A Set of Data Points and the Equations of Two $\sum \mathrm { e } ^ { 2 }$

question 3

Multiple Choice

A set of data points and the equations of two lines are given. For each line, determine $\sum \mathrm { e } ^ { 2 }$ . Then, determine which line fits the set of data points better, according to the least-squares criterion.
- $\begin{array}{c|ccccc}\mathrm{x} & 0 & 1 & 3 & 3 & 5 \\\hline \mathrm{y} & 7 & 6 & 5 & 4 & 2\end{array}$


Line A: $\mathrm { y } = 7.5 - 0.9 \mathrm { x }$
Line $B : y = 8.0 - 1.1 \mathrm { x }$

• A)
• Line A: \(\sum \mathrm { e } ^ { 2 } = 2.29\)
• Line \(B : \sum \mathrm { e } ^ { 2 } = 2.64\)
• Line \(B\) fits the set of data points better.
• B) Line A: \(\sum \mathrm { e } ^ { 2 } = 0.87\)
• Line \(B : \sum \mathrm { e } ^ { 2 } = 0.53\)
• Line \(B\) fits the set of data points better.
• C) Line A: \(\sum \mathrm { e } ^ { 2 } = 2.29\)
• Line \(\mathrm { B } : \sum \mathrm { e } ^ { 2 } = 2.64\)
• Line A fits the set of data points better.
• D) Line \(\mathrm { A } : \sum \mathrm { e } ^ { 2 } = 3.12\)
• Line B: \(\sum \mathrm { e } ^ { 2 } = 3.49\)
• Line \(B\) fits the set of data points better.

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Definitions:

Comparative Negligence

A legal doctrine that reduces the amount of damages a plaintiff can recover in a negligence-based lawsuit, in proportion to the plaintiff's own percentage of fault.

Contributory Negligence

A legal doctrine where a party's own negligence contributes to their harm or loss, potentially limiting or barring their recovery in a lawsuit.

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is a legal doctrine that prevents a plaintiff who has participated in wrongdoing from recovering damages for loss resulting from the wrongdoing.