result = sm.OLS(gold_lookback, silver_lookback ).fit()
After I get the result, how can I get the coefficient and the constant?
In other words,
Cribbing from this answer Converting statsmodels summary object to Pandas Dataframe, it seems that the result.summary() is a set of tables, which you can export as html and then use Pandas to convert to a dataframe, which will allow you to directly index the values you want.
So, for your case (putting the answer from the above link into one line):
df = pd.read_html(result.summary().tables[1].as_html(),header=0,index_col=0)[0]
And then
a=df['coef'].values[1]
c=df['coef'].values[0]