A line of best fit runs through the middle of a cloud of points, as close to as many as possible.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
It need not touch any point
The line summarises the trend. Passing exactly through two points is usually a worse fit.
The slope means something
On a height-against-age plot, a slope of 5 says about 5 cm gained per year.
Do not predict too far
The trend holds over the range of the data. Extending it to age 80 would predict nonsense.
A line through the cloud
A line of best fit summarises a linear trend with a single straight line. It will not pass through most of the points; it passes near as many as possible, with roughly as many above as below.
The slope has a meaning
For height against age, the slope is centimetres of growth per year. Interpreting the slope in the context's units is the most informative thing you can say about a fitted line — more so than the equation itself.
The intercept may be meaningless
For a line fitted to adult heights against ages, the value at age zero is nonsense. An intercept only means something if x = 0 is inside or near the range of the data. Reporting it regardless is a common misuse.
Predicting beyond the data
Using a fitted line far outside the range of the observations is extrapolation, and it is unreliable. A growth trend fitted to childhood data predicts implausible adult heights. The line describes the data you have, not the world in general.
Step 2: Try It Yourself
Adjust the line and judge it against the points.
The slope is 2: for every 1 across, the line goes 2 up.
Step 3: Watch an Example
One step at a time.
Watch Ana Read a Slope
A line of best fit on a height-against-age plot has slope 6.
- Step 1
The x axis is age in years and the y axis is height in centimetres.
Step 4: Your Turn
Practice makes it stick.
The Prediction
Problem 1 of 2
A line of best fit is y = 3x + 5. What is y when x is 4?
The Starting Value
Problem 2 of 2
Same line. What is y when x is 0?
Fit and Interpret
1 of 4
y = 2x + 1. What is y at x = 6?
2 of 4
Must a line of best fit pass through a data point? 1 for yes, 0 for no.
3 of 4
A slope of 4 on a cost-against-items plot. Cost per item?
4 of 4
Is predicting far outside the data reliable? 1 for yes, 0 for no.
Step 5: Quick Check
Show what you know.
Question 1 of 1
y = 5x + 2. What is y at x = 3?
What You Learned
- A line of best fit runs through the middle of the points, not through any particular one.
- Its slope describes how one quantity changes with the other.
- Predictions are only trustworthy across the range of the data.