A further property of r. Suppose all x measurements are changed to x = ax = b and all y measurements to y cy

d, where

a, b, c, and d are fixed numbers Then the correlation coefficient remains unchanged if a and c have the same signs; it changes sign but not numerical value if a and c are of opposite signs.

This property of r can be verified along the lines of Exercise 2.74 in Chapter 2. In particular, the deviations change to and the deviations change to Consequently, and change to 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

Calculate r from the ( x , y ) 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?

Transcribed Image Text:

ac" = r if a and c have the same signs -r if a and c have opposite signs