Financial Risk Manager Part 1
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In a problem involving three independent variables and one dependent variable, assume that the computed coefficient of determination is 0.59. This result means that:
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A
59% of the total variation is explained by the dependent variable.
B
The correlation coefficient is 0.59 as well.
C
At least two of the three independent variables are highly correlated.
D
59% of the total variation in the dependent variable is explained by the independent variables.
Explanation:
Explanation
The coefficient of determination (R-squared) is a statistical measure that shows the proportion of the variance for a dependent variable that's explained by independent variables in a regression model.
Key Points:
- R-squared = 0.59 means that 59% of the total variation in the dependent variable is explained by the independent variables
- This indicates how well the independent variables collectively predict the dependent variable
- The remaining 41% of variation is unexplained and attributed to other factors
Why other options are incorrect:
- A: Incorrect - R-squared measures variation explained by independent variables, not the dependent variable
- B: Incorrect - Correlation coefficient and R-squared are different measures; correlation coefficient would be √0.59 ≈ 0.768
- C: Incorrect - High R-squared doesn't necessarily indicate multicollinearity among independent variables
Interpretation: In this multiple regression context with three independent variables, an R-squared of 0.59 indicates that the model explains 59% of the variability in the dependent variable, which is a moderately good fit.
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