CA Foundation · Quantitative Aptitude · Correlation and Regression
In a scatter diagram for a sample of firms, all plotted points lie exactly on the straight line y = 12 - 2x. Which statement is correct?
The correlation coefficient is -1, a perfect negative correlation. When all points lie exactly on a straight line, the absolute value of r is 1, and the downward slope of -2 makes the sign negative. The slope's size does not matter and r cannot be -2.
- Ar = -1, a perfect negative correlationCorrect
- Br = -2, because the slope is -2
- Cr = +1, because the points lie on a line
- Dr = 0, because the line is not through the origin
Explanation
Points exactly on a straight line give |r| = 1. The slope is negative, so r = -1. The magnitude of r never exceeds 1, so the slope value -2 is not r. The intercept does not affect r.
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