In this section we review plotting scatter diagrams and discuss the different types of correlation that you can expect to see on these diagrams.

*Strong positive correlation* between *x* and *y*. The points lie close to a straight line with

*y increasing as x increases.*

*Weak, positive correlation* between *x* and *y*. The trend shown is that

*y increases as x increases*

but the points are not close to a straight line.

*No correlation* between *x* and *y*; the points are *distributed randomly* on the graph.

*Weak, negative correlation* between *x* and *y*. The trend shown is that

*y decreases as x increases*

but the points do not lie close to a straight line.

*Strong, negative correlation*. The points lie close to a straight line, with

*y decreasing as x increases.*

If the points plotted were all on a straight line we would have *perfect correlation*, but it could be positive or negative as shown in the diagrams above.

The following table lists values of *x* and *y*.

x | 2 | 3 | 5 | 6 | 9 | 11 | 12 | 15 |

y | 10 | 7 | 8 | 5 | 6 | 2 | 5 | 2 |

(a)

Use the data to draw a scatter graph.

(b)

Describe the type of correlation that you observe.

It shows weak, negative correlation.

What sort of correlation would you expect to find between:

(a)

a person's age and their house number,

No correlation, because these two quantities are not linked in any way.

(b)

a child's age and their height,

Positive correlation, because children get taller as they get older.

(c)

an adult's age and their height ?

No correlation, because the height of adults does not change with their age.