4.42. Let the components of X correspond to scores on tests in arithmetic speed (XI)' arithmetic power

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4.42. Let the components of X correspond to scores on tests in arithmetic speed

(XI)' arithmetic power (X2 ), memory for words (X3 ), memory for meaningful symbols (X.1), and memory for meaningless symbols (X;). The observed correlations in a sample of 140 are [Kelley (1928»)

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(a) Find the partial correlation between X4 and Xs, holding X3 fixed.

(b) Find the partial correlation between Xl and X2 , holding X3, X4 , and Xs fixed.

(c) Find the multiple correlation between Xl and the set X3, X. I , and Xs.

(d) Test the hypothesis at the 1% significance level that arithmetic speed is independent of the three memory scores.

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