Lab 3: Data Analysis with R
Hanna Marachkina
Introduction
This report presents the results of exploratory data analysis (EDA) and visualization for the Iris and Mtcars datasets using R. The goal is to identify patterns, relationships, and insights through various analyses.
Data Loading and Preparation
We start by loading the necessary libraries and datasets.
# Load required libraries
library(ggplot2)
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union# Load datasets
data(iris)
data(mtcars)# View the first few rows of each dataset
head(iris)## Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 1 5.1 3.5 1.4 0.2 setosa
## 2 4.9 3.0 1.4 0.2 setosa
## 3 4.7 3.2 1.3 0.2 setosa
## 4 4.6 3.1 1.5 0.2 setosa
## 5 5.0 3.6 1.4 0.2 setosa
## 6 5.4 3.9 1.7 0.4 setosahead(mtcars)## mpg cyl disp hp drat wt qsec vs am gear carb
## Mazda RX4 21.0 6 160 110 3.90 2.620 16.46 0 1 4 4
## Mazda RX4 Wag 21.0 6 160 110 3.90 2.875 17.02 0 1 4 4
## Datsun 710 22.8 4 108 93 3.85 2.320 18.61 1 1 4 1
## Hornet 4 Drive 21.4 6 258 110 3.08 3.215 19.44 1 0 3 1
## Hornet Sportabout 18.7 8 360 175 3.15 3.440 17.02 0 0 3 2
## Valiant 18.1 6 225 105 2.76 3.460 20.22 1 0 3 1Analysis of Iris Dataset
Structure and Summary
Examine the structure and summary statistics of the Iris dataset.
# Display the structure of the Iris dataset
str(iris)## 'data.frame': 150 obs. of 5 variables:
## $ Sepal.Length: num 5.1 4.9 4.7 4.6 5 5.4 4.6 5 4.4 4.9 ...
## $ Sepal.Width : num 3.5 3 3.2 3.1 3.6 3.9 3.4 3.4 2.9 3.1 ...
## $ Petal.Length: num 1.4 1.4 1.3 1.5 1.4 1.7 1.4 1.5 1.4 1.5 ...
## $ Petal.Width : num 0.2 0.2 0.2 0.2 0.2 0.4 0.3 0.2 0.2 0.1 ...
## $ Species : Factor w/ 3 levels "setosa","versicolor",..: 1 1 1 1 1 1 1 1 1 1 ...# Generate a summary of the dataset
summary(iris)## Sepal.Length Sepal.Width Petal.Length Petal.Width
## Min. :4.300 Min. :2.000 Min. :1.000 Min. :0.100
## 1st Qu.:5.100 1st Qu.:2.800 1st Qu.:1.600 1st Qu.:0.300
## Median :5.800 Median :3.000 Median :4.350 Median :1.300
## Mean :5.843 Mean :3.057 Mean :3.758 Mean :1.199
## 3rd Qu.:6.400 3rd Qu.:3.300 3rd Qu.:5.100 3rd Qu.:1.800
## Max. :7.900 Max. :4.400 Max. :6.900 Max. :2.500
## Species
## setosa :50
## versicolor:50
## virginica :50
##
##
## Visualizations
Pair Plot of Numeric Features
A pair plot visualizes the relationships between numeric variables.
pairs(iris[, 1:4], main = "Pair Plot of Iris Dataset")
Boxplot of Sepal Length by Species
The boxplot shows the distribution of Sepal Length across the three species.
ggplot(iris, aes(x = Species, y = Sepal.Length)) +
geom_boxplot(fill = "lightblue") +
ggtitle("Boxplot of Sepal Length by Species") +
xlab("Species") +
ylab("Sepal Length (cm)")
Analysis of Mtcars Dataset
Structure and Summary
We analyze the structure and summary statistics of the Mtcars dataset.
# Structure and summary of Mtcars dataset
str(mtcars)## 'data.frame': 32 obs. of 11 variables:
## $ mpg : num 21 21 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 ...
## $ cyl : num 6 6 4 6 8 6 8 4 4 6 ...
## $ disp: num 160 160 108 258 360 ...
## $ hp : num 110 110 93 110 175 105 245 62 95 123 ...
## $ drat: num 3.9 3.9 3.85 3.08 3.15 2.76 3.21 3.69 3.92 3.92 ...
## $ wt : num 2.62 2.88 2.32 3.21 3.44 ...
## $ qsec: num 16.5 17 18.6 19.4 17 ...
## $ vs : num 0 0 1 1 0 1 0 1 1 1 ...
## $ am : num 1 1 1 0 0 0 0 0 0 0 ...
## $ gear: num 4 4 4 3 3 3 3 4 4 4 ...
## $ carb: num 4 4 1 1 2 1 4 2 2 4 ...summary(mtcars)## mpg cyl disp hp
## Min. :10.40 Min. :4.000 Min. : 71.1 Min. : 52.0
## 1st Qu.:15.43 1st Qu.:4.000 1st Qu.:120.8 1st Qu.: 96.5
## Median :19.20 Median :6.000 Median :196.3 Median :123.0
## Mean :20.09 Mean :6.188 Mean :230.7 Mean :146.7
## 3rd Qu.:22.80 3rd Qu.:8.000 3rd Qu.:326.0 3rd Qu.:180.0
## Max. :33.90 Max. :8.000 Max. :472.0 Max. :335.0
## drat wt qsec vs
## Min. :2.760 Min. :1.513 Min. :14.50 Min. :0.0000
## 1st Qu.:3.080 1st Qu.:2.581 1st Qu.:16.89 1st Qu.:0.0000
## Median :3.695 Median :3.325 Median :17.71 Median :0.0000
## Mean :3.597 Mean :3.217 Mean :17.85 Mean :0.4375
## 3rd Qu.:3.920 3rd Qu.:3.610 3rd Qu.:18.90 3rd Qu.:1.0000
## Max. :4.930 Max. :5.424 Max. :22.90 Max. :1.0000
## am gear carb
## Min. :0.0000 Min. :3.000 Min. :1.000
## 1st Qu.:0.0000 1st Qu.:3.000 1st Qu.:2.000
## Median :0.0000 Median :4.000 Median :2.000
## Mean :0.4062 Mean :3.688 Mean :2.812
## 3rd Qu.:1.0000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :1.0000 Max. :5.000 Max. :8.000Visualizations
Scatter Plot of MPG vs Horsepower
The scatter plot visualizes the relationship between Miles per Gallon (MPG) and Horsepower (HP).
ggplot(mtcars, aes(x = hp, y = mpg)) +
geom_point(color = "blue") +
ggtitle("Scatter Plot: Miles per Gallon vs Horsepower") +
xlab("Horsepower (HP)") +
ylab("Miles per Gallon (MPG)")
Bar Graph: Average MPG by Number of Cylinders
The bar graph shows the average MPG for cars grouped by the number of cylinders.
mtcars %>%
group_by(cyl) %>%
summarise(average_mpg = mean(mpg)) %>%
ggplot(aes(x = as.factor(cyl), y = average_mpg)) +
geom_bar(stat = "identity", fill = "orange") +
ggtitle("Average MPG by Number of Cylinders") +
xlab("Number of Cylinders") +
ylab("Average MPG")
Statistical Tests
ANOVA Test for Iris Dataset
We perform an ANOVA test to check for significant differences in Sepal Length across species.
# ANOVA test for Sepal Length
anova_results <- aov(Sepal.Length ~ Species, data = iris)
summary(anova_results)## Df Sum Sq Mean Sq F value Pr(>F)
## Species 2 63.21 31.606 119.3 <2e-16 ***
## Residuals 147 38.96 0.265
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Interpretation: A low p-value (< 0.05) indicates significant differences in Sepal Length across species.
Correlation Test for Mtcars Dataset
We analyze the correlation between Horsepower (HP) and Miles per Gallon (MPG).
# Correlation test between HP and MPG
cor_test <- cor.test(mtcars$hp, mtcars$mpg)
cor_test##
## Pearson's product-moment correlation
##
## data: mtcars$hp and mtcars$mpg
## t = -6.7424, df = 30, p-value = 1.788e-07
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.8852686 -0.5860994
## sample estimates:
## cor
## -0.7761684Interpretation: The correlation coefficient indicates a strong negative relationship between horsepower and fuel efficiency.
Results
Iris Dataset
The ANOVA test indicates significant differences in Sepal Length among species.
Visualizations confirm that each species has distinct distributions for Sepal Length and other numerical features.
Mtcars Dataset
There is a negative correlation between Horsepower and Miles per Gallon.
Cars with fewer cylinders tend to have higher fuel efficiency, as shown in the bar graph.
Conclusion
This analysis provided the following insights:
Iris Dataset:
- Statistically significant differences in Sepal Length among species.
Mtcars Dataset:
A strong negative correlation exists between Horsepower and Miles per Gallon.
Cars with fewer cylinders are generally more fuel-efficient.