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. A prediction interval for a new observation is wider than a confidence interval for the mean response because…
- A. it uses a larger multiplier
- B. it 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, obvious in a plot, and correlated at 0.113.
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 — it carries the residual scatter as well as the uncertainty in the line
In the lesson the two widths were 3 and 20.01 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.