Grace/C3/Fit-an-Exponential-Decay-Curve/English-timed

Time	Narration
00:01	Welcome to the tutorial on Fit an exponential Decay Curve.
00:07	In this tutorial, we will learn to, Add multiple graph panels to the canvas
00:14	Remove dataset from the graph panel and
00:19	Fit a given set of data points with non-linear regression method.
00:26	To record this tutorial, I am using Ubuntu Linux 16.04 OS
00:35	Grace 5.1.25
00:41	Gedit 3.18.3
00:46	To follow this tutorial, Learner must be familiar with the Grace interface.
00:53	For pre-requisite tutorials, please visit this site.
00:58	Two input files used in this tutorial are provided in the code files link.
01:05	Please download and extract the files.
01:09	I have downloaded and saved them on my Desktop.
01:14	I have opened the Grace interface.
01:18	Click on File, Open to open a project.
01:22	Open the regression.agr project file from the Desktop directory.
01:29	A straight line graph is plotted on this plot window.
01:34	Let's add another graph panel to the canvas.
01:38	Go to the Edit menu, select Arrange graphs option.
01:44	The Arrange graphs window opens.
01:48	Under Matrix, in the Cols drop-down increase the number of columns to 2.
01:55	Click on Apply and then on click Close.
01:59	Notice that one more graph panel is added to the white canvas.
02:05	Notice that the graph panels are now elongated.
02:10	I will resize the graph panels to two squares as seen on the screen.
02:17	I will also reposition the legends in the canvas.
02:22	To select a graph, click on it.
02:25	The selected graph is highlighted with the black squares on the corners.
02:31	Select the newly added graph panel.
02:35	Go to Data, Import, ASCII in the menu.
02:41	Select the file, exponential.txt from Desktop directory.
02:47	Load the data as an XY dataset.
02:51	Click on Ok to plot the graph.
02:55	Then, click on Cancel to close the window.
02:59	From a visual inspection, the data points follow an exponential decay curve.
03:06	Double click on the curve to open the set appearance window.
03:11	Add symbols of your choice and choose no line.
03:17	This helps to differentiate the fitted data from the starting dataset.
03:23	Go to Data and select Transformations.
03:27	A sub-menu opens with many options for data fitting.
03:32	Choose Regression from the sub-menu.
03:36	New Regression dialog box opens.
03:40	Choose the data set of interest from Apply to set.
03:45	Currently only a single set is loaded, shown as (S0).
03:51	It is in the graph panel G1 and set is named S0.
03:57	Choose Exponential for Type of fit.
04:01	This drop-down has few choices with sample functions to do data fitting.
04:08	In the Load drop-down, choose Fitted values.
04:12	For restrictions choose None.
04:15	Click on Accept to run the data fitting.
04:19	The Grace: console dialog box opens.
04:23	Close the dialog box and the generated log file.
04:28	Notice the fitted data in the graph.
04:32	Often, the data may follow a complex mathematical equation.
04:37	Then, we have to define the equation and do a non-linear regression.
04:43	I will demonstrate it.
04:46	I will not save the details of the data fitting.
04:50	I will close the dialog box.
04:53	Let’s delete the fitted dataset loaded on the graph.
04:58	Go to Edit menu and open the Set Operations dialog box.
05:04	In the Source section, select Graph G1 as seen.
05:10	In the set section, select the set G1 S1.
05:16	Right click to open the context menu and choose Kill data.
05:22	A warning popup dialog box opens to confirm the process.
05:28	Click on OK to kill the dataset.
05:32	Different types of set operations are possible in this window.
05:37	I will click on Close, to close the dialog box.
05:42	You may explore further if desired.
05:46	Notice that the fitted data is removed from the graph.
05:51	We can also access the context menu from the set appearance window.
05:57	Select the desired dataset from the Select set form.
06:02	Right click to open the context menu and choose Kill data to remove the data.
06:08	Click on Close, to close the dialog box.
06:12	I will demonstrate to set up non-linear regression process.
06:19	For data fitting, select an equation to fit the data.
06:24	Make an initial guess for the value of the coefficients.
06:29	Run the data fitting algorithm.
06:32	Convergence is usually obtained with few iterations.
06:37	Examine the output parameters for goodness of the fit.
06:42	Plot the function and the data together for visual representation.
06:49	Go to Data, Transformations and select Non-linear curve fitting.
06:55	Under the Main tab, we will enter the desired equation.
07:00	Select 2 for Parameters.
07:04	Two parameters A0 and A1 appear in the form below.
07:10	I will use an exponential decay curve as seen on the interface.
07:16	Let’s type the equation as seen.
07:20	There is also an option to input starting values and define bounds.
07:26	Set Iterations to 20 using the black, up triangle button as seen on the screen.
07:34	Set A0 and A1 initial guess.
07:39	We can make an educated guess for starting values of A0 and A1 from the graph.
07:47	From the graph, A0 could be around point four to point 5.
07:53	Value of A1 is around -0.25.
07:58	Set the initial guess values of the coefficients slightly away.
08:04	Then, the iterative process in the regression algorithm can be observed.
08:11	Input 0.4 for A0 and -0.2 for A1 as initial guess.
08:21	You may apply bounds check box if necessary by clicking on the bounds buttons.
08:28	In the Set section, select the set, G1 S0.
08:34	Click on Apply to run the iterations. The algorithm runs.
08:41	In this window, fitting parameter Chi-square is seen.
08:46	Correlation coefficient, RMS, relative error and Theil coefficient are also seen.
08:54	Examine the chi-square values obtained.
08:58	Low chi-square means, the resulting function is a good fit for the data.
09:04	Residual is the difference between the observed and the fitted values.
09:10	The sum of squares of residuals is minimized in the least square fitting method.
09:17	You may note down the values or save the results.
09:22	Click on File, Save option to save the results.
09:27	A Grace:save logs form appear prompting to give a file name.
09:34	In the form, type 'fitted-values.txt' and click on Apply.
09:41	Click on Close, to close the dialog box.
09:45	Use File, close to close the Grace:console window.
09:50	A curve generated from data fitting, is automatically loaded on the graph.
09:57	The fitted curve traverse between the given data points.
10:03	Click on close to close the non-linear curve fitting window.
10:08	Click on File, save to save the project.
10:12	From top menu, choose File, exit to exit Grace.
10:19	Now, let’s summarize. In this tutorial, we Added multiple graph panels in the canvas
10:29	Learned to delete data sets from a graph panel
10:34	Performed non-linear regression on an exponential decay curve.
10:41	For assignment, please do the following.
10:45	Fit the data given in the file assignment1.txt to a parabola.
10:51	Use an equation of the type, as seen here.
10:56	Fit the given data in the file assignment2.txt, to atan(x).
11:03	Your complete assignment look similar to this.
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11:39	This is Rani, from IIT Bombay. Thank you for joining.

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