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10 March, 22:36

Convert the data to centimeters (1 inchequals=2.54 cm), and recompute the linear correlation coefficient. What effect did the conversion have on the linear correlation coefficient?

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  1. 11 March, 00:28
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    it is not affected by a change of units

    Step-by-step explanation:

    Since the correlation coefficient has no dimensions, it is not affected by a change of units. Then it will remain the same after the conversion

    In fact, the linear correlation coefficient ρ, where

    ρ = Cov (X, Y) / (σx*σy)

    then the units [ ] of ρ are

    [ρ] = [ Cov (X, Y) ] / [σx]*[σy] = σ²/σ² = 1 → dimensionless

    is more useful than using covariance [ Cov (X, Y) ], since dividing by the standard deviations eliminates the units and standardise the variable
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