Question

1. Use the R command X <- iris to assign Fishers’ iris dataset to the data matrix X. Using the head(X) command summarize what each column of the dataset is measuring and represents. Assign Y as a new matrix of dimension 150 by 4 which has the values of X without the species label.

2. Compute and interpret (in summary English) each of the summary statistics X,S,R using R.

3. Visualize the dataset by making a scatterplot of Sepal Length vs. Sepal Width, a scatterplot of Petal Length vs. Petal Width. The pairs function is useful here. Use your plots and stats from #2 to comment on any evident correlations.

Answer 1

Rcode.R

X=iris #assigning iris datset to data matrix X

head(X)

##   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 setosa

# the first column shows the variable Sepal length, which meausres the length of Sepals
# the second column shows the variable Sepal length, which meausres the width of Sepals
# the third column shows the variable Petal width, which meausres the length of Petals
# the fourth column shows the variable Petal width, which meausres the width of Petals

Y=X[,-5] #assigning Y as a matrix of dimension 150*4 having columns of X except the last column(Species) of X

summary(X) #computes the summary for each column of X

##   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
##                
##                
##

attach(X)
#Scatter plots
plot(Sepal.Length,Sepal.Width)

plot(Petal.Length,Petal.Width)

##for correlation interpretaion
pairs(X[1:2]) ## The graph shows no correlation between Sepal length and Sepal width

pairs(X[3:4]) ## The graph shows higher positive correlation between Petal length and Petal width