute to predict.
- Interpret the slope and intercept.
Example 1 — Use the model
A best-fit line is \(y=0.9x+1\). Predict \(y\) at \(x=10\).
Solution
Substitute.
| \(y\) | \(=\) | \(0.9(10)+1=10\) |
Example 2 — Slope meaning
In \(y=0.9x+1\), what does \(0.9\) represent?
Solution
The rate of change per unit \(x\).
Example 3 — Fit quality
When does a line fit the data well?
Solution
When the points cluster closely around it.
Example 4 — Interpolate vs extrapolate
Is predicting inside the data range safer?
Solution
Yes — interpolation is more reliable than extrapolation.
Common pitfalls
Extrapolation is uncertain far from the data.
A trend line is a model, not exact for every point.
Balance the points above and below the line.
Frequently asked questions
What is the line of best fit?
A line that models the trend in scatter data.
What is it used for?
Making predictions from the data.
What does its slope mean?
The rate of change of the trend.
Is prediction outside the data reliable?
Less so — extrapolation is uncertain.
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