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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.
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Footprint
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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
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Ecological footprint F is calculated by this equation:
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Ei = ecological footprint coming from the waste
Ci = product i-thqi = (hectare/kg) reciprocal of the average productivity per hectare produced the i-
th.
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The ecological footprint per capita f is calculated by
dividing for the population N residing in the region
considered:
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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%.
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Ecological footprint in the world
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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
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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
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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
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• usually holiday 1- close to home 2- a short flight away 3- a long flight away
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• I live in a 1 – large house 2 – medium-sized house 3 – small house 4 – flat/apartment 5 – zero emission development
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• 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
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• My heating/cooling bills are relatively 1 – normal 2 – high 3 – low
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• I buy my electricity from 1 – non-renewable sources
2 – renewable sources
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• I tend 1 – not to conserve energy 2 – to conserve energy
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• I am 1 – a regular meat-eater 2 – an occasional meat-eater 3 – a heavy meat-eater 4 – a vegetarian 5 – a vegan
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• usually eat 1 – a mix of fresh and convenience
foods 2 – mostly fresh, locally grown produce 3 – mostly convenience foods
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• I produce 1 – an average 2 – a below average 3 – an above average 4 – half the average amount of domestic waste
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• most of which is 1 – not recycled 2 – recycled
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Aim of our research: to study the impact of specific characteristics of the respondents about their ecological footprint.
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How we made it: For data processing we used methods provided by a branch of statistics known as econometrics.
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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.
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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
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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
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Deterministic Models
1. Hypothesize Exact Relationships2. Suitable When Prediction Error is
Negligible
EPI 809/Spring 2008 27
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Probabilistic Models
1. Hypothesize 2 Components Deterministic Random Error
EPI 809/Spring 2008 28
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Types of Probabilistic Models
ProbabilisticModels
RegressionModels
CorrelationModels
OtherModels
EPI 809/Spring 2008 29
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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
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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
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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
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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
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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
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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
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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
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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
^
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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:
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• 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;
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• independent variables: - age
- usually - Number of people in
household - distance home-school/work
(categorical variable: 1 = 5km, 10km = 2, 3 = 15km)
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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).
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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
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Footprint
a + b age + c sort + d sensation +…. + e
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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.
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Specifically:- the absolute value of the coefficient indicates the
strength of the effect of the independent on the dependent variable.
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What next?Next year the above model will be
estimated using a specific statistics
program : Stata.
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The following slides report our collected data from Footprint quizzes
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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
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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
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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
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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
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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
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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
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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