CA Foundation · Quantitative Aptitude · Correlation and Regression
A scatter diagram of paired observations on X and Y shows all points lying exactly on a straight line that slopes downward from left to right. Which value of Karl Pearson's coefficient of correlation is implied?
The coefficient is -1. When all points fall exactly on one straight line, the correlation is perfect, so its magnitude is 1. Because the line slopes downward, the variables move in opposite directions, which makes the sign negative and r equal to minus one.
- A0
- B-1Correct
- C+1
- D-0.5
Explanation
Points lying exactly on a straight line indicate perfect linear correlation, so |r| = 1. A downward slope means Y decreases as X increases, so r is negative, giving r = -1. Option +1 would need an upward slope.
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