Question

what does it mean when Correlation Coefficient: .500 and the Coefficient of Determination: .25

Answer 1

CORRELATION COEFFICIENT:

The linear correlation coefficient, measures the strength and the direction of a linear relationship between two variables. The value of is such that . The + and – signs are used for positive linear correlations and negative linear correlations, respectively. A correlation greater than 0.8 is generally described as strong, whereas a correlation less than 0.5 is generally described as weak.

The given correlation coefficient is positive and is not close to +1. Thus there is positive moderate linear correlation between independent and dependent variable.

COEFFICIENT OF DETERMINATION:

The coefficient of determination, ,is the proportion of the variance (fluctuation) of one variable that is predictable from the other variable. It is a measure that allows us to determine how certain one can be in making predictions from a certain model.

The coefficient of determination is the ratio of the explained variation to the total variation. The coefficient of determination is such that and denotes the strength of the linear association between x and y. It represents the percent of the data that is the closest to the line of best fit.

Given that , then which means that 25% of the total variation in y can be explained by the linear relationship between x and y (as described by the regression equation). The other 85% of the total variation in y remains unexplained.