Some illustrative data in a DataFrame (MultiIndex) format:
|entity| year |value|
+------+------+-----+
| a | 1999 | 2 |
| | 2004 | 5 |
| b | 20
A function can be applied to a groupby with the apply function. The passed function in this case linregress. Please see below:
In [4]: x = pd.DataFrame({'entity':['a','a','b','b','b'],
'year':[1999,2004,2003,2007,2014],
'value':[2,5,3,2,7]})
In [5]: x
Out[5]:
entity value year
0 a 2 1999
1 a 5 2004
2 b 3 2003
3 b 2 2007
4 b 7 2014
In [6]: from scipy.stats import linregress
In [7]: x.groupby('entity').apply(lambda v: linregress(v.year, v.value)[0])
Out[7]:
entity
a 0.600000
b 0.403226