Question

# The following bivariate data set contains an outlier. x y 48.9 43.4 33.2 483.2 63.3 -182.8...

The following bivariate data set contains an outlier.

x y
48.9 43.4
33.2 483.2
63.3 -182.8
44.5 -22.7
40.6 -84.6
71.1 75.3
45.9 -126.9
16.1 343.7
44.3 77.1
53 -294
30.5 -94.2
53.9 2.1
6.9 491.9
65.5 -13
263.7 2849.6

What is the correlation coefficient with the outlier?
rw =

What is the correlation coefficient without the outlier?
rwo =

Would inclusion of the outlier change the evidence for or against a significant linear correlation?

• Yes. Including the outlier changes the evidence regarding a linear correlation.
• No. Including the outlier does not change the evidence regarding a linear correlation.

correlation coefficient with the outlier-

 X Y (x-x̅)² (y-ȳ)² (x-x̅)(y-ȳ) 48.9 43.4 97.22 37303.06 1904.36 33.2 483.2 653.31 60841.16 -6304.63 63.3 -182.8 20.61 175846.04 -1903.80 44.5 -22.7 203.35 67205.38 3696.76 40.6 -84.6 329.79 103130.90 5831.90 71.1 75.3 152.28 25998.34 -1989.70 45.9 -126.9 165.38 132088.63 4673.84 16.1 343.7 1819.88 11483.27 -4571.45 44.3 77.1 209.09 25421.11 2305.50 53 -294 33.18 281472.69 3055.91 30.5 -94.2 798.63 109388.95 9346.71 53.9 2.1 23.62 54962.11 1139.38 6.9 491.9 2689.46 65208.73 -13242.97 65.5 -13 45.43 62270.21 -1681.90 263.7 2849.6 42000.40 6828082.56 535520.52
 ΣX ΣY Σ(x-x̅)² Σ(y-ȳ)² Σ(x-x̅)(y-ȳ) total sum 881.4 3548.1 49241.62 8040703.14 537780.4 mean 58.760 236.540 SSxx SSyy SSxy

correlation coefficient , r = Sxy/√(Sx.Sy)   =537780.4/√(49241.62*8040703.14) = 0.8547

-------------------------------------

correlation coefficient without the outlier-

 X Y (x-x̅)² (y-ȳ)² (x-x̅)(y-ȳ) 48.9 43.4 22.83 42.16 -31.03 33.2 483.2 119.28 187755.08 -4732.33 63.3 -182.8 367.82 54145.97 -4462.72 44.5 -22.7 0.14 5269.72 -27.48 40.6 -84.6 12.40 18088.33 473.61 71.1 75.3 727.84 645.52 685.45 45.9 -126.9 3.16 31255.71 -314.44 16.1 343.7 785.20 86322.64 -8232.90 44.3 77.1 0.03 740.23 4.86 53 -294 78.83 118262.30 -3053.28 30.5 -94.2 185.54 20762.75 1962.75 53.9 2.1 95.62 2284.16 -467.35 6.9 491.9 1385.43 195370.31 -16452.14 65.5 -13 457.04 3955.51 -1344.56
 ΣX ΣY Σ(x-x̅)² Σ(y-ȳ)² Σ(x-x̅)(y-ȳ) total sum 617.7 698.5 4241.184 724900.39 -35991.5 mean 44.121 49.893 SSxx SSyy SSxy

correlation coefficient , r = Sxy/√(Sx.Sy)   = -35991.5/√(4241.184*724900.39) =    -0.6491

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Yes. Including the outlier changes the evidence regarding a linear correlation

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