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$(2711, 0.62),(3243,1.83),(3846,0.38),(4514,2.42),(5152,0.58),(5723,1.82),(6322,0.38), (6950, 2.44),(7628, 0.57),(8159,1.82),(8757,0.39),(9425,2.44),(10102, 0.56), (10635, 1.82),(11230, 0.41),(11858, 2.41),(12533, 0.57),(13109, 1.81), (13704, 0.44),(14330, 2.38),(15004, 0.58),(15546, 1.8),(14750, 0.55) $

Ok, from this data we need to make a graph (the one bracket and commas are just to separate the data), which i have done. Then we need to remake this graph and find the formula at the same time. What im really asking is that if anyone can find the formula for this data set, so it can be replotted as a graph using the formula made. It doesnt have to be perfect, just near. I have come up with a basic equation to use which is
$2\sin(x_1-4)+0.5\sin(x_1-6)+0.8\sin(x_1-4)+3.02$

Thats as far as i have gotten but im stuck. Please help me solve this, i cant do it.

mahavir
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user133251
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  • user133251 to avoid confusion you should bracket data points as (x,y). Why did you choose that form for your fit? Is there more to this question? – bobbym Mar 05 '14 at 11:00
  • Im have been given those points to make a graph on excel with. I have made that graph. But now i need to find the formula for that graph. I have been toying around on a graphing program using 2sin(1x-4)+0.5sin(1x-6)+0.8sin(1x-4)+3.02, but i can not match it to the graph as accurately as possible. – user133251 Mar 05 '14 at 11:08
  • The last point (14750, 0.55,) looks like it belongs between (14330, 2.38,) and (15004, 0.58,) – bobbym Mar 05 '14 at 11:22
  • They are not in an order, they are 24 hour times over a span of several days – user133251 Mar 05 '14 at 11:27
  • I really only need the formula of the equation. That is all. – user133251 Mar 05 '14 at 11:43

1 Answers1

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The following function is a good fit to your points:

$$ y = 1.29847823 - 0.29759606 \,sin (0.00259178 x - 1.02713312) - 0.85121794 \,sin (2*0.00259178 x)$$

The pattern of your points shows a sum of two periodic functions, where one has twice the frequency of the other. Therefore, I asked my Excel solver to determine a least square fit. Parameters are the average value (added constant), the base frequency, the amplitudes and a phase shift.

Note that there might be a typing error in your values for $14500 .. 15000$. These two values look somewhat odd compared to the other periods.

Axel Kemper
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