The Coefficient of Determination, R2, chart

When there is only one independent variable, the calculation of the Coefficient of Determination is the square of the Correlation between the Independent Variable and the Dependent Variable. Please see the table below.

Correlation Coefficient                            Coefficient of Determination
1                                                                1
0.95                                                           0.90250
0.90                                                           0.81
0.85                                                           0.72250
0.80                                                           0.64
0.75                                                           0.5625
0.70                                                           0.49
0.65                                                           0.4225
0.60                                                           0.36
0.55                                                           0.3025
0.50                                                           0.25
0.45                                                           0.2025
0.40                                                           0.16
0.35                                                           0.1225
0.30                                                           0.09
0.25                                                           0.0625
0.20                                                           0.04
0.15                                                           0.0225
0.10                                                           0.01
0.05                                                           0.0025
0                                                                0

** It is importance to notice the speed of decrease in each site. For the correlation coefficient, the decrease is at a constant decrease of (-.05). For the Coefficient of Determination, the decrease picks up at a faster rate.

For example, at a 0.90 correlation, the independent variable only explains 81% of the dependent variable.

For example, at a 0.80 correlation, the independent variable only explains 64% of the dependent variable.

For example, at a .60 correlatoin, the independent variable only explains 36% of the dependent variable.
So, for a -0.10 decrease in the correlation coefficient from 0.9 to 0.8, the decrease in the Coefficient of Determination (RSquared) decreased by 17%. Also, note that at a value of 0, the model does not correctly explain the variation of the dependent variable at all.

Also, note the Range for the Coefficient of Determination will range from 1 to 0.