Pearson Correlation.docx

1. Manual Computation: X 2 6 4 5 7 7 2 3 5 4 45

x -2.5 1.5 -0.5 0.5 2.5 2.5 -2.5 -1.5 0.5 -0.5

x2 6.25 2.25 0.25 0.25 6.25 6.25 6.25 2.25 0.25 0.25 30.5

zx -1.4315 0.8589 -0.2863 0.2863 1.4315 1.4315 -1.4315 0.8589 0.2863 -0.2863

X2 4 36 16 25 49 49 4 9 25 16 233

Y 8 3 9 7 2 3 9 8 6 7 62

y 1.8 -3.2 2.8 0.8 -4.2 -3.2 2.8 1.8 -0.2 0.8

x̅=4.5 SDX=1.7464 ȳ=6.2 SDy=2.4819 Working Formulas: A. r= ∑xy (N)( SDX)(SDy) =

-39 (10)(1.7464)(2.4819)

=

-39 43.3439 r= -0.90 C. r=

(N) (∑XY) – (∑X) (∑Y) √ {(N) (∑X ) – (∑X)2} {(N) (∑Y2) – (∑Y)2} 2

=

=

=

(10)(240) – (45)(62) √ {(10)(233) – (45)2} {(10)(446) – (62)2} 2,400-2790 √ (305)(616)

-390 433.4513 r= -0.90

y2 3.24 10.24 7.84 0.64 17.64 10.24 7.84 3.24 0.04 0.64 61.6

B. r=

=

=

zy 0.7253 1.2893 1.1282 0.3223 1.6923 1.2893 1.1282 0.7253 0.0806 0.3223

Y2 64 9 81 49 4 9 81 64 36 49 446

∑xy √ (∑x2) (∑y2) -39 √ (30.5) (61.6)

-39 43.3451 r= -0.90

(zx)(zy) -1.0383 1.1074 -0.3230 0.0923 2.4225 1.8456 -1.6150 0.6230 0.0231 -0.0923 3.0453

xy

XY -4.5 16 -4.8 18 -1.4 36 0.4 35 -10.5 14 -8 21 -7 18 -2.7 24 -0.1 30 -0.4 28 -39 240