Find best fit model of y = ax + k, y = ae^kx, or y = ax^k

bbash30

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Apr 8, 2008
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Find a model of the form y=ax+k, y=ae^kx, or y=ax^k, which best fits the data below. Properly compute and than round the values of a and k to 1 decimal place.

a] x= 1, 2, 4, 6, 9
y=0.2, 0.6, 1.8, 3.5, 6.7
-for this one I used Fathom and got y=ax^k that best fit the data since the r squared was closer to 1.0 (correlation), however I'm not sure how to compute for a and k...

b] x= 1, 2, 4, 6, 9
y= 0.3679, 0.1353, 0.0183, 0.0025, 0.0001
-for this one I used Fathom again and got y=ae^kx, but do not know how to do the computations...
any advice?
 

tkhunny

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Logarithms are your friends.

If \(\displaystyle y = ae^{kx}\), then \(\displaystyle log(y) = log(a) + x*k\) and you have a nice linear model.

Similarly, if \(\displaystyle y = ax^{k}\), then \(\displaystyle log(y) = log(a) + k*log(x)\) and you have a nice linear model.

Note: \(\displaystyle R^{2}\) closer to unity is a good measure, but don't mistake it for a formulation that actually makes sense.
 

stapel

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bbash30 said:
I used Fathom and got y=ax^k that best fit the data...however I'm not sure how to compute for a and k...
If you have found the regression equation, so you have found the best form of the equation "y = ax[sup:1nxjzq5j]k[/sup:1nxjzq5j]" and you thus have the values of "a" and "k", how is it that you're still needing to find ("compute") the values of "a" and "k"?

Please clarify. Thank you! :D

Eliz.
 

tkhunny

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I'm guessing "Fathom" provides results but not techniques.
 
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