Key takeaway: A line of best fit is the straight trend line cutting through the middle of a cloud of dots, with similar numbers of dots on each side and small gaps overall.
Grade 88.SP.A.2Statistics and Data
Definition of Line of Best Fit
A line of best fit sums up a straight-line pattern in plotted data, and some books call it a trend line. It will not touch every point; instead it runs through the middle of the data so that the points are balanced above and below and the gaps are small.
Once you have the line, you can write its equation, describe the relationship in words, and make predictions for values that are not in the data. Predictions are trustworthy inside the range of the data and risky far outside it. The steeper the line, the faster the output changes as the input grows.
Formula and notation
The trend line is written like any linear equation:
\[y = mx + b\]
Here \(m\) tells how much the output climbs for each extra input unit, and \(b\) is where the line meets the vertical axis. Choose two points on the line (they need not be data points) and divide rise by run to get \(m\).
Key facts
- A line of best fit matches the trend; it need not pass through any data point.
- The slope tells the average change in y for each increase of 1 in x.
- Use it to predict inside the data range with more confidence than outside it.
- Strong linear patterns have points hugging the line closely.
Line of Best Fit example
Maya’s bike-ride data lie close to a line that passes through (10, 2.6) and (40, 8.6), where \(x\) is minutes ridden and \(y\) is miles. Write the equation, interpret the slope, and predict the distance after 55 minutes.
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Slope: \(m = \frac{8.6 – 2.6}{40 – 10} = \frac{6}{30} = 0.2\) mile per minute.
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Intercept: \(2.6 = 0.2(10) + b\), so \(b = 0.6\). The line is \(y = 0.2x + 0.6\).
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Predict at \(x = 55\): \(y = 0.2(55) + 0.6 = 11.6\).
Maya rides about 0.2 mile per minute, and the model predicts 11.6 miles after 55 minutes.
Common mistake
Watch out
Told that the equation is \(y = 0.2x + 0.6\), Ravi says that Maya rides 0.6 mile for every minute and starts with 0.2 mile.
Why it is wrong
He swapped the roles. The number multiplying \(x\) is the slope: 0.2 mile per minute, the rate. The constant 0.6 is the intercept, the predicted distance at 0 minutes. Read each number from its position in \(y = mx + b\).
Related terms and lessons
Browse the glossary: A–Z list · Grade 8 vocabulary · Statistics and Data