PhET/C3/Curve-Fitting/English-timed
From Script | Spoken-Tutorial
| Time | Narration |
| 00:01 | Welcome to this tutorial on Curve Fitting. |
| 00:05 | In this tutorial, we will demonstrate Curve Fitting PhET simulation. |
| 00:12 | Here I am using, Ubuntu Linux OS version 16.04 |
| 00:21 | Java version 1.8.0 |
| 00:25 | Firefox Web Browser version 60.0.2 |
| 00:31 | The learner should be familiar with topics in high school mathematics. |
| 00:37 | Using this simulation we will look at, Lines |
| 00:43 | Quadratic polynomials |
| 00:46 | Cubic polynomials |
| 00:49 | Quartic polynomials |
| 00:52 | Reduced chi squared statistic and correlation coefficient r squared |
| 00:59 | Let us begin. |
| 01:01 | Use the given link to download the simulation. |
| 01:06 | I have already downloaded the Curve Fitting simulation to my Downloads folder. |
| 01:13 | To open the jar file, open the terminal. |
| 01:17 | At the terminal prompt, type cd Downloads and press Enter. |
| 01:27 | Type java space hyphen jar space curve hyphen fitting underscore en dot jar.
Press Enter. |
| 01:42 | The File opens in the browser in html format. |
| 01:48 | This is the interface of the Curve Fitting simulation. |
| 01:53 | Observe the Help button, the Functions box and the Data Points bucket in the first quadrant. |
| 02:02 | In the Functions box, Linear and Best Fit radio buttons are default selections. |
| 02:11 | Let us click the Help button. |
| 02:15 | A legend for draggable error bars appears in the first quadrant. |
| 02:21 | The data points can be pulled out or put in the bucket. |
| 02:28 | In the fourth quadrant, Best Fit equation is seen with the display boxes for a and b. |
| 02:37 | The equation is y equals a plus bx. Below the display boxes is the correlation coefficient r squared. |
| 02:49 | In the 2nd and 3rd quadrants is a scale for the reduced chi squared statistic. |
| 02:56 | The formula for the chi squared statistic is given in the Help box. |
| 03:02 | Below the formula, we see the conditions for fit. |
| 03:08 | Good or very good fit of data with the equation is seen with a chi squared statistic of or below 1. |
| 03:19 | Let us click on Hide Help to hide these boxes. |
| 03:24 | Drag three data points out of the bucket.
Place them at -10 comma -4, -4 comma 4, and 5 comma 10. |
| 03:40 | Placing the mouse on them will show their co-ordinates. |
| 03:45 | Note that the equation for the best fit line drawn is y equals 6.07 plus 0.912 x. |
| 03:57 | The correlation coefficient r squared for the best fit line is 0.9616. |
| 04:06 | The closer the r squared value is to 1, the better is the prediction of variance in y from x. |
| 04:14 | Note that the reduced chi squared statistic is 6.74. The bar is red. |
| 04:24 | Click on Help and note that this means that the fit is poor. Again click on hide Help. |
| 04:35 | Let us drag another data point and place it at 0 comma 11 on the y axis. |
| 04:44 | Note that the best fit line becomes y equals 7.51 plus 1.004 x. |
| 04:55 | The slope of the best fit line has increased slightly from 0.912 to 1.004. |
| 05:03 | The y intercept has also increased from 6.07 to 7.51. |
| 05:10 | The data point 0 comma 11 is further away from the best fit line than the other points. |
| 05:18 | Note how the r squared value decreases from 0.9616 to 0.8529. |
| 05:28 | The prediction of variance in y from x with this equation has become less reliable. |
| 05:35 | Note also how the reduced chi squared statistic has increased from 6.74 to 18.66. |
| 05:45 | Drag the data point from 0 comma 11 to 0 comma 6. |
| 05:53 | Note how the equation becomes y equals 6.05 plus 0.911 x. |
| 06:03 | The r squared value increases to 0.9635, the reduced chi squared statistic falls to 3.37. |
| 06:15 | Drag the data point from -4 comma 4 to -4 comma 3.5. |
| 06:24 | The r squared value increases to 0.9772. |
| 06:30 | The reduced chi squared statistic falls to 2.12.
The bar now becomes green. |
| 06:39 | Click on Help; the green zone shows good fit. |
| 06:45 | Click on Hide Help. |
| 06:48 | A true best fit line explains all the data and gives a good prediction of y values from x values. |
| 06:58 | Click Adjustable Fit radio button. Drag sliders a and b to values close to 0. |
| 07:08 | Observe how this erases the line drawn earlier. |
| 07:13 | A line parallel to the x axis is seen. |
| 07:18 | Slider a and b values will be displayed in the boxes. |
| 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. |
| 07:35 | The r squared value is 0, meaning poor correlation. |
| 07:41 | Click Best Fit radio button again. |
| 07:45 | Note down the values for a and b (5.94 and 0.918). |
| 07:53 | Again, click Adjustable Fit radio button. Now drag sliders a and b from end to end. |
| 08:04 | Observe the effects of these changes on the line. Drag slider a to 6 and b to 0.97. |
| 08:16 | The line looks like the best fit line we saw earlier.
Note r squared and the reduced chi squared statistic. |
| 08:28 | Check Show deviations and click Best Fit. |
| 08:35 | The vertical lines from the data points to the best fit line show the deviations from the line. |
| 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. |
| 08:59 | R squared approaches 1 and the reduced chi squared statistic becomes 0. |
| 09:06 | The fit has become too good because a line is defined by two points. |
| 09:13 | Without a third point, there is no question of the line being anything but the best fit line. |
| 09:20 | Now, we will look at some information for you to graph a quadratic polynomial. |
| 09:27 | Quadratic polynomials are of the form y equals a plus bx plus c x squared. |
| 09:36 | The degree of the polynomial is 2, hence, it is called quadratic. |
| 09:44 | The function can have a maximum of 2 roots. |
| 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 |
| 10:03 | Note the r squared and reduced chi squared statistic values. |
| 10:09 | Also, click Adjustable Fit and see effects of a, b, c on the fit. |
| 10:17 | This is what the best fit graph for this quadratic polynomial will look like. |
| 10:25 | Cubic polynomials
Now, we will look at some information for you to graph a cubic polynomial. |
| 10:33 | Note the r squared and reduced chi squared statistic values. |
| 10:39 | This is what the best fit graph for this cubic polynomial will look like. |
| 10:46 | Quartic polynomials
Now, we will look at some information for you to graph a quartic polynomial. |
| 10:55 | Note the r squared and reduced chi squared statistic values. |
| 11:01 | This is what the best fit graph for this quartic polynomial will look like. |
| 11:08 | As an assignment, Change the data points and their number. |
| 11:14 | Follow the steps shown earlier to get best fit graphs for all the polynomials. |
| 11:20 | In this tutorial, we have demonstrated the Curve Fitting PhET simulation |
| 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 |
| 11:49 | The video at the following link summarizes the Spoken Tutorial project.
Please download and watch it |
| 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. |
| 12:12 | Please post your timed queries in this forum. |
| 12:16 | This project is partially funded by Pandit Madan Mohan Malaviya National Mission on Teachers and Teaching. |
| 12:24 | Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India.
More information on this mission is available at this link. |
| 12:37 | This is Vidhya Iyer from IIT Bombay signing off.
Thank you for joining. |
