Let r 1 = coefficient of correlation between n pairs of values (Y i , X i

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Let r1= coefficient of correlation between n pairs of values (Yi, Xi) and r2= coefficient of correlation between n pairs of values (aXi+ b, cYi+ d), where a, b, c, and d are constants. Show that r1= r2and hence establish the principle that the coefficient of correlation is invariant with respect to the change of scale and the change of origin.

Apply the definition of r given in Eq. (3.5.13).

Σxy (Σx) (ΣΥ) η ΣΧΥ-(Σ Χ)(Σ Υ) VDΣK-ΣΧ)IΣΥ-ΣΗ

The operations aXi , X+ b, and aXi + b are known, respectively, as the change of scale, change of origin, and change of both scale and origin.

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Basic Econometrics

ISBN: 978-0073375779

5th edition

Authors: Damodar N. Gujrati, Dawn C. Porter

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