OLS Fitting

Basic usage

import ravix

df    = ravix.get_data("Betas.csv")
model = ravix.ols("AAPL ~ SPY", df)
model.summary()

Summary of OLS Regression Analysis:
======================================================

Coefficients:
------------------------------------------------------
              Estimate  Std. Error  t-value    p-value
Intercept     0.014223    0.011989    1.186     0.2437
SPY             1.2266     0.21591    5.681   2.24e-06 ***

Model Statistics:
------------------------------------------------------
Residual Std. Error: 0.069147
R-squared:      0.4870          AIC: -88.2432
Adj. R-squared: 0.4719          BIC: -85.0761
F-statistic: 32.2745 on 1 and 34 DF, p-value: 2.24e-06
======================================================

Formula syntax

Accessing model attributes

The fitted object is a regression model object:

print("R-squared:      ", round(model.rsquared, 4))

R-squared:       0.487

print("Adj. R-squared: ", round(model.rsquared_adj, 4))

Adj. R-squared:  0.4719

print(model.params)

Intercept    0.014223
SPY          1.226589
dtype: float64

model.params          # Series — coefficient estimates
model.resid           # Series — residuals
model.fittedvalues    # Series — fitted values
model.rsquared        # float  — R²
model.rsquared_adj    # float  — Adjusted R²
model.pvalues         # Series — coefficient p-values
model.bse             # Series — coefficient standard errors

Confidence and prediction intervals

model.conf_int(alpha=0.05)

                  0         1
Intercept -0.010142  0.038588
SPY        0.787811  1.665368

import pandas as pd
new_df = pd.DataFrame({"SPY": [0.005, 0.010, 0.015]})
ravix.intervals(model, new_df, interval="confidence")

   Prediction  Lower Bound  Upper Bound
0    0.020356    -0.003498     0.044209
1    0.026489     0.002952     0.050025
2    0.032622     0.009201     0.056043

ravix.intervals(model, new_df, interval="prediction")

   Prediction  Lower Bound  Upper Bound
0    0.020356    -0.122179     0.162890
1    0.026489    -0.115993     0.168971
2    0.032622    -0.109841     0.175085

Logistic Regression

# Get data
df = ravix.get_data("loan_default.csv")
df = df[df.columns[1:]]

# Logistic
logreg = ravix.logistic("Loan_Default ~ Age + Marital_Status + Dependents", df)

# Model Summary
logreg.summary()

Summary of Logistic Regression Analysis:
==========================================================

Coefficients (Log-Odds):
----------------------------------------------------------
                  Estimate  Std. Error  t-value    p-value
Intercept          -1.9135     0.51144   -3.741     0.0002 ***
Age              -0.0081359    0.010230   -0.795     0.4265
Marital_Statu...   0.12677     0.32743    0.387     0.6986
Marital_Statu...   0.42844     0.56198    0.762     0.4458
Marital_Statu... -0.060775     0.33662   -0.181     0.8567
Marital_Statu...   0.68904     0.62056    1.110     0.2668
Dependents       -0.056555    0.090777   -0.623     0.5333

Model Statistics:
----------------------------------------------------------
Log-Likelihood: -395.0289       AIC: 804.0579
Pseudo R-squared: 0.002323      BIC: -7992.44
==========================================================

Poisson Regression

# Get data
df = ravix.get_data("video_engagement.csv")

# Poisson
pois = ravix.poisson("Likes ~ .", df)

# Model summary
pois.summary()

Summary of Poisson Regression Analysis:
======================================================

Coefficients (Log-Rate):
------------------------------------------------------
              Estimate  Std. Error  t-value    p-value
Intercept       10.235   0.0008990 11384.796    < 2e-16 ***
Promoter_B     -2.1581   0.0010739 -2009.636    < 2e-16 ***
Age          0.0048345   2.408e-06 2007.940    < 2e-16 ***
Sentiment    0.0045228   0.0008673    5.215   1.84e-07 ***

Model Statistics:
------------------------------------------------------
Log-Likelihood: -188742.02      AIC: 377492.04
Deviance: 375545.73             BIC: 374772.12
Null Deviance: 12989055.39
Pseudo R-squared: 1
Degrees of Freedom: 3 (Model), 153 (Residual)
======================================================

Textbook reference: OLS fitting is covered in Chapters 3–9 of Applied Linear Regression for Business Analytics with Python.