Module 08 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 correlation near zero means…
- A. no relationship
- B. no straight-line relationship
- C. the data is random
- D. the sample is too small
2. Spearman being noticeably higher than Pearson suggests…
- A. a data error
- B. a monotonic but curved relationship
- C. too few observations
- D. a missing variable
3. A regression slope from observational data should be described as…
- A. the effect of x on y
- B. the association between x and y
- C. the cause of y
- D. the prediction error
4. Between R-squared and the residual standard deviation, the more interpretable is…
- A. R-squared, because it is a proportion
- B. the residual SD, because it is in the outcome's units
- C. neither
- D. R-squared, because it detects the wrong shape
5. obs_ci_lower/upper is wider than mean_ci_lower/upper because…
- A. it uses a larger multiplier
- B. a new observation carries the residual scatter as well as the uncertainty in the line
- C. it uses fewer observations
- D. it assumes non-normality
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Answer Key and Explanations
Check these only after attempting every question.
1. B — no straight-line relationship
The lesson's U-shaped relationship was strong and correlated at −0.002.
2. B — a monotonic but curved relationship
Spearman uses ranks, so it captures any consistently increasing relationship even when it is not a straight line.
3. B — the association between x and y
Nothing was randomised, so the slope reflects whatever else differs between high-x and low-x cases.
4. B — the residual SD, because it is in the outcome's units
R-squared cannot tell you the model is the wrong shape; the curved model had the higher one.
5. B — a new observation carries the residual scatter as well as the uncertainty in the line
In the lesson the widths were 3.83 and 24.96 at the same value of x.
Practical Check
Apply this module to your own work: complete the module activity for *Correlation and Simple Linear Regression*, 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.