Hello,

I need an equation that matches the attached graph. Please help. Data is below the graph.

Thanks,

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- Aug 13th 2011, 06:59 PMpieman91Find an equation from this graph.
Hello,

I need an equation that matches the attached graph. Please help. Data is below the graph.

Thanks, - Aug 13th 2011, 07:04 PMProve ItRe: Find an equation from this graph.
Since there are 40 points, it would fit a polynomial of order 39 exactly.

Let $\displaystyle \displaystyle y = c_0 + c_1x + c_2x^2 + ... + c_{39}x^{39}$.

When you substitute each point, you'll get 40 equations in 40 unknowns which you can solve using technology or MUCH difficulty by hand. - Aug 13th 2011, 10:50 PMpieman91Re: Find an equation from this graph.
- Aug 14th 2011, 12:00 AMCaptainBlackRe: Find an equation from this graph.
- Aug 14th 2011, 01:56 AMpieman91Re: Find an equation from this graph.
Thanks for that. I don't want to seem nit-picky or ungrateful but y=16.467+0.004939x+0.00002781x^2 is just a bit too high for it to match the trendline and therefore I can't use it. I have attached a new graph that shows y=16.467+0.004939x+0.00002781x^2, the trendline and the actual tax percentage. And if that last data becomes an extreme outlier just get rid of it.

I really appreciate everyone's help with this and Captain Black, if you don't want to do it (fair enough), you can show me how to do it and then I can do it. - Aug 14th 2011, 05:43 AMCaptainBlackRe: Find an equation from this graph.
Well if it does not match there is probably a typo in my typing since it passed straight through the data when I was doing the fitting, unfortunately I am not on the machine with the file at present so I cannot check.

However the red curve in your document is not a plot of the quadratic (which is smooth)

Checking my notes, the typo is a wrong sign, it should be:

$\displaystyle y=16.467-0.004939x+0.00002781x^2 $

Also since you already have the equation of the trend line why are you continuing with this thread?

CB - Aug 14th 2011, 05:48 AMzzzoakRe: Find an equation from this graph.
You could use

**interpolation polynomial in the Lagrange form**:

Lagrange polynomial - Wikipedia, the free encyclopedia.

For example:

For k=2: $\displaystyle x_0y_0 \quad x_1y_1 \quad x_2y_2 $

$\displaystyle p(x)=y_0\frac{(x-x_1)(x-x_2)}{(x_0-x_1)(x_0-x_2)}+y_1\frac{(x-x_0)(x-x_2)}{(x_1-x_0)(x_1-x_2)}+y_2\frac{(x-x_0)(x-x_1)}{(x_2-x_0)(x_2-x_1)}$

$\displaystyle p(x_0)=y_0\;\cdot 1+y_1\;\cdot 0+y_2\;\cdot 0=y_0$

$\displaystyle p(x_1)=y_0\;\cdot 0+y_1\;\cdot 1+y_2\;\cdot 0=y_1$

$\displaystyle p(x_0)=y_0\;\cdot 0+y_1\;\cdot 0+y_2\;\cdot 1=y_2$.

For p(x) you don't need to find k coefficients but you have k+1 terms of order k.

You could write a little program for p(x). - Aug 14th 2011, 02:36 PMpieman91Re: Find an equation from this graph.
The trendline is from excel but

**the polynomial of the trendline that excel gives me does not fit the data**. The trendline fits but its the wrong polynomial. The polynomial is the same shape but it does not fit the data. I would use it if it was the actual equation but its not. - Aug 14th 2011, 02:41 PMpieman91Re: Find an equation from this graph.