Ad Revenue Growth Prediction with Polynomial Regression in ML

Digital marketing teams need to forecast next-period ad revenue (USD) based on planning-stage metrics—channel mix, spend, impressions, clicks, and creative complexity—before campaigns launch or budgets are locked in. The relationship between spend and revenue growth is nonlinear: at low spend levels, you get diminishing returns, while at high spend, you may hit saturation or require bid adjustments. A pure linear model underfits these curves, whereas an unregularised high‑degree polynomial overfits. By deploying Polynomial Regression (i.e., linear regression on polynomially expanded features) with ℓ² regularisation (Ridge), we can capture smooth nonlinear effects and deliver reliable, interpretable revenue forecasts to guide budget allocation.

Dataset

Online Advertising Digital Marketing Data

Step-by-Step Code Implementation

1. Libraries Required

import pandas as pd                             # data handling  
import numpy as np                              # numerical operations  

import matplotlib.pyplot as plt                 # plotting  
import seaborn as sns                           # visualization enhancements  

from sklearn.model_selection import train_test_split, GridSearchCV  
from sklearn.preprocessing import PolynomialFeatures, StandardScaler  
from sklearn.linear_model import Ridge  
from sklearn.pipeline import Pipeline  
from sklearn.metrics import mean_squared_error, r2_score

2. Load Data & Libraries

import pandas as pd
import numpy as np

# Load dataset
df = pd.read_csv("data/online_advertising_digital_marketing_data.csv")

# Engineer revenue target
df['Revenue'] = df['Approved_Conversion'] * 100
df['Revenue_Growth'] = df['Revenue'].pct_change().fillna(0)  # growth rate as target

3. Exploratory Analysis

import seaborn as sns
import matplotlib.pyplot as plt

# Inspect nonlinear patterns between Spend and Revenue_Growth
sns.scatterplot(x='Spend', y='Revenue_Growth', data=df, alpha=0.3)
plt.title('Spend vs Growth Rate')
plt.xlabel('Spend (USD)')
plt.ylabel('Revenue Growth (%)')
plt.show()

4. Define Features & Target

# Features at planning stage
X = df[['Spend','Impressions','Clicks']]
y = df['Revenue_Growth']

5. Build Pipeline with PolynomialFeatures

• PolynomialFeatures expands raw spend, impressions, and clicks into their squares and interactions, capturing curved ROI dynamics (e.g., diminishing returns on spend).
• StandardScaler normalises all inputs so the Ridge penalty treats them uniformly.
• Ridge (ℓ²) regularisation shrinks noisy high‑order coefficients, preventing overfitting while preserving key nonlinear patterns.

from sklearn.pipeline import Pipeline
from sklearn.preprocessing import StandardScaler, PolynomialFeatures
from sklearn.linear_model import Ridge

pipe = Pipeline([
    ('scale', StandardScaler()),
    ('poly', PolynomialFeatures(include_bias=False)),
    ('ridge', Ridge())
])

6. Train/Test Split & Hyperparameter Search

GridSearchCV tunes the polynomial degree (1–3) and Ridge α (10⁻³–10³) with 5‑fold CV, optimising for the lowest RMSE on growth‐rate prediction.

from sklearn.model_selection import train_test_split, GridSearchCV

X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.2, random_state=42
)

param_grid = {
    'poly__degree': [1, 2, 3],
    'ridge__alpha': np.logspace(-3, 3, 7)
}

gs = GridSearchCV(
    pipe, param_grid,
    cv=5, scoring='neg_root_mean_squared_error',
    n_jobs=-1, verbose=1
)
gs.fit(X_train, y_train)
print("Best params:", gs.best_params_)

7. Evaluate Model

y_pred = gs.predict(X_test)
rmse = mean_squared_error(y_test, y_pred, squared=False)
r2   = r2_score(y_test, y_pred)

print(f"Test RMSE: {rmse:.4f}")
print(f"Test R²  : {r2:.3f}")

8. Inspect Key Polynomial Coefficients

Coefficient inspection reveals which terms—like Spend², Spend × Clicks, or Clicks²—most strongly drive predicted revenue growth, highlighting areas for spend reallocation or creative focus.

# Feature names
poly = gs.best_estimator_.named_steps['poly']
feat_names = poly.get_feature_names_out(input_features=['Spend','Impressions','Clicks'])

# Coefficients
coefs = gs.best_estimator_.named_steps['ridge'].coef_
coeff_df = pd.Series(coefs, index=feat_names).abs().sort_values(ascending=False)

# Plot top 10
coeff_df.head(10).plot(kind='barh', figsize=(8,5))
plt.gca().invert_yaxis()
plt.title('Top Polynomial Features for Revenue Growth')
plt.xlabel('|Coefficient|')
plt.tight_layout()
plt.show()

Summary

By integrating polynomial feature engineering with Ridge regularisation in a single pipeline, we deliver a model that:

• Accurately predicts revenue growth rate from pre‐launch metrics (low RMSE, strong R²).
• Captures nonlinear campaign dynamics—diminishing returns, synergy effects—without overfitting.
• Provides interpretable insights: the most influential polynomial terms point to optimal spend levels and engagement metrics for maximizing return on ad investments.