Answer: The standard error of the regression coefficient

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.

Author: Nikitesh Somanthe