For the following paired observations, calculate the Pearson product-moment corr
ID: 3436462 • Letter: F
Question
For the following paired observations, calculate the Pearson product-moment correlation coefficient and test for significance at the .01 level.
x x2 y y2 xy
17 289 23 529 391
17 289 19 361 323
18 324 20 400 360
19 361 17 289 323
21 441 15 225 315
22 484 19 361 418
21 441 20 400 420
23 529 19 361 437
22 484 20 400 440
18 324 16 256 288
198 3,966 188 3,582 3,715
Explanation / Answer
=Result Details & Calculation
X Values
? = 198
Mean = 19.8
?(X - Mx)2 = SSx = 45.6
Y Values
? = 188
Mean = 18.8
?(Y - My)2 = SSy = 47.6
X and Y Combined
N = 10
?(X - Mx)(Y - My) = -7.4
R Calculation
r = ?((X - My)(Y - Mx)) / ?((SSx)(SSy))
r = -7.4 / ?((45.6)(47.6)) = -0.1588
Meta Numerics (cross-check)
r = -0.1588
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