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Question 19 10 pts -9. The length x of a leg bone and the length y of an arm bone (in centimeters) in each of five fossils of apparently exceedingly great antiquity were measured. Summary information is 38 < x < 74,41 < y < 84, ī= 58.2, y = 66.0 SSxx = 696.8, SSxy = 834, SSyy - 1010, 8, = 1.975, n = = 25

Answer 1

Salection: a linear we have assuoned Given that, y denotes the length of an arm bone (in em) x denotes the length of leg bone (in cm) to predict the relationship, segression model, Hi=x+pXitei Vi1(1) 25. where ci ind N(0,02). intercept To anscoer the question, whether length of leg bone ( 2 ) is useful to predict the length of am bone (8). We want to test, to: p=0 against his 8 to or to e(x,y) = 0 against #: 2(x,y) cohere e(x,y) - population correlation coefficient between term, p= slope parameter (both unknown) 2 ㅠ X and Y. Test statistic: render Ho, t = Jonas Ji-pa tn-2(t-díst" with af = -2 sample correlation eoeftfcient between x and y Cor(x, y) +3(2-7)(41-4) WÁ Z (2-3)? Why-D 21 (Xi-) (93-7) WZ (24 - 2)² Zi (91-9² & 22 Syy Ivar (x). Varly ssay = 834 696.8 x 1010 = 55.5956. reject to at level d = o. here n=25 = 0.9963. N25-2 (0-9963) observed t = 1 -0.9963² Decision rele: coe = 0.02 if observed It Hote; 1-2 . here It Ho 55.5956 >> 2.5 = tosin-2 - to-01,23 Conclusion: We reject to at x'=0.02 and conclude that this prediction is really worthwile.