Rmarkdown report

Data description

In this project we consider the classical iris data that can be found in the R datasets package. This data has 5 columns named Sepal.Length, Sepal.Width, Petal.Length, Petal.Width, Species and 150 observations.

You can find help on these data here

Descriptive analysis

First, we compute some descriptive statistics with the summary() function:

	Sepal.Length	Sepal.Width	Petal.Length	Petal.Width	Species
	Min. :4.300	Min. :2.000	Min. :1.000	Min. :0.100	setosa :50
	1st Qu.:5.100	1st Qu.:2.800	1st Qu.:1.600	1st Qu.:0.300	versicolor:50
	Median :5.800	Median :3.000	Median :4.350	Median :1.300	virginica :50
	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

Second, we use this code

aggregate(cbind(Sepal.Length, Sepal.Width, Petal.Length, Petal.Width) ~ Species,
  data = iris, mean)

to get the following table that shows the means of the \(4\) numerical variables for each species.

Means by species

Species	Sepal.Length	Sepal.Width	Petal.Length	Petal.Width
setosa	5.006	3.428	1.462	0.246
versicolor	5.936	2.770	4.260	1.326
virginica	6.588	2.974	5.552	2.026

Linear regression

We use the function cor() to get the Pearson’s coefficients of correlation between all our numeric variables:

	Sepal.Length	Sepal.Width	Petal.Length	Petal.Width
Sepal.Length	1.000	-0.118	0.872	0.818
Sepal.Width	-0.118	1.000	-0.428	-0.366
Petal.Length	0.872	-0.428	1.000	0.963
Petal.Width	0.818	-0.366	0.963	1.000

Here are \(3\) scatter plots that show the association between Petal.Length and the other numerical variables.

Study of iris flowers

Now, we would like to explain the variations in the length of the sepal as a function of the length of the petal. To do so, we use the following linear regression lm(Sepal.Length ~ Petal.Length, data = iris). Here is the summary of this model:

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	4.307	0.078	54.939	0
Petal.Length	0.409	0.019	21.646	0

The model’s equation is

\[ Sepal.Length = 4.307+ 0.409 Petal.Length. \]

Here are the data with the regression line:

Finally, we use the plot(mod) command to get some graphical representations of the residuals.