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How do you use a scattergraph and a line of best fit to describe correlation and make predictions?

Drawing and interpreting scattergraphs, describing correlation, drawing a line of best fit, finding its equation and using it to estimate values.

A focused answer to the SQA National 5 Mathematics scattergraph content, covering plotting and interpreting scattergraphs, describing positive, negative and no correlation, drawing a line of best fit, finding its equation, and using it to estimate values.

Generated by Claude Opus 4.89 min answerUpdated 2026-06-14

Reviewed by: AI editorial process; not yet individually human-reviewed

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What this dot point is asking
Reading a scattergraph
Describing correlation
The line of best fit
Using the line to estimate
Finding the equation from the graph
Examples in context
Try this

What this dot point is asking

The SQA wants you to plot and read a scattergraph, describe the correlation it shows, draw a line of best fit, find the equation of that line, and use the equation to estimate a value. The link to the straight line $y = mx + c$ is direct.

Reading a scattergraph

A scattergraph (scatter diagram) plots each pair of values as a single point. The overall shape of the cloud of points shows whether and how the two quantities are related. If the points lie close to a straight-line trend, the relationship is strong; if they are widely scattered, it is weak.

Describing correlation

Correlation describes the direction of the trend, and you should state it in context, not just as a label.

The strength matters too: points hugging a line show strong correlation, while a loose cloud shows weak correlation. Remember that correlation does not prove that one quantity causes the other.

The line of best fit

A line of best fit is a single straight line drawn to follow the trend of the points, with roughly as many points above as below. It should pass through the general middle of the data, not necessarily through the origin or any particular point.

Find the equation of a line of best fit through (0, 4) and (8, 20)

The equation of a straight line is $y = mx + c$ . We need the gradient $m$ (how steeply the line rises) and the $y$ -intercept $c$ (where it crosses the $y$ -axis). Both can be read directly from two points on the line.

Step 1: Find the gradient using the two points

The gradient measures the change in $y$ divided by the change in $x$ between the two points $(0, 4)$ and $(8, 20)$ :

m = \dfrac{20 - 4}{8 - 0} = \dfrac{16}{8} = 2

A gradient of $2$ means $y$ increases by $2$ for every $1$ increase in $x$ .

Step 2: Read the $y$ -intercept and write the equation

One of the given points is $(0, 4)$ , which lies on the $y$ -axis. The $y$ -intercept is therefore $c = 4$ directly. Substituting $m = 2$ and $c = 4$ into $y = mx + c$ :

y = 2x + 4

Final answer: The equation of the line of best fit is $y = 2x + 4$ .

Using the line to estimate

Once you have the equation, you can estimate the value of one quantity for a given value of the other by substituting into $y = mx + c$ .

Finding the equation from the graph

In the exam you usually read two clear points off the line of best fit, then build its equation exactly as in the straight-line topic: find the gradient from the two points, and read the y-intercept where the line crosses the y-axis. Choosing two points that lie neatly on the gridlines makes the gradient easier to calculate accurately.

A line of best fit passes through (2, 7) and (6, 19). Find its equation.

Neither point lies on the $y$ -axis here, so after finding the gradient we must work out the $y$ -intercept algebraically by substituting one point into $y = mx + c$ .

Step 1: Find the gradient

Use the two points $(2, 7)$ and $(6, 19)$ :

m = \dfrac{19 - 7}{6 - 2} = \dfrac{12}{4} = 3

Step 2: Find the $y$ -intercept by substituting one point

We know $m = 3$ and that the point $(2, 7)$ lies on the line, so $7 = 3 \times 2 + c$ , giving $7 = 6 + c$ and therefore $c = 1$ . Alternatively, using $y - 7 = 3(x - 2)$ expands to $y = 3x + 1$ , confirming $c = 1$ .

Final answer: The equation of the line of best fit is $y = 3x + 1$ .

Examples in context

Scattergraphs reveal real-world relationships. A shop plotting temperature against ice-cream sales sees a positive correlation and uses the line of best fit to forecast sales for a hot day. A study plotting a car's age against its value shows negative correlation, helping estimate a fair price. Scientists use lines of best fit to read a trend from experimental data despite measurement scatter.

Try this

Q1. Points fall from upper left to lower right. What correlation is this? [1 mark]

Cue. Negative correlation.

Q2. A line of best fit passes through $(0, 2)$ and $(5, 17)$ . Find its equation. [2 marks]

Cue. Gradient $3$ , so $y = 3x + 2$ .

Q3. Use $y = 3x + 2$ to estimate $y$ when $x = 4$ . [1 mark]

Cue. $y = 14$ .

Exam-style practice questions

Practice questions written in the style of SQA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

SQA National 5 20194 marksA line of best fit passes through

(0, 5)

and

(10, 25)

. Find its equation, and use it to estimate

y

when

x = 6

Show worked answer →

Find the gradient: $m = \dfrac{25 - 5}{10 - 0} = \dfrac{20}{10} = 2$ (1 mark). The line crosses the y-axis at $(0, 5)$ , so $c = 5$ and the equation is $y = 2x + 5$ (1 mark). Substitute $x = 6$ : $y = 2 \times 6 + 5 = 17$ (2 marks). Markers reward the gradient, the equation in $y = mx + c$ form, and the estimate.

SQA National 5 20222 marksA scattergraph shows hours studied against test score, with points rising from lower left to upper right. Describe the correlation and what it suggests.

Show worked answer →

The points rise from lower left to upper right, so there is a positive correlation between hours studied and test score (1 mark). This suggests that, in general, students who study for longer tend to achieve higher test scores (1 mark). Markers reward naming the positive correlation and interpreting it in context. Correlation does not by itself prove that studying causes the higher scores.

Related dot points

Sources & how we know this

SQA National 5 Mathematics Course Specification — SQA (2018)