Linear Regression in Agricultural Science Using R: A Complete Step-by-Step Guide

This article teaches how to apply linear regression in R to analyze and interpret the relationship between agricultural inputs like fertilizer and outcomes like crop yield, equipping readers with practical skills for data-driven decision-making in farming and agronomic research.

Introduction

Agricultural science has become increasingly data-driven, with farmers, agronomists, and researchers using statistical models to better understand the factors influencing crop productivity. Among these models, linear regression is a fundamental technique used to evaluate the relationship between one or more predictor variables and an outcome variable.

This guide provides a hands-on walkthrough of applying linear regression in R, a powerful statistical programming language. We'll use an agricultural example — modeling wheat yield as a function of fertilizer application — to demonstrate how linear regression can guide informed decisions in farming and research.

By the end of this article, you'll be able to:

• Build and interpret a linear regression model in R

• Evaluate model assumptions and performance

• Make predictions and derive actionable insights

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Understanding Linear Regression in Agricultural Applications

What Is Linear Regression?

Linear regression is a statistical technique used to model the relationship between a dependent variable (response) and one or more independent variables (predictors). In simple linear regression, there's one independent variable:

Y=β0+β1X+εY=β0+β1X+ε

Where:

• ( Y ) = Dependent variable (e.g., crop yield)

• ( X ) = Independent variable (e.g., fertilizer)

• ( \beta_0 ) = Intercept

• ( \beta_1 ) = Slope

• ( \varepsilon ) = Random error

Why Use Linear Regression in Agriculture?

Some common applications include:

• Predicting crop yield based on inputs like fertilizer or irrigation

• Analyzing the impact of weather on growth

• Estimating soil response to amendments

• Guiding input optimization strategies

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Defining the Agricultural Problem

In this guide, we’ll explore a real-world scenario:

Research Question:

How does the quantity of fertilizer applied (kg/ha) affect wheat yield (tonnes/ha)?

Variables:

• Independent Variable (X): Fertilizer applied

• Dependent Variable (Y): Wheat yield

Our objective is to fit a regression model that helps us quantify this relationship and use it to predict future yield outcomes.

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Creating and Exploring the Dataset in R

Step 1: Load Required Libraries

# Load necessary packages
library(ggplot2)
library(dplyr)
library(broom)

Step 2: Generate the Dataset

We simulate data for 100 wheat plots. Fertilizer levels vary between 50 and 150 kg/ha, and yield increases with fertilizer plus some random variation.

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