Ridge and Lasso Regression to Predict Soft Soil Settlement from Water Content and Embankment Load

Project info

• Field of studyCivil Engineering and Transportation
• LevelMaster's thesis (S2)
• Method typeRegression
• Estimated build time± 5 working days
• Toolsscikit-learn RidgeCV, LassoCV, StandardScaler, make_pipeline
• PriceUS$22 - US$144

Research goal

Model soil settlement from soil water content and embankment load using Ridge and Lasso Regression and evaluate the model performance.

Variables

Example result

• 0.942R2 Lasso (test)
• 0.941R2 Ridge (test)
• 0.251RMSE Lasso (std.)
• 0.006Best alpha
• 4Non-zero coefs
• 0.058CV MSE min

Lasso retains 4 of 6 predictors for Soil settlement at alpha 0.006 (test R2 0.942), while Ridge reaches R2 0.941.

Computed from illustrative synthetic data, not from a real study.

About Ridge and Lasso Regression

Ridge and Lasso are linear regressions with L2 and L1 penalties that control overfitting and collinearity. They are used when predictors are many or correlated, and Lasso also selects variables.

Steps

1. 1Standardise all predictors
2. 2Split into training and test sets
3. 3Choose the penalty alpha by cross-validation (RidgeCV, LassoCV)
4. 4Fit Ridge and Lasso at the chosen alpha
5. 5Compare RMSE and R2 with ordinary regression
6. 6Show the coefficients and the variables dropped by Lasso

Assumptions to check

• Predictors must be standardised before applying the penalty
• The relationship with the response is roughly linear
• Alpha is chosen on training data only to avoid leakage into the test set

Reading and reporting the results

Report the chosen alpha, test metrics, and the coefficients that shrink or become zero. Explain that coefficients are biased in exchange for lower variance, so they are not read like OLS.

Example Python code

A short starting script with this project's variable names. The delivered version is adapted to your data and fully commented.

import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import RidgeCV, LassoCV, LinearRegression
from sklearn.preprocessing import StandardScaler
from sklearn.pipeline import make_pipeline
from sklearn.model_selection import train_test_split
from sklearn.metrics import mean_squared_error

rng = np.random.default_rng(1)
n, p = 150, 10
X = rng.normal(size=(n, p))
X[:, 1] = X[:, 0] + rng.normal(0, 0.1, n)   # collinear pair
soil_water_content = X[:, 0]
embankment_load = X[:, 1]
soil_settlement = 3 * soil_water_content + 2 * X[:, 2] + rng.normal(0, 1, n)

X_tr, X_te, y_tr, y_te = train_test_split(X, soil_settlement, test_size=0.25, random_state=1)
models = {
    "OLS": make_pipeline(StandardScaler(), LinearRegression()),
    "Ridge": make_pipeline(StandardScaler(), RidgeCV(alphas=np.logspace(-3, 3, 30))),
    "Lasso": make_pipeline(StandardScaler(), LassoCV(cv=5, random_state=1)),
}
coefs = {}
for name, m in models.items():
    m.fit(X_tr, y_tr)
    rmse = mean_squared_error(y_te, m.predict(X_te)) ** 0.5
    coefs[name] = m[-1].coef_
    print(name, "RMSE:", round(rmse, 3))
print("Ridge alpha:", models["Ridge"][-1].alpha_)
print("Lasso alpha:", round(models["Lasso"][-1].alpha_, 4))
print("Lasso zero coefs:", int((coefs["Lasso"] == 0).sum()))

idx = np.arange(p)
for k, (name, c) in enumerate(coefs.items()):
    plt.bar(idx + 0.27 * k, c, width=0.27, label=name)
plt.xlabel("Feature"); plt.ylabel("Coefficient"); plt.legend()
plt.show()

Packages and prices

Choose how much help you need. Each higher package includes everything in the lower ones. Prices exclude 11% VAT.

• Payment: 50% down payment before work starts, balance after the deliverables are handed over
• Tax: Prices exclude 11% VAT
• Data and academic integrity: Results are computed from your own research data; you write and stand behind your manuscript, we help with the analysis and your understanding of it
• Revisions: Up to 2 revisions are included in the price (Package 3: 3 rounds)

Frequently asked questions