ITPEC FE Morning April 2021 Question 4
To compare the entrance exams of the current and previous years, a company required many of its employees to take those exams. The correlation coefficient and the regression line were obtained by assigning the scores of the previous year to the x-axis and the scores of the current year to the y-axis. Which of the following can be derived from the results below?
[Results]
The correlation coefficient is 0.8.
The slope of the regression line is 1.1.
The y-intercept of the regression line is 10.
Explanation
Current-year scores tend to be higher — the regression line y = 1.1x + 10 lies above y = x for every score of 0 or more.
The line predicts the current-year score y from the previous-year score x. Its gap above the diagonal is y − x = 0.1x + 10, which is positive for any x ≥ 0: a candidate is predicted to score 10 points more at 0, 15 more at 50 and 20 more at 100. A correlation of 0.8 is strong, so the tendency is a reliable one.
Answer (a)
Why not others:
- •(b) — the correlation coefficient and slope describe how the two years' scores relate, not whether either exam is well made
- •(c) — the regression line passes through the two means, so the current-year mean is 1.1 times the previous-year mean plus 10, not 1.1 times it
- •(d) — the intercept is the predicted current-year score for someone who scored 0 in the previous year; the option swaps the two years
Key rule: In y = ax + b the slope is the change in y per unit of x and the intercept is y at x = 0; keep track of which variable is on which axis.
Basic Theory · AI-written, may contain errors
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