Mathematics › 📐 Grade 8 › Scatter Plots & the Line of Best Fit

Scatter Plots & the Line of Best Fit

Plot two measurements against each other and a pattern can leap off the page — even before you draw a single line through it.

Grade 8Statistics & Probability

Scatter Plots & the Line of Best Fit — illustration

💡

The big idea: When you measure two things about the same set of objects or people — hours studied and test score, height and shoe size, temperature and ice-cream sales — plotting one against the other on a scatter plot often reveals a pattern called an association. If the pattern is roughly straight, you can sketch a line through the cloud of points by eye and use that line's slope and intercept to describe the relationship and make rough predictions.

🎯 By the end, you'll be able to

Construct a scatter plot from paired (bivariate) measurement data
Describe an association as positive, negative, or none, and as linear or nonlinear, noting clusters and outliers
Fit a straight line to a linear association informally, by eye
Use the line's slope and intercept to make and interpret predictions in context

📎 You should already know

Plotting points on a coordinate plane
Slope-intercept form, y = mx + b

Two measurements, one plot

Suppose you record, for each student in a class, how many hours they studied and what score they got on a quiz. Each student gives you a pair of numbers. Plot every pair as a point — hours on the x-axis, score on the y-axis — and you get a scatter plot: a cloud of points that can reveal a relationship no single number ever could.

🔑 Describing the association

An association is the overall pattern the cloud of points makes. It can be positive (as x increases, y tends to increase), negative (as x increases, y tends to decrease), or show no association at all. A pattern can also be roughly linear (points hug a line) or nonlinear (points curve). Watch, too, for clusters — tight groups of points — and outliers, points that sit far from the rest of the pattern.

Reading the shape of the cloud

Before fitting anything, just look. Do the points trend upward, downward, or scatter with no trend? Do they hug a straight path, or bend like a curve? Is there one point way off to the side — an outlier — that doesn't fit the rest of the story? Naming the shape in words is often the most useful step, because it's the shape that tells you whether a straight line is even the right tool.

📝 Worked example: A scatter plot of hours of TV watched (x) versus hours of homework completed (y) shows points drifting from the upper-left down to the lower-right. Describe the association.

As x (TV hours) increases, the y-values (homework hours) tend to get smaller.
The points fall roughly along a straight downward path, with no obvious outliers.

✓ The association is negative and linear: more TV time is associated with less homework time.

⚠️ Association is not causation

A line through the points describes a pattern — it does not prove that x causes y. Ice-cream sales and drowning incidents both rise together in summer, but ice cream doesn't cause drownings; a third factor, hot weather, drives both. Whenever you describe an association from a scatter plot, resist the urge to claim one variable is causing the other.

Fitting a line by eye

When the association looks roughly linear, you can sketch a single straight line that seems to pass through the “middle” of the cloud — with about as many points above the line as below it. This is called a line of best fit, and at this stage you are drawing it informally, by eye: there is no single correct line, only a reasonable one that tracks the trend.

🎮 Line of Best Fit LIVE

Eyeball a line through the scattered points, then check how well it fits.

Using the line to predict

Once you have a line of best fit, it behaves like any line in slope-intercept form, y = mx + b. The slope tells you, in context, how much y tends to change for every one-unit increase in x. The intercept tells you the predicted y-value when x = 0. Reading a value off the line for an x you didn't directly measure is called interpolation, and it's only a reasonable prediction, not a certainty.

📝 Worked example: A line of best fit for hours studied (x) versus quiz score (y) is y = 5x + 60. Interpret the slope and predict the score for 4 hours of study.

The slope is 5, meaning each extra hour of study is associated with about 5 more points on the quiz.
The intercept 60 is the predicted score for a student who studied 0 hours.
Substitute x = 4: y = 5(4) + 60 = 20 + 60.

✓ The predicted score is 80. Each extra hour of study is associated with roughly 5 more marks — a description of the trend, not a guarantee for any one student.

✨ There's a more precise way — later

Fitting a line “by eye” is a reasonable start, but different people will sketch slightly different lines through the same cloud. The site's Statistics course picks this up formally: it defines the correlation coefficient to measure how tightly the points hug a line, uses residuals (the vertical gaps between each point and the line) to judge a fit's quality, and computes the single best possible line using the least-squares method. For now, focus on reading the pattern and sketching a sensible trend.

⚠️ Don't extrapolate too far

A line fit to data between, say, 0 and 10 hours of study shouldn't be trusted to predict a score at 50 hours — that's far outside the range you actually measured, and the real relationship may not stay linear that far out. Predictions are most trustworthy near the data you started with.

Check your understanding

1. A scatter plot shows that as a car's age increases, its resale value tends to decrease. What kind of association is this?

As one variable (age) increases while the other (value) tends to decrease, that is a negative association.

2. In a scatter plot, a single point sitting far away from the overall pattern of the other points is called a(n):

A point that doesn't fit the general trend of the rest of the data is an outlier.

3. A line of best fit for plant height (cm) versus weeks grown is y = 2x + 5. What does the slope of 2 mean in context?

The slope describes the rate of change: each additional week is associated with about 2 more centimetres of height.

4. Two variables show a strong positive linear association on a scatter plot. What can you correctly conclude?

Association describes a pattern, not a cause. A third factor could be driving both variables, or the link could be coincidental.

5. Why is a line of best fit at this stage drawn 'informally, by eye' rather than with a formula?

Grade 8 asks students to fit a line informally by judging the trend; the precise least-squares calculation and correlation coefficient are treated in a later, more formal course.

✅ Key takeaways

A scatter plot displays paired (bivariate) measurements as points, one axis per variable.
An association can be positive, negative, or none, and linear or nonlinear — watch for clusters and outliers too.
A line of best fit can be sketched informally, by eye, when the association looks roughly linear.
The line's slope and intercept describe the trend in context and support rough predictions.
Association is not causation, and predictions get shakier the further you stray from the data you actually measured.