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Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

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BuyFindarrow_forward

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

A researcher measures three variables, X, Y, and Z, for each individual in a sample of n = 25. The Pearson correlations for this sample are rxy = 0.8, rxz = 0.6, and ryz = 0.7.

  • a. Find the partial correlation between X and Y, holding Z constant.
  • b. Find the partial correlation between X and Z, holding Y constant. (Hint: Simply switch the labels for the variables Y and Z to correspond with the labels in the equation.)

a.

To determine
The Partial correlation of the sample.

Explanation

Given info:

The Pearson correlation between X and Y is 0.8, Pearson correlation between X and Z is 0.6 and Pearson correlation between Y and Z is 0.7. A random sample of size 25 is taken.

Calculation:

Formula to calculate the Partial correlation is,

rXYZ=rXY(rXZrYZ)(1rXZ2)(1rYZ2) (1)

Where rXY is correlation between X and Y, rXZ is the correlation between X and Z and rYZ is the correlation between Y and Z.

Substitute 0.8 for rXY, 0.6 for rXZ and 0

b.

To determine
The Partial correlation of the sample.

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