A weak correlation between age and GPA with a coefficient of 0.019 indicates almost no linear relationship. For high school and freshman college GPAs with a correlation of 0.32, about 90% of the variance in college GPA is unexplained by high school GPA. A ± 0.71 correlation is needed to explain at least 50% of the variance between two variables.
Understanding Correlation and the Coefficient of Determination
If two variables, such as age and GPA, have a correlation coefficient of 0.019, it suggests that there is a weak, practically negligible linear relationship between the two variables. The correlation coefficient measures the strength and direction of the linear relationship between two variables on a scale from -1 to 1, with values close to 0 indicating almost no linear correlation.
Regarding a correlation coefficient of 0.32 between high school GPA and freshman college GPA, we calculate the coefficient of determination (r-squared) by squaring the correlation coefficient: 0.32² = 0.1024. This number represents the proportion of variance in the freshman college GPA that can be explained by high school GPA. The remaining variance, 1 - 0.1024 = 0.8976 or approximately 90%, is not explained by high school GPA.
To achieve a coefficient of determination of at least 0.50, we need to find the square root of 0.50, because the coefficient of determination is the correlation coefficient squared. The required correlation must be at least ±sqrt(0.50), which equals approximately ±0.71 when rounded to two decimal places.
For a university's admissions committee, strong correlations between college GPA and standardized test scores, such as the SAT or ACT, could guide the decision on which students to admit, based on the predictive value of these correlations.