Linear Regression

• aka Ordinary Least Squares (OLS)

• minimizes sum of squared distances between data points and regression line

import pandas as pd
pd.ols(y, x)

import statsmodel.api as sm
sm.OLS(y, x).fit()
# dependent vars = y
# independent vars + constants = x

import numpy as np
np.polyfit(x, y , deg=1)

from scipy import stats
stats.linregress(x, y)

Add constant for linear regression intercept

import statsmodel.api as sm
df = sm.add_constant(df)

Clean data

df = df.dropna()

Regression Output

• coef (SPX_Ret) - slope of regression (beta)

results.params\[1\]

• const: intercept of linear regression

results.params\[0\]

• R-squared - sign = slope sign

• [corr(x,y)]^2 = R^2