78. Let A denote the percentage of one constituent in a randomly selected rock specimen, and let B denote the percentage of a second constituent in that same specimen. Suppose D and E are measurement errors in determining the values of A and B so that measured values are X  A  D and Y  B  E, respectively.

Assume that measurement errors are independent of one another and of actual values.

a. Show that

# 2Corr1Y1, Y2 2 Corr1X, Y2  Corr1A, B2 # 2Corr1X1, X2 2 s2 s X 2 W

s2 E

where X1 and X2 are replicate measurements on the value of A, and Y1 and Y2 are de ned analogously with respect to B. What effect does the presence of measurement error have on the correlation?

b. What is the maximum value of Corr(X, Y) when Corr(X1, X2)  .8100 and Corr(Y1, Y2)  .9025?

Is this disturbing?