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 of
accounts for
% of the variation in