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

#### bbash30

##### New member
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...

#### tkhunny

##### Moderator
Staff member

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

##### Super Moderator
Staff member
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"?

Eliz.

#### tkhunny

##### Moderator
Staff member
I'm guessing "Fathom" provides results but not techniques.