Find An Equation For A Line

I

Inquisitor

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I need to find an equation for a line. I believe the base for it is f(x)= - a√(bx+c) + d but I'm not sure how to manipulate it to make it fit the points I know are on the line (aka what a,b,c, or d are) . The line drops off fairly quick then stays fairly flat from x=50 and beyond. The actual equation includes some minor variation factor on each set output so the numbers in column y may be slightly more or less. I need a line of best fit. Here is a picture of what the graph these points came from looks like: http://s14.postimg.org/f7pljswrl/screenshot_9.png
X
Y
1
75106
3
63477
4
58916
8
46749
71
10158
 
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Inquisitor said:
I need to find an equation for a line. I believe the base for it is f(x)= - a√(bx+c) + d but I'm not sure how to manipulate it to make it fit the points I know are on the line (aka what a,b,c, or d are) . The line drops off fairly quick then stays fairly flat from x=50 and beyond. The actual equation includes some minor variation factor on each set output so the numbers in column y may be slightly more or less. I need a line of best fit. Here is a picture of what the graph these points came from looks like: http://s14.postimg.org/f7pljswrl/screenshot_9.png
XY
175106
363477
458916
846749
7110158
Click to expand...
Do you know how to do a linear regression? To get a good one, you will need many more than five points.

I must tell you that the relevant function I'd think about first would be on the order of y = f(w, x). Those spikes suggest to me that y is not determined solely by x.

Furthermore, if you do want to come up with an approximation based solely on x, I'd start by doing a linear regression of y against u, where
u = 1/x. That may not work, but it looks to me more promising than regressing y against v, where v = sqrt(x).
 
Denis said:
Inquisitor said:
I need to find an equation for a line. I believe... [/QUOTE]
"I believe" doesn't "fit" in a math problem!
Can you post the original problem IN FULL?
Click to expand...

I can not post the original problem because there isn't one. The points I stated were based on the graph linked, which is a simulation of a resource extractor. Uncontrollable environmental factors create variation in the output. And if I can figure out the apx equation of this curve, its part of a more complicated equation for maximizing something else.

JeffM said:
Do you know how to do a linear regression? To get a good one, you will need many more than five points.

I must tell you that the relevant function I'd think about first would be on the order of y = f(w, x). Those spikes suggest to me that y is not determined solely by x.

Furthermore, if you do want to come up with an approximation based solely on x, I'd start by doing a linear regression of y against u, where
u = 1/x. That may not work, but it looks to me more promising than regressing y against v, where v = sqrt(x).
Click to expand...

This is a bit beyond my level of study. While it would be awesome to have an exact equation, the closest I could get would be an approximation of a line of best fit. I'll google linear regressions as I can approximate perhaps 50 points out of the 72 on the graph.

The problem comes from a pc game actually. This particular game is loaded with graphs, stats and numbers - and while its not necessary, I find spreadsheets and equations necessary to maximize effectiveness. You all might enjoy it - link below is a buddy invite I setup for yall. Can never have too many people with good heads nearby!
https://secure.eveonline.com/trial/?invc=fdae8947-c918-4ac0-94c7-c1dc3ed942ba&action=buddy
Click to expand...
 
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lookagain said:
\(\displaystyle f(x) \ = \ -a\sqrt{bx + c \ } + d \ \ \) is not the equation of any line.
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look again - why do you say so? Is it because it is not in the form of y = f(x)?

Definition of a line:

a continuous extent of length, straight or curved, without breadth or thickness; the trace of a moving point.
 
Where did you get that definition? The word "line", without modifiers, implies "straight line".
 
HallsofIvy said:
The word "line", without modifiers, implies "straight line".
Click to expand...

Please site your source. ;)

The implication above is definitely not used in the Seattle Community College District or at the University of Washington.



But you have quoted the second definition while the first is a straight line.
Click to expand...

Halls, you failed to note that the second definition is explicitly listed as the mathematical definition of line.
 
I hesitate somewhat, to post that context is important, but I'm doing so, anyway.

The OP wrote "I need a line of best fit."

The linked histogram shows behavior similar to exponential decay.

The line of best fit ought to be a curved line. :cool:
 
mmm4444bot said:
I hesitate somewhat, to post that context is important, but I'm doing so, anyway.

The OP wrote "I need a line of best fit." **

The linked histogram shows behavior similar to exponential decay.

The line of best fit ought to be a curved line. :cool:
Click to expand...

Then the OP should have stated, "I need a curve of best fit."


**

one of many links:

http://www.investopedia.com/terms/l/line-of-best-fit.asp



A "line of best fit" is synonymous with finding the equation of a straight line
using least squares regression.
 
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