Coefficient of Correlation and Coefficient of Determination

The coefficient of correlation is a measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation.

The coefficient of determination, also known as R-squared, is a measure of the proportion of variance in one variable that is explained by the other variable. It ranges from 0 to 1, where 0 indicates that none of the variance is explained and 1 indicates that all of the variance is explained.

Calculation of Coefficient of Determination

The coefficient of determination can be calculated as the square of the coefficient of correlation. Therefore, if the coefficient of correlation between x and y variables is -0.90, the coefficient of determination can be calculated as follows:

R² = (-0.90)²

R² = 0.81

Interpretation of Coefficient of Determination

The coefficient of determination of 0.81 indicates that 81% of the variance in the y variable is explained by the x variable. This means that the x variable has a strong negative linear relationship with the y variable, and that the x variable is a good predictor of the y variable.

Conclusion

In summary, the coefficient of determination is a measure of the proportion of variance in one variable that is explained by the other variable, and it can be calculated as the square of the coefficient of correlation. In this case, the coefficient of determination is 0.81, indicating a strong negative linear relationship between the x and y variables.

R^2 = (-0.9)^2 = 0.81