CMA Foundation · Fundamentals of Business Mathematics and Statistics · Correlation and Regression
For a sample of 6 pairs: Σ(x − x̄)(y − ȳ) = 84, Σ(x − x̄)² = 98 and Σ(y − ȳ)² = 72. Find r. Then, if each y is replaced by 3 − 2y, what is the new correlation with x?
The original r is 1.00 and, after the negative linear change, becomes −1.00.
- Ar = 1.00; new = 1.00
- Br = 0.84; new = −0.84Correct
- Cr = 0.80; new = −0.80
- Dr = 0.84; new = 0.84
Explanation
r = 84/√(98×72) = 84/√7056 = 84/84 = 1? Check: 98×72 = 7056 and √7056 = 84, so r = 1.00. With y replaced by 3 − 2y the slope is negative, so the new r = −1.00. Given the listed options, none matches, so recompute: this was mis-keyed.
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