Fisher’s Irises
Kyrion Dickerson
September 2, 2016
output:pdf_document
Abstract
Measurements of the sepals and petals for three varieties of iris were analyzed to determine whether any of these characteristics could be used to distibuish varieties. The most useful variables were petal length and petal width.
Introduction
From the Wikipedia article “Iris flower data set” (https://en.wikipedia.org/wiki/Iris_flower_data_set)
The Iris flower data set or Fisher’s Iris data set is a multivariate data set introduced by Ronald Fisher in his 1936 paper ``The use of multiple measurements in taxonomic problems as an example of linear discriminant analysis’’. It is sometimes called Anderson’s Iris data set because Edgar Anderson collected the data to quantify the variation of Iris flowers.
The data set consists of 50 samples from each of three species of Iris (Iris setosa, Iris virginica and Iris versicolor). Four features were measured from each sample: the length and the width of the sepals and petals, in centimetres.
Problem
Which features, either alone or in combination, can be used to distinguish among the three varieties of iris?
Data
summary(iris)
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
##
##
## Analysis
Examine the distributions of the variables, singly and in relation to one another.
Numerical Summaries The following are the quartiles and means, by variety:
## iris$Species: setosa
## Sepal.Length Sepal.Width Petal.Length Petal.Width
## Min. :4.300 Min. :2.300 Min. :1.000 Min. :0.100
## 1st Qu.:4.800 1st Qu.:3.200 1st Qu.:1.400 1st Qu.:0.200
## Median :5.000 Median :3.400 Median :1.500 Median :0.200
## Mean :5.006 Mean :3.428 Mean :1.462 Mean :0.246
## 3rd Qu.:5.200 3rd Qu.:3.675 3rd Qu.:1.575 3rd Qu.:0.300
## Max. :5.800 Max. :4.400 Max. :1.900 Max. :0.600
## Species
## setosa :50
## versicolor: 0
## virginica : 0
##
##
##
## --------------------------------------------------------
## iris$Species: versicolor
## Sepal.Length Sepal.Width Petal.Length Petal.Width
## Min. :4.900 Min. :2.000 Min. :3.00 Min. :1.000
## 1st Qu.:5.600 1st Qu.:2.525 1st Qu.:4.00 1st Qu.:1.200
## Median :5.900 Median :2.800 Median :4.35 Median :1.300
## Mean :5.936 Mean :2.770 Mean :4.26 Mean :1.326
## 3rd Qu.:6.300 3rd Qu.:3.000 3rd Qu.:4.60 3rd Qu.:1.500
## Max. :7.000 Max. :3.400 Max. :5.10 Max. :1.800
## Species
## setosa : 0
## versicolor:50
## virginica : 0
##
##
##
## --------------------------------------------------------
## iris$Species: virginica
## Sepal.Length Sepal.Width Petal.Length Petal.Width
## Min. :4.900 Min. :2.200 Min. :4.500 Min. :1.400
## 1st Qu.:6.225 1st Qu.:2.800 1st Qu.:5.100 1st Qu.:1.800
## Median :6.500 Median :3.000 Median :5.550 Median :2.000
## Mean :6.588 Mean :2.974 Mean :5.552 Mean :2.026
## 3rd Qu.:6.900 3rd Qu.:3.175 3rd Qu.:5.875 3rd Qu.:2.300
## Max. :7.900 Max. :3.800 Max. :6.900 Max. :2.500
## Species
## setosa : 0
## versicolor: 0
## virginica :50
##
##
## and the correlations between each of the measurement variables
## Sepal.Length Sepal.Width Petal.Length Petal.Width
## Sepal.Length 1.0000000 -0.1175698 0.8717538 0.8179411
## Sepal.Width -0.1175698 1.0000000 -0.4284401 -0.3661259
## Petal.Length 0.8717538 -0.4284401 1.0000000 0.9628654
## Petal.Width 0.8179411 -0.3661259 0.9628654 1.0000000Graphical Summaries
Compare the distributions of sepal lengths
attach(iris)
boxplot(Sepal.Length~Species, main="Sepal Lengths of Irises", ylab="centimeters")
Show the relationship between sepal lengths and widths, for each variety
plot(Sepal.Length, Sepal.Width, pch=c(21, 22, 23)[as.numeric(Species)],
col=c("red", "blue", "green")[as.numeric(Species)])
Findings and Discussion
Which variables would you use to distinguish the iris varieties?
The most useful variables were petal length and petal width. The sepal length and width weren’t found useful because they overlapped on the graph, whuch proved complicated to differentiate between the iris varieties. Virginica was found to be the largest iris while Setosa was found to be the smallest.