Financial Risk Manager Part 1
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To construct a confidence interval for a regression coefficient, we need the estimated regression coefficient, the appropriate test statistic, and:
Other
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NNikitesh
A
The F-statistic
B
The standard error of the regression coefficient
C
The coefficient of determination
D
The adjusted R-squared
Explanation:
A confidence interval for a regression coefficient under multiple linear regression modeling is given by:
CI = βⱼ ± (tₐ,ₙ₋ₖ₋₁ * Se(βⱼ))
Where:
- βⱼ is the estimated coefficient of the regression parameter
- Se(βⱼ) is the standard error of the coefficient
- tₐ,ₙ₋ₖ₋₁ is the appropriate t-statistic from the t-distribution with n-k-1 degrees of freedom
The standard error of the regression coefficient is essential because it measures the precision of the coefficient estimate. A smaller standard error indicates more precise estimation, resulting in narrower confidence intervals.
Why other options are incorrect:
- A. The F-statistic: Used for testing the overall significance of the regression model, not individual coefficients.
- C. The coefficient of determination (R²): Measures the proportion of variance explained by the model, not used for coefficient confidence intervals.
- D. The adjusted R-squared: Similar to R² but adjusted for the number of predictors, also not used for coefficient confidence intervals.
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