Question

Another coefficient mentioned in this week's readings is the coefficient of determination, r^2. What information do we obtain from this coefficient?

Answer 1

Coefficient of determination:

The coefficient of determination (denoted by R2) is a key output of regression analysis. It is interpreted as the proportion of the variance in the dependent variable that is predictable from the independent variable.

• The coefficient of determination is the square of thecorrelation (r) between predicted y scores and actual y scores; thus, it ranges from 0 to 1.
• With linear regression, the coefficient of determination is also equal to the square of the correlation between x and y scores.
• An R2 of 0 means that the dependent variable cannot be predicted from the independent variable.
• An R2 of 1 means the dependent variable can be predicted without error from the independent variable.
• An R2 between 0 and 1 indicates the extent to which the dependent variable is predictable. An R2 of 0.10 means that 10 percent of the variance in Y is predictable from X; an R2 of 0.20 means that 20 percent is predictable; and so on.