LOESS Plot (Locally Weighted Scatterplot Smoothing)

Purpose

Fit a smooth non-parametric curve to data to reveal underlying trends and patterns without assuming a specific functional form.

Analysis Type

Bivariate

What to Look For

1. Linearity

• Linear: LOESS will produce a straight line in the plot.
• Non-Linear: Curved or oscillating LOESS lines indicate non-linear relationships.
• Shows true trend without forcing linearity

2. Trend Direction

• Increasing: Positive relationship
• Decreasing: Negative relationship
• Flat: No relationship
• Changing: Relationship varies across range

3. Local Behavior

• How relationship changes in different regions
• Identifies thresholds or breakpoints
• Shows where relationship strengthens or weakens

4. Linearity Assessment

• Linear: (can use linear regression)
  • The LOESS line is almost straight (or close enough that a straight line would match it well).
• Non-Linear: (need polynomial features or transformations)
  • LOESS clearly bends: changes slope, flattens out, turns around, or forms S/U-shapes.
  • The curve shows regions with different behavior (e.g., flat then steep) = classic non-linearity.
  • Even a slight "bow" in the LOESS line is a signal that the relationship isn't perfectly linear.

5. Outlier Impact

• LOWESS is robust to outliers
• Points far from curve are outliers
• Curve shows trend ignoring outliers

Code Example

import statsmodels.api as sm

# Scatter plot with LOWESS curve
x = df['x_variable']
y = df['y_variable']

# Calculate LOWESS
lowess_result = sm.nonparametric.lowess(y, x, frac=0.3)

# Plot
plt.scatter(x, y, alpha=0.5, label='Data')
plt.plot(lowess_result[:, 0], lowess_result[:, 1], color='red', linewidth=2, label='LOWESS')
plt.title("LOWESS Smoothing")
plt.xlabel("X Variable")
plt.ylabel("Y Variable")
plt.legend()
plt.show()

# Seaborn version (easier)
sns.regplot(x='x_variable', y='y_variable', data=df, 
            lowess=True, scatter_kws={'alpha':0.5},
            line_kws={'color':'red', 'linewidth':2})
plt.title("Scatter Plot with LOWESS Curve")
plt.show()