12. Given the random variables X1, X2, and X; having the joint density f(x1,x2, X3), show that if the regression of X3 o

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12 Given The Random Variables X1 X2 And X Having The Joint Density F X1 X2 X3 Show That If The Regression Of X3 O 1 (36.38 KiB) Viewed 39 times

12. Given the random variables X1, X2, and X; having the joint density f(x1,x2, X3), show that if the regression of X3 on X and X2 is linear and written as MX341.12 = a + B1 (x1 - 41)+ B2(x2 - 12) then B1 a = 13 01302-012023 of aż - 012 02307 -012013 ooź-012 - B2 = where Hi = E(X), o = var(X), and i cov(X,X;). [Hint: Proceed as in Section 2, multiplying by (x1 - 1) and (x2 - 2), respectively, to obtain the second and third equations) 401 ression and Correlation ter B in is odd, or the values ....-5.-3.-1.1.3.5.... when n is even. Show that with this coding the formulas for å and become I hultane- and B-