What is the relationship between the covariance and the correlation coefficient

Covariance and correlation coefficient are both statistical concepts that describe the relationship between two variables.

1. Covariance: This is a measure of how much two random variables vary together. It’s similar to variance, but where variance tells you how a single variable varies, covariance tells you how two variables vary together.

2. Correlation Coefficient: This is a statistical measure that calculates the strength of the relationship between the relative movements of two variables. The range of values for the correlation coefficient is -1.0 to 1.0. A correlation of -1.0 shows a perfect negative correlation, while a correlation of 1.0 shows a perfect positive correlation. A correlation of 0.0 shows no linear relationship between the movement of the two variables.

The relationship between covariance and correlation coefficient is that the correlation coefficient is standardized making it not scale dependent, unlike covariance. The correlation coefficient is derived from the covariance of two variables, divided by the product of the standard deviations of the two variables. This standardization allows for the correlation coefficient to be a more useful measure of dependence because it is bound between -1 and 1, which allows for easy comparisons between different pairs of variables.