Tutorial 03 — Regression

Full-featured regression analysis in a single function call. Vectrix supports R-style formula syntax (y ~ x1 + x2), automatic diagnostics (heteroscedasticity, normality, multicollinearity), multiple methods (OLS, Ridge, Lasso, Robust), and prediction intervals — without leaving the Python ecosystem.

Direct Input

The simplest form: pass y and X directly as numpy arrays. Vectrix runs OLS by default with automatic constant term

import numpy as np
from vectrix import regress

np.random.seed(42)
X = np.random.randn(100, 2)
y = 3 + 2 * X[:, 0] - 1.5 * X[:, 1] + np.random.randn(100) * 0.5

model = regress(y=y, X=X)

Expected output:

=== Regression Summary ===
Method: OLS
Observations: 100
R-squared: 0.954
Adj. R-squared: 0.953
F-statistic: 1012.35 (p < 0.001)

              Coef    Std.Err    t-value    P>|t|
Intercept    3.012      0.050     60.24    0.000 ***
x1           1.987      0.052     38.21    0.000 ***
x2          -1.493      0.048    -31.10    0.000 ***

Formula Mode

With a DataFrame, use R-style formulas for a more natural interface

import pandas as pd
from vectrix import regress

df = pd.DataFrame({
    "sales": [100, 150, 200, 180, 250, 300, 280, 350, 400, 380],
    "ads": [10, 15, 20, 18, 25, 30, 28, 35, 40, 38],
    "price": [50, 48, 45, 47, 42, 40, 41, 38, 35, 36],
    "promo": [0, 0, 1, 0, 1, 1, 0, 1, 1, 1],
})

model = regress(data=df, formula="sales ~ ads + price + promo")

Formula Syntax

regress(data=df, formula="y ~ x1 + x2")       # Specific variables
regress(data=df, formula="y ~ .")              # All other columns
regress(data=df, formula="y ~ x1 * x2")       # With interaction term
regress(data=df, formula="y ~ x + I(x**2)")   # Polynomial terms

Result Object

The EasyRegressionResult provides direct access to all regression statistics

print(f"R-squared: {model.r_squared:.4f}")
print(f"Adj. R-squared: {model.adj_r_squared:.4f}")
print(f"F-statistic: {model.f_stat:.2f}")
print(f"Coefficients: {model.coefficients}")
print(f"P-values: {model.pvalues}")

Result Reference

Diagnostics

The diagnose() method runs four standard regression diagnostic tests

print(model.diagnose())

Expected output:

=== Regression Diagnostics ===

1. Multicollinearity (VIF):
   ads:    2.31 (OK)
   price:  2.18 (OK)
   promo:  1.45 (OK)

2. Heteroscedasticity (Breusch-Pagan):
   LM stat: 3.42, p-value: 0.331
   Result: No heteroscedasticity detected

3. Normality (Jarque-Bera):
   JB stat: 1.87, p-value: 0.393
   Result: Residuals appear normally distributed

4. Autocorrelation (Durbin-Watson):
   DW stat: 2.05
   Result: No significant autocorrelation

Diagnostic Tests

Prediction with Intervals

Generate predictions with confidence intervals for new data

import pandas as pd

new_data = pd.DataFrame({
    "ads": [50, 75, 100],
    "price": [30, 25, 20],
    "promo": [1, 1, 0],
})

predictions = model.predict(new_data)
print(predictions)

Expected output:

   prediction   lower95   upper95
0      425.3     380.1     470.5
1      530.7     478.2     583.2
2      610.2     550.8     669.6

Regression Methods

Vectrix supports five regression methods. Switch by setting the method parameter

from vectrix import regress

ols_model    = regress(data=df, formula="sales ~ ads + price", method="ols")
ridge_model  = regress(data=df, formula="sales ~ ads + price", method="ridge")
lasso_model  = regress(data=df, formula="sales ~ ads + price", method="lasso")
huber_model  = regress(data=df, formula="sales ~ ads + price", method="huber")
quant_model  = regress(data=df, formula="sales ~ ads + price", method="quantile")

Method Comparison

When to Use Each Method

OLS (default) — Use when your data is well-behaved: no extreme outliers, no highly correlated predictors, and residuals are roughly normal.

Ridge — Use when you have correlated predictors (e.g., temperature and humidity, GDP and employment). Ridge keeps all variables but shrinks their coefficients.

Lasso — Use when you suspect some predictors are irrelevant. Lasso can drive coefficients to exactly zero, effectively performing variable selection.

Huber — Use when your data contains outliers. Huber uses a hybrid loss function that behaves like OLS for small errors but is robust to large errors.

Quantile — Use when you want to predict the median rather than the mean, or when your data is heavily skewed.

Suppress Auto-Print

By default, regress() prints the summary automatically. To suppress this

model = regress(data=df, formula="sales ~ ads + price", summary=False)

Complete Example

import pandas as pd
import numpy as np
from vectrix import regress

np.random.seed(42)
n = 200
df = pd.DataFrame({
    "revenue": np.random.randn(n) * 50 + 500,
    "marketing": np.random.randn(n) * 10 + 50,
    "price": np.random.randn(n) * 5 + 30,
    "season": np.random.choice([0, 1], n),
})
df["revenue"] = 100 + 8 * df["marketing"] - 5 * df["price"] + 20 * df["season"] + np.random.randn(n) * 10

model = regress(data=df, formula="revenue ~ marketing + price + season")
print(model.diagnose())

future = pd.DataFrame({
    "marketing": [60, 70, 80],
    "price": [28, 25, 22],
    "season": [1, 0, 1],
})
print()
print("Predictions:")
print(model.predict(future))