📘 How to Know if Your Data is Linear, Non-Linear, or Complex

Knowing whether your data is linear, non-linear, or complex helps you choose the right model (like Random Forests for non-linear patterns). Here’s a simple guide:

✅ 1. Visual Inspection

Scatter Plots: Plot your features against the target.

If points form a straight line → likely linear.
If points curve or twist → non-linear.
For multiple features, use pair plots or heatmaps.

Example:

import seaborn as sns
sns.pairplot(df)  # df = your dataset

✅ 2. Correlation Analysis

Compute Pearson correlation for linear relationships.
High correlation (close to ±1) → linear.
Low correlation but still predictive → possibly non-linear.

Code:

df.corr()

✅ 3. Fit a Simple Linear Model

Train a Linear Regression model.
Check R² score:

High R² → data fits linear model well.
Low R² → likely non-linear or complex.

Code:

from sklearn.linear_model import LinearRegression
model = LinearRegression().fit(X, y)
print("R²:", model.score(X, y))

✅ 4. Residual Analysis

Plot residuals (errors) from a linear model.
If residuals show patterns → data is non-linear.

Code:

import matplotlib.pyplot as plt
residuals = y - model.predict(X)
plt.scatter(model.predict(X), residuals)
plt.axhline(0, color='red')

✅ 5. Complexity Indicators
High dimensionality (many features).
Interactions between features.
Non-monotonic patterns (zig-zag relationships).
Use polynomial features or tree-based models to test.

✅ 6. Use Non-Linear Models for Comparison
Train a Random Forest or Decision Tree.
If performance improves significantly over linear regression → data is non-linear.

🔍 Quick Rule of Thumb
Linear: Straight-line relationships, simple patterns.
Non-linear: Curves, interactions, diminishing returns.
Complex: Many features, mixed patterns, noise.

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