{VERSION 4 0 "SUN SPARC SOLARIS" "4.0" } {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 Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 261 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 270 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 302 "" 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 "" 11 12 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 }{PSTYLE "Maple Plo t" 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 "" 0 259 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 }} {SECT 0 {PARA 11 "" 1 "" {TEXT -1 0 "" }{TEXT 256 0 "" }{TEXT 257 9 "M ATH 2270" }}{PARA 260 "" 0 "" {TEXT -1 18 "Friday, November 3" }} {PARA 259 "" 0 "" {TEXT -1 25 "Notes on Body Mass Index." }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 258 "I found a data ba se at the U.S. Center for Disease Control, of national body data colle cted between 1976 and 1980. It is interesting to compare our class da ta to some of the U.S. data. I will use the median heights and weight s for boys and girls, age 2-19." }}{PARA 0 "" 0 "" {TEXT 261 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "with(linalg):with(plots):" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 293 "A1:=matrix([[35.9,38.9,41 .9,44.3,47.2,49.6,51.4,53.6,55.7,\n 57.3,59.8,62.8,66.0,67 .3,68.4,68.9,69.6,69.6],\n [29.8,34.1,38.8,42.8,48.6,54.8,6 0.8,66.5,76.8,82.3,93.8,\n 106.8,124.3,132.6,142.1,145.1,15 5.3,153.2]]);\n #boy heights, weights: medians for ages 2-19" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%#A1G-%'matrixG6#7$74$\"$f$!\"\"$\"$* QF,$\"$>%F,$\"$V%F,$\"$s%F,$\"$'\\F,$\"$9&F,$\"$O&F,$\"$d&F,$\"$t&F,$ \"$)fF,$\"$G'F,$\"$g'F,$\"$t'F,$\"$%oF,$\"$*oF,$\"$'pF,FK74$\"$)HF,$\" $T$F,$\"$)QF,$\"$G%F,$\"$'[F,$\"$[&F,$\"$3'F,$\"$l'F,$\"$o(F,$\"$B)F,$ \"$Q*F,$\"%o5F,$\"%V7F,$\"%E8F,$\"%@9F,$\"%^9F,$\"%`:F,$\"%K:F," }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 260 "B1:=matrix([[35.4,38.4,41.1 ,43.9,46.6,48.9,51.4,53.1,55.7,\n 58.2,61.0,62.6,63.3,64.2, 64.3,64.2,64.1,64.5],\n [28.0,32.6,36.8,41.8,47.0,52.5,60.8, 65.5,76.1,89.0,100.1,\n 108.1,117.1,117.6,122.6,128.8,124.5, 126.0]]);\n #girl data " }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#B1G- %'matrixG6#7$74$\"$a$!\"\"$\"$%QF,$\"$6%F,$\"$R%F,$\"$m%F,$\"$*[F,$\"$ 9&F,$\"$J&F,$\"$d&F,$\"$#eF,$\"$5'F,$\"$E'F,$\"$L'F,$\"$U'F,$\"$V'F,FE $\"$T'F,$\"$X'F,74$\"$!GF,$\"$E$F,$\"$o$F,$\"$=%F,$\"$q%F,$\"$D&F,$\"$ 3'F,$\"$b'F,$\"$h(F,$\"$!*)F,$\"%,5F,$\"%\"3\"F,$\"%r6F,$\"%w6F,$\"%E7 F,$\"%)G\"F,$\"%X7F,$\"%g7F," }}}{PARA 11 "" 1 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "AB:=augment(A1,B1):\n #boy s-girls combined " }}{PARA 12 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "A2:=map(ln, AB): \n #take ln of each mat rix entry" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "A3:=map(evalf, A2): \n #get each decimal value" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "coldim(A3); \n #number of data points " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#O" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "col2:=vector(coldim(A3),1): \n #a vector of 1's." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 131 "A4t:=delrows(A3,2..2): \n \+ #remove the second row of A3, what remains\n #is the first row, whi ch will be the first\n #column of A" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "A4:=transpose(A4t):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "A:=augment(A4,col2): \n #This is our matrix for le ast squares" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "bt:=delrows( A3,1..1):\nb:=transpose(bt):\n #This is the right-hand side for least squares" }}}{PARA 0 "" 0 "" {TEXT -1 75 "The next three commands find the least-squares solution, as in section 8.4." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "ATA:=evalm(t ranspose(A)&*A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ATAG-%'matrixG6 #7$7$$\"+Onc`d!\"($\"+!R\"RP9F,7$F-\"#O" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "ATb:=evalm(transpose(A)&*b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ATbG-%'matrixG6#7$7#$\"+uKpVi!\"(7#$\"+f " 0 "" {MPLTEXT 1 0 69 "linsolve(ATA,ATb);\n #get \+ the slope and intercept for the ln-ln data" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7#$\"+*=)[$f#!\"*7#$!+%40u.'F*" }}}{PARA 0 "" 0 "" {TEXT -1 54 " Graph the least-squares line fit for the ln-ln datat:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "lnlnplot:=pointp lot(\{seq([A3[1,j],A3[2,j]],j=1..coldim(A3))\}):\n #those are the points from the ln-ln data in\n #the A3 matrix" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 197 "line:=plot(2.5934881*x -6.037405, x=3.2. .4.5, color=black):\n #Now x is measuring ln(inches), and this is \n #a good x-range for our data\n #I used the mouse to paste in the coefficients" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "dis play(\{lnlnplot,line\});" }}{PARA 13 "" 1 "" {GLPLOT2D 308 253 253 {PLOTDATA 2 "6&-%'POINTSG6E7$$\"+&HP2e$!\"*$\"+%R3XR$F)7$$\"+^U*4m$F)$ \"+%Q(HHNF)7$$\"+FeGNPF)$\"+Z-UeOF)7$$\"+xY)4z$F)$\"+.\"Qlv$F)7$$\"+$* QRaQF)$\"+JNi$)QF)7$$\"+M3*R!RF)$\"+%>!p.SF)7$$\"+s\"Q'RRF)$\"+*y*e2TF )7$$\"+o!\\:)RF)$\"+[>?(>%F)7$$\"+Z,)*>SF)$\"+SY?TVF)7$$\"+C1I[SF)$\"+ 36P5WF)7$$\"+hc+\"4%F)$\"+c[;TXF)7$$\"+t]&*RTF)$\"+Fz&4n%F)7$$\"+UZl*= %F)$\"+**zpA[F)7$$\"+P-;4UF)$\"+yqL()[F)7$$\"+DGPDUF)$\"+N5`c\\F)7$$\" +yhlKUF)$\"+gJUx\\F)7$$\"+nXwUUF)$\"+I(e`/&F)7$Fbp$\"+dUuJ]F)7$$\"+?=r mNF)$\"+5X?KLF)7$$\"+gu0[OF)$\"+)G7V[$F)7$$\"+A\"3gr$F)$\"+Xy\\0OF)7$$ \"+?V\">y$F)$\"+Sj*Gt$F)7$$\"+T0gTQF)$\"+-w9]QF)7$$\"+'Rx(*)QF)$\"+qJ \"3'RF)7$$\"+GpGO[F)-%'CURVESG6$7S 7$$\"3;+++++++K!#<$\"3h,++?pvhAFav7$$\"3ummT+jLGKFav$\"3)4lGzxY_L#Fav7 $$\"3LLe*Qc\"*HD$Fav$\"3cLUO5**=*R#Fav7$$\"3!om\"H')*=2G$Fav$\"3H-:R]1 5rCFav7$$\"3jm;//-j3LFav$\"31ME[h!)[VDFav7$$\"3OLekk(3kL$Fav$\"3jqY%yU Jbh#Fav7$$\"3%p;Hi/j@O$Fav$\"3G%4b1&[K#o#Fav7$$\"3D+D18,$))Q$Fav$\"3T \\#\\6d&[^FFav7$$\"3xm\"Hso6I#GFav7$$\"3***\\7Q!***QW $Fav$\"3ij)G\"=%3V*GFav7$$\"3aLL3Rut>f`M[KFav7$$\"3ym \"HnE[]g$Fav$\"3N?xozZC7LFav7$$\"3SLL3=dMMOFav$\"3a!3N6PF#)Q$Fav7$$\"3 oLLL-X;fOFav$\"3bCRu#f%f_MFav7$$\"3<+Dc[Y.)o$Fav$\"3eEXVt*ou_$Fav7$$\" 3NLL$)>'*e8PFav$\"33v7K([XPf$Fav7$$\"39+DctuiTPFav$\"3p3uJF8YmOFav7$$ \"3$**\\(oShKoPFav$\"3-d>z-SqNPFav7$$\"3cL$e*)R$='z$Fav$\"3g\"*fhq9&z! QFav7$$\"3cLe9e]w@QFav$\"3?FqH*>(HuQFav7$$\"3ym;aL$e$\\QFav$\"3*R9w1.g e%RFav7$$\"3)o;H<**>!yQFav$\"3'Qp6,q$>?SFav7$$\"39+vV\\+(H!RFav$\"37pD (yP,\\3%Fav7$$\"3qm;H&z;*HRFav$\"3^u!zDW(yaTFav7$$\"3%)****\\?avdRFav$ \"3]Xsx&e')pA%Fav7$$\"36+]7%3!*\\)RFav$\"3'o='zh$>wH%Fav7$$\"30+Dc@5M6 SFav$\"3>(=kW?gfO%Fav7$$\"3b+]([C*fSSFav$\"3#4I_%e5%=W%Fav7$$\"3fLL$)f !*)o1%Fav$\"3HRzp!QB+^%Fav7$$\"3#)***\\([!f\\4%Fav$\"3lW/#HcAGe%Fav7$$ \"3ym\"H2j%R?TFav$\"3M*)**4U%*y[YFav7$$\"3S++DSC?[TFav$\"30P$z^m34s%Fa v7$$\"34Le*=UnV<%Fav$\"3GBXrLsw)y%Fav7$$\"3&)*\\7oO<7MG%Fav$\"3Mtj&obt:2&Fav7$$\"3`m;/GT)4J%Fav$ \"3))R\\ON53V^Fav7$$\"3+Me*3vF$QVFav$\"3q4\"[eR'*R@&Fav7$$\"3-++]+PXjV Fav$\"3\"[rZrCg\"z_Fav7$$\"3/L$3U(3D#R%Fav$\"3S4RZu`%QN&Fav7$$\"30nmm4 u+=WFav$\"3EEBoUYk?aFav7$$\"3e*\\i&[#paW%Fav$\"3u%yi]fm=\\&Fav7$$\"3_+ vVKPvrWFav$\"3#=C274N+c&Fav7$$\"3++++++++XFav$\"3`,++]9HLcFav-%'COLOUR G6&%$RGBG\"\"!FhelFhel-%+AXESLABELSG6$Q\"x6\"Q!6\"-%%VIEWG6$;$\"#K!\" \"$\"#XFffl%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{PARA 0 "" 0 "" {TEXT 270 0 "" } {TEXT 302 458 "You notice that until adolescence the boy and girl data are more or less indistinguishable. The \"baby fat\" of small childr en may explain why the 2-year olds are slightly above the line, and th e peaking near adulthood for both the males and females is quite likel y to be the effect of their respective hormones. But this data IS ver y close to a linear fit. One might wonder what sort of biological adv antage this sort of scaling is a consequence of. I do." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "C:=exp(-6.037406936); #proportiona lity constant\np:=2.593488650; #power. I used the mouse to paste the se" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG$\"+iCu(Q#!#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG$\"+]')[$f#!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "realplot:=pointplot(\{seq([AB[1,j],AB[2,j]],j=1. .coldim(A3))\}):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "powerp lot:=plot(C*x^p,x=0..80,color=black): #Now x is measuring height\n \+ #in inches so this is a good x-range" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "display(\{realplot,powerplot\});" }}{PARA 13 "" 1 "" {GLPLOT2D 342 310 310 {PLOTDATA 2 "6&-%'POINTSG6E7$$\"$f$!\"\"$\"$)HF) 7$$\"$*QF)$\"$T$F)7$$\"$>%F)$\"$)QF)7$$\"$V%F)$\"$G%F)7$$\"$s%F)$\"$'[ F)7$$\"$'\\F)$\"$[&F)7$$\"$9&F)$\"$3'F)7$$\"$O&F)$\"$l'F)7$$\"$d&F)$\" $o(F)7$$\"$t&F)$\"$B)F)7$$\"$)fF)$\"$Q*F)7$$\"$G'F)$\"%o5F)7$$\"$g'F)$ \"%V7F)7$$\"$t'F)$\"%E8F)7$$\"$%oF)$\"%@9F)7$$\"$*oF)$\"%^9F)7$$\"$'pF )$\"%`:F)7$Fbp$\"%K:F)7$$\"$a$F)$\"$!GF)7$$\"$%QF)$\"$E$F)7$$\"$6%F)$ \"$o$F)7$$\"$R%F)$\"$=%F)7$$\"$m%F)$\"$q%F)7$$\"$*[F)$\"$D&F)7$$\"$J&F )$\"$b'F)7$FP$\"$h(F)7$$\"$#eF)$\"$!*)F)7$$\"$5'F)$\"%,5F)7$$\"$E'F)$ \"%\"3\"F)7$$\"$L'F)$\"%r6F)7$$\"$U'F)$\"%w6F)7$$\"$V'F)$\"%E7F)7$Fdt$ \"%)G\"F)7$$\"$T'F)$\"%X7F)7$$\"$X'F)$\"%g7F)-%'CURVESG6$7S7$$\"\"!F`v F_v7$$\"3ELLLLBxV_ON#*45!#>7$$\"3ymmm;$>5E$Fdv$\"3xZ:RVV5@ ^Fgv7$$\"3MLLLLAKn\\Fdv$\"3q2otfFdv7$$\"32+++&[A4]\"Fex$\"3-lMKJXZ%o#Fdv7$$\"3&pmm m3Q\\n\"Fex$\"3a5WWLR\"zc$Fdv7$$\"3aLLLB6@G=Fex$\"3P2#*oZ)HvZ%Fdv7$$\" 3?+++g-w+?Fex$\"3-\"zo2qnul&Fdv7$$\"38++++z,u@Fex$\"3i@ZG)\\0s,(Fdv7$$ \"32+++SP)4M#Fex$\"3>!>A\"fxr,&)Fdv7$$\"3[LLL=Zg#\\#Fex$\"3!)>cV&yU/+ \"Fex7$$\"3#ommms'*Gn#Fex$\"3Ssvp*)Q3*>\"Fex7$$\"3%pmmmqFc#GFex$\"3'4w m=@h\\Q\"Fex7$$\"32+++X,H.IFex$\"3ZrKb:cDA;Fex7$$\"3cmmm1:bgJFex$\"3?5 G]m&[=&=Fex7$$\"3`+++X@4LLFex$\"33B$*))GmcD@Fex7$$\"3K+++N;R(\\$Fex$\" 3\"*yA%*G*y!3CFex7$$\"3Rnmm;4#)oOFex$\"3#)odtUBFEFFex7$$\"3!omm;^Yi#QF ex$\"3)*=a]-I7SIFex7$$\"3ELLL$G^g*RFex$\"3M8h;O-^-MFex7$$\"3uLLL=2VsTF ex$\"3bsj6$e?e!QFex7$$\"37+++N&pfK%Fex$\"3VWJG?,wzTFex7$$\"3)RLLLm&z\" \\%Fex$\"3dk=qM`Fex$\"3a@bw#**o#)>(Fex7$$\"3 Q++++.W2bFex$\"3GuQt.lX=yFex7$$\"3(HLL$ep'Rm&Fex$\"34L*3v6tyS)Fex7$$\" 3%4+++%>4NeFex$\"3Q/7co6k#3*Fex7$$\"3Ommm6s5'*fFex$\"3z+$pbX8qu*Fex7$$ \"3e+++lXTkhFex$\"3`?(\\l3`s/\"!#:7$$\"3Kmmmmd'*GjFex$\"3f\\'**GP/87\" F^bl7$$\"3j*****\\iN7]'Fex$\"3^7[RRj=-7F^bl7$$\"32MLLt>:nmFex$\"3)*zT_ MCQ$G\"F^bl7$$\"3NMLL.a#o$oFex$\"3P>mX\\X\")p8F^bl7$$\"3gnmm^Q40qFex$ \"3d9&RkGu*e9F^bl7$$\"3&3+++3:(frFex$\"3;rNwR)oRa\"F^bl7$$\"3%ymmmXGpL (Fex$\"31k:eGV/X;F^bl7$$\"3GMLL8-V&\\(Fex$\"3')=!>'fe!)Q++ +XhUkwFex$\"3eHvf&o:B%=F^bl7$$\"3)3++]\"oF^bl7$$ \"#!)F`v$\"3FKS]uR()e?F^bl-%'COLOURG6&%$RGBGF`vF`vF`v-%+AXESLABELSG6$Q \"x6\"Q!6\"-%%VIEWG6$;F_vFbel%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{MARK "28 1" 458 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }