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Regression Analysis in R Studio Using Agricultural Dataset
R Codes for Regression Analysis
2026-05-22
N. Uttam Singh¹
Abhishek Thakur¹*
Eric Rani¹
¹ICAR Research Complex for NEH Region
Umiam, Meghalaya
Introduction
Regression analysis is one of the most widely used statistical techniques in agricultural research. It is used to study the relationship between crop yield and various influencing factors such as fertilizer application, rainfall, irrigation, temperature, and soil nutrients.
Multiple regression analysis helps quantify these relationships and enables prediction of crop yield under varying conditions.
R Studio provides an efficient and user-friendly environment for performing regression analysis, graphical visualization, and statistical interpretation.
Objectives
The objectives of this practical tutorial are:
- To understand the concept of multiple regression analysis
- To create and manage agricultural datasets in RStudio
- To fit a multiple linear regression model
- To interpret regression coefficients and statistical output
- To generate regression plots and diagnostic plots
Software Requirements
| Software | Purpose |
|---|---|
| R Software | Statistical Computing |
| RStudio | Integrated Development Environment |
Recommended Versions
- R version 4.0 or above
- Latest version of RStudio
Introduction to R and RStudio
R is an open-source programming language widely used for statistical analysis, data visualization, and predictive modelling.
RStudio is an Integrated Development Environment (IDE) for R.
Agricultural Dataset Description
In this tutorial, a hypothetical agricultural dataset is used to study the effect of:
- Fertilizer application
- Rainfall
- Irrigation
on crop yield.
Variables Used
| Variable | Description | Unit |
|---|---|---|
| fertilizer | Amount of fertilizer applied | kg/ha |
| rainfall | Seasonal rainfall received | mm |
| irrigation | Irrigation hours supplied | hours |
| yield | Crop yield | quintal/ha |
Library Required Packages
library(readxl)
library(ggplot2)
library(dplyr)
library(knitr)
library(car)
library(lmtest)Import Data
Datanew <- read_excel("cropdataregress.xlsx")
head(Datanew)## # A tibble: 6 × 4
## fertilizer rainfall irrigation yield
## <dbl> <dbl> <dbl> <dbl>
## 1 40 820 12 28
## 2 42 790 13 30
## 3 38 760 11 26
## 4 50 880 15 36
## 5 55 910 16 40
## 6 48 850 14 34Structure of Dataset
str(Datanew)## tibble [40 × 4] (S3: tbl_df/tbl/data.frame)
## $ fertilizer: num [1:40] 40 42 38 50 55 48 60 62 45 52 ...
## $ rainfall : num [1:40] 820 790 760 880 910 850 940 960 810 900 ...
## $ irrigation: num [1:40] 12 13 11 15 16 14 17 18 13 15 ...
## $ yield : num [1:40] 28 30 26 36 40 34 44 46 31 38 ...Summary Statistics
summary(Datanew)## fertilizer rainfall irrigation yield
## Min. :38.00 Min. : 760.0 Min. :11.00 Min. :26.00
## 1st Qu.:45.75 1st Qu.: 827.5 1st Qu.:13.00 1st Qu.:31.75
## Median :53.50 Median : 897.5 Median :15.00 Median :38.50
## Mean :53.35 Mean : 889.6 Mean :15.40 Mean :38.40
## 3rd Qu.:60.25 3rd Qu.: 942.5 3rd Qu.:17.25 3rd Qu.:44.25
## Max. :69.00 Max. :1010.0 Max. :20.00 Max. :52.00Scatter Plot
plot(Datanew$fertilizer,
Datanew$yield,
main = "Effect of Fertilizer on Crop Yield",
xlab = "Fertilizer (kg/ha)",
ylab = "Crop Yield (quintal/ha)",
pch = 19)
abline(lm(yield ~ fertilizer, data = Datanew),
col = "blue",
lwd = 2)
Multiple Regression Analysis
Fitting Regression Model
model <- lm(yield ~ fertilizer + rainfall + irrigation,
data = Datanew)
model##
## Call:
## lm(formula = yield ~ fertilizer + rainfall + irrigation, data = Datanew)
##
## Coefficients:
## (Intercept) fertilizer rainfall irrigation
## -17.18765 0.50468 0.02209 0.58514Regression Summary
summary(model)##
## Call:
## lm(formula = yield ~ fertilizer + rainfall + irrigation, data = Datanew)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.99759 -0.24834 -0.02828 0.21340 0.93317
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -17.187649 3.386389 -5.076 1.19e-05 ***
## fertilizer 0.504680 0.069382 7.274 1.44e-08 ***
## rainfall 0.022090 0.007223 3.058 0.00418 **
## irrigation 0.585138 0.176587 3.314 0.00211 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3945 on 36 degrees of freedom
## Multiple R-squared: 0.9976, Adjusted R-squared: 0.9974
## F-statistic: 4913 on 3 and 36 DF, p-value: < 2.2e-16ANOVA Table
anova(model)## Analysis of Variance Table
##
## Response: yield
## Df Sum Sq Mean Sq F value Pr(>F)
## fertilizer 1 2290.04 2290.04 14714.42 < 2.2e-16 ***
## rainfall 1 2.25 2.25 14.43 0.0005402 ***
## irrigation 1 1.71 1.71 10.98 0.0021068 **
## Residuals 36 5.60 0.16
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Understanding Regression Output
Regression Coefficients
The coefficients indicate the effect of each independent variable on crop yield.
- Positive coefficient indicates increase in yield
- Negative coefficient indicates decrease in yield
p-value
Decision rule:
| p-value | Interpretation |
|---|---|
| p < 0.05 | Significant |
| p > 0.05 | Not Significant |
R-squared
R² measures the goodness of fit of the regression model.
| R² Value | Interpretation |
|---|---|
| Close to 1 | Good Fit |
| Close to 0 | Poor Fit |
Regression Diagnostics
par(mfrow=c(2,2))
plot(model)
The above command generates:
- Residual vs Fitted Plot
- Normal Q-Q Plot
- Scale-Location Plot
- Residuals vs Leverage Plot
Interpretation of Diagnostic Plots
Residual vs Fitted Plot
This plot checks:
- Linearity
- Constant variance
Random scatter of points indicates good model fit.
Normal Q-Q Plot
This plot checks normality of residuals.
Residuals should approximately follow a straight line.
Scale-Location Plot
This plot checks homoscedasticity.
Equal spread of residuals indicates constant variance.
Residuals vs Leverage Plot
This plot identifies influential observations and outliers.
Variance Inflation Factor (VIF)
Variance Inflation Factor (VIF) is used to detect multicollinearity among independent variables in a regression model.
car::vif(model)## fertilizer rainfall irrigation
## 97.83653 68.15842 54.81909Interpretation of VIF
- VIF < 5 indicates low multicollinearity
- VIF between 5 and 10 indicates moderate multicollinearity
- VIF > 10 indicates serious multicollinearity problem
Durbin-Watson Test
Durbin-Watson test is used to detect autocorrelation among residuals in regression analysis.
lmtest::dwtest(model)##
## Durbin-Watson test
##
## data: model
## DW = 1.617, p-value = 0.1078
## alternative hypothesis: true autocorrelation is greater than 0Interpretation of Durbin-Watson Test
- Value close to 2 indicates no autocorrelation
- Value less than 2 indicates positive autocorrelation
- Value greater than 2 indicates negative autocorrelation
Applications in Agriculture
Regression analysis has wide applications in agricultural sciences.
Major Applications
- Crop yield prediction
- Fertilizer recommendation studies
- Rainfall impact assessment
- Soil nutrient analysis
- Irrigation management
- Agricultural economic forecasting
- Pest and disease modelling
- Climate change impact studies
Conclusion
Multiple regression analysis is an important statistical tool for agricultural research and decision-making.
RStudio provides a powerful environment for:
- Data analysis
- Model fitting
- Graphical visualization
- Statistical interpretation
- Prediction modelling
The methods explained in this tutorial can be extended to advanced predictive agricultural analytics.
References
- Montgomery, D.C., Peck, E.A. and Vining, G.G. Introduction to Linear Regression Analysis.
- Kutner, M.H., Nachtsheim, C.J., Neter, J. and Li, W. Applied Linear Statistical Models.
- R Core Team. R: A Language and Environment for Statistical Computing.
- https://cran.r-project.org/
- https://posit.co/download/rstudio-desktop/