6 X 159

(b) This is less than the critical value of 0.591 so the null of no rank correlation cannot be rejected.

(c) The differences d should change in sign, but this is eliminated when d2 is calculated, so the result is the same with the rankings reversed.

Exercise 7.4 (a) Using the data and calculations in the answer to Exercise 7.1 we obtain: 12 x 1964 - 60 x 380

(b) A unit increase in the measure of inequality leads to approximately one additional birth per 1000 mothers. The constant has no useful interpretation. The income ratio cannot be zero (in fact, it cannot be less than 0.5).

Exercise 7.5 (a) TSS = £(7, - Y)2 = XY2- nY2 = 12 5 64 - 12 x 31.662 = 5 30.66 7

= 12 564 - 26.443 x 380 - 1.045 x 1139.70 = 463.804

(b) This is the square of the correlation coefficient, calculated earlier as 0.355.

and sb - V0.757 = 0.870 For a the estimated variance is si - s2 x 11 +-W _ , I = 46.3804 x ( — + —— | = 22.793

and hence sa - 4.774. The 95% CIs are therefore 1.045 ± 2.228 x 0.87 = [-0.894, 2.983 ] for b and 26.443 ± 2.228 x 4.774 = [15.806, 37.081].

Not significant.

Exercise 7.7 Excel should give the same answers.

Exercise 7.8 (a) BR = 26.44 + 1.045 x 10 = 36.9. (b)

36.9 - 2.228 x 6.81J— + ^^—, 36.9 + 2.228 x 6.81J— + (10 5)

12 61.26 V12 61.26

36.9 - 2.228 x 6.81.11 + — + ^^—^, 36.9 + 2.228 x 6.81- 1 + — + -(1° 5)

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