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.
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
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
))(())((