Suppose all x measurements are changed to x = ax + b and all y measurements to
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This Property of r can be verified along the line of Exercise 2.74 in Chapter 2. In Particular, the deviations x - Change to a (x - ) and the deviations y - Change to c (y - ). Consequently,
ˆšSxx, ˆšSyy, and Sxy change to |a| ˆšSxx, |c| ˆšSyy, and acSxy,
Respectively (recall that we must take the positive square root of a sum of squares of the deviations). Therefore, r changes to
(a) For a numerical verification of this property of r, consider the data of Exercise 3.18. Change the x and y measurements according to
xʹ = 2x - 3
yʹ = -y + 10
Calculate r from the (xʹ, yʹ) measurements and compare with the result of Exercise 3.18.
(b) Suppose from a data set of height measurements in inches and weight measurements in pounds, the value of r is found to be .86. What would the value of r be if the heights were measured in centimeters and weights in kilograms?
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Related Book For
Statistics Principles And Methods
ISBN: 9780470904114
7th Edition
Authors: Richard A. Johnson, Gouri K. Bhattacharyya
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