Cambridge International Mathematics

TWO VARIABLE ANALYSIS

We often want to know how two variables areassociatedorrelated. We want to know whether an increase

in one variable results in an increase or a decrease in the other.

To analyse the relationship between two variables, we first need to decide which is thedependentvariable

and which is theindependentvariable.

The value of the dependent variabledependson the value of the independent variable.

Next we plot known points on ascatter diagram. The independent variable is placed on the horizontal axis,

and the dependent variable is placed on the vertical axis.

Consider the following two typical scatter diagrams:

In the first scatter diagram the points are quite random.

It is hard to tell how they could be related.

In the second scatter diagram the points are all close

to the red line shown. We say that there is a strong

linear connection orlinear correlationbetween these

two variables. The red line is called theline of best fit

because it best represents the data.

The scatter diagram for theOpening Problemis drawn

alongside. Height is the independent variable and is

represented on the horizontal axis. We see that in general,

as the height increases, the weight increases also.

The weight of a

person is usually

dependenton

their height.

Correlationis a measure of the strength of the relationship or association between two variables.

When we analyse the correlation between two variables, we should follow these steps:

Step 1: Look at the scatter diagram for anypattern.

For a generally upward shape we say that the

correlation ispositive.

As the independent variable increases, the dependent

variable generally increases.

For a generally downward shape we say that the

correlation isnegative.

As the independent variable increases, the dependent

variable generally decreases.

A CORRELATION [11.9]

weight

height

dependent variable

independent variable

75

80

85

90

95

100

105

175 180 185 190 195 200 205

Weight versus Height

height (cm)

weight (kg)

456 Two variable analysis (Chapter 22)

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