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Livre Analyse de données

Outline

Introduction

Principal Component Analysis

Correspondence Analysis

Multiple Correspondence Analysis

Clustering

Multiple Factor Analysis

To conclude

Forum

Computer exercise: female fertility in Europe

We are interested in female fertility in Europe in 2012. To study this, we have constructed a data table with 39 European countries as rows, and age groups as columns: 15-19, 20-24, 25-29, 30-34, 35-39, 40 and over. In the relevant table entry, we have the mean fertility of women for a given country and age group. Here, fertility means the mean number of children born per 1000 women.

To be able to answer the questions, you must run a PCA using the data set available in this file. Here is the line of code you need to import this data into R (don't forget to modify the path):

don = read.table("data_PCA_Fertility.csv", header=TRUE, sep=";", check.names=FALSE, row.names=1, stringsAsFactors = TRUE)

Your aim is to be able to explain and describe female fertility in Europe. After thinking about which variables should be active, and which variables should be supplementary, perform a PCA on this data set (a standardized PCA) and then answer the following questions.

Q1) What is the percentage of inertia associated with the principal 1-2 plane (number between 0 and 100 without the % sign)
22.66 %
61.70 %
84.37 %
100 %

Q2) Which country contributes the most to the construction of the 2nd axis?
France
Spain
Ukraine
Albania
Ireland

Q3) Which variable is most correlated with the 2nd axis?
15-19
20-24
25-29
30-34
35-39
40 et +

Q4) Among the following variables, select those which are strongly positively or negatively correlated with the first axis (those for which the absolute value of their correlation with the first axis is greater than 0.6):
15-19
20-24
25-29
30-34
35-39
40 et +

Q5) Check the statements which are true:
The fertility rate of French women aged 25-29 is very high compared to women of the same age group in the rest of Europe
The fertility rate of Spanish women aged 25-29 is very high compared to women of the same age group in the rest of Europe
The fertility rate of Ukrainian women is higher between the ages of 15 and 19 than between 25 and 29
Ukrainian adolescents have a lot of children compared to adolescents from other European countries
The fertility rate of Estonian women is close to 0 for all age groups
The fertility rate of Estonian women is close to the average fertility rate across Europe for all age group

Q6) Check the statements which are true:
Irish women have more children that other European women from the age of 35 on
For every age group, German and Greek women have (more or less) similar fertility rates
For every age group, Ukrainian and Irish women have (more or less) similar fertility rates
Countries with the highest adolescent fertility rates are those where fertility of women 35 and over is low
Countries with high fertility rates for women aged 25-29 are those where adolescents have low fertility rates

Q7) Interpret the first PCA axes based on a study of the variables and a study of the individuals.
You may also use information contained in the Region variable.
No answer is provided for this question.

Score =
Correct answers: