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Who eats organic?
Gonzague Denise Valentin Jung
ENAC
April 8, 2016
Gonzague Denise Valentin Jung (ENAC) Who eats organic? April 8, 2016 1 / 32
Table of contents
1 IntroductionObjectivesThe SurveyVariables
2 First ModelData AnalysesModelSimplification of themodelFirst linear regression
3 Second ModelSecond linear regressionOptimisation of thesecond Model
4 Third ModelThird linear regressionInterpretation ofcoefficientsValidity of the modelModel Conclusion
5 Testing the modelRamsey RESET TestStrict exogeneity andNormalityHeteroscedasticity
6 ConclusionImprovement
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Objectives
Identify parameters to model the budget per month allocated toorganic food
Obtain the data through a survey
Build a representative model
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How to obtain data?
Our target : consumers
Our survey was made with GoogleForm and distributed through severalmeans like Facebook, e-mail orGoogle. We have acquired 140answers in 5 days, 139 are workable. figure:Our survey
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Data Particularities
Variables with Y/N
Binary code : ”1” or ”0”
Questions with multiple choice answers
With k=0,..,n
All possibilities are observed
Can not take all k
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Variables
Number of variables : k=28
Explanatory variables Special feature
Age NumberSex Man/WomanHeight Height(cm)Weight Weight(kg)Situation Single/Couple/marriedKids NumberFoot Y/NCar Y/NBike Y/NBus Y/NIncome Income per monthTown Big town/mean town/small town
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Variables
Explanatory variables Special feature
Income Income per monthTown Big town/mean town/small townWork Student/worker/OtherStudy Number of years after the BACSort Y/NEggs Code0/Code1/Code2/Code3Chicken Y/NGarden Y/NCompobin Y/NFruitveg Consumption per dayCook Number of cooked meal per week
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Variables
Explanatory variables Special feature
biofood Y/N(regular consumption)Budget Biological budget per monthWherebio Supermarket/biocopTime Time to go to the storeHowmanybio who consume biologicalBio From 1 to 10 BioFastfood fast food per monthDiet diet/Normal diet/No diet
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Use of Log(Budget)
Figure: Log(Budget) against Bio
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Data Analyses
Figure: consumer’s concern forbiological products
Figure: Budget allocated tobiological products per month
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Expression of our First model
Equation for a linear regression:
BUDGET=βX + µ
BUDGET:biological budget per month
X matrix of dimension 139x29 (observations x variables).
β is the vector of coefficients
µ is the vector of the error
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Correlation
The goal of this section is to simplify our model:
Figure:First part of the correlation matrix
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Correlation
Figure:Second part of the correlation matrix
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Correlation
Highly correlated variables (|P | ≥ 50)
Bio-food/Bio = 0.55
Age/Income = 0.60
Age/Kids = 0.80
Age/Work = 0.72
Garden/Compo-Bin = 0.66
Sex/Weight = 0.56
Work/Kids = 0.54
Work/Income = 0.57
We choose to delete Age due to high p-value and the fact that is appears3 times.
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First model
After simplification we obtain for the first linear equation:BUDGET=β0 + β1Bike + β1Bio + β2(Bio − food) + β3Bus + β4Car +β5Chicken + β6(Compo − bin) + β7Cook + β8(Diet = 2) + β9(Diet =1) + β10(Eggs = 0) + β11(Eggs = 1) + β12(Eggs =2) + β13(Fast − food) + β14Foot + β15(Fruit − veg) + β16Garden +β17Height + β18(How −many − bio) + β19Income + β20Kids +β21Sex + β22(Situation = 1) + β23(Situation = 2) + β24(Situation =3) + β25Sort + β26Study + β27Time + β28(Town = 1) + β29(Town =2) + β30Weight + β31(Where − bio) + β32Work
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EViews results for the first Mode
Figure:first regression with EViews
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Study of the model
How improve our model?
The previous model gives incoherent value according to high value inprobability. That is why we decide to delete variables with a |P| ≥50:
Bike
Car
Compo-bin
Diet=1
Diet=2
Eggs=0
Eggs=1
Eggs=2
Chicken
Foot
Fruit-veg
Garden
Time
Town=1
Town=2
Where-bio
Sex
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Second linear regression
We keep only the significant variables:BUDGET = β0 + β1Bio + β2(Bio − food) + β3Bus + β4(Compo −bin) + β5Cook + β6(Fast − food) + β7Height + β8(How −many − bio) +β9Income + β10Kids + β11(Situation = 1) + β12(Situation =2) + β13(Situation = 3) + β14Sort + β15Study + β16Weight + β17WorkIt remain 17 variables on the 32 for the first regression.
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EViews results for the Second regression
Figure:Second regression with EViews
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Analyse of the results
We still have non significant coefficient.
R-squared value
Value First Model Second Model
R-squared 0.48 0.45Adjusted R-squared 0.23 0.37
We decide to delete : Compo-bin, Cook, Situation=1, Situation=2 andSort.We also decide to delete Work because there are to many students.
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Third linear regression
BUDGET = β0 + β1Bio + β2(Bio − food) + β3Bus + β4(Fast − food) +β5Height +β6(How −many −bio) +β7Income +β8Kids +β9(Situation =3) + β10Study + β11WeightIt remain 11 variables on the 32 for the first regression.
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EViews results for the Third regression
Figure:Third regression with EViews
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Interpretation
Variables Effects Consequences
Bio + +6.60 if Bio increaseBio-food + +41.6 if regular consumption of bio foodBus - -20.1 if take the busFast-food + +5.57 if frequency increaseHeight + +0.294 if height increaseHow-many-bio + +1.13 if know more bio consumersIncome + +0.0054 if income increaseKids + +25.0 if kids increaseSituation=3 + +30.7 if marriedstudy - -5.63 if Study increaseWeight - -0.484 if Weight increase
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validity of the model
importance of R-squared and F-statistic
R-squared=0.40
Adjusted R-squared=0.35
Prob(F-statistic)=0.000000
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Model Conclusion
Adjusted R-squared decreases in the third model because we havedeleted Work. The value remains quite low.
We can probably improve the model.
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Ramsey RESET Test
Figure: Ramsey RESET Test result
This test allow us to reject the Null hypothesis. The Classicalassumption of linearity fail.
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Strict exogeneity and Normality
Figure: repartition of the errors
Figure: Normality of the errors
Thanks to Jarque-Bera test wereject the Normality of the errors.
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Heteroscedasticity
Figure: Plot of budget against residuals
Thanks to this graphic it seams that we reject Heteroscedasticity of theerrors if we ignore outliers.
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Heteroscedasticity Test
Figure: Heteroscedasticity Test result result (White)
We do reject the Null, but the White Heteroscedasticity test is to generalfor our data.
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Conclusion
Model
Our model is not perfect. In fact, we can’t verify all of the classicalassumptions.
Problems of our model
Difficult to estimate the budget allocated to biological products
The population is not homogeneous
We could probably improve the results with more answers to oursurvey
We could have improved our survey
It is difficult to include many binary variables
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Improvement of our model
Figure: Test if βincome = 0
According to this test we do notreject H0=(βincome = 0)
Other assumptions
We could have hiddenmulticolinearity
Only few variables really matteraccording to the probabilities
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