r vs. R-squared

r’ is a parameter used in the CORRELATION ANALYSIS. It is also called the correlation coefficient. It is a measure of the strength of the linear relationship between TWO variables. Value of ‘r’ ranges from -1.00 to +1.00; a perfect correlation is indicated by a value of 1.00, positive or negative. A value of 0 indicates that there is no correlation between these two variables.

R-squared is a parameter used in the REGRESSION ANALYSIS. It is also called the coefficient of determination. Just like the ‘r’, R-squared is also an indicator of the strength of the relationship between variables. However, here the relationship could involve MULTIPLE variables. The regression analysis is used to determine the impact of one or more x-variables on the y-variable. R-squared is an indicator on how well the x-variables can be used to predict the value of the y-variable. In other words, R-square indicates the strength of the regression equation which is used to predict the value of the y-variable. Value of R-squared ranges from 0 (poor predictor) to 1 (excellent predictor).

Since the regression analysis is nothing but a correlation analysis involving multiple variables, the R-squared is also known as the multiple correlation coefficient.

So, in simple terms, ‘r’ is an indicator of the strength of the relationship between two variables where R-squared is an indicator of the strength (goodness of fit) of the linear equation that predicts the value of one variable as a function of one or more variables.