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.