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 = - 0.154

1.) Calculate the coefficient of determination. (Round to three decimal places as needed.)

_______

2.) 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.)

3.) 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

r= -0.154 => Correlation coefficient = -0.154

1) Coefficient of determination = (correlation coefficient)2 = r² = (-0.154)² = 0.023716 ~ 0.024

2) As per definition of coefficient of determination, 0.024 i.e 2.4% of the variation can be explained by the regression line.

3) As per definition of Coefficient of determination, (1-0.024) = 0.976 = 97.6% of the variation is unexplained and is due to other factors or to sampling error.

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