PoojaMoolya: Created page with "{|border=1 ||'''Time''' ||'''Narration''' |- ||00:01 ||Welcome to this tutorial on '''Curve Fitting'''. |- ||00:05 ||In this tutorial, we will demonstrate '''Curve Fitting P..."

2018-11-01T07:06:58Z

Created page with "{|border=1 ||'''Time''' ||'''Narration''' |- ||00:01 ||Welcome to this tutorial on '''Curve Fitting'''. |- ||00:05 ||In this tutorial, we will demonstrate '''Curve Fitting P..."

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{|border=1
||'''Time'''
||'''Narration'''

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||00:01
||Welcome to this tutorial on '''Curve Fitting'''.

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||00:05
||In this tutorial, we will demonstrate '''Curve Fitting PhET simulation'''.

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||00:12
||Here I am using, '''Ubuntu Linux OS''' version 16.04

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||00:21
||'''Java''' version 1.8.0

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||00:25
||'''Firefox Web Browser''' version 60.0.2

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||00:31
||The learner should be familiar with topics in high school mathematics.

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||00:37
||Using this '''simulation''' we will look at, Lines

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||00:43
||Quadratic polynomials

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||00:46
||Cubic polynomials

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||00:49
||Quartic polynomials

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||00:52
||'''Reduced chi squared statistic''' and '''correlation coefficient r squared'''

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||00:59
||Let us begin.

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||01:01
||Use the given link to download the '''simulation'''.

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||01:06
||I have already downloaded the '''Curve Fitting simulation''' to my '''Downloads''' folder.

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||01:13
||To open the '''jar file''', open the '''terminal'''.

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||01:17
||At the '''terminal prompt''', type '''cd Downloads''' and press '''Enter'''.

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||01:27
||Type '''java space hyphen jar space curve hyphen fitting underscore en dot jar'''.

Press Enter.

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||01:42
||The '''File''' opens in the '''browser''' in '''html''' format.

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||01:48
||This is the '''interface''' of the '''Curve Fitting simulation'''.

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||01:53
||Observe the '''Help button''', the '''Functions''' box and the '''Data Points''' bucket in the first quadrant.

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||02:02
||In the '''Functions''' box, '''Linear''' and '''Best Fit''' radio buttons are default selections.

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||02:11
||Let us click the '''Help''' button.

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||02:15
||A legend for '''draggable error bars''' appears in the first quadrant.

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||02:21
||The data points can be pulled out or put in the bucket.

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||02:28
||In the fourth quadrant, '''Best Fit equation''' is seen with the '''display''' boxes for '''a''' and '''b'''.

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||02:37
||The equation is '''y equals a plus bx'''. Below the display boxes is the '''correlation coefficient r squared'''.

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||02:49
||In the 2nd and 3rd quadrants is a scale for the '''reduced chi squared statistic'''.

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||02:56
||The formula for the '''chi squared statistic''' is given in the '''Help''' box.

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||03:02
||Below the formula, we see the conditions for '''fit'''.

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||03:08
||Good or very good fit of data with the equation is seen with a '''chi squared statistic''' of or below 1.

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|| 03:19
||Let us click on '''Hide Help''' to hide these boxes.

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||03:24
||Drag three data points out of the bucket.

Place them at '''-10 comma -4''', '''-4 comma 4''', and '''5 comma 10'''.

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||03:40
||Placing the mouse on them will show their '''co-ordinates'''.

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||03:45
||Note that the equation for the best fit line drawn is '''y equals 6.07 plus 0.912 x'''.

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||03:57
||The '''correlation coefficient r squared''' for the '''best fit line''' is 0.9616.

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||04:06
||The closer the '''r squared''' value is to 1, the better is the prediction of '''variance''' in '''y''' from '''x'''.

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||04:14
||Note that the '''reduced chi squared statistic''' is 6.74. The bar is red.

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||04:24
||Click on '''Help''' and note that this means that the fit is poor. Again click on hide Help.

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||04:35
||Let us drag another data point and place it at '''0 comma 11''' on the '''y axis'''.

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||04:44
||Note that the '''best fit line''' becomes '''y equals 7.51 plus 1.004 x'''.

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||04:55
||The slope of the '''best fit line''' has increased slightly from 0.912 to 1.004.

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||05:03
||The '''y intercept''' has also increased from 6.07 to 7.51.

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||05:10
||The data point '''0 comma 11''' is further away from the '''best fit line''' than the other points.

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||05:18
||Note how the '''r squared''' value decreases from 0.9616 to 0.8529.

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||05:28
||The prediction of '''variance''' in '''y''' from '''x''' with this equation has become less reliable.

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||05:35
||Note also how the '''reduced chi squared statistic''' has increased from 6.74 to 18.66.

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||05:45
||Drag the data point from '''0 comma 11''' to '''0 comma 6'''.

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||05:53
||Note how the equation becomes '''y equals 6.05 plus 0.911 x'''.

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||06:03
||The '''r squared''' value increases to 0.9635, the '''reduced chi squared statistic''' falls to 3.37.

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||06:15
||Drag the data point from '''-4 comma 4''' to '''-4 comma 3.5'''.

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||06:24
||The '''r squared''' value increases to 0.9772.

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||06:30
||The '''reduced chi squared statistic''' falls to 2.12.

The bar now becomes green.

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||06:39
||Click on '''Help'''; the green zone shows good fit.

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||06:45
||Click on '''Hide Help'''.

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||06:48
||A true '''best fit line''' explains all the data and gives a good prediction of '''y''' values from '''x''' values.

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||06:58
||Click '''Adjustable Fit radio button'''. Drag '''sliders a''' and '''b''' to values close to 0.

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||07:08
||Observe how this erases the line drawn earlier.

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||07:13
||A line parallel to the '''x axis''' is seen.

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||07:18
||'''Slider a''' and '''b''' values will be displayed in the boxes.

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||07:24
||The data points are still where we placed them.

But the '''reduced chi square statistic''' is very high and in the red zone.

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||07:35
||The '''r squared''' value is 0, meaning poor correlation.

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||07:41
||Click '''Best Fit radio button''' again.

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||07:45
||Note down the values for '''a''' and '''b''' (5.94 and 0.918).

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||07:53
||Again, click '''Adjustable Fit radio button'''. Now drag '''sliders a''' and '''b''' from end to end.

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||08:04
||Observe the effects of these changes on the line. Drag '''slider a''' to 6 and '''b''' to 0.97.

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||08:16
||The line looks like the '''best fit line''' we saw earlier.

Note '''r squared''' and the '''reduced chi squared statistic'''.

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||08:28
||Check '''Show deviations''' and click '''Best Fit'''.

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||08:35
||The vertical lines from the data points to the '''best fit line''' show the deviations from the line.

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||08:43
||Drag the data points at '''-4 comma 3.5''' and '''0 comma 6''' into the bucket.

Note how the line now passes through the two points.

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||08:59
||'''R squared''' approaches 1 and the '''reduced chi squared statistic''' becomes 0.

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||09:06
||The fit has become too good because a line is defined by two points.

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||09:13
||Without a third point, there is no question of the line being anything but the '''best fit line'''.

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||09:20
||Now, we will look at some information for you to graph a '''quadratic polynomial'''.

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||09:27
||'''Quadratic polynomials''' are of the form '''y equals a plus bx plus c x squared'''.

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||09:36
||The degree of the polynomial is 2, hence, it is called '''quadratic'''.

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||09:44
||The '''function''' can have a maximum of 2 roots.

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||09:48
||Drag and place data points at the following '''co-ordinates'''.

'''-9 comma 10''', '''-7 comma 2''', '''2.5 comma -2.5''' and '''5 comma 10'''

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||10:03
||Note the '''r squared''' and '''reduced chi squared statistic''' values.

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||10:09
||Also, click '''Adjustable Fit''' and see effects of '''a''', '''b''', '''c''' on the fit.

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||10:17
||This is what the '''best fit''' graph for this '''quadratic polynomial''' will look like.

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||10:25
||'''Cubic polynomials'''

Now, we will look at some information for you to graph a '''cubic polynomial'''.

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||10:33
||Note the '''r squared''' and '''reduced chi squared statistic''' values.

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||10:39
||This is what the '''best fit''' graph for this '''cubic polynomial''' will look like.

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||10:46
||'''Quartic polynomials'''

Now, we will look at some information for you to graph a '''quartic polynomial'''.

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||10:55
||Note the '''r squared''' and '''reduced chi squared statistic''' values.

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||11:01
||This is what the '''best fit''' graph for this '''quartic polynomial''' will look like.

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||11:08
||As an '''assignment''', Change the data points and their number.

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||11:14
||Follow the steps shown earlier to get '''best fit''' graphs for all the '''polynomials'''.

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||11:20
||In this '''tutorial''', we have demonstrated the '''Curve Fitting PhET simulation'''

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||11:27
|| Using this '''simulation''', we have looked at:

Lines

Quadratic polynomials

Cubic polynomials

Quartic polynomials

'''Reduced chi square statistic χr2''' and '''correlation coefficient r2'''

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||11:49
||The video at the following link summarizes the '''Spoken Tutorial project'''.

Please download and watch it

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||11:58
||The '''Spoken Tutorial Project '''team conducts workshops using '''spoken tutorials''' and gives certificate courses on passing online tests.

For more details, please write to us.

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||12:12
||Please post your timed queries in this forum.

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||12:16
||This project is partially funded by '''Pandit Madan Mohan Malaviya National Mission on Teachers and Teaching'''.

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||12:24
||'''Spoken Tutorial Project''' is funded by '''NMEICT''', MHRD, Government of India.

More information on this mission is available at this link.

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||12:37
||This is '''Vidhya Iyer''' from '''IIT Bombay''' signing off.

Thank you for joining.
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|}

PhET/C3/Curve-Fitting/English-timed - Revision history

PoojaMoolya: Created page with "{|border=1 ||'''Time''' ||'''Narration''' |- ||00:01 ||Welcome to this tutorial on '''Curve Fitting'''. |- ||00:05 ||In this tutorial, we will demonstrate '''Curve Fitting P..."