Multiple Linear Regression to Explain Systolic Blood Pressure in Hypertensive Patients from Body Mass Index and Age

Project info

• Field of studyMedicine and Clinical Data
• LevelUndergraduate thesis (S1)
• Method typeRegression
• Estimated build time± 3 working days
• Toolsscikit-learn LinearRegression, train_test_split, metrics; scipy.stats.shapiro
• PriceUS$16 - US$106

Research goal

Model systolic blood pressure from body mass index and age with multiple linear regression and assess the coefficients and R-squared.

Variables

Example result

• 0.808R2 (test)
• 0.806Adjusted R2 (train)
• 8.01RMSE (test)
• 6.489MAE (test)
• <0.001F-test p-value
• 4.082Coef. Body mass index

Multiple linear regression explains 80.8% of the variance in Systolic blood pressure on the test set (R2 0.808, RMSE 8.010); the Body mass index coefficient is 4.082 and the F-test gives p < 0.001.

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

About Multiple Linear Regression

Multiple linear regression models the linear relationship between one numeric response and several predictors. It suits theses that need to explain the effect of each predictor and also predict the response.

Steps

1. 1Fit the model with ordinary least squares after cleaning data and defining the response and predictors
2. 2Split the data into training and test sets
3. 3Train the model
4. 4Evaluate with R2 and RMSE on the test set
5. 5Check residuals (normality, constant variance)
6. 6Interpret the coefficients and plot actual versus predicted

Assumptions to check

• Relationship between predictors and response is linear
• Residuals are normal with constant variance
• Predictors are not highly collinear (check VIF)

Reading and reporting the results

Report the coefficients, their signs and magnitudes, then R2 and test RMSE. Discuss whether residual assumptions hold and the limits of generalisation.

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
import scipy.stats as st
from sklearn.linear_model import LinearRegression
from sklearn.model_selection import train_test_split
from sklearn.metrics import r2_score, mean_squared_error

rng = np.random.default_rng(42)
n = 200
body_mass_index = rng.normal(50, 10, n)
age = rng.normal(20, 5, n)
systolic_blood_pressure = 5 + 0.8 * body_mass_index - 1.2 * age + rng.normal(0, 4, n)

X = np.column_stack([body_mass_index, age])
X_tr, X_te, y_tr, y_te = train_test_split(X, systolic_blood_pressure, test_size=0.2, random_state=42)
model = LinearRegression().fit(X_tr, y_tr)
pred = model.predict(X_te)
resid = y_te - pred

print("Intercept:", round(model.intercept_, 3), "Coef:", model.coef_.round(3))
print("R2:", round(r2_score(y_te, pred), 3))
print("RMSE:", round(mean_squared_error(y_te, pred) ** 0.5, 3))
print("Shapiro p (residuals):", round(st.shapiro(resid).pvalue, 3))

fig, ax = plt.subplots(1, 2, figsize=(10, 4))
ax[0].scatter(y_te, pred)
ax[0].plot([y_te.min(), y_te.max()], [y_te.min(), y_te.max()], "r--")
ax[0].set_xlabel("Actual"); ax[0].set_ylabel("Predicted")
ax[1].scatter(pred, resid)
ax[1].axhline(0, color="r")
ax[1].set_xlabel("Predicted"); ax[1].set_ylabel("Residual")
plt.tight_layout()
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