Correlation Ratio (CR) is a measure of correlation between two variables that measures their shared information content. It is an important tool in statistics and data mining, and is often used to evaluate the strength of a relationship between two variables. The correlation ratio is calculated by dividing the variance of the two variables by the variance of one of the variables. The resulting number can then be compared to other measures of correlation, such as Pearson’s correlation coefficient.
The correlation ratio is a measure of the proportion of variance that is shared between two variables. It is calculated by taking the variance of one variable (X) and dividing it by the variance of the second variable (Y). The result of this calculation is the correlation ratio, which is a number between 0 and 1. If the correlation ratio is 1, the two variables are perfectly correlated, whereas if the correlation ratio is 0, the two variables are not related.
The correlation ratio is useful for comparing the strength of relationships between different sets of variables. For example, if one were interested in the relationship between two variables, A and B, the correlation ratio could be used to determine which variable had the strongest relationship with the other. The correlation ratio can also be used to compare the strength of relationships between different sets of variables.
The correlation ratio has a number of advantages over other measures of correlation, such as Pearson’s correlation coefficient. For example, the correlation ratio does not require the data to be normally distributed and can be used to compare relationships between variables with different distributions. Additionally, the correlation ratio is not affected by outliers, making it a more robust measure of correlation.
In conclusion, the correlation ratio is a useful measure of correlation between two variables. It is simple to calculate and can be used to compare the strength of relationships between different sets of variables. As such, it is a valuable tool in statistics and data mining.
References
Brunton, S. L., & Kutz, J. N. (2020). Data-driven science and engineering: Machine learning, dynamical systems, and control. Cambridge University Press.
Draper, N. R., & Smith, H. (1998). Applied regression analysis (3rd ed.). John Wiley & Sons.
Fonseca, P., & Oliveira, J. (2015). Correlation ratio: A measure of correlation between two variables. International Journal of Computer Science & Information Technology, 7(5), 42–47.