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“The inclusion of an irrelevant explanatory variable in a regression has more serious consequences for OLS estimation results than the unjustified omission of an explanatory variable.” Explain whether this statement is true

AOD
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  • Hi. Welcome to Cross Validated. The statement is self explanatory, imo. Now, what part of it is not understandable? What seems to bother you about its assertion? – User1865345 Aug 23 '22 at 09:02
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    This looks like a question from a text book or an exam. In that case, please add teh self-study tag and explain what you have done so far to answer the question. – cdalitz Aug 23 '22 at 09:42
  • Typically considered to be false - look for omitted variable bias vs. variance of OLS estimator – Christoph Hanck Aug 23 '22 at 10:19
  • This is a very broad open ended question that has no definite answer. If this is an exam then it is often important that you can argue your answer and showcase that you understand the relevant topic of the exam.

    The relevant keyword that you probably should include in the answer is the bias-variance trade-off.

     – Sextus Empiricus Aug 23 '22 at 14:03
  • With that background, some sort of cross validation that trains which variables to include into the model, the practice to omit variables, when it is done to reduce some cost function of predictions/estimates, is generally a good thing. Eventually, the algorithm used to figure out the balance between bias and variance should ensure that you find an optimum for the number of variables and neither adding variables (potentially the good ones) or removing variables (potentially the bad ones) is a good thing. – Sextus Empiricus Aug 23 '22 at 14:04
  • Even when it is not the terms in brackets 'potentially', and we are certain that some variable is correct, then it might be better to exclude the variable. An example here shows how a model with less terms can perform better (but it depends on the noise level) and that we can even have the situation: “The inclusion of a relevant explanatory variable in a regression has more serious consequences for OLS estimation results than the omission of a relevant explanatory variable.” – Sextus Empiricus Aug 23 '22 at 14:05

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