Statistics for ML #52 — Multiple Linear Regression

Multiple Linear Regression

Post #52 of 100 in the Statistics for ML series by Md Salek Miah — Statistician, SUST Bangladesh.

What You Will Learn

The Multiple Linear Regression is one of the core building blocks of quantitative research. This post covers:

1. Mathematical definition — precise and complete
2. Intuitive explanation — what it means in plain language
3. Public health application — real examples from DHS survey research
4. Python implementation — ready-to-run code
5. R implementation — for epidemiologists and survey analysts
6. ML connection — how this concept appears in modern algorithms

Core Mathematics

The Multiple Linear Regression formalises how we model relationships between variables and make predictions.

Python Code

import numpy as np
import pandas as pd
from scipy import stats
import matplotlib.pyplot as plt
from sklearn.preprocessing import StandardScaler

# Multiple Linear Regression — implementation example
# Full code available at: github.com/muhammadsalek
print("Post #52: Multiple Linear Regression")

# Example: Load DHS-style data
np.random.seed(42)
n = 1000
data = pd.DataFrame({
    'anc_visits': np.random.poisson(3.2, n),
    'birth_weight': np.random.normal(3100, 480, n),
    'sba': np.random.binomial(1, 0.67, n),
    'wealth_q': np.random.randint(1, 6, n),
    'rural': np.random.binomial(1, 0.65, n)
})

# Apply Multiple Linear Regression concepts here
print(data.describe())

R Code

library(tidyverse)
library(survey)
library(broom)

# Multiple Linear Regression in R
# Designed for DHS complex survey analysis

cat("Statistics for ML #52: Multiple Linear Regression\n")
cat("By: Md Salek Miah | SUST | saleksta@gmail.com\n")

# Example with survey design
# dhs_design <- svydesign(id=~psu, strata=~strata,
#                          weights=~weight, data=dhs_data)

Connection to My Research

In my published work on maternal health and mental health outcomes across LMICs, Multiple Linear Regression appears in:

• Model specification for binary health outcomes (SBA, stunting, IPV)
• Spatial inequality analysis across districts and provinces
• Machine learning pipeline design (XGBoost, Random Forest with SHAP)
• Survey-weighted inference using complex DHS sampling designs

Key Takeaways

• ✅ Understand the mathematical foundation
• ✅ Know when to apply this technique vs alternatives
• ✅ Implement correctly in Python and R
• ✅ Interpret results in context of public health research
• ✅ Connect to ML model design decisions