The correlation coefficient measures the strength of the linear association between two variables. It ranges from -1 to +1, and the coefficient of determination represents the percentage of variation in the dependent variable that can be explained by the independent variable.
The correlation coefficient, r, measures the strength of the linear association between two variables, x and y. It ranges from -1 to +1. When r is positive, x and y tend to increase and decrease together. When r is negative, x increases and y decreases, or vice versa.
The coefficient of determination, r², is equal to the square of the correlation coefficient. It represents the percentage of variation in the dependent variable, y, that can be explained by variation in the independent variable, x, using the regression line.
For example, if we have a correlation coefficient of r = 0.9121, it indicates a strong positive linear relationship between x and y. Approximately 91.21% of the variation in y can be explained by the variation in x.