Direction/strength/form of association | Year 10

01 / LEARN

Understand the idea.

Describe three separate features

Describe direction, strength and form separately. Positive means larger horizontal values tend to accompany larger vertical values; negative means they tend to accompany smaller ones. Form tells whether the pattern is approximately straight or curved.

Strength concerns how closely the points follow that pattern. A shallow line can have tightly clustered points and a steep line can have wide scatter. Changing axis units changes the apparent steepness without changing the underlying pairing or its consistency.

Curves can be strong too

A curved relationship can be very strong when points lie close to the curve. Do not call it weak merely because a straight line would fit poorly. Also check whether the direction remains the same across the displayed domain.

Describe unusual observations separately rather than hiding them in an overall label. They can influence fitted summaries and may suggest different conditions. An accurate description of association remains a statement about the observed pattern, rather than proof of causation.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Describe a decreasing pattern

Describe the association between the outside-temperature index and heating-use index shown.

Scatterplot with temperature index from zero to six horizontally and heating-use index from zero to one hundred vertically. Separate points are zero-ninety, one-seventy-eight, two-sixty-five, three-fifty-three, four-forty and five-twenty-eight. No trend line is added.

Worked solution

1
Identify the direction.
Heating-use index tends to decrease as outside-temperature index increases, so the direction is negative.
2
Assess scatter around the pattern.
The observations lie close to the decreasing pattern, supporting a strong association.
3
Name the form.
The pattern is approximately straight, so the full description is strong negative, approximately linear association.

Answer

Strong negative, approximately linear association.

EXAMPLE 02

Describe a curve

The pairs are (0, 0), (1, 1), (2, 4), (3, 9), (4, 16). Describe the pattern.

Worked solution

1
Check how the response changes.
$0 < 1 < 4 < 9 < 16$
Across the given nonnegative horizontal values, the response increases, giving positive direction.
2
Compare successive vertical increases.
$1, 3, 5, 7$
Equal horizontal steps produce increasing vertical changes, so a straight line is unsuitable.
3
Identify the exact curved pattern.
$y = x^{2} (0 \leq x \leq 4 at the listed points)$
Every listed point lies on the quadratic curve, giving a strong positive nonlinear association on this domain.

Answer

Strong positive nonlinear association, not a straight-line relationship.

03 / YOUR TURN

Try it yourself.

Check your understanding

Points lie tightly around a decreasing straight line. Describe direction, strength and form.

Show answer & reasoning

Strong negative linear association.

Decreasing gives negative direction, tight clustering gives strong association, and the straight-line form gives linear: strong negative linear association.

Keep practising

6 worksheet questions · 12 marks

Open worksheet Worked solutions

Read the questions online

Describe the association for $(1, 9)$ , $(2, 7)$ , $(3, 5)$ , $(4, 3)$ , $(5, 1)$ .
2 marks
Describe $(1, 3)$ , $(2, 8)$ , $(3, 2)$ , $(4, 7)$ , $(5, 4)$ .
2 marks
Can a curved pattern be strong? Give a reason.
2 marks
A graph changes from metres to centimetres on one axis. Does that alone strengthen the association?
2 marks
Describe the supplied study-time plot using all three features.
2 marks
A single point lies far from the main pattern. State two sensible next steps.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Describe the association for $(1, 9)$ , $(2, 7)$ , $(3, 5)$ , $(4, 3)$ , $(5, 1)$ .
2 marks
Every increase of 1 in $x$ gives a decrease of 2 in $y$ .
All points lie on $y = 11 - 2 x$ .
Perfect negative linear association.
Describe $(1, 3)$ , $(2, 8)$ , $(3, 2)$ , $(4, 7)$ , $(5, 4)$ .
2 marks
The responses alternate rather than consistently rise or fall.
Five points alone offer limited evidence.
No clear linear direction; the points are scattered.
Can a curved pattern be strong? Give a reason.
2 marks
Strength means closeness to a pattern.
Points may lie very close to a curve.
Yes.
A graph changes from metres to centimetres on one axis. Does that alone strengthen the association?
2 marks
Only the unit scale changes.
The underlying paired observations and relative pattern are unchanged.
No.
Describe the supplied study-time plot using all three features.
2 marks
Scores generally rise with study time.
There is some scatter around a roughly straight trend.
Positive, quite strong, approximately linear association.
A single point lies far from the main pattern. State two sensible next steps.
2 marks
An unusual point is not automatically wrong.
Report and justify any later exclusion.
Check the recording/measurement and investigate its context.

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Curriculum reference & lesson scope

Australian Curriculum v 9 and SA Curriculum Mathematics

Year 10 continuous distributions, bivariate data, two-way categorical tables, bias and investigations, with the approved percentile and standard-deviation content included in the normal chapter.

Official curriculum source ↗

In this lesson

Understand the idea.

Describe three separate features

Curves can be strong too

See the method in action.

Describe a decreasing pattern

Identify the direction.

Assess scatter around the pattern.

Name the form.

Describe a curve

Check how the response changes.

Compare successive vertical increases.

Identify the exact curved pattern.

Try it yourself.

Check your understanding

Keep practising