Slope of a Least-Squares Line
Mediumregressionstatistics
A least-squares line is fitted to the points (1, 2), (2, 5), (3, 7) and (4, 10). The slope of the best-fit line is most nearly:
- A2.0
- B2.3
- C2.6
- D3.0
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Answer: C. 2.6
The least-squares slope is b = Σ(x − x̄)(y − ȳ)/Σ(x − x̄)². With x̄ = 2.5 and ȳ = 6.0 the numerator is 13.0 and the denominator 5.0, giving b = 2.6. Simply taking the endpoints, (10 − 2)/(4 − 1) = 2.67, is close here but ignores the interior points and is not the least-squares result.
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