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.

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, ext.) 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
R^{2} 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 15. 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.

Leave some feedback if you found this interface useful.

This was very helpful since I forgot my calculator! Thank you so much! Would it be possible to add logarithmic or exponential regression to the list of available choices, please?

A most excellent tool. Thank you!

Really great, thanks so much.

Thanks so much, I don't have a graphing calculator with polynomial regression, so helpful.

Thank you, this website helped my group with my engineering project. We got a strange graph by measuring the C02 output of a proof of concept for a mosquito trap mechanism, and we used heptic regression on split up portions of the graph, and obtained a rough estimate of the function of our graph. Thank you.

this website is stupid and u have no life

I needed to find a best fit curve using more coefficients than my spreadsheet software provided. This website was perfect!

Excellent job

stupidest f-ing website ever

doesn't make any f-ing sense and doesn't f-ing work

very helpful indeed

This application help to me to fit easy, confident and fast the test data into the functions to make more confortable my work, thanks.

Very helpful indeed. Thank you so much...

Just awesome, we use this almost on a daily basis.

Thank you for your valuable work. I have checked theresults with Minitab vers. 14.0 and it is OK! Because Minitab works with Microsoft Windows only, and I use (for safety reason ) Ubuntu Linux , your page is a great help !

This was very helpful for checking the results of regression calculations I am doing in the Geometer's Sketchpad.

Thank you, this website helped my group with my engineering project.

it is very helpful .thankyou for posting

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Thank you! I needed a high-precision polynomial regression fit and your site gave me EXACTLY what I needed. Simple and highly functional - perfect. Thanks again.

Very nice. Any hints on how to force a curve that always has a negative or zero slope?

Impressive

you need a data input example

Could you submit your PHP libraries to GitHub, Composer/Packagist?

I stumbled across this site by accident and found it so helpful in my project

I don't get how this works. It makes no sense. I can't enter my data properly.

If users just looked at the the examples provided it's easy to see how to enter data in the correct format. Great format for modeling reliability and validity of assessment item analysis data.

This website was extremely helpful! It was great to be able to take output from a java program in a txt and then just copy and paste! Very very helpful:)

Very helpful. I am using Air Force DATCOM program to calculate some control coefficients for an aircraft design. I have to use experimental CFD wind tunnel data to get the longitudinal coefficients. Well, DATCOM has arrays for the data inputs, and one array wanted slopes of a function (like pitching moment due to alpha). That line is NOT linear, so I entered in the data as two columns, alpha vs. pitching moment and got the nice equation. Then, I took first derivative of the equation and used that in spreadsheet cells to generate the line slopes at any given alpha. Saved me ton of time and grief. Thank you.

this saved my life, multiple times. it works so well!

Thank you taking the time for developing the tool and sharing it with us. Very helpful.

Saved for later. Can't use it this time because my dataset is too big.

Thanks for the development.

very useful, thanks.

Any chance you could show equations model or approximations. How are finding the Coefficient of Determine for higher order Polynomial. Website is Great, its works and its graph and solving

some of my problems. Anyway, I need some help in solving cubic equations in a labview environment. pgmaser@aol.com if anyone wants to suggest somethings.

EXCELLENT! Thank you.

Tried Excel and Matlab - both failed miserably to come up with a curve fit. Your tool worked perfectly! Thanks!

Absolutely amazing resource. There are many tools for curve fitting, but most have very limited data sets. This gives you much more data set freedom, but the real power of this tool is being able to force coefficients. I couldn't find any other tool online that could do that, including paid sites. Well done and thanks for providing this!

Very handy, easy to use. Thanks a lot!

Very good site, but you have a bug on logaritmich regression. The resulthing coefficients are missmatched. It should be f(x) = B*ln(x) + A.

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This is great for use in our robotics class. Our robotic arm has several non-linear relationships towards the ends of its extremes. It would be fairly hard to come up with an efficient and accurate function You helped me produce the formulas for spatial coordination.

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This is great! I created my own version of this a while back but when I got >8 degrees it became slow. But this website can handle 15 degrees with no problem. How??

Very nice, fast.

It would be great to have the maximum error.

Excellent tool, thank you so much!

very good tool, thankful to you.

Thank you very much, this works great and I use it a lot.

Thank you this tool. Usually I use MS Excel to play with polynomials to see how measurements behave, but it is limited to 6 order polynomial only while sometimes I need to verify data against 9- or ever 11-order. A quite helpful tool!

This is great and very useful. I want to fit still higher order and my datapoints is ~8000. where is the link to download php code. I will refer your work.

Hi,

While checking some 2nd degree polynomial R²s produced using your Code against Excel values, I came across some anomalies when a set of data contained a number of values smaller than 0.0001 . However, these anomalies disappeared when I set the bcMaths to bcscale(20).

One example: 0.7142 compared to an Excel value of 0.9629

This post is duplicated on the http://polynomialregression.drque.net/ page

Hope this is helpful & thanks again.

Yours, Walter

Simple to use and got me a great fit equation for an old road using measured coordinates.

Wow, simplest and yet most accurate calculator ever!!! Bomb bomb bomb

Nice tool. Worked great. I don't understand how some users had a problem. Then of course there are the morons. Anyway tool produced a better fit than Excel. Thank you for the effort.

Fantastic tool. Really appreciate the site.

Helped me do linear regression with 15 coefficients! I actually needed that many coefficients but M$ Excel in 2017 limits to the sixth power.

greatt

It isn't clear what order the columns are (x1, x2...xn, and y).

Exactly what I needed. Thanks!

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Very useful.

Fantastic, works a treat, thanks.

Thanks a lot

Wow, It's a great tool. It's very helpful to do our easy job. Thanks for sharing this great info.

Excellent tool. Congratulations, just I'd like to add this comment:

While performing a regression of type f( x ) = a ln x + b something is working bad

I guess that coefficients a and b are swapped.

Thanks a lot for sharing this page.

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Great website and great calculator thanks. I found the high order / degree polynomial regression very useful.

It’s hard to come by experienced people about this subject

Very good write-up. I certainly love this website.

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Highly abnormal as per data entry is concerned. So unable to enter the data.

Extremely abnormal hints for the data.

Suggested to give an example for data entry!

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Very useful. Even if the data has more than 3 columns, the program automatically uses the first 2.

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, ext. 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 a school administrators.

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 school 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.

- May 2014: This page became active in.
- February 2015: Added support for 3 common linearizable functions.
- March 2015: Added support for coefficient forcing.

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.

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.

(C) Copyright 2014-2015 by Andrew Que