Multiple Causes of Food Insecurity: Multiple Regression Analysis

Reference: Gujarati (2004)

THE THREE-VARIABLE MODEL

THE THREE-VARIABLE MODEL

THE THREE-VARIABLE MODEL

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Maternal education and community characteristics as indicators of nutritional

status of children – applicationof multivariate regression

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Main results

• Step 1: Estimating the coefficients of the model(Table 10.2,10.3).• Step 2: Examining how good the model predicts(Table 10.4,10.5).• Step 3: Hypotheses testing.• Tests about the equation(Table 10.6,10.7).• Tests about individual coefficients(Table 10.8,10.9).• Part and partial correlation coefficients.• Step 4: Checking for violations of regression assumptions.• Checking normality of the errors(Table 10.10,Figure 10.1,10.2).• Checking for homogeneity of variance of the residuals(Figure

10.3,10.4).

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Empirical analysis

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Empirical analysis

Data description and methodology

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Table 10.1 Means and standard deviations of variables: Malawi sample

Variables Mean Standard deviation

BFEEDNEW 1.57 0.49

DIARRHEA 0.16 0.37

CALREQ 0.32 0.47

ATTCLINI 1.32 0.59

AGEMNTH 27.29 16.28

CLINFEED 2.29 4.57

DRINKDST 1.98 1.39

EDUCSPOUS 2.23 1.30

LATERINE 0.40 0.49

PXFD 9.00 9.85

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Table 10.2 Determinants of weight for age Z-scoresVariables Model 1 Model 2

Coefficients Std. error Coefficients Std. error

Constant -3.03 0.504 -2.93 0.492

EDUCSPOUS 0.173 0.058 0.156 0.057

ATTCLINI 0.439 0.144 0.439 0.142

DRINKDST -0.143 0.051 -0.147 0.05

LATERINE 0.134 0.152 0.152 0.148

PXFD 0.009 0.008

AGEMNTH -0.084 0.021 -0.088 0.021

AGESQ 0.001 0.0003 0.001 0.0003

CLINFEED 0.717 0.181 0.699 0.179

DIARRHEA -0.608 0.201 -0.620 0.198

BFEEDNEW 0.664 0.226 0.625 0.224

CALREQ 0.566 0.212

HEALTDST -0.094 0.071 -0.06 0.072

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Table 10.3 Determinants of height for age Z-scoresVariables Model 1 Model 2

Coefficients Std. error Coefficients Std. error

Constant -2.159 0.677 -2.564 0.685

EDUCSPOUS 0.048 0.072 0.106 0.074

ATTCLINI 0.514 0.18 0.402 0.177

DRINKDST -0.024 0.064 -0.018 0.062

LATERINE 0.072 0.192 0.114 0.185

PXFD 0.014 0.01

AGEMNTH -0.091 0.034 -0.094 0.034

AGESQ 0.001 0.0004 0.0009 0.0004

CLINFEED 0.686 0.227 0.761 0.224

DIARRHEA -0.829 0.261 -0.932 0.260

BFEEDNEW 0.149 0.305 0.174 0.299

INSECURE 0.252 0.085

HEALTDST -0.106 0.092 -0.127 0.091

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Equations to predict the weight for age Z-scores for model 1

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Table 10.4 Summary of the model for determinants of weight for age Z-scores

Models R R2 Adjusted R2 Std. error of the estimate

1 0.488 0.238 0.203 1.09

2 0.506 0.256 0.222 1.079

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Table 10.5 Summary of the model for determinants of height for age Z-scores

Models R R2 Adjusted R2 Std. error of the estimate

1 0.418 0.174 0.13 1.285

2 0.448 0.201 0.157 1.265

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Table 10.6 Analysis of variance table for weight for age Z-scores

Models Sum of Squares df Mean Square F Sig

I Regression 89.139 11 8.104 6.797 0

Residual 284.936 239 1.192

Total 374.075 250

II Regression 95.757 11 8.705 7.475 0

Residual 278.318 239 1.165

Total 374.075 250

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Table 10.7 Analysis of variance table for height for age Z-scores

Models Sum of Squares df Mean Square F Sig

I Regression 70.948 11 6.45 3.901 0.00

Residual 335.649 203 1.653

Total 406.597 214

II Regression 81.525 11 7.411 4.628 0.00

Residual 325.072 203 1.601

Total 406.597 214

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Table 10.8 Tests of individual coefficients for determinants of weight for age Z-scores

Variables Model 1 Model 2

t-stat P value t-stat P value

Constant -6.016 0.000 -5.956 0.000

EDUCSPOUS 2.987* 0.003 2.70* 0.007

ATTCLINI 3.047* 0.003 3.102* 0.002

DRINKDST -2.817* 0.005 -2.938* 0.004

LATERINE 0.882 0.378 1.03 0.304

PXFD 1.185 0.237

AGEMNTH -4.041* 0.000 -4.282* 0.00

AGESQ 3.096* 0.002 3.386* 0.001

CLINFEED 3.966* 0.000 3.911* 0.00

DIARRHEA -3.018* 0.003 -3.126* 0.002

BFEEDNEW 2.935* 0.004 2.791* 0.006

CALREQ 2.668* 0.008

HEALTDST -1.32 0.188 -0.851 0.396

Note: * denotes at 1 per cent level of significance.

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Table 10.9 Tests of individual coefficients for determinants of height for age Z-scores

Variables Model 1 Model 2t-stat P value t-stat P value

Constant -3.187 0.002 -3.745 0.000

EDUCSPOUS 0.661 0.509 1.437 0.152

ATTCLINI 2.863* 0.005 2.273** 0.024

DRINKDST -0.37 0.712 -0.286 0.775

LATERINE 0.375 0.708 0.615 0.539

PXFD 1.479 0.141

AGEMNTH -2.642* 0.009 -2.78* 0.006

AGESQ 1.949** 0.053 2.022** 0.044

CLINFEED 3.018* 0.003 3.394* 0.001

DIARRHEA -3.171* 0.002 -3.584* 0.00

BFEEDNEW 0.489 0.625 0.580 0.563

INSECURE 2.977* 0.003

HEALTDST -1.15 0.252 -1.395 0.164

Note: * denotes at 1 per cent level of significance, ** denotes at 5 per cent level of significance.

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Table 10.10 Part and partial correlation coefficients for weight for age and height for age

Variables Weight for age Height for agePart correlation Partial correlation Part correlation Partial correlation

EDUCSPOUS 0.169 0.19 0.042 0.046

ATTCLINI 0.172 0.193 0.183 0.197

DRINKDST -0.159 -0.179 -0.024 -0.026

LATERINE 0.05 0.057 0.024 0.026

PXFD 0.067 0.076 0.094 0.103

AGEMNTH -0.228 -0.253 -0.168 -0.182

AGESQ 0.175 0.196 0.124 0.136

CLINFEED 0.224 0.248 0.192 0.207

DIARRHEA -0.17 -0.192 -0.202 -0.217

BFEEDNEW 0.166 0.187 0.031 0.034

HEALTDST -0.075 -0.085 -0.073 -0.08

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Figure 10.1 Histogram of standardized residuals of weight for age

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Figure 10.2 Normal P-P plot of regression standardized residuals

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Figure 10.3 Residuals plotted against predicted values for weight for age

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Figure 10.4 Residuals plotted against predicted values for height for age