Footprint test and

Regression model:

how to deal with data?

Co-finanziatoDal Programma LLP dell’Unione Europea

L’autore è il solo responsabile di questa comunicazione. L’Unione europea declina ogni responsabilità sull’uso che potrà essere fatto delle informazioni in essa contenute.

Footprint

The ecological footprint is a measure of human

demand on the Earth's ecosystems. It is a standardized measure of

demand for natural capital that may be contrasted with the

planet's ecological capacity to regenerate

Ecological footprint F is calculated by this equation:

Ei = ecological footprint coming from the waste

Ci = product i-thqi = (hectare/kg) reciprocal of the average productivity per hectare produced the i-

th.

The ecological footprint per capita f is calculated by

dividing for the population N residing in the region

considered:

Studies carried out on a global scale and in some countries shows that the global footprint is larger than the capacity bioproductive

world. According to Mathis Wackernagel, in 1961 humanity used 70% of the overall capacity of the biosphere, but in 1999 had

increased to 120%.

Ecological footprint in the world

Evidence through observation

To find out whether and how our actions and lifestyle affect our environmentWe selected an appropriate Ecological footprint calculation quiz - as a methods for collecting relevant information related to our environment and lifestyle

We adopted strategies for planning, organizing and most efficiently manage a Footprint quiz

- Pointing out criteria for making right questions in order to ensure accuracy, significance, and fairness about collected data

- Administering the “ Footprint Test” to a quantitative significant sample of people of Pisa area

Footprint TEST• I travel mostly by 1- car ( average

user ) 2- car ( heavy user ) 3- car (light user ) 4- bus/train 5- walking/cycling 6- motorbike

• usually holiday 1- close to home 2- a short flight away 3- a long flight away

• I live in a 1 – large house 2 – medium-sized house 3 – small house 4 – flat/apartment 5 – zero emission development

• that I share with 1 – no other person 2 – one other person 3 – two other person 4 – three other person 5 – four other person 6 – five other person 7 – six other person 8 – more than six

others

• My heating/cooling bills are relatively 1 – normal 2 – high 3 – low

• I buy my electricity from 1 – non-renewable sources

2 – renewable sources

• I tend 1 – not to conserve energy 2 – to conserve energy

• I am 1 – a regular meat-eater 2 – an occasional meat-eater 3 – a heavy meat-eater 4 – a vegetarian 5 – a vegan

• usually eat 1 – a mix of fresh and convenience

foods 2 – mostly fresh, locally grown produce 3 – mostly convenience foods

• I produce 1 – an average 2 – a below average 3 – an above average 4 – half the average amount of domestic waste

• most of which is 1 – not recycled 2 – recycled

Aim of our research: to study the impact of specific characteristics of the respondents about their ecological footprint.

How we made it: For data processing we used methods provided by a branch of statistics known as econometrics.

Econometrics may be defined as a branch of statistics that deals with

the analysis of economic phenomena, or alternatively, can

be considered a sector of the economy devoted to the empirical verification of theoretical models

formulated in scope.

In our survey, - we applied several

statistic methods and techniques to collect data

- we focused on the Regression Model for managing and analyzing quantitative data

The Linear Regression Model

A Math /Stats Model1. Often Describe Relationship between

Variables

2. Types- Deterministic Models (no randomness)

- Probabilistic Models (with randomness)

EPI 809/Spring 2008 26

Deterministic Models

1. Hypothesize Exact Relationships2. Suitable When Prediction Error is

Negligible

EPI 809/Spring 2008 27

Probabilistic Models

1. Hypothesize 2 Components Deterministic Random Error

EPI 809/Spring 2008 28

Types of Probabilistic Models

ProbabilisticModels

RegressionModels

CorrelationModels

OtherModels

EPI 809/Spring 2008 29

Regression Models

Relationship between one dependent variable and explanatory variable(s)

Use equation to set up relationship Numerical Dependent (Response) Variable 1 or More Numerical or Categorical

Independent (Explanatory) Variables

Used Mainly for Prediction & Estimation

EPI 809/Spring 2008 30

Regression Modeling Steps

1. Hypothesize Deterministic Component

Estimate Unknown Parameters

2. Evaluate the fitted Model 3. Use Model for Prediction &

Estimation

EPI 809/Spring 2008 31

Specifying the deterministic component

1. Define the dependent variable and independent variable

2. Hypothesize Nature of Relationship• Expected Effects (i.e., Coefficients’

Signs)

EPI 809/Spring 2008 32

Y Xi i i 0 1

Linear Regression Model

1. Relationship Between Variables Is a Linear Function

Dependent (Response) Variable(e.g., CD+ c.)

Independent (Explanatory) Variable (e.g., Years s. serocon.)

Population Slope

Population Y-Intercept

Random Error

Population Linear Regression Model

Y

X

EPI 809/Spring 2008 34

Y Xi i i 0 1

iXYE 10

Observedvalue

Observed value

i = Random error

Population & Sample Regression Models

EPI 809/Spring 2008 35

Unknown Relationship

Population Random Sample

Y Xi i i 0 1

Y Xi i i 0 1

Model Specification Is Based on Theory

1. Theory of Field (e.g., Epidemiology)

2. Mathematical Theory 3. Previous Research 4. ‘Common Sense’

EPI 809/Spring 2008 36

Sample Linear Regression Model

Y

X

EPI 809/Spring 2008 37

Y Xi i i 0 1

Y Xi i 0 1

Unsampled observation

i = Random

error

Observed value

^

Our data: the application of this methodology of statistical

analysis requires the identification of a dependent

variable and multiple independent variables. The

independent variables will be the ones through which will be

explained the variance of the dependent variable. These are the variables identified for this

project:

• dependent variable: Through a test on

footprint, administered to a large and significant

sample , we will obtain a value that expresses the

footprint of a subject;

• independent variables: - age

- usually - Number of people in

household - distance home-school/work

(categorical variable: 1 = 5km, 10km = 2, 3 = 15km)

sensitization (categorical variable: 1 = "I never discussed the issue of energy and pollution in school or personally," 2 = "I did a course of primary awareness on energy and pollution", 3 = "I have dealt with in

depth and more than once the subject of energy and pollution") where for a categorical variable we mean a variable measured at

different levels (categories).

Estimation model: starting from the estimation

equation: Y = a + bX + c Z + e

(where e is the error of our estimate a,b,c constant, and

together account for the variation in Y not explained by our

dependent variables) we obtain the following equation that

represents our model to estimate

Footprint

a + b age + c sort + d sensation +…. + e

From this equation we will get different values for the

coefficients b, c, d ... that will allow us to see how the

footprint vary with age, gender, and so on.

Specifically:- the absolute value of the coefficient indicates the

strength of the effect of the independent on the dependent variable.

What next?Next year the above model will be

estimated using a specific statistics

program : Stata.

The following slides report our collected data from Footprint quizzes

Sesso Età Dist. Casa scuola

Sensibilità

CO2 (t) Ettari globali

pianeti

M 14 6 2 7,1 4,4 2.7

F 24 5 1 8,8 4,8 3

F 51 10 3 10,3 6,2 3,8

F 47 15 2 8,9 5,2 3,2

F 65 10 2 8,2 4,4 2,7

F 56 3 3 7,5 4,4 2,7

M 16 5 1 7,9 3,8 2,3

M 17 10 1 6 4,4 2,7

M 17 5 1 6,8 4,3 2,6

M 16 5 2 8,7 4,4 2,7

M 16 15 2 6,9 4,1 2,5

M 13 1,5 2 6,5 3,1 1,9

M 16 10 1 9,3 5,3 3,2

F 16 10 1 7,6 5,1 3,1

M 16 20 1 6,4 4 2,4

F 9 3 1 8,2 4,6 2,8

M 18 3,6 1 11,3 5,9 3,6

M 17 7 2 9,5 4,6 2,8

M 18 20 2 10,4 6,1 3,7

M 18 10 1 9,9 5,4 3,3

F 42 5 2 6,3 3,7 2,3

F 20 13 2 7,1 4,3 2,7

F 19 12 1 7,5 4,5 2,8

M 19 5 2 6,3 3,3 2

M 19 5 2 6,3 4,1 2,5

F 54 1,5 2 6,2 3,3 2

m 16 15 2 9,3 5 3,1

F 18 15 3 7 4,2 2,5

M 1 0,1 1 10,4 5,9 3,6

F 10 2 7,1 4,8 2,9

M 17 0,45 1 7,4 3,8 2,3

F 14 10 2 7,8 4,6 2,8

F 14 10 2 9,1 4,5 2,7

M 14 15 2 7,8 3,9 2,4

M 15 5 2 8,4 4,7 2,9

M 17 0,3 2 6,9 3,7 2,3

F 14 10 1 6 3,7 2,3

F 18 30 2 6,6 3,5 2,2

F 17 20 1 6,9 4 2,5

F 16 0,2 1 9,4 4,3 2,6

M 17 2 2 7,7 3,9 2,4

F 16 10 2 7,1 3,9 2,4

F 17 10 2 9,3 5,4 2,3

M 55 5 2 6,1 3,8 2,3

F 15 10 2 6,2 3,8 2,3

F 15 20 2 10,1 5,2 3,2

F 15 15 2 6,8 3,8 2,3

F 15 15 2 7,9 4,6 2,8

F 19 10 1 8,3 4,7 2,8

M 44 10 2 12,3 5,7 3,5

M 15 15 1 6,1 4,4 2,7

M 16 5 1 7 4,2 2,6

F 17 15 3 6,5 3,9 2,4

M 16 0,5 1 6,9 4 2,4

M 16 1 1 8,6 4,8 2,9

F 16 10 2 9,5 5,3 3,2

F 17 10 3 6,8 4,2 2,6

M 16 5 2 10,2 5,1 3,1

F 16 5 1 8,2 4,6 2,8

M 15 10 2 7,1 4,9 3

M 15 5 1 9,1 4,9 3

M 16 10 3 10,4 5 3,1

M 16 5 1 9,2 4,8 3

F 18 5 2 10,6 4,3 2,6

F 16 25 1 7,1 4,4 2,7

M 46 27 2 7,6 4,1 2,5

F 17 0,8 2 6,8 3,4 2,1

f 17 2 2 7,4 4,5 2,7

F 53 10 2 7 4,2 2,6

F 54 10 3 8,9 5,2 3,2

F 17 10 2 11,8 5,8 3,5

M 50 0,3 2 6,7 3,7 2,2

M 17 10 1 15,4 6,8 4,2

M 17 5 2 6,8 4,1 2,5

M 15 10 2 6,1 3,8 2,3

M 16 5 2 7,5 4,5 2,8

M 19 15 2 8 4,5 2,8

M 17 10 2 6,9 4,7 2,9

M 17 5 2 7,9 4,4 2,7

M 17 5 3 7,1 4,8 2,9

M 17 10 2 6,6 3,9 2,4

F 15 5 2 6,5 3,9 2,4

ReferencesEcological footprint analysishttp://www.bestfootforward.com/resources/ecological-footprint/ http://www.epa.vic.gov.au/Ecologicalfootprint/calculators/default.asp http://footprint.wwf.org.uk/ http://myfootprint.org/en/about_the_quiz/what_it_measures// http://www.bestfootforward.com/resources/ecological-footprint/

Scientific American Paper http://sams.scientificamerican.com/article/humans-not-using-more-than-one-planet/

http://www.statsoft.com/Textbook/Multiple-RegressionChap. 11: Simple Linear Regression