Exponential fit in pandas

I have this data:

puf = pd.DataFrame({'id':[1,2,3,4,5,6,7,8],
                    'val':[850,1889,3289,6083,10349,17860,28180,41236]})

The data seems to follow an exponential curve. Let’s see the plot:

puf.plot('id','val')

I want to fit an exponential curve ($$ y = Ae^{Bx} $$, A times e to the B*X)and add it as a column in Pandas. Firstly I tried to log the values:

puf['log_val'] = np.log(puf['val'])

And then to use Numpy to fit the equation:

puf['fit'] = np.polyfit(puf['id'],puf['log_val'],1)

But I get an error:

ValueError: Length of values (2) does not match length of index (8)

My expected result is the fitted values as a new column in Pandas. I attach an image with the column fitted values I want (in orange):

I’m stuck in this code. I’m not sure what I am doing wrong. How can I create a new column with my fitted values?

Answer

Your getting that error because np.polyfit(puf['id'],puf['log_val'],1) returns two values array([0.55110679, 6.39614819]) which isn’t the shape of your dataframe.

This is what you want

y = a* exp (b*x) -> ln(y)=ln(a)+bx
f = np.polyfit(df['id'], np.log(df['val']), 1)

where

a = np.exp(f[1]) -> 599.5313046712091
b = f[0] -> 0.5511067934637022

Giving

puf['fit'] = a * np.exp(b * puf['id'])

   id    val           fit
0   1    850   1040.290193
1   2   1889   1805.082864
2   3   3289   3132.130026
3   4   6083   5434.785677
4   5  10349   9430.290286
5   6  17860  16363.179739
6   7  28180  28392.938399
7   8  41236  49266.644002