An RMarkdown report

Data description

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

To get help about columns, run ?iris.

The data set iris is

Descriptive analysis

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

Descriptive statistics

	Sepal.Length	Sepal.Width	Petal.Length	Petal.Width	Species
	Min. :4.30	Min. :2.00	Min. :1.00	Min. :0.1	setosa :50
	1st Qu.:5.10	1st Qu.:2.80	1st Qu.:1.60	1st Qu.:0.3	versicolor:50
	Median :5.80	Median :3.00	Median :4.35	Median :1.3	virginica :50
	Mean :5.84	Mean :3.06	Mean :3.76	Mean :1.2
	3rd Qu.:6.40	3rd Qu.:3.30	3rd Qu.:5.10	3rd Qu.:1.8
	Max. :7.90	Max. :4.40	Max. :6.90	Max. :2.5

Second, we use the function aggregate 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	5.01	3.43	1.46	0.246
versicolor	5.94	2.77	4.26	1.326
virginica	6.59	2.97	5.55	2.026

Linear regression

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

Pearson’s coefficients of correlation

	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.

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:

Summary of lm: Sepal.Length ~ Petal.Length

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	4.307	0.078	54.9	0.00e+00
Petal.Length	0.409	0.019	21.6	1.04e-47

The model’s equation is \[ \widehat{Sepal.Length} = 4.307+ 0.409 Petal.Length. \]

Here are the data with the regression line:

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

Residuals plot 1

Residuals plot 2