The correlation coefficient is the proportion of total variation in the response variable that is accounted for by changes in the explanatory variable.

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The correlation coefficient measures the strength and direction of the linear relationship between two variables. It is calculated by dividing the covariance of the two variables by the product of their standard deviations. The value of the correlation coefficient can range from -1 to 1, with a value of 0 indicating no correlation, a value of 1 indicating a perfect positive correlation, and a value of -1 indicating a perfect negative correlation. The proportion of total variation in the response variable that is accounted for by changes in the explanatory variable is known as the coefficient of determination, which is the square of the correlation coefficient.

The Correlation Coefficient Is the Proportion of Total Variation in the Response