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Regression Analysis in R Studio Using Agricultural Dataset
Abhishek Thakur
2026-05-20
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 |
Creating Agricultural Dataset
cropdata <- data.frame(
fertilizer = c(40,42,38,50,45,47,43,39,41,44,
46,48,37,36,49,51,52,53,35,34,
55,56,57,58,59,60,61,62,63,64,
65,66,67,68,69,70,71,72,73,74),
rainfall = c(820,790,760,880,850,840,810,770,800,830,
860,870,750,740,890,900,910,920,730,720,
930,940,950,960,970,980,990,1000,1010,1020,
1030,1040,1050,1060,1070,1080,1090,1100,1110,1120),
irrigation = c(12,13,11,15,14,14,13,12,13,14,
15,15,11,10,16,16,17,17,10,9,
18,18,19,19,20,20,21,21,22,22,
23,23,24,24,25,25,26,26,27,27),
yield = c(28,30,26,36,33,34,31,27,29,32,
35,36,25,24,38,39,40,41,23,22,
42,43,44,45,46,47,48,49,50,51,
52,53,54,55,56,57,58,59,60,61)
)
cropdata## fertilizer rainfall irrigation yield
## 1 40 820 12 28
## 2 42 790 13 30
## 3 38 760 11 26
## 4 50 880 15 36
## 5 45 850 14 33
## 6 47 840 14 34
## 7 43 810 13 31
## 8 39 770 12 27
## 9 41 800 13 29
## 10 44 830 14 32
## 11 46 860 15 35
## 12 48 870 15 36
## 13 37 750 11 25
## 14 36 740 10 24
## 15 49 890 16 38
## 16 51 900 16 39
## 17 52 910 17 40
## 18 53 920 17 41
## 19 35 730 10 23
## 20 34 720 9 22
## 21 55 930 18 42
## 22 56 940 18 43
## 23 57 950 19 44
## 24 58 960 19 45
## 25 59 970 20 46
## 26 60 980 20 47
## 27 61 990 21 48
## 28 62 1000 21 49
## 29 63 1010 22 50
## 30 64 1020 22 51
## 31 65 1030 23 52
## 32 66 1040 23 53
## 33 67 1050 24 54
## 34 68 1060 24 55
## 35 69 1070 25 56
## 36 70 1080 25 57
## 37 71 1090 26 58
## 38 72 1100 26 59
## 39 73 1110 27 60
## 40 74 1120 27 61Structure of Dataset
str(cropdata)## 'data.frame': 40 obs. of 4 variables:
## $ fertilizer: num 40 42 38 50 45 47 43 39 41 44 ...
## $ rainfall : num 820 790 760 880 850 840 810 770 800 830 ...
## $ irrigation: num 12 13 11 15 14 14 13 12 13 14 ...
## $ yield : num 28 30 26 36 33 34 31 27 29 32 ...Summary Statistics
summary(cropdata)## fertilizer rainfall irrigation yield
## Min. :34.00 Min. : 720.0 Min. : 9.00 Min. :22.00
## 1st Qu.:43.75 1st Qu.: 827.5 1st Qu.:13.75 1st Qu.:31.75
## Median :54.00 Median : 925.0 Median :17.50 Median :41.50
## Mean :54.00 Mean : 923.5 Mean :17.93 Mean :41.48
## 3rd Qu.:64.25 3rd Qu.:1022.5 3rd Qu.:22.25 3rd Qu.:51.25
## Max. :74.00 Max. :1120.0 Max. :27.00 Max. :61.00Scatter Plot
plot(cropdata$fertilizer,
cropdata$yield,
main = "Effect of Fertilizer on Crop Yield",
xlab = "Fertilizer (kg/ha)",
ylab = "Crop Yield (quintal/ha)",
pch = 19)
abline(lm(yield ~ fertilizer, data = cropdata),
col = "blue",
lwd = 2)
Multiple Regression Analysis
Fitting Regression Model
model <- lm(yield ~ fertilizer + rainfall + irrigation,
data = cropdata)
model##
## Call:
## lm(formula = yield ~ fertilizer + rainfall + irrigation, data = cropdata)
##
## Coefficients:
## (Intercept) fertilizer rainfall irrigation
## -17.47294 0.53455 0.02395 0.44444Regression Summary
summary(model)##
## Call:
## lm(formula = yield ~ fertilizer + rainfall + irrigation, data = cropdata)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.99510 -0.15986 0.03119 0.08189 0.85553
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -17.472943 2.864455 -6.100 5.11e-07 ***
## fertilizer 0.534548 0.077066 6.936 3.98e-08 ***
## rainfall 0.023948 0.006697 3.576 0.001018 **
## irrigation 0.444435 0.122672 3.623 0.000891 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3532 on 36 degrees of freedom
## Multiple R-squared: 0.9992, Adjusted R-squared: 0.9991
## F-statistic: 1.425e+04 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 5331.5 5331.5 42728.315 < 2.2e-16 ***
## rainfall 1 2.3 2.3 18.496 0.0001242 ***
## irrigation 1 1.6 1.6 13.126 0.0008912 ***
## Residuals 36 4.5 0.1
## ---
## 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.
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
Saving Graphs
Graphs can be exported from the Plots window using:
- Export
- Save as Image
- Choose format:
- PNG
- JPEG
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/