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=- 0.873

(a)Calculate the coefficient of determination

(b)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.

(c) About the unexplained variation?

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

Explanation / Answer

a) Coefficient of Determination (R2) is the square of Coefficient of Correlation.
Hence, R2 = (-0.873)2 = 0.762129.

b) R2 gives the proportion of total variability explained by the regression equation.
This implies, 76.21% of the total variation is explained by the regression line.

c) By the same explanation, (100-76.21)% = 23.79% of the variation is unexplained.

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