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Curve Plots
Hello Scott

I am reading a book on ecology where I have found a number of graphs with a curved best fit line (please see attached photo).

I am familiar with the least squares method of fitting a straight line to scattered points, but I did not know there is a technique to fit a curved line--or are these lines merely freehand estimates?

If there is a mathematical technique for curved best fit lines where may I learn about it?

Thanks.

Pete

Whatever estimate you're trying to do must be done to the data.
You have an x value with a y value you are trying to approximate.
If you are trying to fit an exponential to the curve, as in y = Ax^2 + Bx + C.
Let's take the data
1 2
2 5
3 9
4 15
Number = 4
Sum x = 1+2+3+4 = 10
Sum x^2 = 1+4+9+16 = 30
Sum x^3 = 1+8+27+64 = 100
Sum x^4 = 1+16+81+256 = 354

Sum Y = 2+5+9+16 = 32
Sum XY = 2+10+27+60 = 99
Sum (X^2)Y = 2+20+81+240 = 343

Given the sum of X to powers as 4, 10. 30, 100, 354 and
the sum of (x to a power)Y to be 32, 99, 343, we need to set up a matrix.

The matrix to solve would be
4  10  30  32
10  30 100  99
30 100 354 343

The equation would by y = a + bx + cx^2.
a, b, and c are the elements in the matrix, in order.

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#### Scott A Wilson

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I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can also say that I broke 5 minutes for a mile, which is over 12 mph, but is that relevant?

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My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

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Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

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I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

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My clients have been students at OSU, people who live nearby, friends with math questions, and several people every day on the PC. I would guess that you are probably going to be one more.