The data at the bottom pertains to the question that I have. For purposes of this question, only use the data for ages 30-110. Let L x denote the number of survivors at age x . The Mortality Rate at Age x is defined to be ( L x -L x+1 )/L x For example, the Mortality Rate at Age x = 30 is (L x -L x+1 )/L x = (L 30- L 31 )/L 30 = (97,092-96,954)/97,092 = .001421 The Mortality Rate at Age x = 31 is (L x -L x+1 )/L x = (L 31- L 32 )/L 31 = (96,954-96,818)/96,954 = .001402 (a) Calculate the regression of Mortality Rate on age. That is, find the regression line Mortality Rate = a + b (Age). (b) Now, estimate the quadratic regression function

Mortality Rate = a + b(Age) +c(Age²).

(c) What fraction of the variation in Mortality Rate is explained in this model?

(d) Have the computer draw a graph with Age on the horizontal axis and Mortality Rate on the vertical axis, with the quadratic regression function on the graph showing 95% prediction interval bands.

A B Number of Age Survivors 0 100000 1 99249 2 99193 3 99155 4 99126 5 99102 6 99083 7 99066 8 99051 9 99035 10 99019 11 99001 12 98983 13 98963 14 98938 15 98906 16 98860 17 98791 18 98700 19 98580 20 98444 21 98311 22 98163 23 98023 24 97888 25 97752 26 97624 27 97489 28 97359 29 97224 30 97092 31 96954 32 96818 33 96677 34 96522 35 96359 36 96180 37 95997 38 95791 39 95569 40 95337 41 95087 42 94825 43 94542 44 94229 45 93892 46 93529 47 93142 48 92713 49 92254 50 91768 51 91247 52 90707 53 90127 54 89527 55 88839 56 88161 57 87382 58 86542 59 85600 60 84654 61 83582 62 82458 63 81231 64 79920 65 78506 66 76988 67 75391 68 73665 69 71830 70 69875 71 67824 72 65652 73 63335 74 60880 75 58335 76 55655 77 52874 78 50001 79 47012 80 43928 81 40856 82 37568 83 34457 84 31192 85 27975 86 24820 87 21766 88 18852 89 16113 90 13580 91 11277 92 9218 93 7412 94 5857 95 4546 96 3462 97 2586 98 1893 99 1357 100 953 101 600 102 400 103 200 104 100 105 50 106 30 107 15 108 7 109 3 110 1 111 0

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