Line of Best Fit
In short: A line of best fit is the straight line threaded through the middle of a cloud of plotted dots, following the trend closely enough to make predictions.
8th GradeStatistics8.SP.A.2
What is Line of Best Fit?
When dots on a graph climb or fall in a roughly straight band, a line of best fit sums up the trend with one line, placed so that about as many dots lie above it as below it and none are dragged far away.
The line is only a model: it rarely touches every dot. Its equation \(y = mx + b\) has a slope \(m\), the predicted rise in y whenever x grows by one, and an intercept \(b\), the predicted y at \(x = 0\).
How to spot it
- A scatter plot shows dots that cluster around a straight, tilted band.
- The question asks you to predict a value that is not in the data table.
- You are given an equation like \(y = 1.2x + 2\) built from real measurements and asked what the numbers mean.
- The wording mentions trend line, model, fits the data or estimated value.
The method
- Plot the data and check that the dots follow a roughly straight trend.
- Lay a ruler so the line of best fit runs through the middle of the cloud, with similar numbers of dots above and below.
- Pick two points on your line (not necessarily data points) and compute the slope, then read the y-intercept.
- Write \(y = mx + b\), and plug in an x-value to predict y; stay close to the range of the data.
Line of Best Fit: solved example
Problem
A drone pilot’s line of best fit for battery power is \(y = -2.4x + 96\), where x is minutes flown and y is percent of charge left. Interpret the slope and intercept, then predict the charge after 15 minutes and the flight time until empty.
Solution
The slope \(-2.4\) means the battery loses 2.4 percentage points every minute. The intercept 96 means the model starts at 96% charge.
At \(x = 15\): \(y = -2.4(15) + 96 = 60\), so 60% remains. Empty means \(y = 0\): \(2.4x = 96\), so \(x = 40\) minutes.
Try it
Question 1
A trend line is \(y = 0.8x + 12\). Predict y when \(x = 25\).
Show the answer
\(0.8(25) + 12 = 20 + 12 = 32\).
Question 2
Should the same trend line be trusted for \(x = 400\) if the data only cover x from 5 to 40?
Show the answer
No. Such an x is far beyond what was measured, so the answer would be a risky guess.
Line of Best Fit vs. Scatter Plot
The scatter plot is the picture of raw dots, one per observation. The trend line is a model added on top of it, a single line meant to describe all the dots together. You can draw the plot without any line, but the line has no meaning without the plot behind it.
Keep going
Lessons
Worksheets and quizzes
- Using Linear Models to Predict – Worksheet
- Using Linear Models to Predict – Quiz
- Scatter Plots, Lines of Fit and Two-Way Tables – Worksheet
- Scatter Plots, Lines of Fit and Two-Way Tables – Quiz
Related words
Whole dictionary: A–Z · 8th Grade · Statistics