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.
R= 0.581
A) calculate the coefficient of determination (round 3 places)
B) what does this tell us about the explained variation of the data about the regression line? (Round 1 decimal place)
C) what does it say about the variation due to other factors or to sampling error. (Round 1 decimal place) Use the value of the linear correlation coefficient to calculate the coefficient of determination.
R= 0.581
A) calculate the coefficient of determination (round 3 places)
B) what does this tell us about the explained variation of the data about the regression line? (Round 1 decimal place)
C) what does it say about the variation due to other factors or to sampling error. (Round 1 decimal place)
R= 0.581
A) calculate the coefficient of determination (round 3 places)
B) what does this tell us about the explained variation of the data about the regression line? (Round 1 decimal place)
C) what does it say about the variation due to other factors or to sampling error. (Round 1 decimal place)

Explanation / Answer

a) Coefficient of determination = (0.581)2 = 0.338

b) Explained variation = 33.8%

c) Unexplained variation = 100% - 33.8% = 66.2%

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