Based on the linear regression used to predict a team's scoring margin at the end of the season, the authors of the textbook discovered that each offensive turnover has more than double the impact on the scoring margin than each defensive turnover. True or False?

Question

BlackTom AI · Accepted Answer

In linear regression, each predictor’s coefficient measures the expected change in the response (here, scoring margin) associated with a one-unit change in that predictor, holding other variables constant. Thus the coefficients for offensive turnovers and defensive turnovers tell us how many points the scoring margin is expected to change for one additional offensive turnover or one additional defensive turnover.

Step-by-step reasoning:
1. Let b_off be the regression coefficient for offensive turnovers and b_def for defensive turnovers. Interpretation: a one-unit increase in offensive turnovers changes scoring margin by b_off points; similarly for defensive turnovers by b_def points.
2. The statement claims |b_off| > 2·|b_def| (each offensive turnover has more than double the impact of each defensive turnover).
3. The textbook’s reported regression results contradict that inequality: the magnitude of b_def is larger than the magnitude of b_off (defensive turnovers had the greater effect on scoring margin). In algebraic terms the authors found |b_def| > |b_off|, not |b_off| > 2·|b_def|.
4. Therefore the claimed inequality (offensive turnover impact more than double defensive turnover impact) is false.

Why the correct answer is correct:
- Because regression coefficients are the basis for comparing impacts, and the actual coefficients reported by the authors show defensive turnovers reduce scoring margin by more points per turnover than offensive turnovers do. That directly contradicts the “more than double” claim about offensive turnovers.

Why “True” is incorrect:
- Accepting “True” would require the textbook’s coefficients to show offensive turnovers having more than twice the magnitude of effect, which is not what the reported regression shows.

Conclusion: The correct judgment is False, matching the provided answer.

Based on the linear regression used to predict a team's scoring margin at the end of the season, the authors of the textbook discovered that each offensive turnover has more than double the impact on the scoring margin than each defensive turnover. True or False?判断题

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