12. Regression
Coefficient of Determination
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In a given dataset, you determine the value of the correlation coefficient to be . Find the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? What about the unexplained variation?
A
Explained = 91.6%; Unexplained = 8.4%
B
Explained = 95.7%; Unexplained = 4.3%
C
Explained = 8.4%; Unexplained = 91.6%
D
Explained = 4.3%; Unexplained = 95.7%
Verified step by step guidance1
Step 1: Recall the formula for the coefficient of determination (R²), which is the square of the correlation coefficient (r). Mathematically, R² = r².
Step 2: Substitute the given value of r into the formula. Here, r = -0.957, so calculate R² = (-0.957)².
Step 3: Interpret the coefficient of determination (R²). It represents the proportion of the variation in the dependent variable that is explained by the independent variable(s) in the regression model.
Step 4: To find the explained variation, multiply R² by 100 to express it as a percentage. This percentage indicates how much of the total variation in the data is explained by the regression line.
Step 5: To find the unexplained variation, subtract the explained variation percentage from 100%. This represents the proportion of the variation in the data that is not explained by the regression line.
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