ITPEC FE Subject A October 2024 Question 57
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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