# Thread: determining the value of intersection (Excel/2003)

1. ## determining the value of intersection (Excel/2003)

I have a question that has so far stumped myself and coworkers. I have 3 different trendlines plotted in an Excel chart. The lines intersect to form something looking like an H -- so there are two different points of intersection.

How can I determine the values of those two intersecting points? They don't lie on any of the original points I plotted -- they lie on the trendline. I would like to avoid doing this by hand, if possible.

2. ## Re: determining the value of intersection (Excel/2

Could you attach the file? I'm having trouble visualizing the problem.

Here it is!

- Katie

4. ## Re: determining the value of intersection (Excel/2003)

Welcome to Woody's Lounge!

You can use the LINEST function to find the slope and intercept for each of the trend lines from the source data, then use straightforward maths to calculate the intersection points. See screenshot.

(You can also display the equations for the trend lines in the chart, by right clicking a trend line and selecting Format Trend Line, but then you'd still have to do the rest manually)

Post back if you need more help, preferably with a sample workbook.

5. ## Re: determining the value of intersection (Excel/2003)

My lines are curves (I set the trendline to be a 2nd order polynomial) -- is this a problem with using the LINEST or SLOPE function?

6. ## Re: determining the value of intersection (Excel/2

Ah, you had already posted a workbook. Your trend lines are polynomials. It's still possible, though more complicated, to use LINEST to provide the equations for the trend lines. Calculating the intersections is more complicated too - see the attached version.

7. ## Re: determining the value of intersection (Excel/2

Thanks! I really, really, really appreciate your help!

Katie

8. ## Re: determining the value of intersection (Excel/2

To be a little more explicit in something Hans only hinted at:

Each of your curves could have more than one answer and you will have to choose which one you want or have some criteria to choose...

Steve

9. ## Re: determining the value of intersection (Excel/2

And another point (for information only):

In this example, the trend lines are polynomials of degree 2. Calculating their intersection means solving a quadratic equation; this can be done using the famous (or notorious) quadratic formula shown below.

For polynomials of degree 3 and 4, you'd need to solve a cubic or quartic equation. There are explicit formulas for doing so, but they are horribly complicated. For higher degree equations, there simply is no explicit formula. In these cases, the solutions can only be approximated; Excel's Goal Seeker tool could be used for this.

10. ## Re: determining the value of intersection (Excel/2003)

Is there a real theoretical relationship to the curves that you just fit to the quadratic. You might not get the extra and you may be able to solve them easier if you fit to a real relationship. Some relationships are parabolas, but not all curves are parabolic.

These equations, though most likely curved, can be fit relatively well with 3 simple lines and they would be much easier to solve...

Steve

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