Final answer:
The percentage of variability in the dependent variable explained by an independent variable is called the coefficient of determination, or r², which is the square of the correlation coefficient r.
Step-by-step explanation:
The percentage of variability in the dependent variable explained by an independent variable is called the coefficient of determination. This is also known as r², which is the square of the correlation coefficient. The correlation coefficient, denoted as r, measures the strength and direction of a linear relationship between two variables, and can range from -1 to +1. A positive r indicates that as one variable increases, the other also increases, and vice versa. A negative r indicates an inverse relationship where one variable increases as the other decreases
The coefficient of determination, when expressed as a percentage, illustrates the extent to which variation in the dependent variable can be accounted for by the variation in the independent variable. For instance, if r is 0.6631, then r² is 0.6631² or approximately 0.4397. If we convert this to percentage, we can say approximately 44 percent of the variability in the dependent variable is explained by the independent variable through the regression model.