Final answer:
The proportion of variability in the dependent variable explained by the independent variable is called the coefficient of determination, r², not the coefficient of correlation. Coefficient of correlation, r, indicates the strength and direction of the linear relationship between x and y. R², when expressed as a percentage, shows the percentage of variability in y explained by x using the regression line.
Step-by-step explanation:
The statement in question is not completely correct. While the correlation coefficient, commonly denoted by r, does measure the strength and direction of the linear relationship between an independent variable (x) and a dependent variable (y), the proportion of variability of the dependent variable (y) accounted for or explained by the independent variable (x) is actually called the coefficient of determination, which is denoted by r². The correlation coefficient itself is a value between -1 and +1 and indicates the strength of the association between the variables. When r is positive, it means that as x increases, y also tends to increase, and vice-versa. Conversely, a negative r indicates that as x increases, y tends to decrease, and vice versa.
The coefficient of determination, r², is equal to the square of the correlation coefficient. When r² is expressed as a percentage, it describes the percentage of variability in the dependent variable that can be explained by the independent variable, using the regression line. For example, if r² is 0.72, it indicates that 72 percent of the variability in the dependent variable can be attributed to its linear relationship with the independent variable.