Problem-Solving and Data AnalysisVery hardResidual from a line of best fit
Problem-Solving and Data Analysis practice question
A scatterplot shows the number of hours x that students studied and their test scores y. The line of best fit is y = 1.8x + 12. One student studied 20 hours and scored 44. What is the residual (actual score minus predicted score) for that student?
Answer: -4
Predicted score: 1.8(20) + 12 = 48. Residual: 44 − 48 = −4.
Common wrong answers
- If you answered 4
- 4 is predicted minus actual; the residual is actual minus predicted.
- If you answered 48
- 48 is the predicted score, not the residual.
- If you answered -8
- −8 uses a predicted score of 52, from 1.8 × 20 = 40 plus 12 = 52 miscalculated.
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