For three variables X1, X2 and X3, the following information is available: s1 = 10, r12 = 0.90
s2 = 5, r13 = 0.75
s3 = 3, r23 = 0.70
Then partial regression coefficient (b13,2) of X2 on X1 and X3 is:
0.784
The formula for partial regression coefficient is:
b13,2 = (r13 - r12 * r23) / √(1 - r12²)
Substituting the given values:
b13,2 = (0.75 - 0.90 * 0.70) / √(1 - 0.90²) ≈ 0.784.
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