The Correlation Coefficient

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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

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