Question

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ox comparing modeis The total numbers y of AIDs cases by year ot diagnosis in Canada for the years 2005 through 2014 are shown in the table, with 5 corresponding to 2005 (Source: Public Health Agency of Canada) 10 12 43438 31 367 296 276 234223 a. Use the regression capabilities of a graphing utility to find the following models for the data. b. Use a graphing utility to plot the data and graph each of the models. Which model do you think best fits the data? c. Find the rate of change of each of the models in part (a) for the year 2012. Which model is decreasing at the greatest rate in 2012 1157 PM

Answer 1

651.7613 402.2784 406.2409 370.647 635.2724 366.194 358.0035 342.908 620.9889 333.3464 320.8736 315.169 608.3901 303.4452 291.3325 350 671.2637 441.9184 471 287.43 597.12 276.2262 267.2192 259.691 586.925 251.4487 247.1301300 231.952 577.6177 228.8937 230.1119 204.213 569.0558 208.362 215.4935 176.474 561.1287 189.6719 202.7882 200 10 16 y3 4 450 16 10 12 \r\nTo find the best fit, we find the sum of error squares for each of the models as shown belovw. The error is minimum for y3. Hence y3 model is the best fit of the 4 models. (c) The rate of progress can be found by separating every y For yl, the rate of progress is consistent, 27.739 For y2, the rate of progress is 246.3/x For y3, the rate of progress is 7070.9103x *In(0.9103) For y4, the rate of progress is 1765.5 -0.82) * x-1.82 For the year 2012, x 12. So the rate of progress for the 4 models is as beneath Show y1: - 27.739 Show y2: - 246.3/1220.525 Show y3:, 707\"" 0.910312 In(0.9103)9.3424 For y4, the rate of progress is 1765.5 0.82) X-1.82-15.7243 \r\nActual Error Actual Error Actual Error Actual Brar ata Error squared y2 Data Error squared y Data Error squared 5 426.125 4347.875 62.01562 671.2637 434 237.2637 56294.06 441.9184 434 7.918444 62.70175 471.7504434 37.75044 1425.096 6 398.386 398 0.386 0.148996 651.7613398 253.7613 64394.82 402.2784 4.278359 18.30436 406.2409398 8.240948 67.91322 71-12.9965 168.9078 367-33.6536 1132.565 320.8736 367-46.1264 2127.648 296-4.66755 21.786 70.647 371 0.353 0.124609 635.2724 371 264.2724 69839.88 366.194 371 -4.80601 23.09773 358.0035 3 342.908 367-24.092 580.4245 620.9889 367 253.9889 64510.38 333.3464 8 9 15.169 19.169 367.4506 608.3901 296 7.445218 55.43128 291.3325 11.43 130.6449 597.1227321.12 103118.1 276.2262276 0.226182 0.051158 267.2192 296 312.3901 97587.56 303.4452 10 287.43 276 276-8.78076 77.10177 11 259.691234 25.691 660.0275 586.925 234 352.925 124556 251.447 234 17.44869 304.4569 247.1301 234 13.13014 172.4006 12231.952 223 8.952 80.1383 577.6177 223 354.6177 125753.7 228.8937223 5.893746 34.73624 230.1119 223 7.111912 50.57929 13 204.213 226 -21.787 474.6734 569.0558226 343.0558 117687.2 208.36222617.638 311.0999 215.4935 226-10.5065 110.3866 14 176.474 188 -11.526 132.8487 561.1287188 373.1287 139225 189.6719 188 1.671908 2.795275 202.7882 188 14.78822 218.6916 4440.511 234 352.925 124556 251.4487 2488.497 962966.7 1945.24 "",""error"":null,""modified"":1551134599,""source"":""automated""}"