A researcher is planning a logistic regression to model the probability of disease occurrence. The researcher determines the rate of disease occurrence in the population is 1%. For which of the follow

Question

Options

• Aover fitting
• Boversampling
• Cmulticollinearity
• Dsimple random sample

• A
  8% (3)
• B
  13% (5)
• C
  76% (29)
• D
  3% (1)

Explanation

Important note: The stated correct answer of C (multicollinearity) appears to be a likely error in the answer key. The scenario - 1% disease prevalence in a logistic regression - most directly points to B (oversampling) as the correct answer. Here's why:

Why B (oversampling) is most appropriate: A 1% disease rate creates severe class imbalance - for every 1 case, there are 99 non-cases. Logistic regression trained on such skewed data tends to predict the majority class almost exclusively. Oversampling (e.g., SMOTE) of the rare disease cases is the standard remedy, making this study a prime candidate for that technique.

Why the distractors are wrong:

• A (overfitting): Overfitting is a risk of complex models with small samples, but it's not specifically triggered by low prevalence - it depends on model complexity vs. sample size.
• C (multicollinearity): Multicollinearity is about correlated predictors, not about outcome prevalence. Nothing in the 1% rate implies predictor correlation.
• D (simple random sample): A simple random sample is a valid method, not a problem - but with 1% prevalence it would yield too few cases, which is actually an argument for oversampling instead.

Memory tip: When you see "rare outcome" + "logistic regression," think class imbalance → oversampling. Multicollinearity lives on the predictor side; class imbalance lives on the outcome side.

I'd recommend verifying this answer key against your course materials or instructor, as C is not well-supported by standard statistical reasoning for this scenario.

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