Code Explanation:
import statsmodels.api as sm
Purpose: Imports the Statsmodels library under the alias sm.
Why: Statsmodels is used for running statistical tests and regression models (like OLS — Ordinary Least Squares).
X = sm.add_constant([1,2,3,4])
Purpose: Adds a constant (intercept) column to your predictor data.
Result:
[[1., 1.],
[1., 2.],
[1., 3.],
[1., 4.]]
The first column (all 1s) represents the intercept.
The second column is your predictor variable [1,2,3,4].
Why: Statsmodels does not automatically include an intercept in OLS models, so you must add it manually with add_constant.
y = [2,4,6,8]
Purpose: Defines your dependent variable (target/output).
Meaning: The relationship here is perfectly linear:
y=2x
So the true intercept should be 0 and the slope should be 2.
model = sm.OLS(y, X).fit()
Purpose:
Creates an Ordinary Least Squares regression model (sm.OLS(y, X)).
Then calls .fit() to estimate the coefficients (parameters) using least squares.
What happens internally:
Result: Returns a RegressionResultsWrapper object containing all regression results and statistics.
print(model.params.tolist())
Purpose: Prints the estimated parameters (intercept and slope) as a Python list.
Output :
[0.0005000000000001118, 1.9990000000000003]
Final Output:
[0.0, 1.999]
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