STANDARD ERROR OF ESTIMATE 1. For the data of Problem 15.28, find the standard error of estimate of X3 on X1 and X2. 2. For the data of Problem 15.29, find the standard error of estimate of (a) X3 on...

STANDARD ERROR OF ESTIMATE

1. For the data of Problem 15.28, find the standard error of estimate of X3 on X1 and X2.

2. For the data of Problem 15.29, find the standard error of estimate of (a) X3 on X1 and X2 and (b) X1 on X2 and X3.

COEFFICIENT OF MULTIPLE CORRELATION

3. (a) If r₁₂ = r₁₃ = r₂₃ = r ≠ 1, show that

(b) Discuss the case r = 1.

4. If R_1.23 = 0, prove that |^r23| ≥ |r12| and |r23| ≥ |^r13| and interpret.

PARTIAL CORRELATION

5. For the data of compute the coefficients of linear partial correlation r_12.3, r_13.2, and r_23.1. Also use STATISTIX to do these same computations.

6. If r₁₂ = r₁₃ = r₂₃ = r 6 = 1, show that r_12.3 = r_13.2 = r_23.1 = r/(1 + r). Discuss the case r = 1.

7. If r_12.3 = 1, show that (a) |r_13.2| = 1, (b) |r_23.1| = 1, (c) R_1.23 = 1, and (d ) s_1.23 = 0.