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(* Content-type: application/mathematica *)

(*** Wolfram Notebook File ***)(* http://www.wolfram.com/nb *)

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(* Beginning of Notebook Content *)Notebook[{Cell[TextData[{ StyleBox["Calibration: linear relationship, normal distribution.", FontSize->14, FontWeight->"Bold", FontVariations->{"Underline"->True}, FontColor->RGBColor[0, 0, 1]], StyleBox["\n\nSituation:\n\nThere is a linear relationship between a \dependent variable y and an independent variable x:\n y = ", FontColor->RGBColor[0, 0, 1]], StyleBox["\[Beta]", FontColor->RGBColor[0, 0, 1]], StyleBox["0", FontSize->9, FontVariations->{"CompatibilityType"->"Subscript"}, FontColor->RGBColor[0, 0, 1]], StyleBox[" + ", FontColor->RGBColor[0, 0, 1]], StyleBox["\[Beta]", FontColor->RGBColor[0, 0, 1]], StyleBox["1", FontSize->9, FontVariations->{"CompatibilityType"->"Subscript"}, FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontColor->RGBColor[0, 0, 1]], StyleBox["x + ", FontColor->RGBColor[0, 0, 1]], StyleBox["\[Epsilon]", FontColor->RGBColor[0, 0, 1]], StyleBox["\nThe variable x is assumed to be exactly known. The experimental \error ", FontColor->RGBColor[0, 0, 1]], StyleBox["\[Epsilon]", FontColor->RGBColor[0, 0, 1]],

StyleBox[" is a random variable with a normal distribution, an expectation \value of zero, and a standard deviation of ", FontColor->RGBColor[0, 0, 1]], StyleBox["\[Sigma]", FontColor->RGBColor[0, 0, 1]], StyleBox[":\n ", FontColor->RGBColor[0, 0, 1]], StyleBox["\[Epsilon]", FontColor->RGBColor[0, 0, 1]], StyleBox[" ~ N(0,", FontColor->RGBColor[0, 0, 1]], StyleBox["\[Sigma]", FontColor->RGBColor[0, 0, 1]], StyleBox[")\nThe parameters ", FontColor->RGBColor[0, 0, 1]], StyleBox["\[Beta]", FontColor->RGBColor[0, 0, 1]], StyleBox["0", FontSize->9, FontVariations->{"CompatibilityType"->"Subscript"}, FontColor->RGBColor[0, 0, 1]], StyleBox[", ", FontColor->RGBColor[0, 0, 1]], StyleBox["\[Beta]", FontColor->RGBColor[0, 0, 1]], StyleBox["1", FontSize->9, FontVariations->{"CompatibilityType"->"Subscript"}, FontColor->RGBColor[0, 0, 1]], StyleBox[" and ", FontColor->RGBColor[0, 0, 1]], StyleBox["\[Sigma]", FontColor->RGBColor[0, 0, 1]], StyleBox[" are unknown. Estimates b", FontColor->RGBColor[0, 0, 1]], StyleBox["0", FontSize->9, FontVariations->{"CompatibilityType"->"Subscript"}, FontColor->RGBColor[0, 0, 1]], StyleBox[", b", FontColor->RGBColor[0, 0, 1]], StyleBox["1", FontSize->9, FontVariations->{"CompatibilityType"->"Subscript"}, FontColor->RGBColor[0, 0, 1]], StyleBox[" and s are to be determined by a calibration. The values of y are \measured for various choices of x. Subsequently the calibration is to be \applied to measurements of y with the corresponding values of x unknown, \leading to confidence intervals for these x-values.\n\nThis model is also \known as (first kind) Linear Regression.\n\______________________________________________________________________________\\n\nNote: - All names for variables and constants must be spelled with the \proper\n case. Therefore \"True\" is different from \"true\". The \latter\n specification will lead to an error.\n - Use the period \

\".\" as a decimal point, not the comma \",\".\n - None of the variables \specified in the declarative part of this\n notebook is modified in \any way by evaluating the computational part.\n\______________________________________________________________________________\", FontColor->RGBColor[0, 0, 1]]}], "Text", Editable->False, CellHorizontalScrolling->True, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Courier"],

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Cell[TextData[{ "Important: The statements\n Needs[\"Statistics`HypothesisTesting`\"];\n\have to be evaluated only once in a ", StyleBox["Mathematica", FontSlant->"Italic"], " session, though they can be evaluated as many times as desired. However, \they ", StyleBox["must", FontVariations->{"Underline"->True}], " be evaluated ", StyleBox["before", FontVariations->{"Underline"->True}], " any calculation in this notebook is performed. Failing to do so will cause \multiple declarations of some hidden variables, which renders your ", StyleBox["Mathematica", FontSlant->"Italic"], " session useless. Quit and re-launch ", StyleBox["Mathematica", FontSlant->"Italic"], " in the case of diagnostic messages when evaluating the following \statements."}], "Text", Evaluatable->False, CellChangeTimes->{{3.489233930625552*^9, 3.489233934471589*^9}}, AspectRatioFixed->True, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1]],

Cell[BoxData[ RowBox[{ RowBox[{"Needs", "[", "\"\<HypothesisTesting`\>\"", "]"}], ";"}]], "Input", CellChangeTimes->{3.489164182070148*^9}, AspectRatioFixed->True]}, Open ]],


Cell[TextData[{ StyleBox["Specification of the standard deviation", FontVariations->{"Underline"->True}],

"\n\nNormally the standard deviation is estimated from the actual sample \data. Sometimes a (presumably better) estimate is available from an external \source. Sometimes the exact value of the standard deviation is known.\n\Specify whether the standard deviation is known from an external source. \Choose one of the two statements:\n StandardDeviationExternal = True;\n \ StandardDeviationExternal = False;\nIf you declare the standard deviation \as external, specify its value by the statement:\n StdDev = 1.38;\n\Specify the associated number of degrees of freedom as in the following \example:\n NumberOfDegreesOfFreedom = 5;\nIf the standard deviation is \exactly known, specify the value Infinity:\n NumberOfDegreesOfFreedom = \Infinity;\nThe values for the standard deviation and its number of degrees of \freedom are ignored if the standard deviation is to be estimated from the \sample data. Note, however, that the statements, if left in this notebook, \must have the proper syntax, as they are evaluated."}], "Text", Editable->False, CellHorizontalScrolling->True, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1]],

Cell["\<\StandardDeviationExternal = False;StdDev = 1.38;NumberOfDegreesOfFreedom = Infinity;\\>", "Input", ImageRegion->{{0, 1}, {0, 1}}]}, Open ]],


Cell[TextData[{ StyleBox["Specification of the confidence coefficient", FontVariations->{"Underline"->True}], "\n\nThe confidence coefficient 1-", "\[Alpha]", " is the probability associated with the confidence intervals to be \calculated. The confidence coefficient must be a value between 0 and 1, \excluding limits. A typical value is 0.95 leading to the so-called 95% \confidence intervals.\nSpecify the confidence coefficient as in the following \example:\n ConfidenceCoefficient = 0.95;"}], "Text", Editable->False, CellHorizontalScrolling->True, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1]],

Cell["ConfidenceCoefficient = 0.95;", "Input", ImageRegion->{{0, 1}, {0, 1}}]}, Open ]],


Cell[TextData[{ StyleBox["Specification of the calibration data", FontVariations->{"Underline"->True}], "\n\nSpecify the values for x and y, in this sequence, as in the following \example:\n CalibrationData = { { 4.184 , 1.703 } ,\n \ { 3.15 , 1.53*10^2 } ,\n { 1.63 , \0.38*10^-3 } };\nMake sure the punctuation is correct. CalibrationData is a \list of lists. The elements of a list are separated by commas. The delimiters \of a list are braces {}. Blanks and carriage returns are ignored. Their use \is strongly encouraged for the sake of legibility."}], "Text", Editable->False, CellHorizontalScrolling->True, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1]],

Cell["\<\CalibrationData = { { 0 , 0 } , { 0.04855 , 38.21 } , { 0.04855 , 25.37 } , { 0.04855 , \41.57} , { 0.0971 , 54.55 } , { 0.0971 , 56.18 } , { 0.0971 , \54.81 } , { 0.1942 , 92.47 } , { 0.1942 , 100.46 } , { 0.1942 , \95.05 } , { 0.2913 , 142.03 } , { 0.2913 , 128.24 } , { 0.2913 , \141.05 } , { 0.3884 , 144.21 } , { 0.3884 , 137.18 } , { 0.3884 , \132.24 } , { 0.494 , 181.00 } , { 0.494 , 171.97 } , { 0.494 , \173.73 } };\\>", "Input", ImageRegion->{{0, 1}, {0, 1}}]}, Open ]],


Cell[TextData[{ "All results calculated in this notebook can be written into a disk file. \The document to be created will be a ", StyleBox["Mathematica", FontSlant->"Italic"], " notebook. However, it can be opened from within Microsoft Word as a \"text \only\" file. The text can be transferred into a Word document by means of \copying and pasting. The items in the document are separated by tab \characters, which makes formatting straightforward within Word.\nEach time an \input cell that writes to the file is evaluated, the text is appended to the \end of the file. Evaluating a cell twice means a double entry in the file. If \the results should not be written into a file, the corresponding input cells \can be left unevaluated.\nEnter the name of the document as in the following \example:\n FolderName = \"Harddisk:GC:\"\n ResultFileName = \"Fatty \acids\";\nThis would create a file named \"Fatty acids\" on the device named \\"Harddisk\" in folder \"GC\". Note that all folder names must be terminated \by a colon \":\". The folders must already exist. They will not be created by \

", StyleBox["Mathematica", FontSlant->"Italic"], ".\nIf the file already exists, its contents are not to be changed in any \way, unless the variable \"OverwriteFile\" is set \"True\" as in the \following example:\n OverwriteFile = True;\nThis is a rather dangerous \specification since ", StyleBox["Mathematica", FontSlant->"Italic"], " will destroy the file without warning. If you don't explicitly want to \overwrite a file, leave the statement as\n OverwriteFile = False;\nin the \notebook, protecting your results from unintended deletion."}], "Text", Editable->False, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Courier", FontColor->RGBColor[1, 0, 1]],

Cell["\<\FolderName = \"C:\\\\LabSolutions\\\\Data\\\\Lab Course\\\\M2\\\\\";ResultFileName = \"11_Trinkwasser_Cu\";OverwriteFile = True;\\>", "Input", CellChangeTimes->{{3.507880919015625*^9, 3.507880919375*^9}, { 3.50788095128125*^9, 3.507880966234375*^9}, {3.507881073234375*^9, 3.507881107765625*^9}, {3.601987966543277*^9, 3.6019880030629406`*^9}}, ImageRegion->{{0, 1}, {0, 1}}]}, Open ]],


Cell["\<\Evaluate this cell to open the output file for writing. Only a single file \can be open at any one time.\\>", "Text", Editable->False, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Courier", FontColor->RGBColor[1, 0, 1]],


Cell["\<\Module[{},Bad = Head[OutputFileIsOpen]==Integer;If[ Bad , Print[\"Error: There is already a file open: \",OutputFileName] ];If[ Bad , Abort[] ];Bad = True;If[ Head[FolderName]==String , Bad=False ];If[ Bad , Print[\"Error: No folder and file names have been specified.\"] ];If[ Bad , Abort[] ];FileList = FileNames[ ResultFileName , FolderName ];Bad = Length[FileList]>1;If[ Bad , Print[\"Error: Illegal file specification.\"] ];

If[ Bad , Abort[] ];Bad = Length[FileList]==1 && Not[OverwriteFile];If[ Bad , Print[\"Error: The file specified already exists.\"] ];If[ Bad , Print[\" Set variable OverwriteFile to True and \re-evaluate.\"] ];If[ Bad , Abort[] ];Status = OpenWrite[ StringJoin[FolderName,ResultFileName] , FormatType->OutputForm ];Bad = True;If[ Head[Status]==OutputStream , Bad=False ];If[ Bad , Print[\"Error: The file could not be opened.\"] ];If[ Bad , Abort[] ];OutputFileIsOpen = 1;If[ Length[FileList]==0 , FileList=FileNames[ResultFileName,FolderName] ];OutputFileName=FileList[[1]];StreamName = Status;Print[ \"File has been opened and is ready for writing.\" ];Print[ OutputFileName ];];\\>", "Input", Editable->False, CellOpen->False, ImageRegion->{{0, 1}, {0, 1}}],

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Cell["\<\Evaluate this cell to perform the calculation of the calibration part.\\>", "Text", Editable->False, CellHorizontalScrolling->True, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1]],


Cell["\<\CalibrationDone = False;Off[General::spell1,General::spell];CalculationAborted = False;

CheckAbort[ Module[ {} ,NumberOfDigits = 50;Print[ \"Calibration: Linear relationship, normal distribution.\"];Print[ \" \" ];Bad = StandardDeviationExternal != True && StandardDeviationExternal != False;If[ Bad , Print[ \"Illegal value for StandardDeviationExternal: \" , StandardDeviationExternal ] ];If[ Bad , Abort[] ];If[ StandardDeviationExternal , Module[{}, Bad = True; If[Positive[StdDev],Bad=False]; If[Bad,Print[\"Illegal value for StdDev: \", StdDev]]; If[Bad,Abort[]]; Print[\"Standard deviation from external source = \", StdDev]]; Bad = True; If[Positive[NumberOfDegreesOfFreedom],Bad=False]; If[Bad,Print[\"Illegal value for NumberOfDegreesOfFreedom: \", NumberOfDegreesOfFreedom]]; If[Bad,Abort[]]; If[NumberOfDegreesOfFreedom==Infinity, Print[\"(exactly known)\"], Print[\"Associated number of degrees of freedom = \" , NumberOfDegreesOfFreedom] ], Print[\"The standard deviation will be estimated from the sample data.\"] \];Bad = ConfidenceCoefficient >= 1 || ConfidenceCoefficient <= 0;If[ Bad , Print[ \"Illegal value for ConfidenceCoefficient: \" , ConfidenceCoefficient ] ];If[ Bad , Abort[] ];RationalConfidenceCoefficient = Rationalize[100*ConfidenceCoefficient,0];If[ Denominator[RationalConfidenceCoefficient] == 1 , Print[ \"Confidence coefficient = \" , RationalConfidenceCoefficient,\"%\" ] , Print[ \"Confidence coefficient = \" , 100*ConfidenceCoefficient,\"%\" ] ];Print[ \" \" ];Print[\"Results of calibration:\"];Print[\" \"];SampleSize = Length[CalibrationData];Do[ Module[{xx,yy}, Bad=True; xx=CalibrationData[[i,1]]; If[xx<0||xx>=0,Bad=False]; If[Bad,Print[\"Illegal x value in data pair \",i,\": \",xx]]; If[Bad,Print[\"Edit and re-evaluate the definition of CalibrationData.\"]]; If[Bad,Abort[]];

Bad=True; yy=CalibrationData[[i,2]]; If[yy<0||yy>=0,Bad=False]; If[Bad,Print[\"Illegal y value in data pair \",i,\": \",yy]]; If[Bad,Print[\"Edit and re-evaluate the definition of CalibrationData.\"]]; If[Bad,Abort[]] ] , {i,SampleSize} ];x = Table[N[Rationalize[CalibrationData[[i,1]],0],NumberOfDigits],{i,\SampleSize}];y = Table[N[Rationalize[CalibrationData[[i,2]],0],NumberOfDigits],{i,\SampleSize}];XMatrix = Table[ {1,x[[i]]} , {i,SampleSize} ];XTX1 = Inverse[Transpose[XMatrix].XMatrix];{b0,b1} = XTX1 . (Transpose[XMatrix].y);yEstimated = XMatrix . {b0,b1};residuals = y - yEstimated;leverages = Table[Null,{SampleSize}];normalizedResiduals = Table[Null,{SampleSize}];Do[x0 = {{1},{x[[i]]}}; leverages[[i]] = 1/Sqrt[1-(Transpose[x0].XTX1.x0)[[1,1]]]; normalizedResiduals[[i]] = residuals[[i]] * leverages[[i]], {i,SampleSize}];If[ StandardDeviationExternal , s = StdDev , s = Sqrt[(residuals.residuals)/(SampleSize-2)] ];If[ StandardDeviationExternal , nu = NumberOfDegreesOfFreedom , nu = SampleSize-2 ];t95 = If[ nu==Infinity , NormalCI[0,1,ConfidenceLevel->ConfidenceCoefficient][[2]] , StudentTCI[0,1,nu,ConfidenceLevel->ConfidenceCoefficient][[2]] ];sb0 = s * Sqrt[XTX1[[1,1]]];sb0t = t95 * sb0;sb1 = s * Sqrt[XTX1[[2,2]]];sb1t = t95 * sb1;Bad = True;If[ Head[yList]==List , Bad=False\[NonBreakingSpace]];If[ Bad , yList={} ];Clear[yEst,CIyMeanUpper,CIyMeanLower,CIySingleUpper,CIySingleLower];yEst[xx_] := Evaluate[b0+b1*xx];CIyMeanUpper[xx_] := Evaluate[b0+b1*xx+t95*s*Sqrt[{{1,xx}}.XTX1.{{1},{xx}}]];CIyMeanLower[xx_] := Evaluate[b0+b1*xx-t95*s*Sqrt[{{1,xx}}.XTX1.{{1},{xx}}]];CIySingleUpper[xx_] := \Evaluate[b0+b1*xx+t95*s*Sqrt[1+{{1,xx}}.XTX1.{{1},{xx}}]];CIySingleLower[xx_] := \Evaluate[b0+b1*xx-t95*s*Sqrt[1+{{1,xx}}.XTX1.{{1},{xx}}]];CalibrationDone = True;Print[\"Standard deviation of experimental errors = \" , N[s,7] ];Print[\" \"];Print[\"Slope: \",N[b1,7],\" \[PlusMinus] \",N[sb1t,7]];Print[\" upper limit: \",N[b1+sb1t,7]];Print[\" mean: \",N[b1,7]];Print[\" lower limit: \",N[b1-sb1t,7]];Print[\" standard deviation: \",N[sb1,7]];

Print[\" \"];Print[\"Intercept: \",N[b0,7],\" \[PlusMinus] \",N[sb0t,7]];Print[\" upper limit: \",N[b0+sb0t,7]];Print[\" mean: \",N[b0,7]];Print[\" lower limit: \",N[b0-sb0t,7]];Print[\" standard deviation: \",N[sb0,7]];Print[\" \"];Print[TableForm[Table[{N[x[[i]],7],N[y[[i]],7],N[yEstimated[[i]],7],N[residuals[[i]]],N[leverages[[i]]]},{i,SampleSize}],TableHeadings->{None,{\"x\",\"y measured\",\"y \estimated\",\"residual\",\"leverage\"}},TableAlignments->Center,TableSpacing->{0,3}]];] , CalculationAborted=True; ]On[General::spell1,General::spell];If[ CalculationAborted , Abort[] ];\\>", "Input", Editable->False, CellOpen->False, ImageRegion->{{0, 1}, {0, 1}}],

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Cell["\<\Evaluate this cell to write the results of the calibration to disk.\\>", "Text", Editable->False, CellHorizontalScrolling->True, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Courier", FontColor->RGBColor[1, 0, 1]],

Cell["\<\Module[{},Bad = True;If[ Head[CalibrationDone]==Symbol , Bad=False ];If[ Bad , Print[\"Error: First perform calculation on calibration.\"] ];If[ Bad , Abort[] ];Bad = True;If[ CalibrationDone , Bad=False ];If[ Bad , Print[\"Error: First perform calculation on calibration.\"] ];If[ Bad , Abort[] ];Write[StreamName,\"Calibration: Linear relationship, normal distribution.\"];Write[StreamName,\" \"];Write[StreamName,\"Results of calibration:\"];Write[StreamName,\" \"];If[ StandardDeviationExternal , Module[{}, Write[StreamName,\"Standard deviation from external source = \",StdDev]]; If[NumberOfDegreesOfFreedom==Infinity, Write[StreamName,\"(exactly known)\"], Write[StreamName,\"Associated number of degrees of freedom = \" \,NumberOfDegreesOfFreedom] ], Write[StreamName,\"The standard deviation will be estimated from the \sample data.\"] ];Write[StreamName,\"Standard deviation of experimental errors = \" , N[s,7] ];Write[StreamName,\"Associated number of degrees of freedom = \",nu];Write[StreamName,\" \"];Write[StreamName,\"Slope: \",N[b1,7],\" \[PlusMinus] \",N[sb1t,7]];Write[StreamName,\"\\tupper limit:\\t\",N[b1+sb1t,7]];Write[StreamName,\"\\tmean:\\t\",N[b1,7]];Write[StreamName,\"\\tlower limit:\\t\",N[b1-sb1t,7]];Write[StreamName,\"\\tstandard deviation:\\t\",N[sb1,7]];Write[StreamName,\" \"];Write[StreamName,\"Intercept:\\t\",N[b0,7],\" \[PlusMinus] \",N[sb0t,7]];Write[StreamName,\"\\tupper limit:\\t\",N[b0+sb0t,7]];Write[StreamName,\"\\tmean:\\t\",N[b0,7]];Write[StreamName,\"\\tlower limit:\\t\",N[b0-sb0t,7]];Write[StreamName,\"\\tstandard deviation:\\t\",N[sb0,7]];Write[StreamName,\" \"];Write[StreamName,\"\\tx\\ty measured\\ty estimated\\tresidual\\tleverage\"];Do[Write[StreamName,\"\\t\",N[x[[i]],7], \"\\t\",N[y[[i]],7], \"\\t\",N[yEstimated[[i]],7], \"\\t\",N[residuals[[i]],7],

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Cell["\<\Evaluate this cell to close the output file. As soon as the file is closed, \no more output can be appended to the file. Instead a new file must be opened.\\>", "Text", Editable->False, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Courier", FontColor->RGBColor[1, 0, 1]],


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Cell["\<\Evaluate this cell to visualize confidence intervals of the calibration part. \The output cell shows the axes of a coordinate system, the experimental data \pairs as black dots, and the estimated model function as a straight line. In \addition two pairs of confidence intervals around the calibration line are \shown. The outer curves, drawn in green, are the confidence intervals of a \single measurement of y, given a particular (exact) value of x. The inner \curves, drawn in red, correspond to the mean of y, given x.Specify whether the origin of the coordinate system has to be included in the \plot. Choose between one of the following statements: IncludeOrigin = True; IncludeOrigin = False;\\>", "Text", Editable->False, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1]],

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Cell["\<\The size of the plot can be altered by first clicking on the plot and then \dragging a corner of the picture. The plot can be copied to the clipboard by \clicking on the plot and using the Copy function. It can then be pasted into \a Word document.\\>", "Text", Editable->False, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1]],


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Cell["\<\Evaluate this cell to visualize the normalized residuals as black dots.\\>", "Text", Editable->False, ImageRegion->{{0, 1}, {0, 1}},

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Cell["\<\In the following section the calibration can be used to estimate an unknown \value of x from one or several measured values of y. Enter all y-values, \corresponding to the same unknown x, as a list separated by commas as in the \following example: ylist = { 0.619 , 0.526 };The variable ylist must be a list (having the braces around) even if it \contains only a single value: ylist = {4.26};The yList can be edited as many times as desired, followed by a calculation \using the previous calibration.\\>", "Text", Editable->False, CellHorizontalScrolling->True,

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Cell["yList = { 106.70 , 111.53 , 110.07 };", "Input", ImageRegion->{{0, 1}, {0, 1}}],

Cell["\<\Changes in the concentration due to dilution or any other activity can be \specified by setting a global factor to be multiplied to the final \concentration and its confidence limits. Specify the factor as in the \following example: GlobalFactor = 1;\\>", "Text", Editable->False, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1]],

Cell["GlobalFactor = 1;", "Input", ImageRegion->{{0, 1}, {0, 1}}]}, Open ]],


Cell["\<\Evaluate this cell to perform the calculation for the current choice of yList.\\>", "Text", Editable->False, CellHorizontalScrolling->True, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1]],


Cell["\<\CalculationAborted = False;Off[General::spell1,General::spell];CheckAbort[ Module[ {} ,NumberOfValues = Length[yList];If[ NumberOfValues==0 , Print[\"yList is empty\"] ];If[ NumberOfValues==0 , Abort[] ];Do[ Module[{yy},Bad = True; If[ GlobalFactor > 0 , Bad=False ]; If[ Not[Bad] , RationalGlobalFactor = \N[Rationalize[GlobalFactor,0],NumberOfDigits] ]; If[ Bad , Print[ \"Illegal value for GlobalFactor: \" , GlobalFactor ] ]; If[ Bad , Abort[] ]; Bad=True; yy=yList[[i]]; If[yy<0||yy>=0,Bad=False]; If[Bad,Print[\"Illegal y value (item \",i,\"): \",yy]];

If[Bad,Print[\"Edit and re-evaluate the definition of yList.\"]]; If[Bad,Abort[]] ] , {i,NumberOfValues} ];yMean = Sum[N[Rationalize[yList[[i]],0],NumberOfDigits], {i,NumberOfValues}]/NumberOfValues;If[ b1==0 , Print[\"Zero slope. No calculation possible.\"] ];If[ b1==0 , Abort[] ];xEstimated = (yMean-b0) / b1;sx = s * Sqrt[{-1/b1,(b0-yMean)/b1^2}.XTX1.{-1/b1,(b0-yMean)/b1^2}+(1/b1^2)/\NumberOfValues];sxt = t95 * sx;CIxLower = xEstimated-sxt;CIxUpper = xEstimated+sxt;Print[\"List of y-values:\"];Do[ Print[yList[[i]]] , {i,NumberOfValues} ];Print[\" \"];Print[\"Estimated x: \",N[xEstimated*RationalGlobalFactor,7],\" \[PlusMinus] \\",N[sxt*RationalGlobalFactor,7]];Print[\" upper limit: \",N[CIxUpper*RationalGlobalFactor,7]];Print[\" mean: \",N[xEstimated*RationalGlobalFactor,7]];Print[\" lower limit: \",N[CIxLower*RationalGlobalFactor,7]];If[ Denominator[RationalConfidenceCoefficient] == 1 , Print[ \" confidence coefficient: \" \,RationalConfidenceCoefficient,\"%\" ] , Print[ \" confidence coefficient: \" \,100*ConfidenceCoefficient,\"%\" ] ];Print[\" standard deviation: \",N[sx*RationalGlobalFactor,7]];Print[\" associated number of degrees of freedom = \" , nu ];Print[\"Global factor = \" , N[RationalGlobalFactor,7] ];Print[\" \"];] , CalculationAborted=True;\[NonBreakingSpace]];On[General::spell1,General::spell];If[ CalculationAborted , Abort[] ];xCalculationDone = True;\\>", "Input", Editable->False, CellOpen->False, ImageRegion->{{0, 1}, {0, 1}}],

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Cell["\<\Evaluate this cell to visualize confidence intervals of the calibration part. \The output cell shows the axes of a coordinate system, the experimental data \pairs as black dots, and the estimated model function as a straight line. In \addition two pairs of confidence intervals around the calibration line are \shown. The outer curves, drawn in green, are the confidence intervals of a \single measurement of y, given a particular (exact) value of x. The inner \curves, drawn in red, correspond to the mean of y, given x. The y-values, as \specified in yList, are shown as horizontal bars. The confidence intervals \for x are shown as vertical bars.Specify whether the origin of the coordinate system has to be included in the \plot. Choose between one of the following statements: IncludeOrigin = True; IncludeOrigin = False;\\>", "Text", Editable->False,

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Cell["\<\The size of the plot can be altered by first clicking on the plot and then \dragging a corner of the picture. The plot can be copied to the clipboard by \clicking on the plot and using the Copy function. It can then be pasted into \a Word document.\\>", "Text", Editable->False, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1]],


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