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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


Objectives

Identify parameters to model the budget per month allocated toorganic food

Obtain the data through a survey

Build a representative model


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


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


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


Variables


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


Variables


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


Use of Log(Budget)

Figure: Log(Budget) against Bio


Data Analyses

Figure: consumer’s concern forbiological products

Figure: Budget allocated tobiological products per month


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


Correlation

The goal of this section is to simplify our model:

Figure:First part of the correlation matrix


Correlation

Figure:Second part of the correlation matrix


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.


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


EViews results for the first Mode

Figure:first regression with EViews


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


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.


EViews results for the Second regression

Figure:Second regression with EViews


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.


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.


EViews results for the Third regression

Figure:Third regression with EViews


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


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


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.


Ramsey RESET Test

Figure: Ramsey RESET Test result

This test allow us to reject the Null hypothesis. The Classicalassumption of linearity fail.


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.


Heteroscedasticity

Figure: Plot of budget against residuals

Thanks to this graphic it seams that we reject Heteroscedasticity of theerrors if we ignore outliers.


Heteroscedasticity Test

Figure: Heteroscedasticity Test result result (White)

We do reject the Null, but the White Heteroscedasticity test is to generalfor our data.


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


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


Questions?

Thank you for your attention.


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