Aims: To use Pearson’s product moment correlation coefficient to identify the strength of linear correlation in bivariate data. To be able to find the regression (best best fit) line for bivariate data.

 Name: To know what Pearson’s product moment correlation coefficient is.  Describe: How to find the pmcc using a GDC.  Explain: The meaning of the coefficient of the values of r.  Skill: Use a GDC to find the pmcc.

How Good Is Correlation? Which is better at predicting the number of points; wins or losses? How can you tell? Although you can find a regression line for any data it is not sensible to do so... Only if the correlation is good enough.

 The strength of linear correlation is measured with a value called r (Pearson’s Product Moment Correlation Coefficient).  Here is a little bit about it… You look at the product of the differences of x and y from their mean values…

But How? (For Info Not Required Knowledge)  You can see that most of our data is in sections 1 and 3 and the data is negatively corellated.  The differences alone do not tell us this, however, if we multiply the value is positive in 2 and 4 and negative in 1 and

But How?  We work out the average of these values but this is effected by the scale of the axes.  So we divide by the product of the x and y value’s standard deviations this ensures a value of r so that -1≤r≤1

Product Moment Correlation Coefficient (r)  tor!

Calculating and Interpreting  Use the same process as we did for finding the regression line. The value listed as r is the product moment correlation coefficient.

Interpreting  What does this mean...  Well r must be between -1 and 1  -  negative correlation  The closer to 1 the number part is the better the fit to a straight line.  1 is a perfect line so this data is a good fit to a negative linear correlation.

 The following show how r varies with the correlation.

13