Repository: pandas-dev/pandas
Issue category: Feature Request

Issue:
DOC: Improve documentation df.interpolate() for methods   ‘time’, ‘index’ and ‘values’
### Pandas version checks

- [X] I have checked that the issue still exists on the latest versions of the docs on `main` [here](https://pandas.pydata.org/docs/dev/)


### Location of the documentation

https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.interpolate.html

### Documentation problem

It is not possible to understand what exactly the method `interpolate` does from reading the documentation. See e.g. this SE post for more details

https://stackoverflow.com/questions/65511992/pandas-interpolation-type-when-method-index

### Suggested fix for documentation

Rewrite doctstring and documentation page for the method


Hints:
Thanks for the report, agreed this could use clarification. PRs to improve are welcome!
take

Patch:
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 7c2cc5d33a5db..56031f20faa16 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -7668,8 +7668,12 @@ def interpolate(
             * 'linear': Ignore the index and treat the values as equally
               spaced. This is the only method supported on MultiIndexes.
             * 'time': Works on daily and higher resolution data to interpolate
-              given length of interval.
-            * 'index', 'values': use the actual numerical values of the index.
+              given length of interval. This interpolates values based on
+              time interval between observations.
+            * 'index': The interpolation uses the numerical values
+              of the DataFrame's index to linearly calculate missing values.
+            * 'values': Interpolation based on the numerical values
+              in the DataFrame, treating them as equally spaced along the index.
             * 'nearest', 'zero', 'slinear', 'quadratic', 'cubic',
               'barycentric', 'polynomial': Passed to
               `scipy.interpolate.interp1d`, whereas 'spline' is passed to


Test patch: