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     Origin Pro Workbook




                   March 2011
                  Document 083

          Computing Services Department
Contents
     INTRODUCTION                                    4
        What is Origin                               4
        Using this Workbook                          4
        Getting Help                                 5
           Checkpoints                               5
           What is not Covered in Workbook           5

     2 EXERCISE 1 DRAW A GRAPH                        6
       Starting Origin Pro 8.1                        7
       Importing Data into Origin                     7
       Examining the Worksheet                        8
       Creating a Graph                               9
       Setting the Page Size                         10
           Checkpoint 1                              11
       Adding a New Plot to a Graph                  11
       Changing Line Styles                          12
           Checkpoint 2                              12
       Adding a Title, Legend and Axis Titles        13
       Adding Symbols and Downsampling               14
       Changing the Printer Settings                 15
       Saving your Graphs                            16
       Exporting your Graphs                         16
       Creating a Graph using Multi–lines            17
       Zooming in One Part of the Graph              19
       Exiting Origin                                19

     3 EXERCISE 2 DRAW ERROR BARS                    20
       Using the Import Wizard                       21
       Creating the Error Columns in the Worksheet   23
       Creating an Error Bar Plot                    24
       Changing the Error Bar Directions             24
          Checkpoint 1                               25
       Adding a Title                                25
       Adding Another Graph to the Window            26
          Checkpoint 2                               27
       Trying the Polynomial Fitting Routines        27
       Trying Other Curve–Fitting Routines           28
       Changing the Graph Size and Position          29

     4 EXERCISE 3 DRAW A 3D MESH PLOT                30
       Interpolating the Data                        30
           Checkpoint 1                              32
       Adding Original Points                        32
       Changing the Colour Scheme                    33
       Changing the Point of View                    33

     5 EXERCISE 4 DRAW CURVE OF 2D FUNCTION          34
       Using the Function Window                     35
       Adjusting the Axis Scales                     36
          Checkpoint 1                               36
       Changing the Parameters                       36

     6 EXERCISE 5 DRAW MULTIPLE AXES PLOT            38
       Adding Data to the Worksheet                  39
       Creating the Plots                            39
          Checkpoint 1                               40
       Changing the Scales on the Axes               41
                Checkpoint 2                                                              41
             Tidying up the Graph                                                         42

         7 EXERCISE 6 THE HISTOGRAM WIZARD                                                43
           Importing Data to the Worksheet                                                43
           Using the Histogram Wizard                                                     43
           Changing the Bucket Sizes                                                      44
              Checkpoint 1                                                                44
           Creating a Regression Line & Confidence Lines                                  45
           Finding Prediction Intervals and Correlation Coefficient                       47
           Optional Exercise                                                              48

         APPENDIX 1 WORKBOOK DATASETS                                                     49

         APPENDIX 2 LOCAL SETUP OF ORIGIN                                                 53

         APPENDIX 3 PRINTING FROM ORIGIN                                                  53




Format Conventions
   In this document the following format conventions are used:

     Computer output is given in a Courier font.                 Password
     Input which is to be typed by you is in bold                a:\setup
     Input which must be replaced by your details is given       LOGIN user_name
     in bold italics.
     Keys that you press are bold.                               Enter
     Menu options and buttons are given in an Arial font.        File | New
     Notes are indicated by a bulleted book.                      This is a note
     Tips are indicated by a bulleted flag.                          This is a tip
     Warnings are indicated by a bulleted bomb.                      This is a warning

Feedback
   The Computing Services Department welcomes feedback on its documentation. If you notice any
   mistakes in this document, or if you wish to make any suggestions on how the document could be
   improved, please contact Allyson Matthews, Information Officer. Electronic mail should be sent to the
   email address allyson@liv.ac.uk
Introduction
   What is Origin
      Origin is a technical graphing package. It is available to users who have registered for the
      Managed Windows Service. We now have a site licence and you can buy the CD from the
      CSD helpdesk for a nominal cost.

      Origin can be used effectively to produce all types of graphs and charts. It includes a nonlinear
      curve fitter, worksheets that accommodate large datasets and summary statistics. It has what it
      calls a mathematical transform language that allows you to manipulate and analyse data.


   Using this Workbook
      This workbook contains a number of examples that are designed to show you some of the
      facilities available in Origin for creating graphs and to help you navigate the menu system and
      the toolbars.

      For versions of Origin manuals in PDF form, please see the OriginLAB website:

      http://www.originlab.com/index.aspx?s=12&lm=+66

      It is assumed in this workbook that you are familiar with the use of Windows packages; i.e.
      you know what is meant by the following terms:

            Windows
            Clicking
            Double-clicking
            Dragging
            Menus
            Toolbars
            File browsers

      If you are not familiar with using the Managed Windows Service, then it is suggested that you
      look at the following web page

      http://www.liv.ac.uk/csd/mws/index.htm

      We also assume minimal knowledge of spreadsheets; i.e. you know what spreadsheets look
      like and that you can use the mouse or arrow keys to move around the cells.




      4
Getting Help
   When you select Help on the top menu and then select Origin, you will see that Origin uses
   the standard Windows help system. You are presented with four tabs and only one may be
   selected at any one time. These are:

       Contents                         this opens a table of contents where you can
                                        browse various topics

       Index                            this allows you to see a list of index entries. You
                                        can either type a subject or scroll through the list

       Search                           this allows you to search a particular topic or the
                                        entire Help file for a particular word or phrase.

       Favourites                       this allows you to store particular Help topics of
                                        interest and to recall them later.


   Checkpoints
   If you get stuck during an exercise but you do not want to start at the beginning of the exercise
   again, you can load checkpoint files — stored in v:\originexs\chkpoints. At various stages in
   the exercises, you are invited to use a suitable checkpoint file.

   What is not Covered in Workbook
   A workbook has to be selective in the type of examples it chooses to discuss. It is expected
   that the audience will include users from different faculties, not all of whom are computer
   literate or with a strong mathematical background. So a decision was made not to include the
   following topics:

          Advanced Curve Fitting

          Templates

          Themes

          Origin C and Code Builder

   Users are referred to the Origin Tutorial pages or to the Origin User Guide for worked
   examples on these topics. If anyone has suggestions for further exercises in this workbook,
   could they please contact Mary Thorp via the CSD Helpdesk.




                                                                                                   5
2   Exercise 1 Draw a Graph
      The aim of this exercise is to produce the following graph.




      In this exercise, you will be proceeding through the following list of actions. Full instructions
      will be given:

            Starting Origin 8.5
            Importing Data into Origin
            Examining the Worksheet
            Creating a Graph
            Setting the page size
            Adding a New Plot to a Graph
            Changing Line Styles
            Adding a Title, Legend and Axis Titles
            Adding symbols and downsampling
            Changing the printer settings
            Saving your graphs
            Exporting your graphs
            Creating a graph using Multi-lines
            Zooming in on part of the graph
            Exiting Origin




      6
             Starting Origin Pro 8.5
                The following instructions will help you to run Origin.

                      After logging on with your Windows 7 desktop on the screen, double–click the icon for
                       Windows Explorer and select Organise | Folder Options. Click the View tab and
                       check that Hide file extensions for known filetypes is switched off. Close down the
                       Windows Explorer window. This ensures that filetypes are not hidden in file browsers,

                      Then look for Start | All Programs | OriginLab | Origin 8.5 | OriginPro 8.5 and
                       click it if it is there.

                      If this is not present, then you need to install Origin. Click the Install University
                       Applications icon on desktop and look for Origin 8.5 SR1. You should not need to
                       reboot. Then click Start | All Programs | OriginLab | Origin 8.5 | OriginPro 8.5.

                For more details on the installation, see Appendix 2.

                      Maximise the Origin window. You are presented with the following screen. There is
                       usually one other window as well as the main Origin window. This is called Book1. We
                       shall initially concentrate on putting data into the worksheet called Book1.

                      Click Format | Menu and ensure that Full Menus has been switched on.



Standard                                                                                                           Graph
Format                                                                                                             Style




2D Graphs
Status bar


                You will be meeting the Status bar at the bottom and some of the tools on the toolbars later on.
                Some of these toolbars are marked on the above picture (eg Standard, Format etc)

                Note that, once you have installed Origin, you can start Origin in future by using the following
                method. There is also an icon on the Desktop.:

                Select Start | All Programs | OriginLab | Origin 8.5 | OriginPro 8.5.


             Importing Data into Origin
                Make sure that the window called Book 1 is highlighted and then follow these instructions:

                      Select File | Import | Single ASCII.


                                                                                                               7
        Navigate to the directory where the data is stored, in this case v:\originexs\exercises.

        Change the Files of type to All Files *.*.

        Select Exercise1.csv. The first few lines of this file are shown below.




  Note that a comma is used to separate values in the original file. Origin detects that a comma
  is used as a separator. Also, the first row contains column headings T, A1 etc. It is a common
  practice to put column headings in a data file.

        Click on Open.

  The data will now be loaded into the worksheet starting at the cell in Row1, Column 1.


Examining the Worksheet




  An Origin worksheet is a spreadsheet. It consists of rows and columns. Values (data) or labels
  (text) can be put into these cells. Each of the cells has a unique address. For example, the
  address of the cell, which has the label A1, is Book1, 2, 1; i.e. the cell is in Book 1, column 2,
  and row 1.

  Origin is able to detect that there are column headings at the top of the file and so uses those
  by default for the row called Long Name at the top of the worksheet. When you become more
  familiar with using Origin, you will see that it has very comprehensive system for importing
  data from a file or database into a worksheet

  Worksheets can hold data imported from a file, alternatively data can be directly entered into
  the worksheet. Also you can open an Excel spreadsheet in Origin (using File | Open Excel
  not File | Import). Sometimes output worksheets are created as a result of a calculation.




  8
    Creating a Graph
           After you have entered data into the worksheet, a graph can be produced using this data. There
           are two ways of creating a simple 2D graph:

                  EITHER click an icon on the 2D Graphs toolbar near the bottom of the window OR
                   choose one of the options from the Plot menu.

           When more familiar with Origin, you can learn about the other types available, especially
           those in the Template libraries.

           The icons for 2D graph types available from the 2d Graphs toolbar are shown below.

creates a line graph                                 creates a waterfall Z colour mapping graph
creates a horizontal step                            creates a vertical 2 panel graph
creates a vertical step                              creates a horizontal 2 panel graph
creates a connected spline                           creates a 4 panel graph
creates a scatter graph.                             creates a 9 panel graph
c reates a scatter central plot                      creates a stack of graphs
creates a Y Error graph                              creates multiple panels by label
creates a X Y Error graph                            creates a box chart
creates a vertical drop line graph                   creates a histogram
creates a bubble graph                               creates a histogram with probabilities
creates a colour map graph                           creates stacked histograms
creates bubble & colour map graph                    creates a QC (X-bar R) chart
creates a line & symbol graph                        creates Pareto chart binned data
creates a line series                                creates Pareto chart raw data
creates a 2-point segment                            creates a scatter matrix
creates a 3-point segment                            creates a probability plot
creates a column graph                               creates a Q-Q plot
creates a column plus label graph                    creates an area graph.
creates a bar graph                                  creates a stack area graph.
creates a stacked column chart                       creates a fill area graph.
creates a stacked bar chart                          creates a polar theta (X) r(Y) graph
creates a floating column                            creates a polar theta (Y) r(X) graph

creates a floating bar                               creates a windrose binned graph
creates a 3D pie chart.                              creates a windrose raw graph
creaes a B&W pie chart.                             creates a ternary graph.
creates a double y axis graph                        creates a Smith Chart
creates a 3Ys Y-YY graph                             creates a XYAM (X,Y, angle, magnitude) vector graph
creates a 3Ys Y-Y-Y graph                            creates a XYXY (start XY, end XY) vector graph.
creates a 4Ys Y-YYY graph                           creates a zoom graph
creates a 4Ys YY-YY graph                           creates a high-low-close chart
creates multiple Y axes                             creates a Japanese Candlestick
stack lines by Y off sets                            creates an OHLC bar chart


                                                                                                        9
creates a waterfall graph                              creates an OHLC Volume
creates a waterfall Y colour mapping graph             opens the Select Template dialog box (Template Library).
           When using the 2D graph toolbar, you can select some columns or a block of data. If no data
           has been selected, Origin assumes you want all the data.

           We want to produce a line graph showing A1 against T. To do this,

                 Click on the heading for column A(X) and drag over to the heading for B(Y). Both
                  columns should be highlighted.

                 Select the Line icon from the 2D Graphs toolbar. If a window appears about System
                  Theme, click the little box Don’t show this message in future and then click OK.




   Setting the Page Size
           It is a good idea to set the printer before doing major work. In this particular exercise, we want
           an A4 plot in Landscape orientation.

                 Go to File | Print and check that you are using one of the A4 laser printers. Click
                  Cancel

                 Click File | Page Setup. The Paper Size should already have been set to A4 and the
                  Orientation should have been set to Landscape. Click OK

           Next, check that you are using millimetres for your units:

                 Go to Format | Page and click the Print/Dimensions tab

                 Change the Units to mm if necessary and then click OK

           You may want to resize the plot, so that it fills the page. To do this:

                 Click somewhere on the white space inside the graph box (where the two axes are two
                  sides of the rectangular box). The box is highlighted.

                 Resize the plot. Drag it to wherever you wish. Also, you can move the legend.




           10
   Checkpoint 1
   If you have not obtained the picture below, then you can either load the file EX1CH1.OPJ
   from v:\originexs\chkpoints\ or you can start from scratch.




Adding a New Plot to a Graph
   A layer has one set of controlling axes. On the top left of the Graph window, the number 1
   refers to Layer 1. Another exercise later shows how to add another layer with new set of axes.

   To add another line to the first line on this layer:

         Click on the Worksheet window. (If this is not visible, then click Window | Exercise1
          – Exercise1.csv). Select the heading A(X) and then pressing the CTRL key, select the
          column heading C(Y). You should now have 2 columns highlighted.

   You may have noticed that, when switching between the Worksheet window and the Graph
   window, the menu at the top changed. For instance the Statistics menu only appears when the
   Worksheet window is active. The Graph menu only appears when the Graph window is active.

         Click on the Graph window (called Graph1) and then select Graph | Add Plot to
          Layer | Line

         Notice that the legend is not correct now. Select Graph | New Legend

   You should now be presented with the following graph:




                                                                                               11
Changing Line Styles
   We will now change the formatting of the lines so that the lines can be more easily
   distinguished on the laser printer.

         Select Format | Plot. The Plot Details window appears, with the Line tab showing.




         Click the first line T(X).A1(Y) and make its Colour Red. Change the Colour of the
          second line Navy and its Style to Dot. You may need to change its Width. Click OK.

   Checkpoint 2
   If you have not obtained the picture below, then you can either load the file EX1CH2.JNB
   and start here or load the file EX1CH1.JNB and retrace the steps from Checkpoint 1.




   12
Adding a Title, Legend and Axis Titles
   It is worth pointing out at this stage that Origin has an object–oriented rationale. Double–
   clicking on any object will allow you to change the properties of that object. For instance, try
   double–clicking on one of the curves.

   To change the X axis title, first:

         Click Format | Axis Titles | X Axis Title. Or simply right-click T on the graph and
          choose Properties.

         Make the axis title Time (mseconds)

         Repeat for the Y axis so that the title for the Y axis is Amplitude.

   To change the graph title and the legends.

         Click on the Text tool on the toolbar on the left and add the title Sound Waves.
          Note that the title moves with the graph if you select the graph box. The title is part of
          the layer. To move the title around, click outside the text box and then click the Text
          box again and move it.

         Return to the data worksheet and click the Long Name entry (currently A2) on the
          B(Y) column. Change this to High. Change the Long Name (currently A3) for the
          C(Y) column into Low.

         Click on the Graph window and select Graph | Update Legend | Open Dialog. Click
          OK on next box. The legend should be updated now.




                                                                                                   13
Adding Symbols and Downsampling
  You could have requested a line and scatter plot initially instead of asking just for a line plot
  but you can also add symbols to your line plots at any stage of creating a graph.

        Right-click one of the lines on the graph to select it. Choose Change Plot to | Line
         and Symbol.

        To change the symbols, go to the Plot Details window (via the Format | Plot menu
         item). There are various details that you can change – for instance, the Symbol Type.
         As an exercise, try changing the symbol types to a Solid Triangle Up and to a Hollow
         Triangle Down.

  Sometimes, you may have too many data points to view and you may decide you only want to
  see a subset of them. You can downsample the data.

        Select Format | Layer and choose the Size/Speed tab. There should be a tick by
         Worksheet Data, maximum points per curve. Change the default number to 14.




  14
Changing the Printer Settings




   To print your finished graph,

         Undo the downsampling before doing the next set of instructions to print the graph.

         Select File | Print.

         Change the Printer Name to the desired print-queue/printer. Use an A4 printer such as
          the Colour Laser printer. You can change any of the printer settings at this stage by
          clicking the Properties button.

         Click on OK and your plot will be added to the queue.

         Before using Origin, you should normally make the desired printer to be your default
          printer, because the page sizes available in Origin are dependent upon which printer
          you have chosen. See Appendix 3 for more details.

   If you want to check your print-out before printing, use File | Print Preview.

   You can create a layout (similar to a slide in PowerPoint) in Origin via the File | New |
   Layout menu item. You can then put both the graph and part of the worksheet on the layout
   using the Layout menu. Objects on a layout can be rearranged using the Object Edit toolbar
   (see View | Toolbars) and then the layout can be printed.

   Although the Layout facilities in Version 8 of Origin have improved, we still do not consider
   this topic any further in this workbook since most people would prefer to use PowerPoint or
   Corel Draw to create a poster (another term for layout).




                                                                                                 15
Saving your Graphs
   To save your Origin file containing both the graph and the worksheet:

         Select File | Save Project As. Navigate to where you want to save your file, e.g.
          M:\originexs




         Enter a File name for the Origin Project (please call it Exercise1.opj) and click Save.

   At this stage, it is worth while pausing to look at the structure of an Origin Project.

         Do not close the project down but look at the bottom and close any panels at the bottom
          and on the left and the Results log window, if they are present. Click View | Project
          Explorer and move the new window (on the left) so that it is docked at the bottom. The
          Project Explorer should currently show that you have one open project which contains
          one graph and one worksheet. You may need to expand the headers so that you see a
          similar picture as the one below.




   When you save a project, you save the whole structure of Origin child windows, including the
   pages, layouts, scripts, matrices, worksheets, graphs, notes and Excel workbook windows.
   You can also use Project Explorer to append a second project or to find windows within the
   current project file


Exporting your Graphs
   To export your graphs as pictures, for inclusion in another program,

         Click on the Graph window again and then select File | Export Graphs. Make sure
          you have the Image tab clicked.

         Select the desired File Type, (there are a number of choices, including TIFF, GIF,
          WMF, JPEG and Encapsulated PostScript).

         Enter a File name (for example, type Exercise1.emf if you have chosen Enhanced
          Metafile for the File Type)


   16
         For the Path, navigate to where you want to export your file, i.e. M:\originexs




         Click Preview (or AutoPreview). Then click OK unless you wish to explore the
          Export Settings or change the Image Size.


Creating a Graph using Multi–lines
   We are going to start a new page and we shall be using the default settings for multiple lines.

         Remove the old page by closing the Graph1 window. You are asked if you want to
          delete or hide the window. Choose Delete.

         Click on the Worksheet window and change the Long Name for columns 2 and 3 back
          to A1 and A2. Select all the columns so they are highlighted. A quick way of doing this
          is to move to the top left white space, next to A(X) and, when the pointer change to a
          diagonal arrow, click.

         Select Plot | Line and Symbol | Line + Symbol and a new window appears. If you
          have received a Reminder Message, just click OK on the dialog box.




         Select the menu item Format | Plot to obtain the Plot Details box. It looks different!

   The Group tab is now available since we have multiple plots on this layer. You can edit the
   colours and line styles for each individual line, independently of the other lines on this layer.
   Or you can edit the lines as a group, where the colours and line styles of each line depends on


                                                                                                   17
the group schemes. The advantage of working in groups is that if you add a new layer to the
same page, the new graphs by default use the same group schemes as those in the first layer.

      Keeping the Dependent option ticked, go to the colours (under Details) on the same
       row as Line Colour. Right-click and choose Load | Colour.List. Rainbow.OTH
       option. You should have By One for the Increment for both Line Colour, Symbol
       Type

      Change the Increment for the Symbol Interior to By One. Right-click on the symbol
       interiors on the same line and choose Load | Symbol.Interior.OpenClose.OTH. The
       PlotDetails box should look like the one below:




      Click OK




You can create your own incrementing schemes for line types, symbol types, patterns and for
colours but that process is not covered here in this workbook.




18
Zooming in One Part of the Graph
   You can obtain the usual zoom in and out functions using the Zoom In and Zoom out keys on
   the Graph toolbar at the top. But there is another type of zooming (called Enlarging). This
   rescales the axis of the graph to show only the region of interest.

         Click the Scale In button on the Tools toolbar on the left. Drag a rectangle around
          some of the graph as shown below.




   The result is shown below. To return to the original, click Scale Out on the same toolbar.




Exiting Origin
   To exit Origin:

         Select File | Exit. You will be prompted to save any modified files at this stage.




                                                                                                19
3   Exercise 2 Draw Error Bars
      The aim of the first part of this exercise is to produce the following graph.



                                                                                          Plus Error



                                                               Datapoint

                                                                                          Minus Error




      In this exercise, you will be proceeding through the following list of actions. Full instructions
      will be given:

            Using the Import Wizard
            Creating the Error Columns in the Worksheet
            Creating an Error Bar Plot
            Changing the Error Bar Directions
            Adding a Title
            Adding another graph window
            Trying the polynomial fitting routines
            Trying other curve–fitting routines
            Changing the graph size and position




      20
Using the Import Wizard
        Start Origin. There should be a new datasheet called Book1.

   Use a Text Editor such as WordPad (via Start | All Program | Accessories) to have a look at
   the data file stored in v:\originexs\exercises\Exercise2.txt. The data items in this file are
   separated by tab characters. Here is the file with extra comments:

  1       Header 1            This is to show how Origin imports a file of data with multple

  2       Header 2            line headers and multiple column headers.

  3       Header 3

  4       Header 4

  5       Long Name           T                Ymean                Ymin                  Ymax

  6       Comments            (secs)           Average              Minimum               Maximum

  7       Comments

  8       Data                2                36                   34                    39

  9       Data                4                39                   35                    42

  10      Data                7                44                   39                    48

  11      Data                10               52                   46                    57

  12      Data                12               64                   58                    73

  13      Data                14               81                   72                    87

        In Origin, click File | Import | Import Wizard. The following dialog box appears.




                                                                                               21
      First we want to import the file. Click the box with dots (marked with red arrow on
       picture above) and the usual file browser box appears. Find the file stored in
       v:\originexs\exercises\Exercise2.txt using Text(*.txt) for the File type and click Add
       File then OK on the Open dialog box..

      Click Next on the Import Wizard – Source box and on next panel, click Next again.

As you can see, there is flexibility for importing headers, subheaders and variable names.




Origin has picked up that there are 4 header lines with descriptive text or blank lines at the top
of the file and that there are also 3 subheader lines. If you did want to change these numbers,
you can switch off Auto determines subheader line.

      In our file, we are not interested in Short Names. The Long Names is in the first line of
       the subheaders (line 5 of the file). There are no Units in our file. We want to read lines
       2 and 3 of the subheading (lines 6 and 7 of the file) as Comments. So we need to
       change the Units to <None> and Comments so it reads lines 2 to 3. Make sure your
       panel looks like the picture below before clicking Next.




      Click Next again. Origin has detected that the TAB character is the delimiter. Either
       click Next twice more and then Finish or just click Finish



22
Creating the Error Columns in the Worksheet
   We want to store the errors in two new columns. We also open a script window for executing
   some commands.

         Select Column | Add New Columns and add two new columns. These are
          automatically assumed to be storing Y values and have headings E(Y) and F(Y).

         Select column 5, then right-click the column header for E(Y) and choose Properties.
          Give a name YMinus and change the Plot Designation to YError. Add a Comment if
          wished. Click OK. Repeat for F(Y) but call it YPlus.




         Select Window | Script Window and a new window appears

   The Script Window is useful for (amongst other things) simple calculations and for getting or
   setting the value of a variable.

   Enter the following two lines: (no spaces !)

          col (E) = col (B) - col (C)

          col (F) = col (D) - col (B)

   Notice that when you press the Enter key at the end of each line, the line is executed. When
   you have checked the values in the two columns are correct, close the script window.




                                                                                                  23
Creating an Error Bar Plot
   Since we are not intending to plot Ymin or Ymax, you have to use the Ctrl Key to select
   columns A(X), B(Y), E(yEr+-) and F(yEr+-) on the worksheet. Leave the Ymin and Ymax
   columns unselected.




        Select the menu item Plot | Symbol | YError. Select the legend and drag it slightly.




   Notice that the Long Names have been used to label the axes and for the legend.


Changing the Error Bar Directions
        To change the directions of the error bars, go to the Plots Details window (via Format |
         Plot). On the left hand side, select the set for Yplus(yEr). On the right hand side for the
         Direction, remove the tick for the Minus box.




   24
         Remove the Plus direction for the Yminus(yEr) dataset and click OK.




   In this picture, the bars are given different colours just to emphasise Plus and Minus errors!



                                                                                      Plus Error

                                                           Datapoint

                                                                                      Minus Error




   Checkpoint 1
   If you have not obtained the picture above (don’t worry about different colours!), then you can
   either load the file EX2CH1.opj or you can start from scratch


Adding a Title
         Click on the Text tool on the toolbar down the left hand side. Click on the page where
          you want the title and type Y-Mean & Error Levels.




                                                                                                    25
Adding Another Graph to the Window
  We want to have two graphs on the same page, one showing the Error Bars and the other
  showing a line. We already have done one of these. We are going to scrap this graph but still
  keep the worksheet. Origin has a neat way of adding two graphs to the same page.

        Ensure that the graph window is current and close the window. You will be asked if
         you want to hide or delete the window. Choose Delete. Deselect the columns on the
         worksheet by clicking outside the columns.

        Select the menu item Plot | Multi-Curve | Vertical 2 Panel. The new dialog box may
         be a little confusing to begin with! At the bottom, there are two layers. If you cannot
         see these, click the blue symbol in bottom right of dialog box. The up arrows mean
         ‘Hide’ and the down ones mean ‘Show’ Remember a layer holds one set of axes.
         Layer1 is to hold the line plot and Layer2 is to hold the Error Bars.

         Layer 1 should be highlighted. Click Line from the list of Plot Type and then put a
         tick in the X box for the Long name T and a tick in the Y box for Ymean. Then click
         Add




        Now select Layer2 on the bottom and then choose Scatter from the list of Plot Types.
         Put a tick in the X box for T, a tick in the Y box for Ymean, a tick in the YError box
         for Yplus and a tick in the YError box for Yminus. Click Add

        Click OK. The graphs look a bit squashed so go to File | Page Setup and change to
         Portrait Orientation.

        Select the figure 2 (this is for Layer 2) in the top left of the Graph window and then
         change the Error Bar directions.




  26
   You should be presented with a picture showing two graphs similar to the one below.




   Checkpoint 2
   If you have not obtained the picture above, then you can either load the file EX2CH2.opj or
   you can start from scratch.


Trying the Polynomial Fitting Routines
   Origin has a library of over 100 built–in equations which can be used as curve fitting
   functions. We now try a least-squares fit of the data to a polynomial of order 3.

   Discard the top graph, by selecting it and then pressing the Delete key. Return to Landscape
   mode (use File | Page Setup).

          To find a linear fit for Y-mean, click Analysis | Fitting | Linear Fit | Open Dialog
          and click OK. Say No when asked about the report Sheet.




                                                                                                  27
         To delete the linear fit, click Format | Layer and delete the fitting line from the layer.
          Update the legend – try moving graph around to remove any unwanted text.

         To find a polynomial fit for Y-mean, click Analysis | Fitting | Polynomial Fit. Try an
          order of 2 first and click OK. Then try order 3. You should now have two red curves.
          Delete the polynomial of order 2 curve (use Format | Plot to delete unwanted curves),
          leaving the polynomial fit for order 3. Reset the Legend (Graph | New Legend).




   Polynomial Regression for Ymean: Y = Intercept + B1*X + B2*X^2 + B3*X^3

   Intercept         30.38947           B1       3.6168

   B2                -0.493             B3       0.03526

   with a value for Adjusted R-Square of                   0.99909


Trying Other Curve–Fitting Routines
   On the Analysis | Fitting menu, there are a number of choices for the fitting function. In many
   cases, you just choose the fitting function and you do not have to input any parameters.




   The Nonlinear Curve Fit option on the menu above is for the more advanced non-linear least
   squares fitting. With this, you can build up a fitting function. You can using Origin scripts or
   incorporate Origin C programs to help you define your fitting function. If you are interested in
   these facilities, then have a look at the Origin User Guide or the online help pages.




   28
         Delete the old Polynomial Fit curve (use Format | Plot to delete unwanted curves),
          leaving the original line. Reset the Legend (Graph | New Legend).

         Click Analysis | Fitting | Nonlinear Curve Fit or one of the other fitting functions.
          Choose Rational for the Category and Reciprocal for the Function. Click Fit. A
          window appears which shows the fitting function, the coefficients and the statistics.




Changing the Graph Size and Position
   You may need to fix the size and position of a graph.

         Double-click the background of the graph which is on Layer 1. This is a different way
          of obtaining the Plot Details window.

         Click the Size / Speed tab and switch the Units to mms. Give values 40 for Left, 220
          for Width, 20 for Top and 150 for Height.

         Click File | Exit and leave Origin




                                                                                                  29
4   Exercise 3 Draw a 3D Mesh Plot
       The aim of this exercise is to produce the following mesh plot.




       In this exercise, you will be proceeding through the following list of actions. Full instructions
       will be given:

             Interpolating the data
             Adding the original points
             Changing the Colour Scheme
             Changing the point of view


    Interpolating the Data
             Start Origin.

             Import the file v:\originexs\exercises\Exercise3.txt (use Single Ascii) and keep the
              worksheet window active. Select then right-click the C(Y) column. Click Set as | Z

       The data consists of a set of (x,y,z) triplets and is not on a regular grid. It is advised to
       interpolate the data into a regular grid, before drawing a 3D mesh since there is then more
       control over the smoothing.

       Origin has a window type called a matrix window in which a single two dimensional data set
       (Z) is displayed in rows and columns. This is used to store a regular grid.




       30
      Keep the Z column selected. Click Worksheet | Convert to Matrix | XYZ Gridding

Open the Gridding Setting s section by clicking the little plus sign. There are five gridding
methods and we are going to try several of these. First try Random Renka Cline for the
Gridding Method and Parameters, type 7 for both Rows and Columns (remove the ticks by
these!) and ask for 3D Colour Map Surface for the Preview Map Type. Also click the
Preview Result tab. The Preview button appears then on the bottom.




Next try Random Kriging Correlation for the Gridding Method. Keep the grid 7 rows by 7
columns and keep the other parameters as suggested by Origin. This time, click OK




A new window appears – this stores the interpolation results in a7 by 7 matrix.

      Keep the Matrix window as the current window and click Plot | 3D Surface | Colour
       Map Surface click OK




This is not a suitable place to discuss the merits of all the different smoothing algorithms for
this particular set of data and the effects of changing the parameters. However, as you have



                                                                                                   31
   probably already realised, it is important that you take care in choosing a method and in
   choosing particular values for the other parameters!

   Checkpoint 1
   If you have not obtained the picture on previous page, then you can either load the file
   EX3CH1.JNB or you can start from scratch.


Adding Original Points
         Reselect the Graph window and click Graph | Plot Setup. There should be three parts
          to the window – if there are not, then click the blue symbols on the right side of the
          dialog box.

          Select Layer1 in the bottom third of the dialog window, if this is not already selected.
          We want to add a graph to that layer, one showing the original points. In the top section
          click Worksheets in Project instead of Matrices and then click Exercise 3. For the
          Plot Type (in the middle) choose 3D Line.




          In the middle, you can specify what columns are to be X,Y,Z. Click the X box on the
          row which has A for the Column, the Y box for B and the Z box for C. Click Add.

         At the bottom of the dialog box, click Apply then click OK




   32
Changing the Colour Scheme
      Select Format | Plot to obtain the Plot Details dialog.box. On the left hand side of this
       dialog box, make sure that the surface not the 3d line has been selected. The Color
       Map tab should then be selected.

      Click the Fill header and ask for Limited Mixing. Change the From colour to Olive and
       the To colour to Wine. You can change the contour levels on the Color Map panel, if
       you wish.

      Click the Surface tab and click Use Colour Map instead of the Single colour. Also
       click the Surfaces/Projections tab and add ticks for Bottom Contour for both Fill and
       Contour lines. Click Apply to see the changes.

      Next, click the plus sign by the Exercise3 graph on the left hand side. Click Original
       (these mean the original points) and then change the Symbol into a solid red circle size
       8 and remove the Drop Lines.

      Click Apply and OK to apply changes.

      To change the backplanes, click Format | Layer and click the Planes tab. Switch off
       all three planes. You can switch off the axes and axis titles (look at the Display tab)




Changing the Point of View
      You may have noticed that there is a new toolbar opened near the top. This is the 3D
       Rotation toolbar. At the right of this toolbar, choose 20 for the 3D Rotation Angle.

      Try clicking the Rotate Counter-clockwise twice then the Tilt Down twice. Then try
       the Tilt Up about 4 or 5 times. You can see from the rotations how far the original data
       points are from the surface.

      If you want, you can choose Reset Rotation to return to the default position. As an
       exercise, see if you can reproduce the picture at the start of this exercise!




                                                                                              33
5   Exercise 4 Draw Curve of 2D
    Function
      This exercise is to draw a 2D curve which describes the following function:

      y = cos ( m*x ) * sin (n*x)

      where m and n are parameters and x has values between 0 and 720 degrees.

      For the initial picture shown here, m = 8 and n = 1. There are other interesting curves, when
      we vary m and n.

      Origin has a Function window in which you can type a function and it automatically plots the
      function without your having to calculate the X and Y values. You can specify a range for X
      and how many points are to be on the range. You should try to have a reasonably large number
      for the sample points.

      In this example, we have 145 sample points ranging from 0 to 720.




      In this exercise, you will be proceeding through the following list of actions:

            Using The Function Window

            Adjusting the axes scales

            Changing the parameters




      34
Using the Function Window
       If you have not left Origin, then close the old Project and start a new Project.

       To change the trigonometric units to degrees, click Tools | Options. Click the tab for
        Numeric Format and choose Degree. Unless you definitely prefer to keep Radian for
        your normal startup, choose Yes when asked if you want to save this in your Startup
        options. Otherwise you will see peculiar results if you leave Origin and return to doing
        this example!

       Click File | New | Function and click OK. The Plot Details window appears.

       In the blank area next to F1(X)=, you can type:

        cos(2*x) * sin(2*x)

  The Plot Details window should look like the following picture. Notice that the Auto X
  Range has been switched off and values of 0 and 720 have been inserted for the start and end
  of range. The number of Total Points is 145. Click OK




       The plot window appears. You may need to click Rescale on the Function window to
        obtain the picture as shown below.




                                                                                             35
Adjusting the Axis Scales
         First, remove the legend (select then right-click and choose Delete).

         Double-click the X axis. Click the Scale tab and change the From value to 0 and the
          To value to 720 and make the Increment 80.

         Next click the Title & Format tab and remove the axis title. Ask for Major Ticks to be
          Out and the Minor ticks to be None. Next remove the gridlines by clicking the
          GridLines tab and switch off both Major and Minor Grids. Do not click OK yet.

         Still on the dialog box for Axes, click Title and Format and click on the icon for the
          Left axis. Remove the axis title, remove the gridlines, change the scale to -1,1,
          increement to 0.2 and change the ticks. Click OK. If you still have a line at Y=0, then
          double-click the X axis, click the Grid Lines tab and remove the tick in the Additional
          Lines section..




   Checkpoint 1
   If you have not obtained the picture above, then you can either load the file EX4CH1.JNB or
   you can start from scratch. Change to Degree (Tools | Options | Numeric Format) if
   necessary.


Changing the Parameters
         With the Function window current, go to Format | Plot

         Change the equation so that it now reads:

          F1(x)= cos(8*x)*sin(1*x)

   You should obtain a picture similar to the one shown at the front of this exercise. Now change
   the 8 into 16 instead.




   36
Try plotting the function y = cos(4*x)*cos(8*x)*sin(0.5*x) instead .




                                                                       37
6   Exercise 5 Draw Multiple Axes Plot
      This exercise is to draw the following. There are 3 lines to be plotted using different scales:




      There are many occasions when one wants to plot multiple datasets that have different orders
      of magnitude and hence one has420 to use axes with different scales. In this example, we have
      three plots, each of which has one line. We create three Y axes and each one of these axes are
      assigned to a different layer.

      When a new plot is added to a graph, it is automatically assigned to the Y axis which is on the
      left of the graph. This axis adjusts its scales (if necessary) to accommodate the new dataset. If
      there is already a dataset assigned to that axis and if the datasets have different orders of
      magnitude, then one of the datasets may possibly disappear or become a straight horizontal
      line.

      In this exercise, you will be proceeding through the following list of actions:

            Adding data to the worksheet
            Creating the plots
            Changing the scales on the axes.
            Tidying up the graph




      38
Adding Data to the Worksheet
         Start Origin or start with a new Project.

         Add two new columns to the worksheet (via Column | Add New Column) Type the
          following data into the worksheet. Keep Column B blank.




         Use Window | Script Window to calculate the data for the second column of data. Add
          the following statements: (The semi-colon is a statement separator).

          temp = col ( D ) ; col ( B ) = ln ( temp )

         and press the ENTER key. The resultant worksheet should look like this:




   If we put all 3 lines into one layer with one pair of axes, one line would become horizontal
   since the range on the Y axis is so large. Instead, we add more layers and separate Y axes.


Creating the Plots
         Create a graph with a line plot using the data in columns A and B. Remove the legend
          for the moment – we shall sort that out later.




                                                                                                  39
      Select the menu item Graph | New Layer (Axes) | Right Y (Linked, X Scale &
       Dimension). A new axis appears in the Graph window. Notice that you have a new
       layer (see 2 in top left of the Graph window).

      Return to the worksheet and just select columns A and C only (use CTRL key to select
       columns). Make the Graph window current, keep layer 2 as the current layer and select
       Graph | Add Plot to Layer | Line.

      A new line should be added and the axis on the right should show a different scale.




      Repeat the last three steps to add a new line for columns A and D. You can select the
       axis on the right and move it using the horizontal right arrow key.

Checkpoint 1
If you have not obtained the picture below, then you can either load the file EX5CH1.opj or
you can start from scratch.




To show that each layer has one line, click Format | Plot to obtain the Plot Details dialog.
Open up the Layers. Each layer has one line. In theory, it is possible to have many linked
layers, each containing one or more lines or symbol sets but, in practice, of course, the
resultant graph would be very confusing! Close down the Plot Details dialog box.

NB There was a new facility in version 8.1 in which you could have just selected all four
columns and asked for Plot | Multi-curve | Multiple Y Axes. However, we decided to keep
the example as it is since it helps to understand the principle of adding new layers better.




40
Changing the Scales on the Axes
   Origin chooses a range larger than required for all the axes. We want to tidy up the axis scales.

         Double–click the Y axis on the left. If you hit the actual axis, the dialog box opens with
          the Scale tab showing but if you hit the labels, the Tick Labels tab is showing. Notice
          that it picks up that you are working on Layer 1. We want the Scale tab showing.

   When making the following changes, you can use Apply or OK to see the effects on the graph.
   If you use OK, then you may have to reopen the Axis dialog box by double–clicking an axis.

         Change the range from 8.4 to 10.1. The increment is 0.34. If you click Apply, you will
          see that the axis still looks untidy.

         Still with the Scale tab showing, look at the Rescale options and choose Fixed from.
          Give a value of 8.4 for the First Tick.




         Click OK. For the second Y axis, change the range so that it is from 420 to 2920. the
          increment value is 500 and the first tick is at 420. Click OK.

         For the third axis, repeat the process using a range from 4200 to 24200. We want an
          Increment value of 4000 and the first tick is at 4200. Click OK .

         Double-click the X axis. Change the range from 10 to 50. Click OK to see the changes.

   Checkpoint 2
   If you have not obtained the picture below, then either load the file EX5CH2.JNB and start
   here or you could load the file EX5CH1.JNB and retrace the steps from Checkpoint 1.




                                                                                                  41
Tidying up the Graph
       First we need to sort out the legends. Go to the menu item Format | Page and choose
        the Legends/Titles tab. Switch on the option Include Data Plots from all Layers

       As an exercise, try to reproduce the picture below, without adding new plots or deleting
        old ones. Note that the sets containing a line with connecting symbol and
        corresponding axis header are drawn in different colours. The lines are thickened and
        the axis headers are done in bold text. To change the control of an axis title, right–click
        it and choose Label control. Attach it to the Page rather than Label and Scales.




   42
7   Exercise 6 The Histogram Wizard
       This exercise shows how to create a histogram with different bucket sizes.




       In this exercise, you will be proceeding through the following list of actions:

             Importing data to the worksheet
             Using the Histogram Wizard
             Changing the bucket sizes
             Creating a Regression Line and Confidence Lines.
             Finding the Prediction lines and Correlation Coefficient


    Importing Data to the Worksheet
             Start Origin. Import the data file v:\originexs\exercises\exercise6.txt using File | Import
              | Single Ascii There are two columns giving the age and cholesterol level of 100
              people. Your worksheet should look like the one shown below (after you have adjusted
              the column width!).




    Using the Histogram Wizard
       A histogram for the Ages column only is our first objective.



                                                                                                      43
         First, we want to change the Age column so it is a Y column not X. Right-click on the
          A(X) column and choose Set As | Y. Keep that column selected.

         Select Plot | Statistics | Histogram




Changing the Bucket Sizes
   Currently the Bucket size is 5. We want to change this to 10 and to change the Start and End
   points to 15 and 75 so that the centres of the histogram bars are at 20, 30, 40, 50, 60 and 70.

         On the graph window, right-click on the histogram itself and choose Plot Details.

         Pick the Data tab and switch off Automatic Binning. Put 10 for the Bin Size, 15 for
          the Begin and 75 for the End. Click OK

         You may need to click Graph | Rescale to Show All

   Checkpoint 1
   If you have not obtained the picture below, then you can either load the file EX6CH1.JNB or
   you can start from scratch.




   44
   As an exercise, see if you can reproduce the following picture, using the Plot Details dialog
   and other dialog boxes.




Creating a Regression Line & Confidence Lines
         To create a scatter plot of Age & Cholesterol, right-click the Age heading on the
          worksheet and click Set As | X. Then select both columns and click Plot | Symbol |
          Scatter.

         Remove the legend and change the axis scales.




         Click Analysis | Fitting | Polynomial Fit. Use the Open Dialog as usual! and change
          the Polynomial Order from 2 to 1. Click OK at the bottom. A red line appears – this is
          the regression line. (Up to you about seeing the Report Sheet or not).




                                                                                                   45
      Undo and repeat but this time open the Fitted Curves Plot dialog (see above) and click
       Confidence Bands. Scroll down and note that the confidence levels are 95%. Click
       OK. This time two green lines appear. Remove the table.

 Confidence intervals describe the range where the regression line will appear a percentage of
time for repeated measurements. In other words, we are 95% confident that in another sample
of the same size the regression line will be between the two confidence curves.




46
Finding Prediction Intervals and Correlation
Coefficient
   Prediction intervals describe the range where the data will appear a percentage of time for
   repeated measurements.

         Undo and repeat the Fit Polynomial operation but switch on Prediction Bands and
          click OK. The Prediction Bands are just under the Confidence Bands on the same panel
          as before




         Does this data provide evidence of a correlation between Age and Cholesterol? To
          show this, find the Table that has been created. This appears on the Graph Window but
          you might have deleted this. If you have, then you can just undo the deletion or repeat
          the instructions! The correlation coefficient is shown on the list of results as Adj R
          square.

   R ² = 0.7194

   This shows it is a fair prediction to say that there is a dependency relationship between Age
   and Cholesterol.




                                                                                                   47
Optional Exercise
   Try to reproduce the following picture. The data is in a file called vib.txt stored in
   v:\originexs\exercises. The first column stores the X values. The column e0 represents the Y
   values for the graph on the left and the column e5 represents the Y values for the graph on the
   right.




   Hints:

           Use Import | Single Ascii when importing the file.

           First, create graph on left which is a line plot of x vs e0

           Use log10 scaling (instead of linear) for axes and change scaling on axes.

           Add grid lines (both major and minor), remove legend, change title.

           Thicken axes and plot.

           Copy and paste graph then move second graph to the right. Check that there are now
            two layers and that Layer 2 is current.

           Click Graph | Plot Setup. The second graph should be selected. Change the value for
            Y for that graph to variable e5 instead of e0 and click Replace. You may need to alter
            the axis scales again.




   48
Appendix 1 Workbook Datasets
     The following dataset is used in Exercise 1

      X        Y1             Y2            Y3        Y4        Y5
      5        17.7           14.7          18.2      17.2      10.8
      10       14.2           12.1          19.1      16.2      13.2
      15       11             13.4          17.6      17.3      13.7
      20       14.2           15.6          17.6      16.9      12.5
      25       19.2           12.1          12.7      15        13.1
      30       18.7           9.8           16.6      12.8      10.7
      35       6.2            8.8           10.9      14.5      11.3
      40       5.5            9.9           15.5      15.5      12.1
      45       11.6           12.5          16.2      18.1      10.6
      50       11.9           8.3           15.2      12.7      9.8
      55       6.2            14.2          18.1      11.2      10.5
      60       18.9           11.2          16.2      12.8      11
      65       14.2           10.9          16.9      12.9      11.7
      70       15.5           14.8          17        13.4      10.5
      75       6.9            12.1          16.2      12.7      11.9
      80       17.8           9.5           17.7      12.2      13.1
      85       14.8           12.1          19        10.9      9.9
      90       21.4           12.5          18.2      13.8      10.2
      95       17.5           16            16.9      15        11.9
      100      17.346         14.406        17.836    16.856    10.584
      105      13.916         11.858        18.718    15.876    12.936
      110      10.78          13.132        17.248    16.954    13.426
      115      13.916         15.288        17.248    16.562    12.25
      120      18.816         11.858        12.446    14.7      12.838
      125      18.326         9.604         16.268    12.544    10.486
      130      6.076          8.624         10.682    14.21     11.074
      135      5.39           9.702         15.19     15.19     11.858
      140      11.368         12.25         15.876    17.738    10.388
      145      11.662         8.134         14.896    12.446    9.604
      150      6.076          13.916        17.738    10.976    10.29
      155      18.522         10.976        15.876    12.544    10.78
      160      13.916         10.682        16.562    12.642    11.466
      165      15.19          14.504        16.66     13.132    10.29
      170      6.762          11.858        15.876    12.446    11.662
      175      17.444         9.31          17.346    11.956    12.838
      180      14.504         11.858        18.62     10.682    9.702
      185      20.972         12.25         17.836    13.524    9.996
      190      17.15          15.68         16.562    14.7      11.662
      195      16.9991        14.1179       17.4793   16.5189   10.3723
      200      13.6377        11.6208       18.3436   15.5585   12.6773




                                                                          49
The following dataset is used in Exercise 2
This is to show how Origin imports a file of data with multple
line headers and multiple column headers.



  T          Y-mean                                 Ymin              Ymax
  (secs)     Average                                Minimum           Maximum


  2          36                                     34                39
  4          39                                     35                42
  7          44                                     39                48
  10         52                                     46                57
  12         64                                     58                73
  14         81                                     72                87



The following dataset is used in Exercise 3

  0                0             0
  4                -42           -2.71329
  6.53333          -36.4667      -3.4446
  9.06667          -30.9333      -3.78734
  11.6             -25.4         -4.09721
  14.1333          -19.8667      -6.15704
  16.6667          -14.3333      -16.2005
  19.2             -8.8          -45.9343
  21.7333          -3.26667      -92.6726
  24.2667          2.26667       -130.143
  26.8             7.8           -140.923
  29.3333          13.3333       -110.025
  31.8667          18.8667       -7.63413
  34.4             24.4          92.7351
  36.9333          29.9333       113.672
The following dataset is used in Exercise 6

  AGE        Cholesterol         AGE        Cholesterol          AGE         Cholesterol
  24         106                 46         186                  66          193
  63         261                 36         107                  45          146
  34         160                 47         196                  26          99
  39         149                 59         227                  39          164
  46         186                 39         108                  54          161
  50         230                 44         191                  44          157
  58         228                 38         182                  51          160
  38         116                 56         268                  50          141
  36         104                 51         155                  61          280
  49         210                 61         171                  27          115
  50         161                 24         75                   50          174
  36         127                 52         232                  59          229
  50         223                 64         197                  51          184
  33         101                 62         180                  41          163
  35         137                 31         106                  26          116
  27         91                  58         270                  58          252
  50         177                 62         202                  62          202
  32         125                 68         196                  24          93
  41         122                 33         153                  32          98
  27         128                 24         69                   23          80
  64         231                 41         195                  61          238



50
61   258   40   132   21   81
66   238   32   128   33   139
66   244   63   175   66   267
58   231   27   87    39   108
41   121   52   238   24   107
52   220   59   229   53   163
54   232   58   164   62   256
54   159   47   224   23   77
27   130   50   169   65   230
54   174   28   91    46   215
26   121   42   123   58   182
67   295




                                 51
This dataset is the one used in the Optional Exercise. Not all the rows are shown here.
"x" "e0" "e1" "e2" "e3" "e4" "e5"
0.1 1.0101 1.0101 1.0101 1.0101 1.01 1.0097
0.10476 1.0111 1.0111 1.0111 1.0111 1.011 1.0106
0.10975 1.0122 1.0122 1.0122 1.0122 1.012 1.0116
0.11498 1.0134 1.0134 1.0134 1.0134 1.0132 1.0127
0.12045 1.0147 1.0147 1.0147 1.0147 1.0145 1.0139
0.12619 1.0162 1.0162 1.0162 1.0161 1.0159 1.0152
0.13219 1.0178 1.0178 1.0178 1.0177 1.0175 1.0166
0.13849 1.0196 1.0196 1.0195 1.0195 1.0192 1.0181
0.14508 1.0215 1.0215 1.0215 1.0214 1.021 1.0198
0.15199 1.0236 1.0236 1.0236 1.0236 1.0231 1.0216
0.15923 1.026 1.026 1.026 1.0259 1.0253 1.0235
0.16681 1.0286 1.0286 1.0286 1.0285 1.0278 1.0256
0.17475 1.0315 1.0315 1.0315 1.0313 1.0305 1.0279
0.18307 1.0347 1.0347 1.0346 1.0345 1.0335 1.0304
0.19179 1.0382 1.0382 1.0381 1.038 1.0368 1.033
0.20092 1.0421 1.0421 1.042 1.0418 1.0403 1.0359
0.21049 1.0464 1.0463 1.0463 1.046 1.0443 1.039
0.22051 1.0511 1.0511 1.051 1.0507 1.0486 1.0423
0.23101 1.0564 1.0563 1.0562 1.0559 1.0533 1.0458
0.24201 1.0622 1.0622 1.0621 1.0616 1.0585 1.0495
0.25354 1.0687 1.0686 1.0685 1.0679 1.0641 1.0535
0.26561 1.0759 1.0758 1.0757 1.075 1.0704 1.0577
0.27826 1.0839 1.0839 1.0836 1.0828 1.0772 1.0622
0.29151 1.0929 1.0928 1.0925 1.0914 1.0846 1.0669
0.30539 1.1029 1.1027 1.1024 1.1011 1.0928 1.0718
0.31993 1.114 1.1139 1.1135 1.1119 1.1018 1.077
0.33516 1.1265 1.1264 1.1259 1.1239 1.1115 1.0823
0.35112 1.1406 1.1404 1.1398 1.1373 1.1222 1.0878
……………….
……………….
……………….
……………….
3.9442 0.068697 0.07382 0.08737 0.12757 0.2698 0.48026
4.132 0.062214 0.067294 0.080603 0.11955 0.25616 0.46058
4.3288 0.056376 0.061413 0.074479 0.11219 0.24332 0.44153
4.5349 0.051111 0.056106 0.068928 0.10542 0.23122 0.42312
4.7508 0.04636 0.051314 0.063888 0.099169 0.21981 0.40535
4.977 0.042068 0.046981 0.059305 0.093395 0.20903 0.3882
5.214 0.038189 0.043059 0.055131 0.088049 0.19884 0.37167
5.4623 0.034678 0.039507 0.051323 0.08309 0.18921 0.35575
5.7224 0.031501 0.036288 0.047844 0.07848 0.18009 0.34044
5.9948 0.028622 0.033366 0.04466 0.074188 0.17145 0.32572
6.2803 0.026013 0.030714 0.041742 0.070186 0.16326 0.31156
6.5793 0.023648 0.028303 0.039064 0.066447 0.1555 0.29798
6.8926 0.021502 0.026111 0.036602 0.062949 0.14814 0.28493
7.2208 0.019554 0.024117 0.034335 0.059673 0.14114 0.27242
7.5646 0.017786 0.0223 0.032244 0.056599 0.1345 0.26041
7.9248 0.01618 0.020644 0.030313 0.053712 0.12819 0.24891
8.3022 0.014722 0.019133 0.028527 0.050997 0.1222 0.23789
8.6975 0.013396 0.017753 0.026872 0.048441 0.1165 0.22733
9.1116 0.012192 0.016493 0.025337 0.046032 0.11107 0.21721
9.5455 0.011097 0.01534 0.02391 0.043759 0.10591 0.20753
10.0 0.010101 0.014284 0.022582 0.041614 0.101 0.19827




52
Appendix 2 Local Setup of Origin
      To install Origin:

            Logon to the Managed Windows Service (MWS).

            Select Start on the Taskbar. Choose All Programs | Install University Applications
             then click Graphics in the list of categories

            Click on Origin 8.5 SR1. You should not need to reboot.

      Note that a working directory called origin8.5 is created on your M: drive. By default, Origin
      templates, themes, filters etc are stored in that directory.

      If you have used Origin before using version 8.5, you may like to tidy up your M: drive since
      there may be old Origin directories stored there. Transfer any project files that you have
      created to M:\orogin85\; also any special themes or templates etc.

      To run Origin, you can:

            Click Start on the taskbar at the bottom and then click All Programs. Click OriginLab
             | Origin 8.5 | OriginPro 8.5.




Appendix 3 Printing from Origin
      Origin is integrated with Windows. The new version of Origin does now allow you to choose a
      paper size other than the ones associated with the currently selected printer. For example, if
      your current default printer is the A4 laser printer, then you are still allowed to choose A3 or
      A2 or larger sizes.

      In Origin, you should change the paper size at the start which is the desired output for your
      chosen printer.

            When a graph or chart is first created, you should select File | Page Setup and select a
             page size. This step should be done at this stage since it is possible that, after making
             alterations and then choosing a new paper size or orientation, the layout of the
             presentation will be spoilt.

            To obtain a hardcopy, select File | Print Choose a printer first.

            You should check that the correct orientation and paper size have been set for your
             chosen printer by selecting Properties.




                                                                                                      53

				
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