Let the components of X correspond to scores on tests in arithmetic speed (X1)' a rithmetic power (X2 ), memory for words (X3), memory for meaningful symbols (X4), an d memory for meaningless symbols (Xs). The observed correla- tions in a sample of 14 O are [Kelley (1928)) (1.0000 0.4248 0.0420 0.0215 0.0573) 0.4248 1.0000 0.1487 0.2489 0.2843 0.0420 0.1487 1.0000 0.6693 0.4662 0.0215 0.2489 0.6693 1.0000 0.6915 (0.0573 0.2843 0.4662 0.6915 1.0000 (a) Find the partial correlation between X4 and Xs, holding X3 fixed. (b) Find the partial correlation between X, and X2 , holding X3, X4 , and X, fixed. (C) Find the multiple correlation between X1 and the set X3, X1 , and X.

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Let the components of X correspond to scores on tests in arithmetic speed (X1)' a
rithmetic power (X2), memory for words (X3), memory for meaningful symbols (X4), an
d memory for meaningless symbols (Xs). The observed correla- tions in a sample of 14
O are [Kelley (1928)]
1.0000 0.4248 0.0420 0.0215 0.0573
0.4248 1.0000 0.1487 0.2489 0.2843
0.0420 0.1487 1.0000 0.6693 0.4662
0.0215 0.2489 0.6693 1.0000 0.6915
(0.0573 0.2843 0.4662 0.6915 1.0000
(a) Find the partial correlation between X4 and X5, holding X3 fixed.
(b) Find the partial correlation between X, and X2 , holding X3, X4 , and Xg fixed.
(C) Find the multiple correlation between X1 and the set X3, X1 , and Xg.
(d) Test the hypothesis at the 1% significance level that arithmetic speed is independen
t of the three memory scores.
Transcribed Image Text:Let the components of X correspond to scores on tests in arithmetic speed (X1)' a rithmetic power (X2), memory for words (X3), memory for meaningful symbols (X4), an d memory for meaningless symbols (Xs). The observed correla- tions in a sample of 14 O are [Kelley (1928)] 1.0000 0.4248 0.0420 0.0215 0.0573 0.4248 1.0000 0.1487 0.2489 0.2843 0.0420 0.1487 1.0000 0.6693 0.4662 0.0215 0.2489 0.6693 1.0000 0.6915 (0.0573 0.2843 0.4662 0.6915 1.0000 (a) Find the partial correlation between X4 and X5, holding X3 fixed. (b) Find the partial correlation between X, and X2 , holding X3, X4 , and Xg fixed. (C) Find the multiple correlation between X1 and the set X3, X1 , and Xg. (d) Test the hypothesis at the 1% significance level that arithmetic speed is independen t of the three memory scores.
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