The Iris data set

We will explore the iris dataset that comes with R, based on data collected by Edgar Anderson (1935) and analyzed by R. A. Fisher (1936).

Numerical Summaries

We start by loading the data set:

data(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  
##                 
##                 
##

We see that the dataset contains four numerical variables and one categorical variable:

  1. Sepal.Length: The sepal length, in centimeters,
  2. Sepal.Width: The sepal width, in centimeters,
  3. Petal.Length: The petal length, in centimeters,
  4. Petal.Width: The petal width, in centimeters,
  5. Species: The three different species of iris considered: setosa, versicolor and virginica

The summary command gave us five-number summaries for the numerical variables and a frequency table for the categorical variable.

We can also create these numerical summaries on their own:

favstats(~Sepal.Length, data=iris)
##  min  Q1 median  Q3 max     mean        sd   n missing
##  4.3 5.1    5.8 6.4 7.9 5.843333 0.8280661 150       0
tally(~Species, data=iris)
## Species
##     setosa versicolor  virginica 
##         50         50         50

We can also produce summaries within each Species:

favstats(~Petal.Length|Species, data=iris)
##      Species min  Q1 median    Q3 max  mean        sd  n missing
## 1     setosa 1.0 1.4   1.50 1.575 1.9 1.462 0.1736640 50       0
## 2 versicolor 3.0 4.0   4.35 4.600 5.1 4.260 0.4699110 50       0
## 3  virginica 4.5 5.1   5.55 5.875 6.9 5.552 0.5518947 50       0

Basic Graphs

We can easily generate histograms:

histogram(~Petal.Length, breaks=20, col="purple", data=iris)

histogram(~Petal.Length|Species, data=iris, layout=c(1, 3))

And some boxplots:

bwplot(Species~Petal.Length, data=iris)

A scatterplot:

xyplot(Sepal.Length~Petal.Length, data=iris, groups=Species, 
       fill=brewer.pal(3, "Dark2"), pch=21:23, lwd=2, col="black",
       main="Iris data (green=setosa, orange=versicolor, purple=virginica)",
       xlab="Petal Length (cm)",
       ylab="Sepal Length (cm)", 
       type=c("p", "smooth"))

A labeled dotplot of the mean Petal Length for each species:

mean(~Petal.Length|Species, data=iris) %>% sort() %>% dotplot()

Linear Regression

setosaFit <- lm(Sepal.Length~Petal.Length, 
                    data=iris %>% filter(Species == "setosa"))
summary(setosaFit)
## 
## Call:
## lm(formula = Sepal.Length ~ Petal.Length, data = iris %>% filter(Species == 
##     "setosa"))
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.57238 -0.20671 -0.03084  0.17339  0.93608 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    4.2132     0.4156  10.138 1.61e-13 ***
## Petal.Length   0.5423     0.2823   1.921   0.0607 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3432 on 48 degrees of freedom
## Multiple R-squared:  0.07138,    Adjusted R-squared:  0.05204 
## F-statistic:  3.69 on 1 and 48 DF,  p-value: 0.0607

As anticipated, the linear model for setosa is weak.

Residual plot:

residPlot <- xyplot(resid(setosaFit)~fitted(setosaFit), 
       xlab="Predicted Values", ylab="Residuals")
ladd(panel.abline(h=0, lwd=2, col="black"), plot=residPlot)