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A Set of Data Points and the Equations of Two e2\sum \mathrm { e } ^ { 2 }

Question 21

Multiple Choice

A set of data points and the equations of two lines are given. For each line, determine e2\sum \mathrm { e } ^ { 2 } . Then, determine which line fits the set of data points better, according to the least-squares criterion.
- x01335y76542\begin{array}{c|ccccc}\mathrm{x} & 0 & 1 & 3 & 3 & 5 \\\hline \mathrm{y} & 7 & 6 & 5 & 4 & 2\end{array}


Line A: y=7.50.9x\mathrm { y } = 7.5 - 0.9 \mathrm { x }
Line B:y=8.01.1xB : y = 8.0 - 1.1 \mathrm { x }


A)
Line A: e2=2.29\sum \mathrm { e } ^ { 2 } = 2.29
Line B:e2=2.64B : \sum \mathrm { e } ^ { 2 } = 2.64
Line BB fits the set of data points better.

B) Line A: e2=0.87\sum \mathrm { e } ^ { 2 } = 0.87
Line B:e2=0.53B : \sum \mathrm { e } ^ { 2 } = 0.53
Line BB fits the set of data points better.

C) Line A: e2=2.29\sum \mathrm { e } ^ { 2 } = 2.29
Line B:e2=2.64\mathrm { B } : \sum \mathrm { e } ^ { 2 } = 2.64
Line A fits the set of data points better.

D) Line A:e2=3.12\mathrm { A } : \sum \mathrm { e } ^ { 2 } = 3.12
Line B: e2=3.49\sum \mathrm { e } ^ { 2 } = 3.49
Line BB fits the set of data points better.

Correct Answer:

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