Page 268 - F2 - MA Integrated Workbook STUDENT 2018-19

Chapter 12

4.3 The coefficient of determination

This squares the correlation in order to express the strength of the relationship
between the variables as a percentage.

2
The coefficient of determination, r , gives the proportion of changes in y that can be
explained by changes in x, assuming a linear relationship between x and y.

For example:

2
If a correlation coefficient r = +0.9, then r = 0.81 and we could state that 81% of the
observed changes in y can be explained by the changes in x and that 19% of the
changes must be due to other factors.

Test your understanding 4

If the correlation coefficient is 0.8, what is the coefficient of determination?

A 0.64

B 89

C 20.8

D 0.4

260