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

[bbash30]

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]

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]

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!

Eliz.

 

[tkhunny]

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