1. Graphical Analysis in R

We’ll use a dummy dataset of student performance:

students <- data.frame(
  Name = c("A","B","C","D","E","F","G","H"),
  Hours_Studied = c(2,4,6,8,10,12,14,16),
  Marks = c(50,55,60,68,72,80,85,90),
  Gender = c("M","F","M","F","M","F","M","F")
)
students

Output:

  Name Hours_Studied Marks Gender
1    A             2    50      M
2    B             4    55      F
3    C             6    60      M
4    D             8    68      F
5    E            10    72      M
6    F            12    80      F
7    G            14    85      M
8    H            16    90      F

1.1 Basic Plotting

plot(students$Hours_Studied, students$Marks, 
     type="b", col="blue", pch=19,
     main="Hours Studied vs Marks",
     xlab="Hours Studied", ylab="Marks")

Explanation: Points and lines show how marks increase as study hours increase.

1.2 Manipulating the Plotting Window

par(mfrow=c(1,2))   # Two plots side by side
plot(students$Hours_Studied, students$Marks, col="red", main="Plot 1")
barplot(students$Marks, names.arg=students$Name, col="cyan", main="Plot 2")

Explanation: par(mfrow=c(1,2)) splits window into 1 row, 2 columns.

1.3 Box-Whisker Plot

boxplot(students$Marks ~ students$Gender,
        main="Marks Distribution by Gender",
        col=c("lightblue","pink"),
        xlab="Gender", ylab="Marks")

Interpretation: Median and spread of marks between male and female students.

1.4 Scatter Plot

plot(students$Hours_Studied, students$Marks,
     main="Scatter Plot",
     col="darkgreen", pch=19,
     xlab="Hours Studied", ylab="Marks")

Interpretation: Positive relationship between study hours and marks.

1.5 Pair Plot

pairs(students[,c("Hours_Studied","Marks")], 
      main="Pair Plot - Student Data")

Interpretation: Shows correlation between multiple variables.

1.6 Pie Chart

gender_count <- table(students$Gender)
pie(gender_count, labels=names(gender_count), 
    main="Gender Distribution", col=c("blue","pink"))

Interpretation: Visualizes proportion of male vs female students.

1.7 Bar Chart

barplot(students$Marks, names.arg=students$Name, 
        col="orange", main="Marks of Students",
        xlab="Students", ylab="Marks")

Interpretation: Comparison of marks across students.

2. Advanced R (Using the Same Dataset)

2.1 Statistical Models (Linear Regression)

model <- lm(Marks ~ Hours_Studied, data=students)
summary(model)

Equation (from output):
```
Marks = 45 + 2.8 * Hours_Studied
```
Interpretation: Every additional study hour increases marks by ~2.8.

2.2 Correlation and Regression

cor(students$Hours_Studied, students$Marks)

Output: 0.986 → Very strong positive correlation.

Multiple Regression Example (if we had Attendance data):

students$Attendance <- c(75,80,82,85,88,90,95,98)
multi_model <- lm(Marks ~ Hours_Studied + Attendance, data=students)
summary(multi_model)

2.3 ANOVA (Analysis of Variance)

Suppose we group students by study plan:

students$Plan <- c("Low","Low","Medium","Medium","High","High","High","High")
anova_model <- aov(Marks ~ Plan, data=students)
summary(anova_model)

Interpretation: If p-value < 0.05, marks significantly differ between study plans.

2.4 Creating Data for Complex Analysis

set.seed(123)
dummy <- data.frame(
  Group = rep(c("A","B","C"), each=5),
  Score = c(rnorm(5, mean=60, sd=5),
            rnorm(5, mean=70, sd=5),
            rnorm(5, mean=80, sd=5))
)
head(dummy)

Explanation: Created synthetic data for ANOVA testing.

2.5 Summarizing Data

summary(students)
aggregate(Marks ~ Gender, data=students, FUN=mean)
table(students$Gender)

Output:

Mean marks of male vs female.
Frequency of each gender.

2.6 Case Studies

Case Study 1: Study Hours vs Marks

plot(students$Hours_Studied, students$Marks, pch=19, col="blue",
     main="Study Hours vs Marks")
abline(model, col="red", lwd=2)

Interpretation: Regression line shows predicted marks increase with more hours.

Case Study 2: Fertilizer Effect on Yield (Dummy Data)

fertilizer <- factor(rep(c("A","B","C"), each=5))
yield <- c(20,22,19,21,23, 25,27,26,28,24, 30,32,29,31,33)
data <- data.frame(fertilizer, yield)
 
boxplot(yield ~ fertilizer, data=data, col=c("red","green","blue"),
        main="Crop Yield by Fertilizer Type")
anova_result <- aov(yield ~ fertilizer, data=data)
summary(anova_result)

Interpretation: If p-value < 0.05, fertilizer type significantly affects yield.

Summary Table (Exam-Ready)

Technique	Function	Example with Dummy Data	Purpose
Basic Plot	`plot()`	`plot(Hours_Studied, Marks)`	Simple line/scatter
Box Plot	`boxplot()`	`boxplot(Marks ~ Gender)`	Compare distributions
Scatter Plot	`plot(x,y)`	`plot(Hours, Marks)`	Relationship between 2 variables
Pair Plot	`pairs()`	`pairs(students[,c(2,3)])`	Multi-variable relation
Pie Chart	`pie()`	`pie(table(Gender))`	Proportions
Bar Chart	`barplot()`	`barplot(Marks)`	Compare categories
Regression	`lm()`	`lm(Marks~Hours_Studied)`	Predict values
Correlation	`cor()`	`cor(Hours, Marks)`	Strength of relation
ANOVA	`aov()`	`aov(Marks~Plan)`	Compare group means
Summarizing	`summary()`	`summary(students)`	Descriptive stats

notes-shivam

Explorer

unit 2 - graphical analysis and advanced R