Wondering what's the most efficient/accurate way to estimate these parameters (a0, a1, a2, a3) with Python in the model:
col_4 = a0 + a1*col_1 + a2*col_2 + a3*col_3
The sample dataset would be:
inputs = {
'col_1': np.random.normal(15,2,100),
'col_2': np.random.normal(15,1,100),
'col_3': np.random.normal(0.9,1,100),
'col_4': np.random.normal(-0.05,0.5,100),
}
_idx = pd.date_range('2021-01-01','2021-04-10',freq='D').to_series()
data = pd.DataFrame(inputs, index = _idx)
statsmodels provides a pretty simple way to estimate linear models like that:
import statsmodels.formula.api as smf
results = smf.ols('col_4 ~ col_1 + col_2 + col_3', data=data).fit()
print(results.summary())
The coef column shows your aX parameters:
OLS Regression Results
==============================================================================
Dep. Variable: col_4 R-squared: 0.049
Model: OLS Adj. R-squared: 0.019
Method: Least Squares F-statistic: 1.637
Date: Wed, 29 Dec 2021 Prob (F-statistic): 0.186
Time: 17:25:00 Log-Likelihood: -68.490
No. Observations: 100 AIC: 145.0
Df Residuals: 96 BIC: 155.4
Df Model: 3
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
Intercept 0.2191 0.846 0.259 0.796 -1.461 1.899
col_1 -0.0198 0.023 -0.854 0.395 -0.066 0.026
col_2 -0.0048 0.051 -0.093 0.926 -0.107 0.097
col_3 0.1155 0.056 2.066 0.042 0.005 0.226
==============================================================================
Omnibus: 2.292 Durbin-Watson: 2.291
Prob(Omnibus): 0.318 Jarque-Bera (JB): 2.296
Skew: -0.351 Prob(JB): 0.317
Kurtosis: 2.757 Cond. No. 370.
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
That includes the intercept (a0) by default. If you want to remove it, just add a -1 to the formula