Use the value of the linear correlation coefficient to calculate the coefficient

Question

Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation? r = -0.683 Calculate the coefficient of determination. (Round to three decimal places as needed.) What does this tell you about the explained variation of the data about the regression line? % of the variation can be explained by the regression line. (Round to one decimal place as needed.) About the unexplained variation? % of the variation is unexplained and is due to other factors or to sampling error. (Round to one decimal place as needed.)

Explanation / Answer

coefficient of determination = square of coefficient of linear = r2 = 0.6832 = 0.466489 = 0.4665

The coefficient of determination (denoted by R2) is a key output of regression analysis. It is interpreted as the proportion of the variance in the dependent variable that is predictable from the independent variable.

percentage of variation can be explained by linear coefficient R^2 = 0.466 = 46.6%

percentage of variation is unexplained and is due to the other factors is 1- R^2 = 1- 0.466 = 0.534 = 53.4%

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