Each experimental point carries a small random error. A best-fit line smooths these errors to show the underlying relationship, while joining every dot would record the errors as though they were real.
This lesson is part of uncertainty and practical-data reasoning. It builds on plotting a graph with appropriate scale and units.
What makes a good best-fit line?
Check these three things.
- One line: a single straight line or smooth curve, not a chain of segments.
- Balance: roughly equal numbers of points above and below it.
- Closeness: the points lie near it, with no pattern of long runs on one side.
Worked example: a resistor
An original experiment measures the current I through a resistor and the potential difference V across it.
| I (A) | 0.10 | 0.20 | 0.30 | 0.40 | 0.50 |
|---|---|---|---|---|---|
| V (V) | 0.52 | 0.98 | 1.53 | 2.01 | 2.47 |
The points lie close to a straight line but not exactly on it. Draw one best-fit line. Suppose it passes through (0.10, 0.50) and (0.50, 2.46).
Gradient = (2.46 − 0.50) ÷ (0.50 − 0.10) = 1.96 ÷ 0.40 = 4.9 Ω.
The gradient of a V-I graph is the resistance, so the resistor is about 4.9 Ω.
Why joining the dots fails
A zigzag line through all five dots has different gradients for each section, such as (0.98 − 0.52) ÷ 0.10 = 4.6 Ω and (1.53 − 0.98) ÷ 0.10 = 5.5 Ω. These two values differ because of small reading errors, not because the resistance changes.
A single best-fit line gives one value for the whole range, which is the quantity the experiment is designed to find.
The mistake that costs marks
The common slip is a vague explanation such as “because the line must be straight”. A marker wants the reason.
| Answer | Verdict |
|---|---|
| “Because the line should be straight.” | Weak: no reason |
| “The points scatter because of random errors in reading, so one best-fit line gives the underlying trend and a consistent gradient.” | Strong: gives cause and effect |
Check yourself
A student joins all the dots on a V-I graph with a zigzag line and reads the gradient from the steepest part. Give two reasons this is wrong and describe the correct line.
Answer
Reason 1: the scatter is caused by random errors in measurement, so the zigzag records errors rather than the true relationship.
Reason 2: the gradient changes from section to section, and a gradient from the steepest part over-estimates the resistance.
The correct line is one straight best-fit line with about equal numbers of points on each side, and the gradient is found from a large triangle on that line.
What to study next
Continue with identifying a systematic offset from a supplied calibration example. The graph evidence and fair-comparison lab lets you practise drawing lines.
If you want a teacher to check your best-fit lines and explanations, see online one-to-one Physics tuition.