(************** Content-type: application/mathematica ************** Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 47638, 1269]*) (*NotebookOutlinePosition[ 48306, 1292]*) (* CellTagsIndexPosition[ 48262, 1288]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Initialization", "Subsubsection", CellFrame->True, Background->GrayLevel[0.849989]], Cell[BoxData[ \(<< \ Statistics`LinearRegression`\)], "Input"], Cell[BoxData[ \(<< \ Graphics`Graphics`\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["The LSFit Routine", "Subsubsection", CellFrame->True, Background->GrayLevel[0.849989]], Cell[BoxData[ \(\(\( (*\(\(\(**\)\(**\)\(**\)\(**\)\(**\)\(**\)\(**\)\(**\)\(**\)\(**\)\ \(**\)\(**\)\(**\)\(**\)\(**\)\(**\)\(**\)\(**\)\(**\)\(**\)\(**\)\(**\)\(**\)\ \(**\)\(**\)\(**\)\(**\)\(**\)\(**\)\(\n\)\(\t\)\(If\)\)\ this\ looks\ \ horribly\ ugly ... \)\ that' s\ because\ it\ is . \n\t\t\tAll\ it\ does\ is\ take\ the\ brain\ \ damaged\ output\ format\ of\n\t\t\tthe\ Regress\ comand\ \((in\ \ Statistics`LinearRegression`)\)\ and\n\t\t\textract\ the\ useful\ \((for\ us)\ \)\ values . \ \ \n\t\(\(**\)\(**\)\(**\)\(**\)\(**\)\(**\)\(**\)\(**\)\(**\)\ \(**\)\(**\)\(**\)\(**\)\(**\)\(**\)\(**\)\(**\)\(**\)\(**\)\(**\)\(**\)\(**\)\ \(**\)\(**\)\(**\)\(**\)\(**\)\)******) \)\(\n\)\(\n\)\(LSFit[X_, \ Y_, \ Yerr_]\ := \ Block\ [{\n\t\t\tRegressResult, paramTable, \ anovaTable, \n\t\t\tfitm, \ fitb, \ fitdm, \ fitdb, \ TStat, \ PValue, \n\t\t\tr2val, \ sy, \ SSModel, \ SSRes, \ SSTotal\n\t\t\t}, \ \((\n\t\t\n\t\t (*\ Perform\ Fit\ *) \n\t\tRegressResult = \ Regress[Transpose[{X, \ Y}], \ {1, \ x}, \ x, \ Weights\ -> \ 1/Yerr^2]; \n\t\t\t\n\t\t (*\ Get\ Fit\ and\ Uncertainty\ *) \t\n\t\tparamTable\ = \ ParameterTable\ /. \ RegressResult; \n\t\t{{fitb, \ fitm}, \ {fitdb, \ fitdm}, \ TStat, \ PValue}\ = \ \n\t\t\t\((\((FullForm[ paramTable])\)[\([1, 1]\)])\) // Transpose; \n\t\t\n\t\t (*\ Get\ R^2\ value\ *) \n\t\tr2val\ = \ RSquared\ /. \ RegressResult; \n\t\t\t\n\t\t (*\ Get\ Model\ Sum\ of\ Squares\ and\ Residual\ Sum\ of\ Squares\ \ *) \n\t\tanovaTable\ = \ \((FullForm[ ANOVATable\ /. \ RegressResult])\)\ [\([1, 1]\)]; \n\t\t{SSModel, \ SSRes, \ SSTotal}\ = \ \n\t\t\t\t{anovaTable[\([1, 2]\)], \ anovaTable[\([2, 2]\)], \ anovaTable[\([3, 2]\)]}; \t\t\t\t\n\t\t\t\t\n\t\t{{fitm, \ fitb}, \ \n\t\t\t{fitdm, \ fitdb}, \n\t\t\t{r2val, \ syNotYet}, \n\t\t\t{SSModel, \ SSRes}}\ \n\ )\)]\)\)\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["Set up an array", "Subsubsection", CellFrame->True, Background->GrayLevel[0.849989]], Cell[BoxData[{ \(\({m, \ b, nonlin, \ \ noise, \ \ uncertainty}\ = \ {\(-5\), \ \(-2\), \ .4, \ \ 0, \ .3};\)\), "\n", \(\(X\ = \ Range\ [1, \ 10];\)\), "\n", \(\(Y\ = \ \((m\ X\ + \ b\ + \ nonlin\ m\ X\^2\ )\)\ *\ \((1 + \ noise\ *Sin[4.32\ X])\);\)\), "\n", \(\(Yerr\ = \ Abs[uncertainty\ *\ Y\ *\ \((1 + \ noise\ *Sin[2.7\ X])\)\ + \ 0.01];\)\)}], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(\(Transpose[{X, \ Y, \ Yerr}]\ // N[#, 5]\ &\) // TableForm\)], "Input"], Cell[BoxData[ FormBox[ TagBox[GridBox[{ {"1.`", \(-9.`\), "2.69`"}, {"2.`", \(-20.`\), "5.99`"}, {"3.`", \(-35.`\), "10.49`"}, {"4.`", \(-54.`\), "16.189999999999998`"}, {"5.`", \(-77.`\), "23.089999999999996`"}, {"6.`", \(-104.`\), "31.189999999999998`"}, {"7.`", \(-135.`\), "40.49`"}, {"8.`", \(-170.`\), "50.99`"}, {"9.`", \(-209.`\), "62.69`"}, {"10.`", \(-252.`\), "75.58999999999999`"} }, RowSpacings->1, ColumnSpacings->3, RowAlignments->Baseline, ColumnAlignments->{Left}], Function[ BoxForm`e$, TableForm[ BoxForm`e$]]], TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(anovaTable\ = \ \ \ \((ANOVATable\ /. \ Regress[Transpose[{X, \ Y}], \ {1, \ x}, \ x, \ Weights\ -> \ 1/Yerr^2])\)\)], "Input"], Cell[BoxData[ FormBox[ InterpretationBox[GridBox[{ { FormBox["\<\"\"\>", "TraditionalForm"], FormBox["\<\"DF\"\>", "TraditionalForm"], FormBox["\<\"SumOfSq\"\>", "TraditionalForm"], FormBox["\<\"MeanSq\"\>", "TraditionalForm"], FormBox["\<\"FRatio\"\>", "TraditionalForm"], FormBox["\<\"PValue\"\>", "TraditionalForm"]}, { FormBox["\<\"Model\"\>", "TraditionalForm"], "1", "63.01390981739658`", "63.01390981739658`", "103.93105301787463`", "7.348953852792661`*^-6"}, { FormBox["\<\"Error\"\>", "TraditionalForm"], "8", "4.850439439427914`", "0.6063049299284893`", "\<\"\"\>", "\<\"\"\>"}, { FormBox["\<\"Total\"\>", "TraditionalForm"], "9", "67.8643492568245`", "\<\"\"\>", "\<\"\"\>", "\<\"\"\>"} }, RowSpacings->1, ColumnSpacings->3, RowAlignments->Baseline, ColumnAlignments->{Left}], TableForm[ {{1, 63.013909817396581, 63.013909817396581, 103.93105301787463, .73489538527926612*^-5}, {8, 4.8504394394279142, .60630492992848928}, {9, 67.864349256824497}}, TableHeadings -> {{"Model", "Error", "Total"}, {"DF", "SumOfSq", "MeanSq", "FRatio", "PValue"}}]], TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(ErrorListPlot[Transpose[{X, \ Y, \ Yerr}]];\)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.0952381 0.603319 0.00179677 [ [.21429 .59082 -3 -9 ] [.21429 .59082 3 0 ] [.40476 .59082 -3 -9 ] [.40476 .59082 3 0 ] [.59524 .59082 -3 -9 ] [.59524 .59082 3 0 ] [.78571 .59082 -3 -9 ] [.78571 .59082 3 0 ] [.97619 .59082 -6 -9 ] [.97619 .59082 6 0 ] [.01131 .06429 -24 -4.5 ] [.01131 .06429 0 4.5 ] [.01131 .15413 -24 -4.5 ] [.01131 .15413 0 4.5 ] [.01131 .24396 -24 -4.5 ] [.01131 .24396 0 4.5 ] [.01131 .3338 -24 -4.5 ] [.01131 .3338 0 4.5 ] [.01131 .42364 -24 -4.5 ] [.01131 .42364 0 4.5 ] [.01131 .51348 -18 -4.5 ] [.01131 .51348 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .21429 .60332 m .21429 .60957 L s [(2)] .21429 .59082 0 1 Mshowa .40476 .60332 m .40476 .60957 L s [(4)] .40476 .59082 0 1 Mshowa .59524 .60332 m .59524 .60957 L s [(6)] .59524 .59082 0 1 Mshowa .78571 .60332 m .78571 .60957 L s [(8)] .78571 .59082 0 1 Mshowa .97619 .60332 m .97619 .60957 L s [(10)] .97619 .59082 0 1 Mshowa .125 Mabswid .07143 .60332 m .07143 .60707 L s .11905 .60332 m .11905 .60707 L s .16667 .60332 m .16667 .60707 L s .2619 .60332 m .2619 .60707 L s .30952 .60332 m .30952 .60707 L s .35714 .60332 m .35714 .60707 L s .45238 .60332 m .45238 .60707 L s .5 .60332 m .5 .60707 L s .54762 .60332 m .54762 .60707 L s .64286 .60332 m .64286 .60707 L s .69048 .60332 m .69048 .60707 L s .7381 .60332 m .7381 .60707 L s .83333 .60332 m .83333 .60707 L s .88095 .60332 m .88095 .60707 L s .92857 .60332 m .92857 .60707 L s .25 Mabswid 0 .60332 m 1 .60332 L s .02381 .06429 m .03006 .06429 L s [(-300)] .01131 .06429 1 0 Mshowa .02381 .15413 m .03006 .15413 L s [(-250)] .01131 .15413 1 0 Mshowa .02381 .24396 m .03006 .24396 L s [(-200)] .01131 .24396 1 0 Mshowa .02381 .3338 m .03006 .3338 L s [(-150)] .01131 .3338 1 0 Mshowa .02381 .42364 m .03006 .42364 L s [(-100)] .01131 .42364 1 0 Mshowa .02381 .51348 m .03006 .51348 L s [(-50)] .01131 .51348 1 0 Mshowa .125 Mabswid .02381 .08226 m .02756 .08226 L s .02381 .10022 m .02756 .10022 L s .02381 .11819 m .02756 .11819 L s .02381 .13616 m .02756 .13616 L s .02381 .17209 m .02756 .17209 L s .02381 .19006 m .02756 .19006 L s .02381 .20803 m .02756 .20803 L s .02381 .226 m .02756 .226 L s .02381 .26193 m .02756 .26193 L s .02381 .2799 m .02756 .2799 L s .02381 .29787 m .02756 .29787 L s .02381 .31584 m .02756 .31584 L s .02381 .35177 m .02756 .35177 L s .02381 .36974 m .02756 .36974 L s .02381 .38771 m .02756 .38771 L s .02381 .40567 m .02756 .40567 L s .02381 .44161 m .02756 .44161 L s .02381 .45958 m .02756 .45958 L s .02381 .47755 m .02756 .47755 L s .02381 .49551 m .02756 .49551 L s .02381 .53145 m .02756 .53145 L s .02381 .54942 m .02756 .54942 L s .02381 .56738 m .02756 .56738 L s .02381 .58535 m .02756 .58535 L s .02381 .04632 m .02756 .04632 L s .02381 .02835 m .02756 .02835 L s .02381 .01038 m .02756 .01038 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .002 w .11905 .58231 m .11905 .59198 L s .015 w .11905 .58715 Mdot .002 w .21429 .55662 m .21429 .57815 L s .015 w .21429 .56738 Mdot .002 w .30952 .52158 m .30952 .55928 L s .015 w .30952 .54043 Mdot .002 w .40476 .4772 m .40476 .53538 L s .015 w .40476 .50629 Mdot .002 w .5 .42348 m .5 .50646 L s .015 w .5 .46497 Mdot .002 w .59524 .36041 m .59524 .4725 L s .015 w .59524 .41645 Mdot .002 w .69048 .288 m .69048 .43351 L s .015 w .69048 .36075 Mdot .002 w .78571 .20625 m .78571 .38949 L s .015 w .78571 .29787 Mdot .002 w .88095 .11515 m .88095 .34043 L s .015 w .88095 .22779 Mdot .002 w .97619 .01472 m .97619 .28635 L s .015 w .97619 .15053 Mdot % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHggoo00<007ooOol01Woo 000ROol00`00Oomoo`3oOolkOol00`00Oomoo`06Ool0029oo`800?moocaoo`03001oogoo00Ioo`00 8Woo00<007ooOol0ogoo>goo00<007ooOol01Woo000ROol00`00Oomoo`3oOolkOol00`00Oomoo`06 Ool0029oo`03001oogoo0?mooc]oo`03001oogoo00Ioo`008Woo00<007ooOol0ogoo>goo00<007oo Ool01Woo000ROol00`00Oomoo`3oOolkOol00`00Oomoo`06Ool0029oo`800?moocaoo`03001oogoo 00Ioo`008Woo00<007ooOol0ogoo>goo00<007ooOol01Woo000ROol00`00Oomoo`3oOolkOol00`00 Oomoo`06Ool000Qoo`<000Eoo`@000Aoo`@000Ioo`03001oogoo0?mooc]oo`03001oogoo00Ioo`00 1goo00D007ooOomoo`0000=oo`03001oogoo009oo`04001oogoo0004Ool00`00Oomoo`03Ool00`00 Oomoo`3oOolkOol00`00Oomoo`06Ool000]oo`05001oogooOol00004Ool01000Oomoo`0017oo00<0 07ooOol00goo00<007ooOol0ogoo>goo00<007ooOol01Woo00050006Ool01@00Oomoogoo000017oo 00@007ooOol000Aoo`03001oogoo00=oo`<00?mooc]oo`03001oogoo00Ioo`002Goo0P0017oo00<0 07ooOol00Woo00@007ooOol000Aoo`03001oogoo00=oo`03001oogoo0?mooc]oo`03001oogoo00Io o`002goo00D007ooOomoo`0000Aoo`04001oogoo0004Ool00`00Oomoo`03Ool00`00Oomoo`3oOolk Ool00`00Oomoo`06Ool000Moo`05001oogooOol00003Ool00`00Oomoo`02Ool01000Oomoo`0017oo 00<007ooOol00goo00<007ooOol0ogoo>goo00<007ooOol01Woo0008Ool30005Ool40004Ool40006 Ool00`00Oomoo`3oOolkOol00`00Oomoo`06Ool0029oo`03001oogoo0?mooc]oo`03001oogoo00Io o`008Woo0P00ogoo?7oo00<007ooOol01Woo000ROol00`00Oomoo`3oOolkOol00`00Oomoo`06Ool0 029oo`03001oogoo0?mooc]oo`03001oogoo00Ioo`008Woo00<007ooOol0ogoo>goo00<007ooOol0 1Woo000ROol00`00Oomoo`3oOolkOol00`00Oomoo`06Ool0029oo`03001oogoo0?mooc]oo`03001o ogoo00Ioo`008Woo0P00ogoo?7oo00<007ooOol01Woo000ROol00`00Oomoo`3oOolkOol00`00Oomo o`06Ool0029oo`03001oogoo0?mooc]oo`03001oogoo00Ioo`008Woo00<007ooOol0ogoo>goo00<0 07ooOol01Woo000ROol00`00Oomoo`3oOolkOol00`00Oomoo`06Ool0029oo`03001oogoo0?mooa]o o`03001oogoo01eoo`03001oogoo00Ioo`008Woo0P00ogoo77oo00<007ooOol07Goo00<007ooOol0 1Woo000ROol00`00Oomoo`3oOolKOol00`00Oomoo`0MOol00`00Oomoo`06Ool0029oo`03001oogoo 0?mooa]oo`03001oogoo01eoo`03001oogoo00Ioo`008Woo00<007ooOol0ogoo6goo00<007ooOol0 7Goo00<007ooOol01Woo000ROol00`00Oomoo`3oOolKOol00`00Oomoo`0MOol00`00Oomoo`06Ool0 029oo`03001oogoo0?mooa]oo`03001oogoo01eoo`03001oogoo00Ioo`008Woo0P00ogoo77oo00<0 07ooOol07Goo00<007ooOol01Woo000ROol00`00Oomoo`3oOolKOol00`00Oomoo`0MOol00`00Oomo o`06Ool0029oo`03001oogoo0?mooa]oo`03001oogoo01eoo`03001oogoo00Ioo`001goo1@0017oo 100017oo10001Woo00<007ooOol0ogoo6goo00<007ooOol07Goo00<007ooOol01Woo0007Ool01@00 Oomoogoo00000goo00<007ooOol00Woo00@007ooOol000Aoo`03001oogoo00=oo`03001oogoo0?mo oa]oo`03001oogoo01aoo`8000Qoo`0027oo00<007ooOol02Goo00@007ooOol000Aoo`03001oogoo 00=oo`03001oogoo0?mooa]oo`03001oogoo01]oo`@000Moo`001@0017oo00<007ooOol027oo00@0 07ooOol000Aoo`03001oogoo00=oo`<00?mooa]oo`03001oogoo01]oo`@000Moo`002Woo00<007oo Ool00goo10000goo00<007ooOol00Woo00<007ooOol00goo00<007ooOol0ogoo6goo00<007ooOol0 77oo0P0027oo000;Ool00`00Oomoo`02Ool00`00Oomoo`04Ool00`00Oomoo`02Ool00`00Oomoo`03 Ool00`00Oomoo`3oOolKOol00`00Oomoo`0MOol00`00Oomoo`06Ool000Moo`05001oogooOol00004 Ool00`00Oomoo`04Ool00`00Oomoo`02Ool00`00Oomoo`03Ool00`00Oomoo`3oOolKOol00`00Oomo o`0MOol00`00Oomoo`06Ool000Qoo`<000Eoo`D000=oo`@000Ioo`03001oogoo0?mooa]oo`03001o ogoo01eoo`03001oogoo00Ioo`008Woo00<007ooOol0ogoo6goo00<007ooOol07Goo00<007ooOol0 1Woo000ROol2003oOolLOol00`00Oomoo`0MOol00`00Oomoo`06Ool0029oo`03001oogoo0?mooa]o o`03001oogoo01eoo`03001oogoo00Ioo`008Woo00<007ooOol0ogoo6goo00<007ooOol07Goo00<0 07ooOol01Woo000ROol00`00Oomoo`3oOolKOol00`00Oomoo`0MOol00`00Oomoo`06Ool0029oo`03 001oogoo0?mooa]oo`03001oogoo01eoo`03001oogoo00Ioo`008Woo00<007ooOol0ogoo6goo00<0 07ooOol07Goo00<007ooOol01Woo000ROol2003oOolLOol00`00Oomoo`0MOol00`00Oomoo`06Ool0 029oo`03001oogoo0?mooa]oo`03001oogoo01eoo`03001oogoo00Ioo`008Woo00<007ooOol0ogoo 6goo00<007ooOol07Goo00<007ooOol01Woo000ROol00`00Oomoo`3oOolKOol00`00Oomoo`0MOol0 0`00Oomoo`06Ool0029oo`03001oogoo0?mooa]oo`03001oogoo01eoo`03001oogoo00Ioo`008Woo 00<007ooOol0ogoo6goo00<007ooOol07Goo00<007ooOol01Woo000ROol2003kOol00`00Oomoo`0M Ool00`00Oomoo`0MOol00`00Oomoo`06Ool0029oo`03001oogoo0?Yoo`03001oogoo01eoo`03001o ogoo01eoo`03001oogoo00Ioo`008Woo00<007ooOol0nWoo00<007ooOol07Goo00<007ooOol07Goo 00<007ooOol01Woo000ROol00`00Oomoo`3jOol00`00Oomoo`0MOol00`00Oomoo`0MOol00`00Oomo o`06Ool0029oo`03001oogoo0?Yoo`03001oogoo01eoo`03001oogoo01eoo`03001oogoo00Ioo`00 8Woo00<007ooOol0nWoo00<007ooOol07Goo00<007ooOol07Goo00<007ooOol01Woo000ROol2003k Ool00`00Oomoo`0LOol2000OOol00`00Oomoo`06Ool0029oo`03001oogoo0?Yoo`03001oogoo01]o o`@001ioo`03001oogoo00Ioo`008Woo00<007ooOol0nWoo00<007ooOol06goo10007Woo00<007oo Ool01Woo0007Ool50004Ool40004Ool40006Ool00`00Oomoo`3jOol00`00Oomoo`0LOol2000OOol0 0`00Oomoo`06Ool000Moo`05001oogooOol00003Ool00`00Oomoo`02Ool01000Oomoo`0017oo00<0 07ooOol00goo00<007ooOol0nWoo00<007ooOol07Goo00<007ooOol07Goo00<007ooOol01Woo0008 Ool00`00Oomoo`04Ool00`00Oomoo`02Ool01000Oomoo`0017oo00<007ooOol00goo00<007ooOol0 nWoo00<007ooOol07Goo00<007ooOol07Goo00<007ooOol01Woo00050004Ool00`00Oomoo`03Ool0 0`00Oomoo`02Ool01000Oomoo`0017oo00<007ooOol00goo0`00nWoo00<007ooOol07Goo00<007oo Ool07Goo00<007ooOol01Woo000:Ool00`00Oomoo`02Ool00`00Oomoo`02Ool01000Oomoo`0017oo 00<007ooOol00goo00<007ooOol0nWoo00<007ooOol07Goo00<007ooOol07Goo00<007ooOol01Woo 000;Ool01@00Oomoogoo000017oo00@007ooOol000Aoo`03001oogoo00=oo`03001oogoo0?Yoo`03 001oogoo01eoo`03001oogoo01eoo`03001oogoo00Ioo`001goo00D007ooOomoo`0000=oo`03001o ogoo009oo`04001oogoo0004Ool00`00Oomoo`03Ool00`00Oomoo`3jOol00`00Oomoo`0MOol00`00 Oomoo`0MOol00`00Oomoo`06Ool000Qoo`<000Eoo`@000Aoo`@000Ioo`03001oogoo0?Yoo`03001o ogoo01eoo`03001oogoo01eoo`03001oogoo00Ioo`008Woo00<007ooOol0nWoo00<007ooOol07Goo 00<007ooOol07Goo00<007ooOol01Woo000ROol2003kOol00`00Oomoo`0MOol00`00Oomoo`0MOol0 0`00Oomoo`06Ool0029oo`03001oogoo0?Yoo`03001oogoo01eoo`03001oogoo01eoo`03001oogoo 00Ioo`008Woo00<007ooOol0nWoo00<007ooOol07Goo00<007ooOol07Goo00<007ooOol01Woo000R Ool00`00Oomoo`3jOol00`00Oomoo`0MOol00`00Oomoo`0MOol00`00Oomoo`06Ool0029oo`03001o ogoo0?Yoo`03001oogoo01eoo`03001oogoo01eoo`03001oogoo00Ioo`008Woo00<007ooOol0nWoo 00<007ooOol07Goo00<007ooOol07Goo00<007ooOol01Woo000ROol2003kOol00`00Oomoo`0MOol0 0`00Oomoo`0MOol00`00Oomoo`06Ool0029oo`03001oogoo0?Yoo`03001oogoo01eoo`03001oogoo 01eoo`03001oogoo00Ioo`008Woo00<007ooOol0nWoo00<007ooOol07Goo00<007ooOol07Goo00<0 07ooOol01Woo000ROol00`00Oomoo`3KOol00`00Oomoo`0LOol00`00Oomoo`0MOol00`00Oomoo`0V Ool0029oo`03001oogoo0=]oo`03001oogoo01aoo`03001oogoo01eoo`03001oogoo02Ioo`008Woo 00<007ooOol0fgoo00<007ooOol06goo0P007goo00<007ooOol09Woo000ROol2003LOol00`00Oomo o`0JOol4000NOol00`00Oomoo`0VOol0029oo`03001oogoo0=]oo`03001oogoo01Yoo`@001ioo`03 001oogoo02Ioo`008Woo00<007ooOol0fgoo00<007ooOol06goo0P007goo00<007ooOol09Woo000R Ool00`00Oomoo`3KOol00`00Oomoo`0LOol00`00Oomoo`0MOol00`00Oomoo`0VOol0029oo`03001o ogoo0=]oo`03001oogoo01aoo`03001oogoo01eoo`03001oogoo02Ioo`008Woo00<007ooOol0fgoo 00<007ooOol077oo00<007ooOol07Goo00<007ooOol09Woo000ROol2003LOol00`00Oomoo`0LOol0 0`00Oomoo`0MOol00`00Oomoo`0VOol0029oo`03001oogoo0=]oo`03001oogoo01aoo`03001oogoo 01eoo`03001oogoo02Ioo`008Woo00<007ooOol0fgoo00<007ooOol077oo00<007ooOol07Goo00<0 07ooOol09Woo0008Ool50003Ool40004Ool40006Ool00`00Oomoo`3KOol00`00Oomoo`0LOol00`00 Oomoo`0MOol00`00Oomoo`0VOol000Yoo`03001oogoo009oo`03001oogoo009oo`04001oogoo0004 Ool00`00Oomoo`03Ool00`00Oomoo`3KOol00`00Oomoo`0LOol00`00Oomoo`0MOol00`00Oomoo`0V Ool000Yoo`03001oogoo00Moo`04001oogoo0004Ool00`00Oomoo`03Ool00`00Oomoo`3KOol00`00 Oomoo`0LOol00`00Oomoo`0MOol00`00Oomoo`0VOol000D000Eoo`03001oogoo00Moo`04001oogoo 0004Ool00`00Oomoo`03Ool3003KOol00`00Oomoo`0LOol00`00Oomoo`0MOol00`00Oomoo`0VOol0 00Yoo`03001oogoo00=oo`@000=oo`03001oogoo009oo`03001oogoo00=oo`03001oogoo0=]oo`03 001oogoo01aoo`03001oogoo01eoo`03001oogoo02Ioo`002Woo00<007ooOol00goo00<007ooOol0 17oo00<007ooOol00Woo00<007ooOol00goo00<007ooOol0fgoo00<007ooOol077oo00<007ooOol0 7Goo00<007ooOol09Woo0008Ool30005Ool00`00Oomoo`04Ool00`00Oomoo`02Ool00`00Oomoo`03 Ool00`00Oomoo`3KOol00`00Oomoo`0LOol00`00Oomoo`16Ool000Yoo`03001oogoo00=oo`D000=o o`@000Ioo`03001oogoo0=]oo`03001oogoo01aoo`03001oogoo04Ioo`008Woo00<007ooOol0fgoo 00<007ooOol077oo00<007ooOol0AWoo000ROol2003LOol00`00Oomoo`0LOol00`00Oomoo`16Ool0 029oo`03001oogoo0=]oo`03001oogoo01aoo`03001oogoo04Ioo`008Woo00<007ooOol0fWoo0P00 7Woo00<007ooOol0AWoo000ROol00`00Oomoo`2kOol00`00Oomoo`0KOol4000MOol00`00Oomoo`16 Ool0029oo`03001oogoo0;]oo`03001oogoo01]oo`@001eoo`03001oogoo04Ioo`008Woo00<007oo Ool0^goo00<007ooOol077oo0P007Woo00<007ooOol0AWoo000ROol2002lOol00`00Oomoo`0MOol0 0`00Oomoo`0LOol00`00Oomoo`16Ool0029oo`03001oogoo0;]oo`03001oogoo01eoo`03001oogoo 01aoo`03001oogoo04Ioo`008Woo00<007ooOol0^goo00<007ooOol07Goo00<007ooOol077oo00<0 07ooOol0AWoo000ROol00`00Oomoo`2kOol00`00Oomoo`0MOol00`00Oomoo`0LOol00`00Oomoo`16 Ool0029oo`03001oogoo0;]oo`03001oogoo01eoo`03001oogoo01aoo`03001oogoo04Ioo`008Woo 00<007ooOol0^goo00<007ooOol07Goo00<007ooOol077oo00<007ooOol0AWoo000ROol2002lOol0 0`00Oomoo`0MOol00`00Oomoo`0LOol00`00Oomoo`16Ool0029oo`03001oogoo0;]oo`03001oogoo 01eoo`03001oogoo01aoo`03001oogoo04Ioo`008Woo00<007ooOol0^goo00<007ooOol07Goo00<0 07ooOol0IGoo000ROol00`00Oomoo`2kOol00`00Oomoo`0MOol00`00Oomoo`1UOol0029oo`03001o ogoo0;]oo`03001oogoo01eoo`03001oogoo06Eoo`008Woo00<007ooOol0^goo00<007ooOol07Goo 00<007ooOol0IGoo000ROol2002lOol00`00Oomoo`0MOol00`00Oomoo`1UOol0029oo`03001oogoo 0;]oo`03001oogoo01eoo`03001oogoo06Eoo`008Woo00<007ooOol0^Woo0P007goo00<007ooOol0 IGoo0008Ool50003Ool40004Ool40006Ool00`00Oomoo`2iOol4000NOol00`00Oomoo`1UOol000Yo o`03001oogoo009oo`03001oogoo009oo`04001oogoo0004Ool00`00Oomoo`03Ool00`00Oomoo`2i Ool4000NOol00`00Oomoo`1UOol000Yoo`03001oogoo009oo`03001oogoo009oo`04001oogoo0004 Ool00`00Oomoo`03Ool00`00Oomoo`2jOol2000OOol00`00Oomoo`1UOol000D000Eoo`03001oogoo 009oo`03001oogoo009oo`04001oogoo0004Ool00`00Oomoo`03Ool3002KOol00`00Oomoo`0MOol0 0`00Oomoo`0MOol00`00Oomoo`1UOol000Yoo`03001oogoo009oo`03001oogoo009oo`04001oogoo 0004Ool00`00Oomoo`03Ool00`00Oomoo`2KOol00`00Oomoo`0MOol00`00Oomoo`0MOol00`00Oomo o`1UOol000Yoo`03001oogoo009oo`03001oogoo009oo`04001oogoo0004Ool00`00Oomoo`03Ool0 0`00Oomoo`2KOol00`00Oomoo`0MOol00`00Oomoo`0MOol00`00Oomoo`1UOol000Qoo`<000Aoo`03 001oogoo009oo`04001oogoo0004Ool00`00Oomoo`03Ool00`00Oomoo`2KOol00`00Oomoo`0MOol0 0`00Oomoo`0MOol00`00Oomoo`1UOol000Yoo`03001oogoo00=oo`@000Aoo`@000Ioo`03001oogoo 09]oo`03001oogoo01eoo`03001oogoo08Eoo`008Woo00<007ooOol0Vgoo00<007ooOol07Goo00<0 07ooOol0QGoo000ROol2002LOol00`00Oomoo`0MOol00`00Oomoo`25Ool0029oo`03001oogoo09]o o`03001oogoo01eoo`03001oogoo08Eoo`008Woo00<007ooOol0Vgoo00<007ooOol07Goo00<007oo Ool0QGoo000ROol00`00Oomoo`2KOol00`00Oomoo`0MOol00`00Oomoo`25Ool0029oo`03001oogoo 09]oo`03001oogoo01eoo`03001oogoo08Eoo`008Woo00<007ooOol0Vgoo00<007ooOol07Goo00<0 07ooOol0QGoo000ROol2002LOol00`00Oomoo`0MOol00`00Oomoo`25Ool0029oo`03001oogoo09Yo o`8001moo`03001oogoo08Eoo`008Woo00<007ooOol0VGoo10007Woo00<007ooOol0QGoo000ROol0 0`00Oomoo`2IOol4000NOol00`00Oomoo`25Ool0029oo`03001oogoo09Yoo`8001moo`03001oogoo 08Eoo`008Woo00<007ooOol0Vgoo00<007ooOol0YGoo000ROol2001lOol00`00Oomoo`0MOol00`00 Oomoo`2UOol0029oo`03001oogoo07]oo`03001oogoo01eoo`03001oogoo0:Eoo`008Woo00<007oo Ool0Ngoo00<007ooOol07Goo00<007ooOol0YGoo000ROol00`00Oomoo`1kOol00`00Oomoo`0MOol0 0`00Oomoo`2UOol0029oo`03001oogoo07]oo`03001oogoo01eoo`03001oogoo0:Eoo`008Woo00<0 07ooOol0Ngoo00<007ooOol07Goo00<007ooOol0YGoo000ROol2001lOol00`00Oomoo`0MOol00`00 Oomoo`2UOol0029oo`03001oogoo07]oo`03001oogoo01eoo`03001oogoo0:Eoo`008Woo00<007oo Ool0NWoo0P007goo00<007ooOol0YGoo000@Ool40004Ool40006Ool00`00Oomoo`1iOol4000NOol0 0`00Oomoo`2UOol000moo`03001oogoo009oo`04001oogoo0004Ool00`00Oomoo`03Ool00`00Oomo o`1iOol4000NOol00`00Oomoo`2UOol001Aoo`04001oogoo0004Ool00`00Oomoo`03Ool00`00Oomo o`1jOol20037Ool000Moo`H000Moo`04001oogoo0004Ool00`00Oomoo`03Ool3001kOol00`00Oomo o`35Ool0011oo`@000=oo`03001oogoo009oo`03001oogoo00=oo`03001oogoo07]oo`03001oogoo 0Eoo`008Woo00<007ooOol0Fgoo0P00iWoo000ROol2001MOol0 0`00Oomoo`3TOol0029oo`03001oogoo05aoo`03001oogoo0>Aoo`008Woo00<007ooOol0?7oo00<0 07ooOol07Goo00<007ooOol0i7oo000ROol00`00Oomoo`0iOol5000NOol00`00Oomoo`0LOol3000l Ool3000kOol4000hOol50003Ool40003Ool0029oo`03001oogoo03Uoo`03001oogoo008003ioo`03 001oogoo03Yoo`05001oogooOol0000iOol00`00Oomoo`02Ool00`00Oomoo`0gOol00`00Oomoo`02 Ool00`00Oomoo`02Ool10001Ool1Ool0029oo`03001oogoo03Yoo`<003moo`03001oogoo03Yoo`05 001oogooOol0000iOol00`00Oomoo`02Ool00`00Oomoo`0gOol00`00Oomoo`02Ool00`00Oomoo`02 Ool10001Ool1Ool0029oo`8003]oo`@003Yoo`H003]oo`05001oogooOol0000iOol00`00Oomoo`02 Ool00`00Oomoo`0gOol00`00Oomoo`02Ool00`00Oomoo`02Ool10001Ool1Ool0029oo`03001oogoo 03Yoo`@003]oo`04001oogoo000lOol4000kOol4000jOol00`00Oomoo`02Ool00`00Oomoo`02Ool1 0001Ool1Ool0029oo`03001oogoo03]oo`<003]oo`04001oogoo000lOol00`00Oomoo`0kOol00`00 Oomoo`02Ool00`00Oomoo`0gOol00`00Oomoo`02Ool00`00Oomoo`02Ool10001Ool1Ool0029oo`03 001oogoo03Uoo`03001oogoo008003aoo`03001oo`0003eoo`03001oogoo03Yoo`03001oogoo009o o`03001oogoo03Eoo`<000Aoo`03001oogoo009oo`40005oo`5oo`008Woo00<007ooOol0>Woo0`00 ?Woo0P00?Woo0`00>Woo1000>Woo00<007ooOol00goo10000goo000ROol00`00Oomoo`0KOol2003o OolWOol0029oo`8001]oo`@00?moobIoo`008Woo00<007ooOol06Woo1000ogoo9Woo000ROol00`00 Oomoo`0KOol2003oOolWOol0029oo`03001oogoo0?moodAoo`008Woo00<007ooOol0ogooA7oo000R Ool00`00Oomoo`3oOom4Ool001Yoool004l000008Woo00<007ooOol03Goo00<007ooOol037oo00<0 07ooOol03Goo00<007ooOol03Goo00<007ooOol03Goo00<007ooOol03Goo00<007ooOol03Goo00<0 07ooOol037oo00<007ooOol03Goo00<007ooOol03Goo00<007ooOol03Goo00<007ooOol03Goo00<0 07ooOol03Goo00<007ooOol03Goo00<007ooOol037oo00<007ooOol03Goo00<007ooOol03Goo00<0 07ooOol03Goo00<007ooOol03Goo00<007ooOol03Goo00<007ooOol01Woo000ROol00`00Oomoo`0l Ool00`00Oomoo`0lOol00`00Oomoo`0mOol00`00Oomoo`0lOol00`00Oomoo`0mOol00`00Oomoo`06 Ool0029oo`03001oogoo0?moodAoo`008Woo00<007ooOol0ogooA7oo000ROol00`00Oomoo`3oOom4 Ool00?moofUoo`00ogooJGoo003oOomYOol00?moofUoo`00ogooJGoo003oOomYOol00?moofUoo`00 \ \>"], ImageRangeCache->{{{0, 359}, {221.375, 0}} -> {-1.07792, -348.925, \ 0.0394428, 2.09067}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Test it out", "Subsubsection", CellFrame->True, Background->GrayLevel[0.849989]], Cell[CellGroupData[{ Cell[BoxData[ \(\(({{fitm, \ fitb}, \ \n\t{fitdm, \ fitdb}, \n\t{r2val, \ sy}, \n\t{SSReg, \ SSRes}}\ = \ LSFit[X, Y, \ Yerr]\ )\) // TableForm\)], "Input"], Cell[BoxData[ FormBox[ TagBox[GridBox[{ {\(-18.18588851873487`\), "10.739060470591705`"}, {"1.7838644912529482`", "3.1430300724635627`"}, {"0.9285274301964938`", "syNotYet"}, {"63.01390981739658`", "4.850439439427914`"} }, RowSpacings->1, ColumnSpacings->3, RowAlignments->Baseline, ColumnAlignments->{Left}], Function[ BoxForm`e$, TableForm[ BoxForm`e$]]], TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\( (*\(Notice\ that\ our\ function\ is\ not\ very\ linear ... \)\ \ this\ is\ to\ show\ the\ effect\ of\ the\ \(weights!\)*) \)\(\ \[IndentingNewLine]\)\(DisplayTogether[{\n\t\tErrorListPlot[ Transpose[{X, \ Y, \ Yerr}]], \n\t\tPlot[ fitm\ x\ + \ fitb, \ {x, \ 0, \ 10}]}]\)\)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.0952381 0.584636 0.00173974 [ [.21429 .57214 -3 -9 ] [.21429 .57214 3 0 ] [.40476 .57214 -3 -9 ] [.40476 .57214 3 0 ] [.59524 .57214 -3 -9 ] [.59524 .57214 3 0 ] [.78571 .57214 -3 -9 ] [.78571 .57214 3 0 ] [.97619 .57214 -6 -9 ] [.97619 .57214 6 0 ] [.01131 .06271 -24 -4.5 ] [.01131 .06271 0 4.5 ] [.01131 .1497 -24 -4.5 ] [.01131 .1497 0 4.5 ] [.01131 .23669 -24 -4.5 ] [.01131 .23669 0 4.5 ] [.01131 .32368 -24 -4.5 ] [.01131 .32368 0 4.5 ] [.01131 .41066 -24 -4.5 ] [.01131 .41066 0 4.5 ] [.01131 .49765 -18 -4.5 ] [.01131 .49765 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .21429 .58464 m .21429 .59089 L s [(2)] .21429 .57214 0 1 Mshowa .40476 .58464 m .40476 .59089 L s [(4)] .40476 .57214 0 1 Mshowa .59524 .58464 m .59524 .59089 L s [(6)] .59524 .57214 0 1 Mshowa .78571 .58464 m .78571 .59089 L s [(8)] .78571 .57214 0 1 Mshowa .97619 .58464 m .97619 .59089 L s [(10)] .97619 .57214 0 1 Mshowa .125 Mabswid .07143 .58464 m .07143 .58839 L s .11905 .58464 m .11905 .58839 L s .16667 .58464 m .16667 .58839 L s .2619 .58464 m .2619 .58839 L s .30952 .58464 m .30952 .58839 L s .35714 .58464 m .35714 .58839 L s .45238 .58464 m .45238 .58839 L s .5 .58464 m .5 .58839 L s .54762 .58464 m .54762 .58839 L s .64286 .58464 m .64286 .58839 L s .69048 .58464 m .69048 .58839 L s .7381 .58464 m .7381 .58839 L s .83333 .58464 m .83333 .58839 L s .88095 .58464 m .88095 .58839 L s .92857 .58464 m .92857 .58839 L s .25 Mabswid 0 .58464 m 1 .58464 L s .02381 .06271 m .03006 .06271 L s [(-300)] .01131 .06271 1 0 Mshowa .02381 .1497 m .03006 .1497 L s [(-250)] .01131 .1497 1 0 Mshowa .02381 .23669 m .03006 .23669 L s [(-200)] .01131 .23669 1 0 Mshowa .02381 .32368 m .03006 .32368 L s [(-150)] .01131 .32368 1 0 Mshowa .02381 .41066 m .03006 .41066 L s [(-100)] .01131 .41066 1 0 Mshowa .02381 .49765 m .03006 .49765 L s [(-50)] .01131 .49765 1 0 Mshowa .125 Mabswid .02381 .08011 m .02756 .08011 L s .02381 .09751 m .02756 .09751 L s .02381 .11491 m .02756 .11491 L s .02381 .1323 m .02756 .1323 L s .02381 .1671 m .02756 .1671 L s .02381 .1845 m .02756 .1845 L s .02381 .20189 m .02756 .20189 L s .02381 .21929 m .02756 .21929 L s .02381 .25409 m .02756 .25409 L s .02381 .27148 m .02756 .27148 L s .02381 .28888 m .02756 .28888 L s .02381 .30628 m .02756 .30628 L s .02381 .34107 m .02756 .34107 L s .02381 .35847 m .02756 .35847 L s .02381 .37587 m .02756 .37587 L s .02381 .39326 m .02756 .39326 L s .02381 .42806 m .02756 .42806 L s .02381 .44546 m .02756 .44546 L s .02381 .46285 m .02756 .46285 L s .02381 .48025 m .02756 .48025 L s .02381 .51505 m .02756 .51505 L s .02381 .53244 m .02756 .53244 L s .02381 .54984 m .02756 .54984 L s .02381 .56724 m .02756 .56724 L s .02381 .04532 m .02756 .04532 L s .02381 .02792 m .02756 .02792 L s .02381 .01052 m .02756 .01052 L s .02381 .60203 m .02756 .60203 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .002 w .11905 .5643 m .11905 .57366 L s .015 w .11905 .56898 Mdot .002 w .21429 .53942 m .21429 .56026 L s .015 w .21429 .54984 Mdot .002 w .30952 .5055 m .30952 .54199 L s .015 w .30952 .52374 Mdot .002 w .40476 .46252 m .40476 .51886 L s .015 w .40476 .49069 Mdot .002 w .5 .41051 m .5 .49085 L s .015 w .5 .45068 Mdot .002 w .59524 .34944 m .59524 .45797 L s .015 w .59524 .4037 Mdot .002 w .69048 .27933 m .69048 .42021 L s .015 w .69048 .34977 Mdot .002 w .78571 .20017 m .78571 .37759 L s .015 w .78571 .28888 Mdot .002 w .88095 .11197 m .88095 .33009 L s .015 w .88095 .22103 Mdot .002 w .97619 .01472 m .97619 .27773 L s .015 w .97619 .14622 Mdot .5 Mabswid .02381 .60332 m .06244 .59048 L .10458 .57649 L .14415 .56334 L .18221 .5507 L .22272 .53724 L .26171 .52429 L .30316 .51052 L .34309 .49725 L .3815 .48449 L .42237 .47092 L .46172 .45784 L .49955 .44527 L .53984 .43189 L .57861 .41901 L .61984 .40532 L .65954 .39212 L .69774 .37944 L .73838 .36593 L .77751 .35293 L .81909 .33912 L .85916 .32581 L .89771 .313 L .93871 .29938 L .97619 .28693 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHggoo00<007ooOol01Woo 000ROol00`00Oomoo`3oOolkOol00`00Oomoo`06Ool0029oo`800?moocaoo`03001oogoo00Ioo`00 8Woo00<007ooOol0ogoo>goo00<007ooOol01Woo000ROol00`00Oomoo`3oOolkOol00`00Oomoo`06 Ool0029oo`03001oogoo0?mooc]oo`03001oogoo00Ioo`008Woo00<007ooOol0ogoo>goo00<007oo Ool01Woo000ROol00`00Oomoo`3oOolkOol00`00Oomoo`06Ool0029oo`800?moocaoo`03001oogoo 00Ioo`008Woo00<007ooOol0ogoo>goo00<007ooOol01Woo000ROol00`00Oomoo`3oOolkOol00`00 Oomoo`06Ool000Qoo`<000Eoo`@000Aoo`@000Ioo`03001oogoo0?mooc]oo`03001oogoo00Ioo`00 1goo00D007ooOomoo`0000=oo`03001oogoo009oo`04001oogoo0004Ool00`00Oomoo`03Ool00`00 Oomoo`3oOolkOol00`00Oomoo`06Ool000]oo`05001oogooOol00004Ool01000Oomoo`0017oo00<0 07ooOol00goo00<007ooOol0ogoo>goo00<007ooOol01Woo00050006Ool01@00Oomoogoo000017oo 00@007ooOol000Aoo`03001oogoo00=oo`<00?mooc]oo`03001oogoo00Ioo`002Goo0P0017oo00<0 07ooOol00Woo00@007ooOol000Aoo`03001oogoo00=oo`03001oogoo0?mooc]oo`03001oogoo00Io o`002goo00D007ooOomoo`0000Aoo`04001oogoo0004Ool00`00Oomoo`03Ool00`00Oomoo`3oOolk Ool00`00Oomoo`06Ool000Moo`05001oogooOol00003Ool00`00Oomoo`02Ool01000Oomoo`0017oo 00<007ooOol00goo00<007ooOol0ogoo>goo00<007ooOol01Woo0008Ool30005Ool40004Ool40006 Ool00`00Oomoo`3oOolkOol00`00Oomoo`06Ool0029oo`03001oogoo0?mooc]oo`03001oogoo00Io o`008Woo0P00ogoo?7oo00<007ooOol01Woo000ROol00`00Oomoo`3oOolkOol00`00Oomoo`06Ool0 029oo`03001oogoo0?mooc]oo`03001oogoo00Ioo`008Woo00<007ooOol0ogoo>goo00<007ooOol0 1Woo000ROol00`00Oomoo`3oOolkOol00`00Oomoo`06Ool0029oo`800?moocaoo`03001oogoo00Io o`008Woo00<007ooOol0ogoo>goo00<007ooOol01Woo000ROol00`00Oomoo`3oOolkOol00`00Oomo o`06Ool0029oo`03001oogoo0?mooc]oo`03001oogoo00Ioo`008Woo00<007ooOol0ogoo>goo00<0 07ooOol01Woo000ROol00`00Oomoo`3oOolKOol00`00Oomoo`0MOol00`00Oomoo`06Ool0029oo`80 0?mooaaoo`03001oogoo01eoo`03001oogoo00Ioo`008Woo00<007ooOol0ogoo6goo00<007ooOol0 7Goo00<007ooOol01Woo000ROol00`00Oomoo`3oOolKOol00`00Oomoo`0MOol00`00Oomoo`06Ool0 029oo`03001oogoo0?mooa]oo`03001oogoo01eoo`03001oogoo00Ioo`008Woo00<007ooOol0ogoo 6goo00<007ooOol07Goo00<007ooOol01Woo000ROol00`00Oomoo`3oOolKOol00`00Oomoo`0MOol0 0`00Oomoo`06Ool0029oo`800?mooaaoo`03001oogoo01eoo`03001oogoo00Ioo`008Woo00<007oo Ool0ogoo6goo00<007ooOol07Goo00<007ooOol01Woo000ROol00`00Oomoo`3oOolKOol00`00Oomo o`0MOol00`00Oomoo`06Ool000Moo`D000Aoo`@000Aoo`@000Ioo`03001oogoo0?mooa]oo`03001o ogoo01eoo`03001oogoo00Ioo`001goo00D007ooOomoo`0000=oo`03001oogoo009oo`04001oogoo 0004Ool00`00Oomoo`03Ool00`00Oomoo`3oOolKOol00`00Oomoo`0LOol20008Ool000Qoo`03001o ogoo00Uoo`04001oogoo0004Ool00`00Oomoo`03Ool00`00Oomoo`3oOolKOol00`00Oomoo`0KOol4 0007Ool000D000Aoo`03001oogoo00Qoo`04001oogoo0004Ool00`00Oomoo`03Ool3003oOolKOol0 0`00Oomoo`0KOol40007Ool000Yoo`03001oogoo00=oo`@000=oo`03001oogoo009oo`03001oogoo 00=oo`03001oogoo0?mooa]oo`03001oogoo01aoo`8000Qoo`002goo00<007ooOol00Woo00<007oo Ool017oo00<007ooOol00Woo00<007ooOol00goo00<007ooOol0ogoo6goo00<007ooOol07Goo00<0 07ooOol01Woo0007Ool01@00Oomoogoo000017oo00<007ooOol017oo00<007ooOol00Woo00<007oo Ool00goo00<007ooOol0ogoo6goo00<007ooOol07Goo00<007ooOol01Woo0008Ool30005Ool50003 Ool40006Ool00`00Oomoo`3oOolKOol00`00Oomoo`0MOol00`00Oomoo`06Ool0029oo`03001oogoo 0?mooa]oo`03001oogoo01eoo`03001oogoo00Ioo`008Woo0P00ogoo77oo00<007ooOol07Goo00<0 07ooOol01Woo000ROol00`00Oomoo`3oOolKOol00`00Oomoo`0MOol00`00Oomoo`06Ool0029oo`03 001oogoo0?mooa]oo`03001oogoo01eoo`03001oogoo00Ioo`008Woo00<007ooOol0ogoo6goo00<0 07ooOol07Goo00<007ooOol01Woo000ROol00`00Oomoo`3oOolKOol00`00Oomoo`0MOol00`00Oomo o`06Ool0029oo`800?mooaaoo`03001oogoo01eoo`03001oogoo00Ioo`008Woo00<007ooOol0ogoo 6goo00<007ooOol07Goo00<007ooOol01Woo000ROol00`00Oomoo`3oOolKOol00`00Oomoo`0MOol0 0`00Oomoo`06Ool0029oo`03001oogoo0?mooa]oo`03001oogoo01eoo`03001oogoo00Ioo`008Woo 00<007ooOol0ogoo6goo00<007ooOol07Goo00<007ooOol01Woo000ROol00`00Oomoo`3oOolKOol0 0`00Oomoo`0MOol00`00Oomoo`06Ool0029oo`800?]oo`03001oogoo01eoo`03001oogoo01eoo`03 001oogoo00Ioo`008Woo00<007ooOol0nWoo00<007ooOol07Goo00<007ooOol07Goo00<007ooOol0 1Woo000ROol00`00Oomoo`3jOol00`00Oomoo`0MOol00`00Oomoo`0MOol00`00Oomoo`06Ool0029o o`03001oogoo0?Yoo`03001oogoo01eoo`03001oogoo01eoo`03001oogoo00Ioo`008Woo00<007oo Ool0nWoo00<007ooOol07Goo00<007ooOol07Goo00<007ooOol01Woo000ROol00`00Oomoo`3jOol0 0`00Oomoo`0LOol2000OOol00`00Oomoo`06Ool0029oo`800?]oo`03001oogoo01]oo`@001ioo`03 001oogoo00Ioo`008Woo00<007ooOol0nWoo00<007ooOol06goo10007Woo00<007ooOol01Woo000R Ool00`00Oomoo`3jOol00`00Oomoo`0LOol2000OOol00`00Oomoo`06Ool000Moo`D000Aoo`@000Ao o`@000Ioo`03001oogoo0?Yoo`03001oogoo01eoo`03001oogoo01eoo`03001oogoo00Ioo`001goo 00D007ooOomoo`0000=oo`03001oogoo009oo`04001oogoo0004Ool00`00Oomoo`03Ool00`00Oomo o`3jOol00`00Oomoo`0MOol00`00Oomoo`0MOol00`00Oomoo`06Ool000Qoo`03001oogoo00Aoo`03 001oogoo009oo`04001oogoo0004Ool00`00Oomoo`03Ool00`00Oomoo`3jOol00`00Oomoo`0MOol0 0`00Oomoo`0MOol00`00Oomoo`06Ool000D000Aoo`03001oogoo00=oo`03001oogoo009oo`04001o ogoo0004Ool00`00Oomoo`03Ool3003jOol00`00Oomoo`0MOol00`00Oomoo`0MOol00`00Oomoo`06 Ool000Yoo`03001oogoo009oo`03001oogoo009oo`04001oogoo0004Ool00`00Oomoo`03Ool00`00 Oomoo`3jOol00`00Oomoo`0MOol00`00Oomoo`0MOol00`00Oomoo`06Ool000]oo`05001oogooOol0 0004Ool01000Oomoo`0017oo00<007ooOol00goo00<007ooOol0nWoo00<007ooOol07Goo00<007oo Ool07Goo00<007ooOol01Woo0007Ool01@00Oomoogoo00000goo00<007ooOol00Woo00@007ooOol0 00Aoo`03001oogoo00=oo`03001oogoo0?Yoo`03001oogoo01eoo`03001oogoo01eoo`03001oogoo 00Ioo`0027oo0`001Goo100017oo10001Woo00<007ooOol0nWoo00<007ooOol07Goo00<007ooOol0 7Goo00<007ooOol01Woo000ROol00`00Oomoo`3jOol00`00Oomoo`0MOol00`00Oomoo`0MOol00`00 Oomoo`06Ool0029oo`800?]oo`03001oogoo01eoo`03001oogoo01eoo`03001oogoo00Ioo`008Woo 00<007ooOol0nWoo00<007ooOol07Goo00<007ooOol07Goo00<007ooOol01Woo000ROol00`00Oomo o`3jOol00`00Oomoo`0MOol00`00Oomoo`0MOol00`00Oomoo`06Ool0029oo`03001oogoo0?Yoo`03 001oogoo01eoo`03001oogoo01eoo`03001oogoo00Ioo`008Woo00<007ooOol0nWoo00<007ooOol0 7Goo00<007ooOol07Goo00<007ooOol01Woo000ROol2003kOol00`00Oomoo`0MOol00`00Oomoo`0M Ool00`00Oomoo`06Ool0029oo`03001oogoo0?Yoo`03001oogoo01eoo`03001oogoo01eoo`03001o ogoo00Ioo`008Woo00<007ooOol0nWoo00<007ooOol07Goo00<007ooOol07Goo00<007ooOol01Woo 000ROol00`00Oomoo`3KOol00`00Oomoo`0LOol00`00Oomoo`0MOol00`00Oomoo`0VOol0029oo`03 001oogoo0=]oo`03001oogoo01aoo`03001oogoo01eoo`03001oogoo02Ioo`008Woo00<007ooOol0 fgoo00<007ooOol06goo0P007goo00<007ooOol077oo0P0027oo000ROol2003LOol00`00Oomoo`0J Ool4000NOol00`00Oomoo`0JOol2000:Ool0029oo`03001oogoo0=]oo`03001oogoo01Yoo`@001io o`03001oogoo01Moo`<000aoo`008Woo00<007ooOol0fgoo00<007ooOol06goo0P007goo00<007oo Ool057oo0`003goo000ROol00`00Oomoo`3KOol00`00Oomoo`0LOol00`00Oomoo`0MOol00`00Oomo o`0BOol2000BOol0029oo`03001oogoo0=]oo`03001oogoo01aoo`03001oogoo01eoo`03001oogoo 00moo`<001Aoo`008Woo00<007ooOol0fgoo00<007ooOol077oo00<007ooOol07Goo00<007ooOol0 2goo10005goo000ROol2003LOol00`00Oomoo`0LOol00`00Oomoo`0MOol00`00Oomoo`08Ool3000K Ool0029oo`03001oogoo0=]oo`03001oogoo01aoo`03001oogoo01eoo`03001oogoo00Aoo`@001io o`008Woo00<007ooOol0fgoo00<007ooOol077oo00<007ooOol07Goo00@007ooOomoo`<0029oo`00 27oo1@000goo100017oo10001Woo00<007ooOol0fgoo00<007ooOol077oo00<007ooOol07Goo1000 9Goo000:Ool00`00Oomoo`02Ool00`00Oomoo`02Ool01000Oomoo`0017oo00<007ooOol00goo00<0 07ooOol0fgoo00<007ooOol077oo00<007ooOol06goo0`00:7oo000:Ool00`00Oomoo`07Ool01000 Oomoo`0017oo00<007ooOol00goo00<007ooOol0fgoo00<007ooOol077oo00<007ooOol067oo0`00 0Woo00<007ooOol09Woo00050005Ool00`00Oomoo`07Ool01000Oomoo`0017oo00<007ooOol00goo 0`00fgoo00<007ooOol077oo00<007ooOol05Goo0`001Goo00<007ooOol09Woo000:Ool00`00Oomo o`03Ool40003Ool00`00Oomoo`02Ool00`00Oomoo`03Ool00`00Oomoo`3KOol00`00Oomoo`0LOol0 0`00Oomoo`0BOol30008Ool00`00Oomoo`0VOol000Yoo`03001oogoo00=oo`03001oogoo00Aoo`03 001oogoo009oo`03001oogoo00=oo`03001oogoo0=]oo`03001oogoo01aoo`03001oogoo011oo`80 00]oo`03001oogoo02Ioo`0027oo0`001Goo00<007ooOol017oo00<007ooOol00Woo00<007ooOol0 0goo00<007ooOol0fgoo00<007ooOol077oo00<007ooOol03Goo0`00=Woo000:Ool00`00Oomoo`03 Ool50003Ool40006Ool00`00Oomoo`3KOol00`00Oomoo`0LOol00`00Oomoo`0:Ool3000iOol0029o o`800=aoo`03001oogoo01aoo`03001oogoo00Moo`<003aoo`008Woo00<007ooOol0fgoo00<007oo Ool077oo00<007ooOol00goo1000?goo000ROol00`00Oomoo`3JOol2000NOol00`00Oomoo`030013 Ool0029oo`03001oogoo0;]oo`03001oogoo01]oo`@001aoo`@004Ioo`008Woo00<007ooOol0^goo 00<007ooOol06goo10006Goo0`0000=oo`00Ool0Agoo000ROol00`00Oomoo`2kOol00`00Oomoo`0L Ool2000HOol20004Ool00`00Oomoo`16Ool0029oo`800;aoo`03001oogoo01eoo`03001oogoo01=o o`<000Ioo`03001oogoo04Ioo`008Woo00<007ooOol0^goo00<007ooOol07Goo00<007ooOol047oo 0`002Goo00<007ooOol0AWoo000ROol00`00Oomoo`2kOol00`00Oomoo`0MOol00`00Oomoo`0>Ool2 000Ool40009Ool2000NOol00`00Oomoo`35Ool0029o o`03001oogoo04]oo`<000aoo`@00>Eoo`008Woo00<007ooOol0BGoo0P003goo1000iGoo000ROol0 0`00Oomoo`16Ool3000BOol2003VOol0029oo`8004Aoo`<001Ioo`03001oogoo0>Aoo`008Woo00<0 07ooOol0@Goo0P006Goo00<007ooOol0i7oo000ROol00`00Oomoo`0iOol8000KOol00`00Oomoo`0L Ool3000lOol3000kOol4000hOol50003Ool40003Ool0029oo`03001oogoo03Uoo`D001ioo`03001o ogoo01eoo`03001oogoo03Yoo`05001oogooOol0000iOol00`00Oomoo`02Ool00`00Oomoo`0gOol0 0`00Oomoo`02Ool00`00Oomoo`02Ool10001Ool1Ool0029oo`03001oogoo03Moo`@00003Ool007oo 03ioo`03001oogoo03Yoo`05001oogooOol0000iOol00`00Oomoo`02Ool00`00Oomoo`0gOol00`00 Oomoo`02Ool00`00Oomoo`02Ool10001Ool1Ool0029oo`03001oogoo03=oo`@000Aoo`8003]oo`H0 03]oo`05001oogooOol0000iOol00`00Oomoo`02Ool00`00Oomoo`0gOol00`00Oomoo`02Ool00`00 Oomoo`02Ool10001Ool1Ool0029oo`80035oo`<000Moo`@003]oo`04001oogoo000lOol4000kOol4 000jOol00`00Oomoo`02Ool00`00Oomoo`02Ool10001Ool1Ool0029oo`03001oogoo02eoo`<000Yo o`@003]oo`04001oogoo000lOol00`00Oomoo`0kOol00`00Oomoo`02Ool00`00Oomoo`0gOol00`00 Oomoo`02Ool00`00Oomoo`02Ool10001Ool1Ool0029oo`03001oogoo02Yoo`<000aoo`03001oo`00 008003aoo`03001oo`0003eoo`03001oogoo03Yoo`03001oogoo009oo`03001oogoo03Eoo`<000Ao o`03001oogoo009oo`40005oo`5oo`008Woo00<007ooOol09goo0`0047oo0`00?Woo0P00?Woo0`00 >Woo1000>Woo00<007ooOol00goo10000goo000ROol00`00Oomoo`0TOol3003oOolMOol0029oo`03 001oogoo01]oo`8000Eoo`800?moob1oo`008Woo0P006goo100000Aoo`0000000?moob9oo`008Woo 00<007ooOol06Woo1@00ogoo9Goo000ROol00`00Oomoo`0JOol3003oOolWOol0029oo`03001oogoo 01Moo`<00?moobYoo`008Woo00<007ooOol04goo1000ogoo;Goo000ROol00`00Oomoo`0@Ool3003o OolaOol001Yoool004l000008Woo00<007ooOol02Goo0`0000=oo`00Ool03Goo00<007ooOol03Goo 00<007ooOol03Goo00<007ooOol03Goo00<007ooOol03Goo00<007ooOol03Goo00<007ooOol037oo 00<007ooOol03Goo00<007ooOol03Goo00<007ooOol03Goo00<007ooOol03Goo00<007ooOol03Goo 00<007ooOol03Goo00<007ooOol037oo00<007ooOol03Goo00<007ooOol03Goo00<007ooOol03Goo 00<007ooOol03Goo00<007ooOol03Goo00<007ooOol01Woo000ROol00`00Oomoo`07Ool2000cOol0 0`00Oomoo`0lOol00`00Oomoo`0mOol00`00Oomoo`0lOol00`00Oomoo`0mOol00`00Oomoo`06Ool0 029oo`03001oogoo00Aoo`<00?mooceoo`008Woo00@007ooOomoo`<00?mood1oo`008Woo1000ogoo @goo000ROol2003oOom5Ool0029oo`03001oogoo0?moodAoo`008Woo00<007ooOol0ogooA7oo000R Ool00`00Oomoo`3oOom4Ool0029oo`03001oogoo0?moodAoo`008Woo00<007ooOol0ogooA7oo003o OomYOol00?moofUoo`00ogooJGoo003oOomYOol00?moofUoo`00ogooJGoo003oOomYOol00001\ \>"], ImageRangeCache->{{{0, 359}, {221.375, 0}} -> {-1.07792, -349.624, \ 0.0394428, 2.15921}}], Cell[BoxData[ FormBox[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False], TraditionalForm]], "Output"] }, Open ]] }, Open ]] }, FrontEndVersion->"4.1 for Microsoft Windows", ScreenRectangle->{{0, 1600}, {0, 1089}}, WindowSize->{975, 609}, WindowMargins->{{-3, Automatic}, {Automatic, -27}}, Magnification->1.25 ] (******************************************************************* Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. *******************************************************************) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[1727, 52, 93, 2, 57, "Subsubsection"], Cell[1823, 56, 66, 1, 35, "Input"], Cell[1892, 59, 56, 1, 35, "Input"] }, Open ]], Cell[CellGroupData[{ Cell[1985, 65, 96, 2, 57, "Subsubsection"], Cell[2084, 69, 2181, 35, 728, "Input"] }, Open ]], Cell[CellGroupData[{ Cell[4302, 109, 94, 2, 57, "Subsubsection"], Cell[4399, 113, 435, 9, 99, "Input"], Cell[CellGroupData[{ Cell[4859, 126, 101, 2, 35, "Input"], Cell[4963, 130, 760, 19, 238, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[5760, 154, 174, 3, 35, "Input"], Cell[5937, 159, 1584, 38, 116, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[7558, 202, 80, 1, 35, "Input"], Cell[7641, 205, 18859, 489, 238, 4039, 301, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[26549, 700, 90, 2, 57, "Subsubsection"], Cell[CellGroupData[{ Cell[26664, 706, 183, 3, 98, "Input"], Cell[26850, 711, 515, 13, 112, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[27402, 729, 332, 5, 98, "Input"], Cell[27737, 736, 19703, 523, 238, 4483, 331, "GraphicsData", "PostScript", \ "Graphics"], Cell[47443, 1261, 167, 4, 35, "Output"] }, Open ]] }, Open ]] } ] *) (******************************************************************* End of Mathematica Notebook file. *******************************************************************)