IPA FE Subject A 2024 Question 19
A question IPA Japan published in 令和６年度 基本情報技術者試験 科目A 公開問題 問19, translated into English. ITPEC is based on the same exams.
Same question on ITPEC: Oct 2024 Q57
The relationship between the value “x” of a certain factor in the manufacture of a product and the value “y” of a quality characteristic of the product is plotted in the figure below. Which of the following is an appropriate interpretation of this figure?
Explanation
The correlation coefficient is negative — the points fall from upper left to lower right.
In the scatter plot, larger values of x go with smaller values of y, and the band of points is roughly straight. That is a negative linear relationship, so the correlation coefficient r lies between -1 and 0.
Answer (b)
Why not others:
- •(a) — the points form a straight band, not a curve, so simple linear regression is enough; nothing calls for a quadratic term
- •(c) — a positive coefficient would show the points rising from lower left to upper right
- •(d) — the regression of y on x minimises vertical errors and that of x on y minimises horizontal errors; the two lines coincide only when the points lie exactly on a line, |r| = 1
Key rule: Read the sign of the correlation from the direction of the point cloud (falling is negative, rising is positive) and its strength from how tightly the points hug a line.
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This question comes from the past questions IPA Japan publishes, translated into English by ITPEC Practice. ITPEC Practice is an independent study tool and is not affiliated with IPA or ITPEC. See the original paper (PDF) or Report an issue.