Decoding Regression Models in Biostatistics: A Simple Guide

In biology and medical research, we often ask questions like:
Does age affect body weight?
Can a specific diet improve growth in animals?
Is there a link between exposure to a chemical and disease risk?

To answer these questions with numbers, we use a powerful statistical tool called regression analysis.

Regression is a way to explore the relationship between two or more variables. For example, if we want to understand how body weight changes with age, we can use linear regression to draw a line through data points that best explains this trend. It helps us predict outcomes, identify patterns, and make sense of complex data.

In biostatistics, regression is everywhere. Whether you’re working with plants, animals, microbes, or human health data, regression models can help uncover relationships between genetics, environment, treatment, or behavior.

There are different types of regression:

• Simple linear regression looks at one predictor (e.g., age).
• Multiple regression uses several predictors (e.g., age + diet + treatment).
• Generalized linear models (GLM) handle special types of outcomes, like disease status (yes/no) or counts.
• Mixed models account for repeated measurements or individual variation (like measuring the same hen multiple times).

The best part? You don’t need to be a mathematician to use these tools. With user-friendly software like R, biologists can run regression models and interpret results with just a few lines of code.

So whether you’re studying chickens, crops, or clinical trials — regression is your friend when it comes to understanding biological patterns and making data-driven decisions.

Simple Linear Regression

Imagine you’re studying how the body weight of a hen is influenced by different factors like how many hours she spends outside, what kind of feed she gets, or how old she is. One way to explore this is through a method called linear regression.

Think of it like drawing a straight line through your data points to summarize the relationship between two things: one predictor (also called independent variable, like age) and one outcome (also called dependent variable, like weight). If the line slopes upward, it means as the hen gets older, her weight tends to increase; if it slopes downward, it means the opposite. The goal of linear regression is to find the best-fitting line that describes how changes in one variable are related to changes in another. It’s very basic but powerful for simple relationships.

# Base R (no package needed)
#lm function used = Fits a linear regression model to your data. It's used when you want to predict a numeric outcome (like hen weight) from one or more predictors (like age, feed type).

data <- data.frame(
  Weight = c(1.2, 1.5, 1.6, 1.9, 2.0),
  Age = c(10, 12, 14, 16, 18)  # in weeks
)

model1 <- lm(Weight ~ Age, data = data)
summary(model1)

Multiple Regression

What if you want to consider more than one factor at the same time? That’s where multiple regression comes in. It’s just like linear regression, but now you’re drawing a line in more dimensions — for example, considering age, outdoor activity, and feed type all together to predict body weight. This helps you understand which variables matter most when others are controlled for. You can ask questions like, “Does feed type still affect weight after I account for the hen’s age?” Multiple regression helps disentangle complex biological influences that don’t act in isolation.

# FeedType is a categorical variable here
data$FeedType <- as.factor(c("A", "A", "B", "B", "C"))

model2 <- lm(Weight ~ Age + FeedType, data = data)
summary(model2)

General Linear Regression

Sometimes you deal with data that’s not just numbers, but categories — like different treatment groups or breeds. This is where the general linear model (GLM) is useful. It’s a flexible extension of the simple linear models that allows you to include both numeric and categorical variables.

For example, you might compare the weight of hens across three types of feed while still adjusting for age. The GLM handles this by translating categories into numbers behind the scenes so you can still model the outcome using linear methods. It’s a broader framework that includes both simple and multiple regressions.

# GLM with binary outcome (logistic regression)
#glm function Fits models where the outcome is not necessarily continuous — like binary (yes/no), counts, or proportions. Very useful for logistic regression (e.g., disease = yes/no).

data$Overweight <- c(0, 0, 0, 1, 1)

model3 <- glm(Overweight ~ Age + FeedType, data = data, family = binomial)
summary(model3)

Linear Mixed Models

In real biological studies, you often have grouped or repeated measures — like measuring the same hens over multiple days, or having hens nested within different farms or cages. This kind of structure breaks the assumption that every data point is totally independent, which is important in basic regression. Linear mixed models (LMMs) handle this by allowing some parts of the model to vary depending on the group. For instance, each hen might have her own baseline behavior, but you’re still interested in overall trends across all hens. These models include both fixed effects (variables you care about and are trying to estimate precisely, like feed type or treatment) and random effects (variables that introduce natural variation, like individual hen identity or cage).

# Install lme4 if not already installed
#Fits mixed models where you have both: Fixed effects (like treatment, feed type ) Random effects (like hen ID, cage number)

install.packages("lme4")
library(lme4)

# Example dataset with repeated measurements per hen
data_mixed <- data.frame(
  Weight = c(1.2, 1.3, 1.4, 1.5, 1.6, 1.7),
  Age = c(10, 12, 10, 12, 10, 12),
  FeedType = as.factor(c("A", "A", "B", "B", "C", "C")),
  HenID = as.factor(c("Hen1", "Hen1", "Hen2", "Hen2", "Hen3", "Hen3"))
)

# HenID is a random effect
model4 <- lmer(Weight ~ Age + FeedType + (1 | HenID), data = data_mixed)
summary(model4)

#1 | HenID is random effect here 

So what’s the difference between fixed and random effects?

In summary: fixed effects = what you want to study; random effects = where variation is coming from but you’re not directly analyzing it.

Limitations of Regression Models in Biology

Linear models such as linear regression, multiple regression, general linear models (GLMs), and linear mixed models (LMMs) are powerful tools that are widely used in biology. They help researchers explore relationships between variables, make predictions, and control for confounding effects. However, like all statistical models, they come with important limitations, especially when applied to complex biological systems.

Also learn to overcome challenges in data analysis in biology

Biological Relationships Are Rarely Truly Linear

One of the biggest assumptions of linear regression and related models is that the relationship between variables is linear — that is, a straight line fits the data well. But in biology, many relationships are nonlinear. For example:

• The effect of temperature on enzyme activity shows a bell-shaped curve.
• Weight gain may plateau after a certain age.
• Dose-response relationships often follow a logarithmic or sigmoidal curve.

If you use a linear model in such cases, it may give misleading results because it cannot capture these curves. You can sometimes fix this by transforming variables (e.g., using log()), but you must recognize when linearity doesn’t hold.

Collinearity Among Predictors (In Multiple Regression)

In multiple regression, you may include several predictors (e.g., age, feed type, activity level). But if some of them are strongly correlated with each other (a situation called multicollinearity), it becomes hard to separate their individual effects.

For example, if older hens are more likely to receive a specific feed, then age and feed type are correlated. Your model might struggle to tell which one actually affects weight. This leads to unstable estimates and inflated standard errors, reducing the reliability of your conclusions.

Small Sample Sizes and Overfitting

Biological studies often involve limited sample sizes due to ethical, logistical, or financial constraints. Linear models require a sufficient number of observations per predictor to produce stable and reliable estimates.

If you include too many variables in your model compared to your sample size, you risk overfitting — the model fits your current dataset well but won’t generalize to new data. This is especially problematic in genetic studies, where the number of SNPs or genes may far exceed the number of animals.

Categorical Variables and Reference Bias

When using categorical predictors (e.g., breed, treatment group), linear models automatically set one category as the reference level. The estimated effects of other levels are compared to this reference, which may bias interpretation if not chosen thoughtfully.

Also, if a category has very few observations, the model may not estimate its effect accurately. This can happen in field studies where some treatments or conditions are rare.

Violation of Assumptions

All these models rely on several key assumptions:

• Linearity: relationship is linear.
• Normality of residuals: model errors follow a normal distribution.
• Homoscedasticity: constant variance of residuals across levels of predictors.
• Independence: observations are independent.

Violating these assumptions reduces the validity of the model results. For example, if the residuals are not normally distributed, your p-values and confidence intervals may not be trustworthy. These assumptions must be tested (e.g., with residual plots or statistical tests) and dealt with accordingly — often through variable transformation, model change, or robust alternatives.

Biological Meaning vs. Statistical Significance

It’s possible for a linear model to produce statistically significant results that lack biological meaning. For example, you might find that “treatment A increases weight by 2.3g with p < 0.001”, but that difference could be biologically irrelevant.

Linear models are good at detecting small differences, especially with large datasets, but researchers must always ask whether those differences matter in the biological context.

Limited Flexibility for Complex Biological Processe

Biological systems are often dynamic, hierarchical, and interactive, with feedback loops, gene-environment interactions, and nonlinear growth. Linear models may not be flexible enough to capture this complexity.

In such cases, you might need more advanced approaches like:

• Generalized additive models (GAMs) for nonlinear trends
• Bayesian models for hierarchical uncertainty
• Machine learning models for interaction-heavy data (with caution)

Ready to dive deeper into the world of biostatistics without getting lost in technical jargon? Our website is your go-to hub for mastering the latest tools, from basic regression models to advanced machine learning — all explained in a way that biologists, students, and life science researchers can easily understand. Whether you want to analyze experiments, improve your data skills, or keep up with cutting-edge techniques like R, mixed models, GWAS, or DESeq2, we’ve got you covered. So don’t stop here — explore our tutorials, guides, and real-world examples and take your research skills to the next level!