## The Correlation Coefficient

Regression coefficients tell us how good a fit our data is to a straight line. The regression coefficient is a number between -1 and 1. -1 means a perfect relationship. All the points are on a straight line, and the graph slopes down. 1 means a perfect relationship. All the points are on a straight line and the graph slopes up. Some values, along with the data they summarise, are given below.

The first has a perfect positive linear correlation, with correlation coefficient 1.

The second has a perfect negative correlation with correlation coefficient -1.

The third has a positive but not perfect correlation The correlation coefficient may be about 0.8.

The third has a negative but not perfect correlation The correlation coefficient may be about -0.8.

We want to find the correlation coefficient for the data in this table.

x | 2 | 4 | 7 | 3 | 5 | 1 |

y | 10 | 5 | 2 | 9 | 4 | 10 |

To find the correlation coefficient it is most efficient to first find the summary statistics. Your calculator may have functions to help. They are

The correlation coefficient is then calculated from

r=

This means the data is a very close fit to a straight line.

The variation ofaccounts for% of the variation in