Financial Risk Manager Part 1

Explanation

An extraneous variable, in the context of regression diagnostics, is a variable that is unnecessarily included in the model. Its actual coefficient and consistently approximated value is 0 in large sample sizes. This means that the variable does not contribute significantly to the model's predictive power or accuracy.

Key Points:

• Definition: A variable whose true coefficient is zero in the population
• Impact: Does not improve model prediction in large samples
• Cost: Including such variables is computationally expensive and can lead to overfitting
• Identification: Should be identified and removed to improve model efficiency

Why Other Options Are Incorrect:

• Choice A: Incorrect because extraneous variables are not eliminated to "increase effectiveness" - they are removed because they have no real effect on the dependent variable
• Choice C: Incorrect because sample size appropriateness is not the criterion for extraneous variables
• Choice D: Incorrect because variables needed to control confounding are important and necessary, not extraneous

Practical Implications:

Extraneous variables can:

• Increase model complexity unnecessarily
• Reduce degrees of freedom
• Lead to multicollinearity issues
• Make interpretation more difficult
• Decrease model performance on new data