Online Calculator

[Christy Knudsen]

Does anyone know of a good website for a graphing calculator? I am looking for one that has the ability to come up with an equation based on points that are inputted in.

Thanx!
Christy

[Timothy Kim]

Ooops, I accidentally deleted my post:

Are you talking about a linear regression graphing calculator?

http://www.alcula.com/calculators/statistics/linear-regression/

Just type in these data pairs without the parenthesis but with the comma (you need at least 5 pairs):

2,4

3,6

4,9

5,11

6,11

and submit for the line the of best fit.

Does this work for you?

[Christy Knudsen]

I am actually not fitting my points to a linear. It should be a polynomial. And the students will need to find the line of best fit, whether it is cubic, quartic, or a higher power.

[Steve Cates]

The "line" or really curve of best fit will always be based on the number of points.  Two points determine a line... three a parabola... four a cubic.... n a x^(n-1) polynomial.

Not much statistical curve approximating is done beyond parabolic (there are exponential and log fits as well like a^bx or a*log bx).  Excel offers all of these fits.

Put in your points, select graph and do scatter plot.  Right click on a point on the graph and select "Add trendline" there are options to use different types of fits including polynomial and selecting the order.  You can check to "Display Equation on Chart"

See my example attached.

[Steve Cates]

BTW, the method of hand calculating this is solving simultaneous equations.

beyond three points would really require matrix methods that should really be done by a computer.

Example of solving for the three point:

y = ax^2+bx+c

(1,2)

(2,3)

(4,2)

You plug in the three points for x and y and get three equations with a,b, and c as your unknowns and you solve the system.  Not easy but doable. When you go to 6 points and you're solving for 6 coefficients with 6 equations nobody does that by hand and that's only an order 5 polynomial. Imagine a statistical data set of 100 points!  Also, sometimes it's impossible to have a fit, if two points have the same x value and different y vaules because then it's not a function.

[Christy Knudsen]

Thanx Steve. I didn't even think about excel. That will definitely work. Doing it by hand will be really tricky for the task that I developed.

[Steve Cates]

I just figured out how to do this with GeoGebra.  It might be better to use GeoGebra over excel, since we'll be using it more with other modules and excel might not be on student computers.

I show how to input 3 or 4 points in the video below and FitPoly.  I prefer putting them in the spreadsheet view first but I show the click method as well.

Then great part is that it's dynamic and you can move the points around and see the formula change.

See this video.

[Christy Knudsen]

Thanx Steve! Using GeoGebra will be a lot more efficient for the task I made. In Excel, you can only fit a polynomial to degree 6. GeoGebra looks like you can make it any degree.