You can do this using interpolate:

df['Price'].interpolate(method='linear', inplace=True)

Result:

    Price   Date
0   NaN     1
1   NaN     2
2   1800.000000     3
3   1900.000000     4
4   1933.333333     5
5   1966.666667     6
6   2000.000000     7
7   2200.000000     8

As you can see, this only fills the missing values in a forward direction. If you want to fill the first two values as well, use the parameter limit_direction="both":

df['Price'].interpolate(method='linear', inplace=True, limit_direction="both")

There are different interpolation methods, e.g. quadratic or spline, for more info see the docs: https://pandas.pydata.org/pandas-docs/stable/generated/pandas.Series.interpolate.html

You can use apply and lambda for this:

missing_data_df['horsepower']= missing_data_df.apply(
    lambda row: 
            0.25743277 * row.displacement + 0.00958711 * row.weight + 25.874947903262651 
            if np.isnan(row.horsepower) else row.horsepower, axis=1)

Use:

dfreg = df[df['A'].notna()]
dfimp = df[df['A'].isna()]

from sklearn.neural_network import MLPRegressor    
regr = MLPRegressor(random_state=1, max_iter=200).fit(dfreg['B'].values.reshape(-1, 1), dfreg['A'])
regr.score(dfreg['B'].values.reshape(-1, 1), dfreg['A'])

regr.predict(dfimp['B'].values.reshape(-1, 1))

Note that in the provided data correlation of the A and B columns are very low (less than .05). For replacing the imputed values with empty cells:

s = df[df['A'].isna()]['A'].index
df.loc[s, 'A'] = regr.score(dfreg['B'].values.reshape(-1, 1), dfreg['A'])

Output:

scikit-learn has an "Imputer" class you should look into.

• API
• Overview
• Demo

EDIT: Looks like this class doesn't support imputing from a linear model. You could always try modifying the sklearn code to support it, maybe even submit a pull request: https://github.com/scikit-learn/scikit-learn/blob/master/sklearn/preprocessing/imputation.py

EDIT2: Looks like you might have better luck with the more versatile imputation faculties available in the Orange library.