{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 "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 1 14 0 0 0 0 0 1 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 0 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 } {CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 266 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 267 "" 0 1 0 0 0 0 0 0 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 "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 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 "" 0 256 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 0 0 0 0 0 0 0 0 0 }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 0 0 0 0 0 0 0 0 0 }3 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 0 0 0 0 0 0 0 0 0 }3 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 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 13 263 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 11 "" 0 "" {TEXT -1 0 "" }}{PARA 11 "" 1 "" {TEXT 256 13 "ACCESS - MATH" }}{PARA 257 "" 0 "" {TEXT -1 9 "July 2009" }}{PARA 256 "" 0 "" {TEXT -1 49 "Notes on Body Mass Index and Actual National \+ Data" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 28 "What is the Body Mass Index?" }}{PARA 0 "" 0 "" {TEXT -1 383 " If you read newspapers and magazines it i s likely that once or twice a year you run across an article about the body mass index (B.M.I.) , and its use in determining health risk fac tors for overweight and underweight people. If you search the interne t for \"body mass index\" you will find many sites which let you compu te your B.M.I., and which tell you a little bit about it. " }}{PARA 0 "" 0 "" {TEXT -1 931 " A person's B.M.I. is computed by dividin g their weight by the square of their height, and then multiplying by \+ a universal constant. If you measure weight in Newtons, i.e. mass in \+ kilograms, and height in meters, this constant is the fine number one. If you use pounds and inches instead, and are good at conversions you will work out that the constant is about 703. Or you might just find a calculator on the internet which confirms this. Since your B.M.I. \+ is supposed to indicate health risks, proponants of the B.M.I index a re claiming that if for two different people, their weights are the s ame multiple (i.e. their common B.M.I.) of their heights-squared, then these people have comparable health risks. Thus, unless height itsel f is a health risk, the B.M.I. hypothesis can be interpreted as a biom etric scaling law that says that on average, weight should scale propo rtionately to the square of height in people." }}{PARA 0 "" 0 "" {TEXT -1 876 " If people were to scale equally in all directions ( \"self-similar\") when they grew, volume and hence weight would 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 migh t expect the best predictive power for weight as a function of height \+ to be somewhere between 2 and 3, if one expected a power law at all. \+ If there is a predictive power, and if it is much larger than 2, then \+ one could argue that the body mass index might need to be modified to \+ reflect this fact. (In fact, when you find body mass index tables, the y often explain how and why you should modifiy the acceptable BMI valu es for children. Is it possible that if a different power law had been used, no such modification would have been needed?)" }}{PARA 0 "" 0 " " {TEXT -1 172 " Each group will use our common data, see if it i s consistent with a power law relating weights to heights, and decide \+ whether the B.M.I. power of 2 is a good choice. " }}{PARA 0 "" 0 "" {TEXT -1 982 " Several years ago I found a national data base at t he U.S. Center for Disease Control web site. It contained a wide vari ety of body measurements collected between 1976 and 1980 (when America ns were skinnier), including national median heights and weights for b oys and girls, age 2-19. By using only the national medians, a lot of the variance has been taken out of the data, compared to what yours w ill look like. The national data is very consistent with a power law, \+ with power = 2.6. When you do a literature and internet search into \+ the history of the B.M.I. index and height-weight scaling laws, as par t of your project work for this week, you might discover that (by cent uries) we're not the first people to stumble upon a power close to tha t value, based on empirical data. As far as I know there is no mathem atical model to explain any power law for height-weight scaling in peo ple, despite the empirical evidence which shows that the data does see m to follow one." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 259 31 "How do you test for power laws?" }}{PARA 0 "" 0 "" {TEXT -1 154 " Yesterday I explained how to look for power law fi ts to data points: you look for a best line fit to the corresponding \+ ln-ln data points. Recall: " }}{PARA 0 "" 0 "" {TEXT -1 148 " Su ppose we have a set of \"n\" data points, which you can think of as yo ur height-weight data, but which could really be any set of paired dat a:" }}{PARA 258 "" 0 "" {XPPEDIT 18 0 "[[x[1], y[1]], [x[2], y[2]], [x [3], y[3]], `...`, [x[n], y[n]]];" "6#7'7$&%\"xG6#\"\"\"&%\"yG6#F(7$&F &6#\"\"#&F*6#F/7$&F&6#\"\"$&F*6#F5%$...G7$&F&6#%\"nG&F*6#F<" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 68 "We want to see if there is a p ower m and a proportionality constant " }{XPPEDIT 18 0 "b;" "6#%\"bG" }{TEXT -1 21 " so that the formula" }}{PARA 259 "" 0 "" {XPPEDIT 18 0 "y = b*x^m;" "6#/%\"yG*&%\"bG\"\"\")%\"xG%\"mGF'" }{TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 36 "effectively mirrors the real data. " } {TEXT 258 60 "Taking (natural) logarithms of the proposed power law yi elds" }}{PARA 260 "" 0 "" {XPPEDIT 18 0 "ln(y) = ln(b)+m*ln(x);" "6#/- %#lnG6#%\"yG,&-F%6#%\"bG\"\"\"*&%\"mGF,-F%6#%\"xGF,F," }{TEXT -1 1 ". " }}{PARA 0 "" 0 "" {TEXT -1 16 "So, if we write " }{XPPEDIT 18 0 "Y = ln(y);" "6#/%\"YG-%#lnG6#%\"yG" }{TEXT -1 7 " and " }{XPPEDIT 18 0 "X = ln(x);" "6#/%\"XG-%#lnG6#%\"xG" }{TEXT -1 3 ", " }{XPPEDIT 18 0 "B = ln(b);" "6#/%\"BG-%#lnG6#%\"bG" }{TEXT -1 59 ", this becomes the \+ equation of a line in the new variables " }{XPPEDIT 18 0 "X;" "6#%\"XG " }{TEXT -1 5 " and " }{XPPEDIT 18 0 "Y;" "6#%\"YG" }{TEXT -1 1 ":" }} {PARA 261 "" 0 "" {XPPEDIT 18 0 "Y = mX+B;" "6#/%\"YG,&%#mXG\"\"\"%\"B GF'" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 5 "Thus," }{TEXT 261 1 " " }{TEXT 262 207 "in order for there to be a power law for the origi nal data, the ln-ln data should (approximately) satisfy the equation o f a line, and vise verse. If we get a good line fit to the ln-ln data , then the slope " }{XPPEDIT 18 0 "m" "6#%\"mG" }{TEXT 266 75 " of thi s line is the power relating the original data, and the exponential " }{XPPEDIT 18 0 "exp(B);" "6#-%$expG6#%\"BG" }{TEXT 263 8 " of the " } {XPPEDIT 18 0 "Y" "6#%\"YG" }{TEXT 267 43 "-intercept is the proportio nality constant " }{XPPEDIT 18 0 "b" "6#%\"bG" }{TEXT 264 26 " in the \+ original relation " }{XPPEDIT 18 0 "y = b*x^m" "6#/%\"yG*&%\"bG\"\"\") %\"xG%\"mGF'" }{TEXT 265 3 ". " }{TEXT -1 161 "With real data it is n ot too hard to see if the ln-ln data is well approximated by a line, i n which case the original data is well-approximated by a power law. \+ " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" } {TEXT 260 24 "National data example: " }}{PARA 0 "" 0 "" {TEXT -1 31 " Here is the national data." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plo ts):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 334 "boyhw:=[[35.9,29.8 ],[38.9,34.1],[41.9,38.8],[44.3,42.8],\n [47.2,48.6],[49.6,54.8 ],[51.4,60.8],[53.6,66.5],\n [55.7,76.8],[57.3,82.3],[59.8,93.8 ],[62.8,106.8],\n [66.0,124.3],[67.3,132.6],[68.4,142.4],[68.9, 145.1],\n [69.6,155.3],[69.6,153.2]]:\n#boy heights (inches) we ights (pounds): Ntl medians for ages 2-19" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 336 "girlhw:=[[35.4,28.0],[38.4,32.6],[41.1,36.8],[43.9 ,41.8],\n [46.6,47.0],[48.9,52.5],[51.4,60.8],[53.1,65.5],\n \+ [55.7,76.1],[58.2,89.0],[61.0,100.1],[62.6,108.1],\n [63.3 ,117.1],[64.2,117.6],[64.3,122.6],[64.2,128.8],\n [64.1,124.5], [64.5,126]]:\n#girl heights(inches) weights (pounds): Ntl medians for \+ ages 2-19 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 133 "boys:=point plot(boyhw,color=blue):\ngirls:=pointplot(girlhw,color=pink): #plots \+ of the points for girl\n #and boy height-weights.\n\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "display(\{boys,girls\},title=`plot \+ of [height,weight], National medians ages 2-19`);" }}}{PARA 0 "" 0 "" {TEXT -1 187 " In order to use Maple's statistical package we'll ne ed to change the structure of these data sets somewhat. But otherwise , it's not much harder than what we did yesterday in the lab." }} {PARA 0 "" 0 "" {TEXT -1 133 " We want the ln-ln data. If you wan t to see what some of the intermediate commands are doing replace the \+ colons with semicolons." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "w ith(linalg): #one of two linear algebra packages in Maple" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 252 "B:=evalm(boyhw): #\"evalm\" stand s for evaluate as a matrix,\n #converts an array of points\n #into a matrix structure, which will be \n #easiser to manipulate in Mapl e\nG:=evalm(girlhw):\nBG:=stackmatrix(B,G): #stack the matrices on to p of eachother." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 261 "lnBGa:= map(ln,BG): #take ln of the boy and girl height-weights\nlnBG:=map(ev alf,lnBGa): #Get decimal (floating point) values.\n #This speeds up \+ computations later in the\n #least squares fit - otherwise Maple trie s working\n #symbolically and has an epic fail." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "lnlnplot:=pointplot(lnBG):\ndisplay(lnlnplot, title=`ln-ln data`);\n" }}}{PARA 0 "" 0 "" {TEXT -1 119 "Notice the ln -ln plot really does seem close to a line! So there will be an empiri cal power law for the original data." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 270 "Xs:=convert(col(lnBG,1),list): #convert the first co lumn of\n #the ln-ln data into a list of the \"x's\" The MAPLE least squares\n #command wants to have lists input, not matrix columns, ev en\n #though it's hard for us to see any difference\nYs:=convert(col( lnBG,2),list):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "with(stat s): #time for the statistical package" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 142 "fit[leastsquare[[X,Y]]]([Xs,Ys]);#this is the bizarr e syntax\n #we saw yesterday. Luckily you'll be just be able to copy it\n #for your data\n" }}}{PARA 263 "" 0 "" {TEXT -1 65 "We can past e in the equation of the line and see how well we did." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 132 "line:=plot(-6.038703303+2.59382800 4*X, X=3.4..4.5,Y=2.7..5.7,\n color=black):\ndisplay(\{line,lnlnplot \}, title=`least squares fit`);\n" }}}{PARA 0 "" 0 "" {TEXT -1 70 "Fin ally, we can go back from the least squares line fit to a power law" } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "m:=2.593828004; #power\nb:= exp(-6.038703303); #proportionality constant\n" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 173 "Finally, here's a graph \+ showing the power law we derived, and the national boy/girl data point s. Boys are blue and girls are pink. Notice in the command lines bel ow how to" }}{PARA 0 "" 0 "" {TEXT -1 20 " (i) make a title" }} {PARA 0 "" 0 "" {TEXT -1 63 " (ii) get the axes labeled \"h\" and \+ \"w\" for height and weight" }}{PARA 0 "" 0 "" {TEXT -1 243 " (iii) get the display to include appropriate ranges of height and weight - \+ to contain all our data\n (iv) Create plots of the boy and girl ht- wt data points, a plot of the power function, and then display all thr ee graphs in one picture." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 162 "boys:=pointplot(boyhw,color=blue): #we actually did this earlier \ngirls:=pointplot(girlhw,color=pink): #plots of the points for girl \n #and boy height-weights." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "powerplot:=plot(b*h^m,h=0..80,w=0..200,color=black):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 187 "display(\{powerplot,boys,gi rls\},title=\n `power law for national height-weight data`);\n#by cal ling the variables h and w, and giving their ranges, I\n#get Maple to \+ label the axes as I want\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 283 "Notice that the power graph fits the data pretty well. What power will you get from the ACCESS data? \+ Would either power be different if you disallowed kids younger than 4 , with the claim that their baby-fat and big heads are messing with ho w people may scale later on? Just asking." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 148 "Also, if Iyouwant to save a plot \+ or picture after I've removed output, you can just (size) copy and pas te it into a text field, as I have done here:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 11 "" 1 "" {GLPLOT2D 408 342 342 {PLOTDATA 2 "6( -%'CURVESG6$7S7$$\"\"!F)F(7$$\"3ELLLLBxV7$$ \"3ymmm;$>5E$F-$\"319/e#z@l6&F07$$\"3MLLLLAKn\\F-$\"3#o8EUZ9U_\"!#=7$$ \"3]MLLLc$\\o'F-$\"3EqC(yGZHH$F;7$$\"3ammm;bQ%R)F-$\"3kHb'pX\">WfF;7$$ \"3lLLL$Qk#z**F-$\"3Zj`k_)R#4$*F;7$$\"3#******\\YJ?;\"!#;$\"3/[5L:'3F-7$$\"32+++&[A4]\"FN$\"3asM8\"FN7$$\"3%pmmmqFc#GFN$\"3SIf=/it %Q\"FN7$$\"32+++X,H.IFN$\"3%)ot??c-A;FN7$$\"3cmmm1:bgJFN$\"3X+&[.4=;&= FN7$$\"3`+++X@4LLFN$\"3-bj.B/MD@FN7$$\"3K+++N;R(\\$FN$\"3lr%\\Y(>'yS#F N7$$\"3Rnmm;4#)oOFN$\"3kKQ^*)42EFFN7$$\"3!omm;^Yi#QFN$\"3MwhK6=%*RIFN7 $$\"3ELLL$G^g*RFN$\"3(y#Qwb!3YFN7 $$\"33+++!G5Jm%FN$\"3xu9L,t(y2&FN7$$\"3C+++5#32$[FN$\"3ZSL29#>\\c&FN7$ $\"3W+++Dy'G*\\FN$\"3Zl8%)=(4D1'FN7$$\"3++++I%=H<&FN$\"3@9_IHS*fk'FN7$ $\"35mmm1>qM`FN$\"3[()eFA=l)>(FN7$$\"3Q++++.W2bFN$\"3^q#\\@(o&*=yFN7$$ \"3(HLL$ep'Rm&FN$\"3Q#euS<\"\\3%)FN7$$\"3%4+++%>4NeFN$\"3^44:nmFN$\"3zb>&=!ya$G\"Faw7$$\"3NMLL.a#o$oFN$\"3zc9UPF+q8 Faw7$$\"3gnmm^Q40qFN$\"3z![pJw'=f9Faw7$$\"3&3+++3:(frFN$\"3yM`cN^?W:Fa w7$$\"3%ymmmXGpL(FN$\"3g1\\*[u4`k\"Faw7$$\"3GMLL8-V&\\(FN$\"3ey$*\\+++XhUkwFN$\"3^z&>oBSE%=Faw7$$\"3)3++]\"oFaw7$$\"#!)F)$\"3yv8C@mEf?Faw-%'COLOURG6&%$RGBGF)F)F)-%'POINTSG657 $$\"$f$!\"\"$\"$)HFc[l7$$\"$*QFc[l$\"$T$Fc[l7$$\"$>%Fc[l$\"$)QFc[l7$$ \"$V%Fc[l$\"$G%Fc[l7$$\"$s%Fc[l$\"$'[Fc[l7$$\"$'\\Fc[l$\"$[&Fc[l7$$\"$ 9&Fc[l$\"$3'Fc[l7$$\"$O&Fc[l$\"$l'Fc[l7$$\"$d&Fc[l$\"$o(Fc[l7$$\"$t&Fc [l$\"$B)Fc[l7$$\"$)fFc[l$\"$Q*Fc[l7$$\"$G'Fc[l$\"%o5Fc[l7$$\"$g'Fc[l$ \"%V7Fc[l7$$\"$t'Fc[l$\"%E8Fc[l7$$\"$%oFc[l$\"%C9Fc[l7$$\"$*oFc[l$\"%^ 9Fc[l7$$\"$'pFc[l$\"%`:Fc[l7$Fb`l$\"%K:Fc[l-Fjz6&F\\[lF(F($\"*++++\"! \")-F^[l657$$\"$a$Fc[l$\"$!GFc[l7$$\"$%QFc[l$\"$E$Fc[l7$$\"$6%Fc[l$\"$ o$Fc[l7$$\"$R%Fc[l$\"$=%Fc[l7$$\"$m%Fc[l$\"$q%Fc[l7$$\"$*[Fc[l$\"$D&Fc [lF_]l7$$\"$J&Fc[l$\"$b'Fc[l7$Fj]l$\"$h(Fc[l7$$\"$#eFc[l$\"$!*)Fc[l7$$ \"$5'Fc[l$\"%,5Fc[l7$$\"$E'Fc[l$\"%\"3\"Fc[l7$$\"$L'Fc[l$\"%r6Fc[l7$$ \"$U'Fc[l$\"%w6Fc[l7$$\"$V'Fc[l$\"%E7Fc[l7$F[el$\"%)G\"Fc[l7$$\"$T'Fc[ l$\"%X7Fc[l7$$\"$X'Fc[l$\"$E\"F)-Fjz6&F\\[l\"\"\"$\"*w6%Hv!\"*$\"+9Vyg z!#5-%&TITLEG6#%Jpower~law~for~national~height-weight~dataG-%+AXESLABE LSG6$Q\"h6\"Q\"wFbgl-%%VIEWG6$;F(Fez;F($\"$+#F)" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" }} {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 77 "Your ACCESS 2009 data are in the file \"htwts09.mws\", on the week 1 home page." }}}{MARK "61 0 " 46 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }