Correlation 1

Scatter diagramsMeasurement of correlation

Using a calculatorUsing the formula

Practice qs

Scatter diagramsScatter diagrams illustrate bivariate data that is when two variables are

compared.

Draw scatter diagrams to illustrate positive correlation, negative correlation and no correlation.

How well the variables fit to a straight line of best fit is the measure of correlation they exhibit.

The two types of correlation are positive and negative.

Product Moment Correlation Coefficient (PMCC)The product moment correlation coefficient r is a statistical

measure of how well each data point lies on a straight line

It has a value between 1 (perfect positive correlation) and -1 (perfect negative correlation).

In the exam questions if the original data is given then it is acceptable to use a calculator to calculate r.

Some times summary statistics are given instead of the original data then the formula for r given in the formula book is used.

Jan 07 q3

Using a calculator to calculate PMCC

x 1 3 5

y 3 7 11

Stats mode

Enter the data as two lists

GRPH F1 (should draw a scatter graph for the data)

CALC (note F1 leads to the statistics for each data set separately)

F2 which looks like a X, then F2 ( a + bx)

This should give the results a = 1, b = 2 and r = 1 the other results can be ignored

June 06 q1 (example of using a calculator calculate PMCC

One for you to try (June 07 q1)

Product Moment Correlation CoefficientThe product moment correlation coefficient, r, has a value between 1 (perfect positive correlation) and -1 (perfect negative correlation). It can be calculated from summary statistics as follows:

yyxx

xy

SS

Sr

n

xxxxSxx

222 )(

)(

n

yyyyS yy

222 )(

)(

n

yxxyyyxxSxy

))(())((

Jan 08 (q2 using the formula)