12. Regression

Coefficient of Determination

12. Regression

Coefficient of Determination

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Multiple Choice

In a given dataset, you determine the value of the correlation coefficient to be $r = - 0.957$ . 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?

Explained = 91.6%; Unexplained = 8.4%

Explained = 95.7%; Unexplained = 4.3%

Explained = 8.4%; Unexplained = 91.6%

Explained = 4.3%; Unexplained = 95.7%

Verified step by step guidance

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.