r
2
– Coefficient of Determination
The slope of the regression line depends on the correlation between the two
variables, among other factors.
The stronger the correlation between the two variables, the higher the slope.
The correlation coefficient also helps identify the percentage of the response
variable that is explained by or can be attributed to the explanatory variable.
In other words, how good a variable is at predicting the other variable.
This percentage can be obtained by squaring the correlation coefficient. The
result represents the coefficient of determination and is denoted by r
2
.
r
2
– the percentage of the response variable that can be explained by the
explanatory variable
Example:
r = 0.3
r
2
= 0.09
In the example, the correlation coefficient is 0.30, a fairly small correlation.
Squaring this number results in 0.09
This means that only 9% of the variation in students’ self-esteem scores can
be explained by their GPA.
Correlations above 0.7 are considered strong because if r = 0.7, then r
2
= 0.49.
This means approximately 50% of the variance in the response variable can
be explained by the explanatory variable.
The rest of the variance remains unexplained and is attributed to other
factors that were not included in the regression equation.