Final answer:
In statistics, R, or the correlation coefficient, measures the strength and direction of the linear relationship between two variables. It ranges from -1 to +1, with -1 or +1 indicating a strong linear relationship. The coefficient of determination, r², represents the percentage of variation in the dependent variable explained by the independent variable using the regression line.
Step-by-step explanation:
In statistics, R or the correlation coefficient measures the strength and direction of the linear relationship between two variables, commonly represented as x and y.
The correlation coefficient, denoted as r, is a value between -1 and +1. When r is positive, it indicates that as one variable increases, the other variable tends to increase as well, and when r is negative, it indicates that as one variable increases, the other tends to decrease. The strength of the relationship is indicated by how close the value of r is to 1 or -1. A value of 0 indicates no linear relationship between the variables.
The coefficient of determination, denoted as r², is the square of the correlation coefficient. This value represents the percentage of variation in the dependent variable that can be explained by the independent variable when using the regression line. For instance, if r is 0.6631, then r² is approximately 0.4397, indicating that about 44 percent of the variation can be explained by the relationship between the variables.