Logarithmic Graph Interpolation

Don't use a graph. Use the LINEST function to work with your transformed variables. See
Trendline Coefficients and Regression Analysis
http://www.tushar-mehta.com/publish_train/data_analysis/16.htm

wirehead said:

Alright, I think I’ve looked everywhere and can't find what I’m looking for; so here is my question. I have a Lin-Log graph (lin "y" axis-log "x" axis) i have multiple points in the graph and want to interpolate points that i don't have plotted. I thought this would be an easy task but has been quite difficult. I don't know the mathematical relationships between the X&Y variables; I transposed the graph out of printed document. I want to be able to input a value for X and have the graph spit out the Y value. I saw a thread about a log-log graph but that didn't help me. Thanks for any help that anyone can provide.<?xml:namespace prefix = o ns = "urn:schemas-microsoft-comfficeffice" /><o></o>

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wirehead said:

I transposed the graph out of printed document<o></o>

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So all you have is an image?
Or do you have coordinates? If so how have you arranged these values on the sheet?

p45cal said:

So all you have is an image?
Or do you have coordinates? If so how have you arranged these values on the sheet?

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sorry for the late reply. I do have the coordinates and have arranged and ploted them on the graph. I'm just trying to find the ones in-between the knowns. thanks for the help.

wirehead said:

sorry for the late reply. I do have the coordinates and have arranged and ploted them on the graph. I'm just trying to find the ones in-between the knowns. thanks for the help.

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so

Originally Posted by p45cal
Or do you have coordinates? If so how have you arranged these values on the sheet?

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Are there gaps? Vertically in a range? How?

Like I wrote previously. Use LINEST to solve your problem.

wirehead said:

sorry for the late reply. I do have the coordinates and have arranged and ploted them on the graph. I'm just trying to find the ones in-between the knowns. thanks for the help.

Click to expand...

If your data are linear when plotted as y vs log(x), then the data has a logarithmic relationship, as you pointed out. For example,


The formula in B2 and down is =2*LN(A2) + 1

If you plot it with a logarithmic y axis, it's linear (perfectly linear; yours surely isn't if it's measurement data).

You can extract the log trend using LINEST. Select two side-by-side cells (say D2:E2), and paste this in the formula bar:

=LINEST(B2:B6, LN(A2:A6))

Don't press Enter; instead, press and hold the Ctrl and Shift keys, then press Enter. You'll see


So let's add some noise. Change the formula in B2 and down to

=2*LN(A2) + 1 + (RAND()-0.5)/10

Then you might see


The values in D2 and E2 tell you the best fit for the trendline

y = m * ln(x) + b

Now, suppose you want to interpolate y for x=1.5. You have two choices: interpolate along the trendline, or do a piecewise interpolation between the points x=1 and x=2. Which do you want?