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. In revenue ~ spend * C(channel), the term spend:C(channel)[T.social] is…
- A. the social channel's slope
- B. the difference between the two slopes
- C. the social channel's intercept
- D. an error term
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 38 when the next largest is 0.09 should be…
- A. deleted
- B. investigated, and the model reported with and without it
- C. ignored
- D. replaced with the mean
5. Twenty pure-noise predictors on n = 60 produced R-squared 0.26 and adjusted R-squared −0.12. This shows…
- A. the model is useful
- B. R-squared always rises with more terms while adjusted R-squared penalises them
- C. an error in the fit
- D. that n was too large
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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 888 to 82 once experience entered, and 50 was the truth.
2. B — the difference between the two slopes
The social slope was 3.099 − 2.136 = 0.963. Reporting −2.136 as the slope is a common misread.
3. B — the model is the wrong shape
The curved model's mean residuals swung +4.85, −10.24, +5.39 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 — R-squared always rises with more terms while adjusted R-squared penalises them
A negative adjusted R-squared is the honest verdict on a model fitting pure noise.
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.