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 = 0.732

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

Solution :

Given that,

r = -0.732

coefficient of determination = r2 = (-0.732)2 = 0.536

53.6% of the variation can be explained by the regression line .

1 - 53.6% = 46.4%

46.4% of the variation is unexplained and is due to other factors or to sampling error

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