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Two variables X and Y are said to have a spurious correlation if their correlation solely reflects each variable's relationship to a third (antecedent) variable Z (and possibly to other variables). The table below presents zero-order correlations based on the responses of 34 subjects. .202 674 430 360 532 Xi .303 X2 Determine the partial correlations ryxI(x2, Tyxix. Exixzy and ryx2x3 b) Test the significance of the partial correlations c) Comment relationships between the variables using both zero-order and partial correlations Variable Constant X, x4=( x, x2) Coefficient Standard deviation 4904 01523 6388 6298 02039 01974 pa (approximate) 1.1361 07648 7433 8239 02772 03204 X5 (-X, X,)

Answer 1

(3 X 1 0. 360 o.532202 0:303 . 67y X2 10:532-10:203 X3 0.2020.30 2- YX Ci ㅡ 0.5325 (1-0.305

(3 X 1 0. 360 o.532202 0:303 . 67y X2 10:532-10:203 X3 0.2020.30 2- YX Ci ㅡ 0.5325 (1-0.305

X1r C1-0:202 C-e16.sus724) 0-136)48 072 3503 二0.188 0.303-(0360(o.s32) 84 0.71676) 78997 o. 14112- 0.532- (o.22 (0.430) 1-0, 20 2つ(I-o,y30 9591 (o 8151) o 38422 .503427 02 tn-2-t 92 614 0.2463) 1.4 P-valueo,.ogsy のt: o.is8)8./ 1-02-218亘lo,06MG 3 :5.5368 (о.)5W8) P-value 0.15065 1.05

지X2ly p-valve = o. 22025 P-value o.ooi55 Yx21X3 signi cant

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