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.
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
This means the data is a very close fit to a straight line.
The variation ofaccounts for% of the variation in