Why does adding more variables to a regression not necessarily improve it?
Correct Answer
D) The model may fit noise in this particular sample
Why this is correct: Adding more variables may not improve a regression because the model may fit noise in this particular sample. This is called overfitting. As the original explanation states, R-squared always rises with added variables, but a model tuned to sample-specific randomness will perform poorly on new data. Why the other choices are wrong: R-squared always rises (or stays the same) when variables are added; it does not fall. Extra variables do not each need to be tested separately in the way this option implies. The dependent variable (e.g., sale price) does not change with each variable addition. Exam tip: If a model fits your sample data perfectly but seems too complex, it's likely overfitting. Use adjusted R-squared or out-of-sample testing to check.
Why This Is the Correct Answer
Why this is correct: Adding more variables may not improve a regression because the model may fit noise in this particular sample. This is called overfitting. As the original explanation states, R-squared always rises with added variables, but a model tuned to sample-specific randomness will perform poorly on new data. Why the other choices are wrong: R-squared always rises (or stays the same) when variables are added; it does not fall. Extra variables do not each need to be tested separately in the way this option implies. The dependent variable (e.g., sale price) does not change with each variable addition. Exam tip: If a model fits your sample data perfectly but seems too complex, it's likely overfitting. Use adjusted R-squared or out-of-sample testing to check.
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