Module 09 Knowledge Check
5 questions. Pass mark 4 out of 5. Answer every question before checking the answer key below, then retry after reading the feedback.
1. A coefficient in a multiple regression is…
- A. the total association with the outcome
- B. the association holding the other predictors fixed
- C. always smaller than the simple regression version
- D. a causal effect
2. A factor with four levels contributes…
- A. four coefficients
- B. three coefficients, all relative to the reference
- C. one coefficient
- D. one coefficient per observation
3. A systematic pattern in residuals against fitted values indicates…
- A. a large sample
- B. the model is the wrong shape
- C. high R-squared
- D. multicollinearity
4. An observation with a Cook's distance of 29 when the next largest is 0.07 should be…
- A. deleted
- B. investigated, and the model reported with and without it
- C. ignored
- D. replaced with the mean
5. Two predictors correlated at 0.996 will typically produce…
- A. a lower R-squared
- B. inflated standard errors and non-significant coefficients
- C. an error message
- D. a better model
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Answer Key and Explanations
Check these only after attempting every question.
1. B — the association holding the other predictors fixed
The training coefficient went from 853 to 52 once experience entered, and 50 was the truth.
2. B — three coefficients, all relative to the reference
R encodes one fewer indicator than there are levels, and each is a difference from the reference.
3. B — the model is the wrong shape
The curved model's mean residuals swung +4.60, -9.83, +5.23 while its R-squared was the higher of the two.
4. B — investigated, and the model reported with and without it
It may be the most informative observation you have, or a data entry error. Only investigation tells you which.
5. B — inflated standard errors and non-significant coefficients
The standard error went from 0.043 to 0.511 and p from 4e-27 to 0.174, while R-squared barely moved.
Practical Check
Apply this module to your own work: complete the module activity for *Multiple Regression and Diagnostics*, then write one sentence naming what your result shows and one naming what it does not.
Strong Answer Pattern
A strong answer names the task, the evidence used, the check performed, and the remaining limitation. It avoids "proved", "guaranteed", or "always" unless the evidence genuinely supports it.