2. 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.

3.  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.

4. 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.

5.  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…

6. 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 3. 1 2 3 4

7. 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

8. Product Moment Correlation Coefficient (r)  tor!

9. 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.

10. 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.

11.  The following show how r varies with the correlation.

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