Answers and explanations · Describe an association without inventing a cause

Lesson 10 answers

10A. Fitted value=12.6622+1.8058×40=84.8942 minutes, approximately 84.89. Residual=90−84.8942=+5.1058 minutes. The hypothetical shipment was about 5.11 minutes slower than the line's fitted value. Using full-precision coefficients gives a slightly different last decimal, which is rounding rather than a method disagreement.

10B. Correlation does not establish cause. r is not a percentage of delay explained, and the fitted outcome is actual delivery minutes, not the late indicator. The dataset is fictional and observational. A better sentence: “Recorded distance and actual minutes have a strong positive linear association in this synthetic fixture, r≈0.923; route/service mix and shared weekly conditions limit causal and inferential interpretation.” R²≈0.851 describes in-sample variation around the mean, not a causal share.

10C. Zero and 100 km lie outside the observed range, so intercept interpretation and a 100-km prediction require extrapolation assumptions. Look for curvature, changing residual spread, unusual influential observations and patterns by time or service. A high R² does not rule them out.