Two exercises are proposed to illustrate the simple linear regression. The first one is based on the famous Galton's data set on heredity. We use the lm R command and get coefficients estimates, standard error of the error, R2, residuals …In the second example, devoted to data related to the vapor tension of mercury, we fit a simple linear regression, predict values, and anticipate on multiple linear regression.

This pratical session is an excerpt from practical exercises proposed by A. Dalalyan at EPNC (see Exercises 1 and 2 of http://certis.enpc. fr/∼dalalyan/Download/TP_ENPC_4.pdf).

An exercise is proposed to illustrate the logistic regression. One investigates the different risk factors in the apparition of coronary heart disease. It has been proposed in Chapter 5 of the book of D.G. Kleinbaum and M. Klein, “Logistic Regression”, Statistics for Biology and Health, Springer Science Business Media, LLC (2010) and also by D. Chessel and A.B. Dufour in Lyon 1 (see Sect. 6 of http://pbil.univ-lyon1.fr/R/pdf/tdr341.pdf). This example is based on data given in the file evans.txt coming from http://www.sph.emory.edu/dkleinb/logreg3.htm#data.

An introduction to R is proposed. This pratical session is an excerpt from practical exercises proposed by A. Dalalyan at EPNC (see http://certis.enpc.fr/∼dalalyan/Download/TP_ENPC_1.pdf). Datas are also extracted from a practical session proposed by hydrologic data from Amazonia proposed by D. Chessel A.B. Dufour in Lyon 1 (website indicated in the text below) and from other practical exercises proposed by A. Dalalyan at ENPC (same address as above but ended by /TP_ENPC_4.pdf).

Three exercises are proposed to illustrate the simple linear regression. In the first one investigates the influence of several factors on atmospheric pollution. It has been proposed by D. Chessel and A.B. Dufour in Lyon 1 (see Sect. 6 of http://pbil.univ-lyon1.fr/R/ pdf/tdr33.pdf) and is based on data coming from 20 cities of U.S. Exercise 2 is an introduction to model selection whereas Exercise 3 provides a first example of analysis of variance. Exercises 2 and 3 have been proposed by A. Dalalyan at ENPC (see Exercises 2 and 3 of http://certis.enpc.fr/ dalalyan/Download/TP_ENPC_5.pdf).

We consider stationary processes with long memory which are non-Gaussian and representedas Hermite polynomials of a Gaussian process. We focus on the corresponding waveletcoefficients and study the asymptotic behavior of the sum of their squares since this sumis often used for estimating the long–memory parameter. We show that the limit is notGaussian but can be expressed using the non-Gaussian Rosenblatt process defined as aWiener–Itô integral of order 2. This happens even if the original process is definedthrough a Hermite polynomial of order higher than 2.