Gnuplot/C2/Error-bars-and-data-fitting/English - Revision history

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Ranipv076: Created page with "'''Title of script''': '''Error bars and Data fitting''' '''Author: '''Rani Parvathy '''Keywords:'''..."

2018-12-04T07:25:23Z

Created page with "'''Title of script''': '''Error bars and <span style="color:#000000;">D</span><span style="color:#000000;">ata fitting'''</span> '''Author: '''Rani Parvathy '''Keywords:'''..."

New page

'''Title of script''': '''Error bars and <span style="color:#000000;">D</span><span style="color:#000000;">ata fitting'''</span>

'''Author: '''Rani Parvathy

'''Keywords:''' gnuplot, video tutorial, spoken tutorial, data fitting, regression, error bars

{| style="border-spacing:0;width:6.8472in;"
|-
! align=center style="background-color:#993366;border-top:1pt solid #000000;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | Visual Cue
! align=center style="background-color:#993366;border:1pt solid #000000;padding:0.0382in;" | Narration
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | <div style="color:#000000;">'''Slide Number 1'''</div>

<div style="color:#000000;">'''Title Slide '''</div>

<div style="color:#000000;">'''Data fitting and error bars'''</div>
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">Welcome to the tutorial on </div>

<div style="color:#000000;">'''Data fitting and error bars'''</div>
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | <div style="color:#000000;">'''Slide Number 2'''</div>

<div style="color:#000000;">'''Learning Objectives'''</div>

| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">In this tutorial, we will learn,</div>

* <div style="color:#000000;">Learn to add error bars in a graph</div>
* <div style="color:#000000;">Learn data fitting</div>
* <div style="color:#000000;">Fit a given dataset to an equation </div>
* <div style="color:#000000;">Run non-linear regression and generate fitting parameters</div>

|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | <div style="color:#000000;">'''Slide Number 3'''</div>

<div style="color:#000000;">'''System and Software Requirement'''</div>

<div style="color:#000000;"></div>
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">Debian Linux</div>

<div style="color:#000000;">Gedit 3.22.0</div>

<div style="color:#000000;">and</div>

<div style="color:#000000;">Have Gnuplot 5.2.5 installed</div>
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | <div style="color:#000000;">'''Slide Number 4'''</div>

<div style="color:#000000;">'''Samson Microphone'''</div>

| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">To record audio, I am using '''Samson''' '''USB''' portable microphone was used.</div>

<div style="color:#000000;">The model number '''SAGOMIC'''</div>

<div style="color:#000000;">I bought it from '''amazon''' website, for about rupees four thousand</div>

<div style="color:#000000;"><span style="background-color:transparent;">It may be available in other websites.</span></div>
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | <div style="color:#000000;">'''Slide Number 5'''</div>

<div style="color:#000000;">'''Pre-requisites'''</div>

<div style="color:#000000;"></div>
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">To follow this tutorial, learner’s must be familiar with, </div>

<div style="color:#000000;">Basic computer and internet skills</div>

<div style="color:#000000;">Concept of graphing </div>

<div style="color:#000000;">and </div>

<div style="color:#000000;">College level Mathematics skills</div>
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | <div style="color:#000000;">'''Slide Number 6'''</div>

<div style="color:#000000;">'''Pre-requisites'''</div>

<div style="color:#000000;"></div>
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <span style="background-color:transparent;color:#000000;">Please locate this tutorial on our web page, </span><span style="background-color:transparent;color:#000000;">'''spoken hyphen tutorial dot org'''</span><span style="background-color:transparent;color:#000000;"> </span>

<div style="color:#000000;">Prerequisite '''spoken''' '''tutorials''', if any, will be mentioned in this page </div>
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | Go to '''Desktop'''.
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">First, we will first learn to incorporate error bars in a graph.</div>

<div style="color:#000000;">First, Go to '''Desktop'''.</div>

<div style="color:#000000;">I have a, x y yerror type data, in a text file. </div>
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | Double click to open the file.
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">It is saved in '''Desktop''' directory for me. </div>

<div style="color:#000000;">Double click on the file icon to open it in a text editor.</div>

<div style="color:#000000;">The file opens in gedit for me.</div>

<div style="color:#000000;">This file is provided to you with the tutorial.</div>
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | The first column is '''x''' data.

Second column is '''y''' data.

The third column is '''y''' data error bar in measurement.
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | Close '''gedit'''
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | Close '''gedit''' by clicking on the x-sign.
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | <div style="color:#000000;">Press '''ctrl alt t'''</div>

<div style="color:#000000;">'''cd ~/Desktop'''</div>
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | Press '''ctrl alt t''' keys together to open a '''terminal'''.

Change directory to '''Desktop''' as seen on the screen.
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | <div style="color:#000000;">ctrl+alt+T</div>

<div style="color:#000000;">>'''gnuplot'''</div>
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | Open '''gnuplot'''.

Type '''gnuplot''' and '''enter'''
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | Show qt on screen.
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">'''Set''' '''terminal''' as necessary. </div>

<div style="color:#000000;">For me it is already in '''qt'''.</div>
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | '''Ctrl-l'''
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | I will clear screen with command control l.

This takes terminal prompt to top of the screen for clarity in video.
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | First, let's plot the data to see the trend and for visual inspection.
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | '''plot 'error-bar.txt' using 1:2:3 with yerrorbars'''
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | Enter the plot command as seen on the screen.
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | If error limits are on the x data, we can use, x error bars term for plotting.

The graphic window opens.
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | The colon 3 with y error bars in the plot command adds the error to the plot.
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | Hover mouse over decay curve.
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | Next, let's fit this graph to an equation.
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | This data likely represent an exponential decay.
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | The points may be off the ideal curve due to measurement errors.
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | We will fit the given data points to an exponential decay function.
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | Let's see a few steps involved in fitting data points to an equation.
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | <span style="color:#000000;">'''Slide Number </span><span style="color:#000000;">7'''</span>

'''Steps in data fitting'''

Find a function to represent the data

Initial guess values for constants

A good fitting, measured by chi square

Find the 'optimal' value of the constants in the function

<div style="color:#000000;">Display the fitted data</div>
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | First, define a function to represent the data

Make initial guess values for constants

A good fitting, measured by '''chi square''' value

Find the 'optimal' value of the constants in the function

and Display the fitted data
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | '''f(x) = a * exp(-k*x)'''
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">First, let's define the function.</div>

<div style="color:#000000;">Type '''f''' of '''x''' is equal to a times '''e''' to the power minus '''k x'''</div>

<div style="color:#000000;">Use the syntax as seen on the screen</div>
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | Go to graphical window.
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">Let's make an educated initial guess for the initial guess values of a and k</div>

<div style="color:#000000;">Go to graphical window.</div>
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;color:#000000;" | From the graph, I will place the initial value of a at one lakh fitfty thousand
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;color:#000000;" | For an exponential decay, I will place the initial guess of k around 0.5
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | Close the graphical window and go to gnuplot terminal prompt.
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | <div style="color:#000000;">'''a=150000 '''</div>

<div style="color:#000000;">'''k=0.5'''</div>

| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">Enter commands to set the values of a and k</div>

<div style="color:#000000;">Enter a equal to fifteen hundred thousand</div>

<div style="color:#000000;">Enter k equal to zero point five</div>
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | '''fit f(x) “error-bar.txt” using 1:2:3 via a,k'''
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">To fit the data use command as seen on the screen.</div>

<div style="color:#000000;">Fit space f of x space in double quotes error hyphen bar dot txt. </div>

<div style="color:#000000;">Then Space using space 1 colon 2 colon 3 via a comma k</div>
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | If column 3 is not mentioned, the y axis uncertainties is not considered for data fitting.
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | The software does the fitting and gives output values.
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;color:#000000;" | Let's scroll up the screen.
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;color:#000000;" | I see an error , warning message on top
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;color:#000000;" | Notice a table with chi square and new values of a and k after each iteration.
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">Program reports, the fitting process converged after a few iterations.</div>

<div style="color:#000000;">It is 8 iteractions.</div>
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">Many fitting parameters are reported in the output.</div>

<div style="color:#000000;">Program reports, final sum of square of residuals.</div>
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">Notice, relative change in values after the last iteration.</div>

<div style="color:#000000;">The number is very small</div>
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;color:#000000;" | Degrees of freedom is 9
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;color:#000000;" | The root mean square or RMS is around 0.17
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | Updated values of a and k and their error in estimation is also shown.
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | The correlation matrix of variables is at the end of the output.
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | Now we have a function that fits the given data points.
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | Let's plot the data points and function together.
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">Then, we can see, how well the equation fit the given points.</div>

<div style="color:#000000;">I will clear the screen with command control l for clarity in video again.</div>
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | '''plot f(x) lw 2 title 'fitted data', "error-bar-fitting.txt" using 1:2:3 with yerrorbars pt 7 ps 1.5 notitle'''
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">Then, enter the plot command as seen on the screen.</div>

|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">I will modify to change legend as '''fitted data''' for f of x.</div>

<div style="color:#000000;">It is represented by a line with width 2.</div>
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">I have specified no legend title for the starting data set.</div>

<div style="color:#000000;">Data points are represented only by symbols with error bar and have no line.</div>

<div style="color:#000000;">I have specified a filled circle symbol and 1.5 for point size</div>
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | '''set xrange [0.95:5.05]'''
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">Please pause video as necessary to practice.</div>

Let's also set x axis limits with set xrange command as seen in the video.
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | '''replot'''
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | Replot to see the results.
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | <div style="color:#000000;">'''Slide Number 8'''</div>

<div style="color:#000000;">'''Summary'''</div>
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | Now let’s summarize.

In this tutorial, we learned to

* Display error bars in a graph
* Fit a given set of data points to an equation<br/>and
* Display fitted curve along with parent data

|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | <div style="color:#000000;">'''Slide Number 9'''</div>

<div style="color:#000000;">'''Assignment'''</div>

<div style="color:#000000;"></div>
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">For assignment activity, please do the following.</div>

<div style="color:#000000;">For data file assignment.txt, plot x and y error bars in graph.</div>

<div style="color:#000000;">The file is provided to you along with the tutorial.</div>

<div style="color:#000000;">Fit the data to a double exponential decay curve.</div>
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | <div style="color:#000000;">'''Slide Number 10'''</div>

<div style="color:#000000;">'''Spoken Tutorial Project'''</div>

| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <span style="color:#000000;">This video summarises the</span><span style="color:#000000;"> Spoken Tutorial Project </span>

<div style="color:#000000;">If you do not have good bandwidth, you may download and watch it.</div>
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | <div style="color:#000000;">'''Slide Number 11'''</div>

<div style="color:#000000;">'''Spoken Tutorial workshops'''</div>

| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <span style="color:#000000;">We</span><span style="color:#000000;"> conduct workshops using spoken tutorials and give certificates. </span>

<span style="color:#000000;">P</span><span style="color:#000000;">lease write to us.</span>
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | <div style="color:#000000;">'''Slide Number 12'''</div>

<div style="color:#000000;">'''Forum for specific questions:'''</div>

| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;color:#000000;" | Post your timed queries in the forum.
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | <div style="color:#000000;">'''Slide Number 13'''</div>

<span style="color:#000000;">'''Acknowledgemen'''</span><span style="color:#000000;">t</span>

| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India.</div>

|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;color:#000000;" | Thank you for joining.
|-
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | '''plot f(x) lw 2, "error-bar-fitting.txt" using 1:2:3 with yerrorbars pt 7 ps 1.5'''
| style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;color:#000000;" |
|-
|}
<div style="color:#000000;margin-left:0in;margin-right:0in;"></div>

@@ Line 66: / Line 66: @@
 || Close '''gedit'''.
 Press '''Ctrl+Alt+T'''.
-|| Close the file.
+||
 Open a '''terminal'''.

@@ Line 22: / Line 22: @@
 || '''Slide Number 3'''
 '''Learning Objectives'''
-|| In this tutorial, we will,
+||
 * Fit the dataset to the equation
 * Draw an arrow object in the graph
@@ Line 31: / Line 31: @@
 || To record this tutorial, I am using,
 * '''Ubuntu Linux''' 16.04 OS
-* '''Gnuplot''' v 5.2.6 and
+* '''Gnuplot''' version 5.2.6 and
-* '''Gedit''' v 3.18
+* '''Gedit''' version 3.18
 |-
@@ Line 52: / Line 52: @@
 || Go to '''Desktop'''.
 || Go to '''Desktop'''.
 I have a, '''x,''' '''y,''' '''y'''-error type data, in a text file.
@@ Line 66: / Line 67: @@
 Press '''Ctrl+Alt+T'''.
 || Close the file.
 Open a '''terminal'''.
@@ Line 144: / Line 146: @@
 || Go to graphical window.
 || Make an educated initial guess for the values of '''a''' and '''k'''.
 Go to the graphical window.
@@ Line 240: / Line 243: @@
 || Cursor on the '''terminal'''.
 || Now we have a function that fits the given data points.
 Let's plot the data points and the function together.
@@ Line 249: / Line 253: @@
 || Enter the command, '''plot f(x) lw 2 title 'fitted data', "xydy.txt" using 1:2:3 with yerrorbars pt 7 ps 1.5 notitle''' .
 || Enter the command as seen on the screen.
 This plots the data and the function together.
@@ Line 256: / Line 261: @@
 || Hover mouse near the legend.
 || The fitted data is represented by a line with a line.
 I am specifying the legend for '''f of x''' as '''fitted data'''.
-No legend title is added for the starting dataset as no '''notitle''' is
+No legend title is added for the starting dataset as no '''notitle''' is mentioned.
 mentioned.
 I have specified a filled circle '''symbol''' and 1.5 for point size.

@@ Line 258: / Line 258: @@
 I am specifying the legend for '''f of x''' as '''fitted data'''.
-No legend title is added for the starting data set as no '''notitle''' is
+No legend title is added for the starting dataset as no '''notitle''' is
 mentioned.
 |-
@@ Line 265: / Line 267: @@
 Show symbol with error bar.
 || Data points are represented by symbols with '''error bar''' and without a line style.
 |-
@@ Line 287: / Line 287: @@
 |-
 || Move the mouse on the screen to show the arrow placement around ('''1.63,77200 to 1.7, 62000''').
-|| In the graph, I want to add an arrow between these two points to highlight it.
+|| In the graph, I want to add an arrow.
 |-

@@ Line 8: / Line 8: @@
 '''Title Slide '''
 || Welcome to the tutorial on
-'''Error bars and data fitting '''in gnuplot.
+'''Error bars and data fitting '''in '''gnuplot'''.
 |-

@@ Line 118: / Line 118: @@
 |-
-|| '''Slide Number 6'''
+|| '''Slide Number 7'''
 '''Steps for Fitting Data'''
 ||
@@ Line 126: / Line 126: @@
 |-
-|| '''Slide Number 7'''
+|| '''Slide Number 8'''
 '''Steps for Fitting Data'''
@@ Line 346: / Line 346: @@
 |-
-|| '''Slide Number 8'''
+|| '''Slide Number 9'''
 '''Summary'''
 || To summarize, in this tutorial, we
@@ Line 355: / Line 355: @@
 |-
-|| '''Slide Number 9'''
+|| '''Slide Number 10'''
 '''Assignment'''
 || For the assignment activity, please do the following.
@@ Line 362: / Line 362: @@
 |-
-|| '''Slide Number 9'''
+|| '''Slide Number 11'''
 '''Assignment'''
 ||
@@ Line 374: / Line 374: @@
 |-
-|| '''Slide Number 10'''
+|| '''Slide Number 12'''
 '''Spoken Tutorial Project'''
 || This video summarises the '''Spoken Tutorial''' Project .
@@ Line 380: / Line 380: @@
 |-
-|| '''Slide Number 11'''
+|| '''Slide Number 13'''
 '''Spoken Tutorial workshops'''
 || We conduct workshops and give certificates.
@@ Line 387: / Line 387: @@
 |-
-|| '''Slide Number 12'''
+|| '''Slide Number 14'''
 '''Forum for specific questions:'''
@@ Line 393: / Line 393: @@
 |-
-|| '''Slide Number 13'''
+|| '''Slide Number 15'''
 '''Acknowledgement'''
 || Spoken Tutorial Project is funded by '''MHRD''', '''Government of India'''.

@@ Line 33: / Line 33: @@
 '''Pre-requisites'''
 [https://spoken-tutorials.org https://spoken-tutorials.org]
-|| To follow this tutorial, * Learner must be familiar with the basics of '''gnuplot'''.
+|| To follow this tutorial,
 * For the prerequisite tutorials, please visit this site.
@@ Line 39: / Line 40: @@
 || '''Slide Number 5'''
 '''Code files'''
-|| The input file used in this tutorial is provided in the '''code file''' link.
+||
-Please download and extract the files.
+* The input file used in this tutorial is provided in the '''code file''' link.
 |-
@@ Line 50: / Line 52: @@
 || Hover mouse over '''x''', '''y''' and '''dy''' columns on the screen for the file.
 || The first column is x data.
 The second column is '''y''' data.
 The third column is error in the '''y''' data.
@@ Line 62: / Line 66: @@
 || Enter the command '''cd Desktop '''.
 Enter the command '''gnuplot'''.
 || Change the directory to '''Desktop''' and open '''gnuplot'''.
@@ Line 83: / Line 88: @@
 || Hover mouse over '''yerrorbars'''.
 || If error limits are on the '''x''' data, we have to use, '''x''' errorbars term for plotting.
 The graphic window opens.
@@ Line 96: / Line 102: @@
 || Hover mouse on the graph.
 || The points may deviate from an accurate exponential decay.
 This could be due to measurement errors.
@@ Line 113: / Line 120: @@
 * Make initial guess values for the coefficients in the equation.
 * Optimal values for the coefficients is found by an iterative process.
 |-
@@ Line 121: / Line 127: @@
 ||
 * Check for goodness of the fit
-* A good fitting is measured by a low value of chi square
+* A good fitting is measured by a low value of chi square and
 * Display the fitted data with the starting dataset
-−
-−
-and * Display the fitted data with the starting dataset
 |-
@@ Line 131: / Line 134: @@
 and press '''Enter'''.
 || First, let's define the function.
 In the '''gnuplot''' prompt, type f of x is equal to a times e to the power minus k x.
@@ Line 155: / Line 159: @@
 '''k=0.5'''
 || Enter commands to set initial guess values.
 Set '''a''' to 150 thousand and '''k''' to 0.5 .
@@ Line 161: / Line 166: @@
 and press '''Enter'''.
 || To fit the data type the command,
 '''fit f of x''' in single quotes the file name.
 Here it is '''error dash bar dot txt'''.
 Then '''using 1 colon 2 colon 3''' via a comma k .
 Here '''a''' and '''k''' are the '''coefficients'''.
@@ Line 176: / Line 185: @@
 Data fitting is seen on the screen.
 || Press '''Enter''' to run the data fitting algorithm.
 The coefficients in the equation are optimized by an iterative process.
 The output is generated on the screen.
@@ Line 235: / Line 246: @@
 || Enter the command, '''plot f(x) lw 2 title 'fitted data', "xydy.txt" using 1:2:3 with yerrorbars pt 7 ps 1.5 notitle''' .
 || Enter the command as seen on the screen, to plot both data together.
 We are plotting the fitted equation fit along with the initial data points.
@@ Line 241: / Line 253: @@
 || The fitted data is represented by a line with a line.
 I am specifying the legend for '''f of x''' as '''fitted data'''.
 No legend title is added for the starting data set as no '''notitle''' is
 mentioned.
@@ Line 248: / Line 261: @@
 Show symbol with error bar.
 || Data points are represented by symbols with '''error bar''' and without a line style.
 I have specified a filled circle '''symbol''' and 1.5 for point size.