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). It is calculated as 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 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. Multiply R² by 100 to express it as a percentage.
Step 4: Calculate the unexplained variation. This is the remaining percentage of variation not explained by the regression model, which is given by (1 - R²) × 100.
Step 5: Compare the calculated explained and unexplained percentages to the provided answer choices to determine the correct interpretation of the data.
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