Statistics

Scatter graphs

Change points and investigate a line of best fit.

Predict, test and explain

Step 1 of 3

Predict

The observed x values run from 1 to 8. A line predicts a value at x = 9. What is this called?

\text{your line: }y=x

Scroll the diagram sideways to see every label.

Your prediction

\hat y=4

Positive trend. Green is your estimated line; red dashes, when shown, are an automatic comparison. Correlation does not establish causation. This prediction is within the observed x range.

Editable data points
Point	x	y
1	1	2
2	2	4
3	3	3
4	4	5
5	5	7
6	6	6
7	7	8
8	8	9

Explore and compare

Choose the investigation above. Predict what will change before you move a control.

Predict

Try it in the simulation. Change one thing at a time.

Explain

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Hints, self-check and connections

Try a self-check

Fixed values, separate from the diagram controls.

The pairs (1, 2), (2, 4) and (3, 6) form what association? Does the plot alone prove causation?

$(1,2),\;(2,4),\;(3,6)$

Hint

Follow what happens to y as x increases. A pattern does not explain its cause.

Reveal answer

Perfect positive correlation: all three points lie on an increasing straight line. The plot alone does not prove that x causes y.

$y=2x$

Build an explanation

Hint 1

Each point represents a pair of measurements. Look for the overall pattern rather than joining the points.

Hint 2

An upward pattern suggests positive correlation; a downward pattern suggests negative correlation. A line of best fit follows the overall trend, with points roughly balanced around it.

Hint 3

Use the line to estimate one variable from the other. Predictions inside the observed range are interpolation; those outside are extrapolation and may be less reliable.

Worked example

This example uses fixed values, separate from the diagram controls.

A line of best fit is y = 2x + 5, using observations with x between 2 and 6. Estimate y at x = 4 and explain why a prediction at x = 20 needs care.

Substitute x = 4 into the line: y = 2 × 4 + 5 = 13.
This is interpolation because 4 lies inside the observed range from 2 to 6.
x = 20 lies outside that range. Extending the line assumes the same trend continues, which the observations do not establish.

Answer: Estimated y = 13 at x = 4. A prediction at x = 20 is extrapolation and may be unreliable.

Connect this idea

Watch out: Correlation does not prove that one variable causes the other. A best-fit line estimates the trend; individual points need not lie on it.