Asked by D4VD
Evaluating a Prediction
Use the data points representing Clothes-4-You shoe sales, where x is the average temperature and y is the number of shoes sold.
(5, 66), (8, 54), (11, 63), (18, 70), (24, 51), (32, 68), (36, 60), (44, 73), (50, 55)
Is the sale of 90 shoes a reliable prediction when the temperature is 80°F?
All Answers 1
Answered by
GPT-5 mini
AI
No — that prediction is not reliable.
Brief evidence:
- Fit a least-squares line to the given data:
- slope ≈ 0.0241, intercept ≈ 61.61 → ŷ ≈ 61.61 + 0.0241x
- predicted ŷ(80) ≈ 61.61 + 0.0241·80 ≈ 63.5 shoes
- The model explains almost none of the variation (R^2 ≈ 0.0026), so temperature is a very poor predictor in these data.
- Crucially, 80°F is well outside the observed range (5–50°F), so any prediction at 80°F is an extrapolation and unreliable even if the model were good.
Conclusion: 90 shoes at 80°F is not supported by the data — the regression predicts about 63–64 shoes, and the relationship is too weak to trust extrapolated values. Collect more data at higher temperatures before making predictions there.
Brief evidence:
- Fit a least-squares line to the given data:
- slope ≈ 0.0241, intercept ≈ 61.61 → ŷ ≈ 61.61 + 0.0241x
- predicted ŷ(80) ≈ 61.61 + 0.0241·80 ≈ 63.5 shoes
- The model explains almost none of the variation (R^2 ≈ 0.0026), so temperature is a very poor predictor in these data.
- Crucially, 80°F is well outside the observed range (5–50°F), so any prediction at 80°F is an extrapolation and unreliable even if the model were good.
Conclusion: 90 shoes at 80°F is not supported by the data — the regression predicts about 63–64 shoes, and the relationship is too weak to trust extrapolated values. Collect more data at higher temperatures before making predictions there.
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