{VERSION 5 0 "SUN SPARC SOLARIS" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "" -1 256 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 258 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 259 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 260 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 261 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE " " 0 262 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 256 "" 0 "" {TEXT -1 11 "Math 2270-2" }}{PARA 257 "" 0 " " {TEXT -1 25 "Solution Template, part A" }}{PARA 258 "" 0 "" {TEXT 256 41 "A Power Law For Human Heights and Weights" }{TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 23 "Type in \+ your name here:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 258 15 "Body Mass Index" }}{PARA 0 "" 0 "" {TEXT -1 517 " In this part of your project you will use the \+ method of least squares to find a power law which (approximately) rela tes human weights to heights. Within the past few years you might ha ve noticed a series of newspaper and magazine articles about the so-ca lled body mass index, and its use in determining risk factors for over weight (and underweight) people. If you search the internet for \"bod y mass index\" you will find many sites which let you compute your B.M .I., and which tell you a little bit about it. " }}{PARA 0 "" 0 "" {TEXT -1 1194 " A person's body mass index (B.M.I.) is computed b y dividing their weight by the square of their height, and then multip lying by a universal constant. (If you measure weight in kilograms, \+ and height in meters, this constant is the number one.) Thus, the prop onants of the B.M.I index seem to be assuming, or claiming, that for adults at equal risk levels (but different heights), weight should be proportional to the square of height. It is easy to deduce that if p eople were to scale equally in all directions when they grew, weight w ould scale as the cube of height. That particular power law seems a \+ little high, since adults don't look like uniformly expanded versions \+ of babies; we seem to get relatively stretched out when we grow taller . One would expect the best predictive power to be somewhere between \+ 2 and 3. If the power is much larger than 2 then one could argue that the body mass index might need to be modified to reflect this fact. O f course, the sample heights and weights which we have collected may o r may not be representative of a healthy population, but let's proceed anyway. (In previous years our experimental power has come out betw een 2.35 and 2.65.)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 549 " Here is the height- weight data which you have pr ovided to me. Thanks to all who contributed, especially Travis. Afte r I tried out your data, I noticed a big hole between 30 and 50 inches , so I took all data points between those heights from last year's cla ss. (We also had a teacher in that class, only she must have had smal ler students.) The first number of each pair is a height, in inches, \+ the second number is a weight, in pounds. Heights vary from baby (19 \+ inches) to tall person (78 inches). Weights vary from 6 to 250 pounds . . " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "restart:with(linalg ):with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1037 "S:=[[60 ,116],[63,132],[71,181],[63,118],[61,115],\n [20,6.0+10/16], [20,7.0 +1/16],[19,6.0+6/16],\n [20,7.0+5/16],[19,6.0+2/16],[19.5,8.0+1/16], \n [21,8.0+13/16],[20,7.0+11/16],[20,8.0+8/16],\n [70,150],[68,135 ],[64,135],[69,132],[68,137],\n [54,70],[73,142],[72,154],[74,170],[ 63,113],\n [72,165],[30,30],[77,230],[73,180],[72,145],\n [66,132] ,[75,250],[72,220],[78,185],[71,165],\n [72,210],[73,180],[67,160],[ 64,110],[63,112],\n [66,120],[76,230],[75,190],[43,41],[27,18],\n \+ [67,120],[73,182],[68,120],[69,154],[66,118],\n [75,185],[67,145],[6 0,98],[64,93],[59,84],\n [60,82],[48,82],[65,90],[49,64],[48,79],[59 ,84],\n [60,92],[59,95],[57,61],[61,90],[53,58],[54,69],\n [50,51] ,[54,77],[54,60],[52,63],[67,130],[63,135],\n [60,105],[66,110],[61, 110],[72,189],[60,100],\n [64,156],[64,140],[69.5,145],[75,180],[67, 138],\n [73,132],[66,187],[74,240],[64,140],[72,187],\n [55,79],[6 7,126],[40,37.5],[42,41.5],[43,41],\n [43,43],[44,42.5],[44,38.5],[4 4,40.5],[45,55],\n [45,46.5],[47,54.5],[48,70.5],[48,43.5],[49,49]]: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "A1:=convert(S,matrix): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 259 "" 0 "" {TEXT -1 122 "1) As in the worked example, find a least squares line \+ fit to the ln-ln data which you obtain from A1. Show your work! " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 260 "" 0 "" {TEXT -1 85 "2) Create a plot display which shows the ln- ln data and your least squares line fit." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 261 "" 0 "" {TEXT -1 163 "3) Deduce a power law for our class height-weight data. Create a pl ot display which shows the graph of the power function and the pointpl ot of our original data." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 259 126 "4) What does yo ur power law predict for the weights of \"average\" people, at heights of 5 feet, 51/2 feet, 6 feet, and 61/2 fe" }{TEXT -1 1 "e" }{TEXT 260 2 "t?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 262 "" 0 "" {TEXT -1 315 "5) Compare the power law you o btained with the one which I obtained from national data. (It's poste d on our Maple page.) Are the two power laws close? How do they comp are to the BMI index? Does this tell you anything about whether one \+ should use the BMI index (without adjustment) on both children and adu lts?" }}}{MARK "16 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }