Answer: It is one that is unnecessarily included in the model, whose actual coefficient and consistently approximated value is 0 in large sample sizes. If we add these variables is costly.

The correct answer is B. An extraneous variable is one that is unnecessarily included in the model, whose actual coefficient and consistently approximated value is 0 in large sample sizes. Adding these variables is costly because: 1. **Statistical Cost**: Including irrelevant variables increases the variance of the estimated coefficients for the relevant variables, reducing the precision of the model. 2. **Computational Cost**: More variables require more computational resources and time. 3. **Interpretation Cost**: Unnecessary variables complicate model interpretation and can lead to overfitting. Option A is incorrect because extraneous variables are those that are included unnecessarily, not eliminated. Option C is incorrect because extraneous variables are not included as a precaution for sample size issues - they are simply irrelevant variables that should not be in the model. Option D is incorrect because option B accurately describes extraneous variables.

Author: Nikitesh Somanthe