Data entry
There are three forms of weighting the data. The first is to use a third column to specify a weighting term for each individual point. There is also a linear and exponentiation weighting. Each term is weighted by the index of that term. For linear weighting, the weighting term is the slope. The slope term is multiplied by the data point index to determine the weight for that point. For exponentiation, the weighting term is the power. The index raised to this power determines the weighting for the term.
There are times when one or more of the coefficients are known. The most typical case is a zero intercept, where the first coefficient is known to be 0. The same technique can be applied to any coefficient.
To force a coefficient, use the Add a forcing term button to insert a forcing term. The first box specifies which coefficient to force. The second is the value to use for that coefficient.
The math can be done using an arbitrary amount of precision. The number of decimal digits can be specified for more exact answers and higher precision can make answers more accurate.
Polynomial Regression Online Interface
This interface is designed to allow the graphing and retrieving of the coefficients for polynomial regression. This includes the mean average and linear regression which are both types of polynomial regression. Higher-order polynomials are possible (such as quadratic regression, cubic regression, etc.) making this tool useful for a range of analysis.
The data to analyze is placed in the text area above. It must be formatted so the first column is the x-values, and the second column the y-values. Columns may be separated by any character such as a comma. This character used for separation has to be specified. The same is true for the row separators. Generally a comma, space, or tab is used to separate columns and a linefeed to separate rows. Copying data from common spreadsheet software uses a tab to separate columns, and a linefeed to separate rows.
The regression analysis has several results that can be displayed. The equation displays the function that will produce the regression line. The coefficient check box will enable the individual coefficients to be printed from lowest order to highest. This is useful for copying the coefficients. A graph of the data and the regression line can also be made. This allows visual inspection of the data and the fit of the regression function. Lastly the R2 value can be displayed. This is a value that ranges between 0 (the worst fit) to 1 (a perfect fit) and used to determine the goodness of fit. The time needed to run the regression analysis is always displayed and reflects how long the server spent calculating the data.
Examples are provided to demonstrate various regression plots, and how the data is entered. To show the example, check the "Show examples" check box, and then select an example to display. After an example has been selected, the data for the example will be loaded into the form. Submitting this data will run the regression analysis and display the results. Each example displays the starting function so the fit can be compared.
Because this is a server-side script, the amount of data that can be entered is limited to 10000 points. The maximum number of coefficients to use in the regression analysis is limited to 25. Lastly, the precision of the data is limited to 20 decimal places. Should you require more data or coefficients, feel free to download the PHP library and run this program on your own computer.
User comments
Feel free to leave some feedback. A subset of Markdown is supported.
Opinions are not censored, but all advertisements—in particular those for south Asian educational institutes—will unceremoniously be deleted.
Feedback
2021-10-17
Thanks to all the who have reached out and left feedback. Your comments make my efforts worthwhile.
Greetings to all the scientists, researchers and fellow engineers who have used this tool in their work. May your efforts help build a better future. Greetings also to the many professors and teachers from around the world who use this site as part of their curriculum. May your students gain a better understanding of applied mathematics.
Good luck to all the students using this site from the many universities and schools around the world. May your studies enhance your abilities without stifling your desire to learn more.
Although I deplore censorship, I remove advertisements from the comments. If you want to advertise there are plenty of places to buy ad space, but this site isn't one of them. This tool is free and free from advertisements, tracking, data mining, click bating and all other such nuisance.
2015-03-14
I want to thank everyone who has used this site and left feedback. This page is now the most active on my server. The popularity of the site has inspired me to add improvements. Comments about how the site is used is both gratifying as well as useful. Seeing applications where polynomial regression can be applied is useful to me as well as students who also use this site.
Feel free to make requests for features, interface options, etc. I can't promise I can implement them all, but getting a feeling for features/changes people want helps me consider where to concentrate improvement efforts.
Not everyone is always happy with this site—or having to use this site. Even primary school students from the Las Virgenes Unified School District in Los Angeles County, California are still free to voice their opinion. As long as the comments are not inundated with extraneous/malice remarks I support the right of students to voice their discontent. Disgruntled users may consider pointing out what they don't like about the site, why they don't like having to use the site, or why they don't enjoy the subject. Remember: what is written here cannot be censored by school administrators.
Educators
One of the goals of this page was not only to provide a tool for calculating polynomial regression, but examples of how such techniques are used in real-world scenarios, and some of the mathematical phenomena exhibited.
Here are some articles on the mathematics of polynomial regression:
This site has been used by people from primary schools through distinguished universities. My hope is to provide something that can be useful to each level of user. I do not expect that high school students will be able to follow partial differentiation and the linear algebra necessary for the equations behind the regression technique. However, a pre-calculus student might be able to visually understand the concept of minimizing a quadratic function. For university level students I hope the explanations are detailed enough to give a comprehensive picture of how and why the algorithms work.
These goals require feedback. Suggestions, additions, clarifications, corrections, and criticisms are all welcome. Language is not my strong point, and while I have tried to convey ideas in the most clear manner I don't always succeed. And while I am better at math I am far from above mistakes. So proof reading and peer review would be nice.
History
- May 2014: This page became active in.
- February 2015: Added support for 3 common linearizable functions.
- March 2015: Added support for coefficient forcing.
- 2020-05-21: Our server is having issues that is causing the graphs not to function.
- 2020-07-17: A server upgrade earlier this month should have fixed the problem with graphs.
- 2021-10-17:
- Updated comment system.
- Added variable precision.
- 2023-12-25: General maintenance. No functionality changes.
- Updated to Polynomial Regression class 1.3.0.
- Updated to X/Y Plot 1.4.1.
- Switched to PHP 8.
- Cleaned up backend directory structure.
- 2025-05-15: Minor bug fixes.
- The coefficients on logarithmic and power regression were shown in reverse order.
- Misspelling of
linear
corrected.
Privacy
The data submitted is analyzed server-side, and saved for the duration of the session (which is 24 minutes). Aside from the mathematics performed on the data, no other analysis is done. The data is not kept, and will never be shared—even with the site's author. We are not a data mining company. Nonetheless, this site does not use a secure connection (i.e. no encryption or authentication), and thus it isn't recommended this site be used to analyze highly sensitive sets of data.
We do, however, keep records for basic Web analytics. These are used for statistical purposes such as the number of visitors a day and tracking spam robots.
About
This page is designed and maintained by Andrew Que. To get in touch with Andrew Que, visit his contact page. It uses the Polynomial Regression class to preform the regression calculations and X/Y Plot to graph the results.