Topic 18 multiple regression

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Topic 18 multiple regression

  1. 1. Multiple Causes of Food Insecurity: Multiple Regression Analysis Reference: Gujarati (2004)
  2. 2. THE THREE-VARIABLE MODEL
  3. 3. THE THREE-VARIABLE MODEL
  4. 4. THE THREE-VARIABLE MODEL
  5. 5. Maternal education and community characteristics as indicators of nutritional status of children – application of multivariate regression Nutritional Status of Children 5
  6. 6. 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). Nutritional Status of Children 6
  7. 7. Empirical analysis Nutritional Status of Children 7
  8. 8. Empirical analysis Data description and methodology Nutritional Status of Children 8
  9. 9. Table 10.1 Means and standard deviations of variables: Malawi sampleVariables Mean Standard deviationBFEEDNEW 1.57 0.49DIARRHEA 0.16 0.37CALREQ 0.32 0.47ATTCLINI 1.32 0.59AGEMNTH 27.29 16.28CLINFEED 2.29 4.57DRINKDST 1.98 1.39EDUCSPOUS 2.23 1.30LATERINE 0.40 0.49PXFD 9.00 9.85 Nutritional Status of Children 9
  10. 10. Table 10.2 Determinants of weight for age Z-scoresVariables Model 1 Model 2 Coefficients Std. error Coefficients Std. errorConstant -3.03 0.504 -2.93 0.492EDUCSPOUS 0.173 0.058 0.156 0.057ATTCLINI 0.439 0.144 0.439 0.142DRINKDST -0.143 0.051 -0.147 0.05LATERINE 0.134 0.152 0.152 0.148PXFD 0.009 0.008AGEMNTH -0.084 0.021 -0.088 0.021AGESQ 0.001 0.0003 0.001 0.0003CLINFEED 0.717 0.181 0.699 0.179DIARRHEA -0.608 0.201 -0.620 0.198BFEEDNEW 0.664 0.226 0.625 0.224CALREQ 0.566 0.212HEALTDST -0.094 0.071 -0.06 0.072 Nutritional Status of Children 10
  11. 11. Table 10.3 Determinants of height for age Z-scoresVariables Model 1 Model 2 Coefficients Std. error Coefficients Std. errorConstant -2.159 0.677 -2.564 0.685EDUCSPOUS 0.048 0.072 0.106 0.074ATTCLINI 0.514 0.18 0.402 0.177DRINKDST -0.024 0.064 -0.018 0.062LATERINE 0.072 0.192 0.114 0.185PXFD 0.014 0.01AGEMNTH -0.091 0.034 -0.094 0.034AGESQ 0.001 0.0004 0.0009 0.0004CLINFEED 0.686 0.227 0.761 0.224DIARRHEA -0.829 0.261 -0.932 0.260BFEEDNEW 0.149 0.305 0.174 0.299INSECURE 0.252 0.085HEALTDST -0.106 0.092 -0.127 0.091 Nutritional Status of Children 11
  12. 12. Equations to predict the weight for age Z-scores for model 1 Nutritional Status of Children 12
  13. 13. Table 10.4 Summary of the model for determinants of weight for age Z-scores Adjusted R2 Std. error of Models R R2 the estimate 1 0.488 0.238 0.203 1.09 2 0.506 0.256 0.222 1.079 Nutritional Status of Children 13
  14. 14. Table 10.5 Summary of the model for determinants of height for age Z-scores Adjusted R2 Std. error of Models R R2 the estimate 0.418 0.174 0.13 1.285 1 2 0.448 0.201 0.157 1.265 Nutritional Status of Children 14
  15. 15. Table 10.6 Analysis of variance table for weight for age Z-scores Sum ofModels df Mean Square F Sig Squares 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 Nutritional Status of Children 15
  16. 16. Table 10.7 Analysis of variance table for height for age Z-scores Sum of Models df Mean Square F Sig Squares 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 Nutritional Status of Children 16
  17. 17. Table 10.8 Tests of individual coefficients for determinants of weight for age Z-scoresVariables Model 1 Model 2 t-stat P value t-stat P valueConstant -6.016 0.000 -5.956 0.000EDUCSPOUS 2.987* 0.003 2.70* 0.007ATTCLINI 3.047* 0.003 3.102* 0.002DRINKDST -2.817* 0.005 -2.938* 0.004LATERINE 0.882 0.378 1.03 0.304PXFD 1.185 0.237AGEMNTH -4.041* 0.000 -4.282* 0.00AGESQ 3.096* 0.002 3.386* 0.001CLINFEED 3.966* 0.000 3.911* 0.00DIARRHEA -3.018* 0.003 -3.126* 0.002BFEEDNEW 2.935* 0.004 2.791* 0.006CALREQ 2.668* 0.008HEALTDST -1.32 0.188 -0.851 0.396 Note: * denotes at 1 per centof Children Nutritional Status level of significance. 17
  18. 18. Table 10.9 Tests of individual coefficients for determinants of height for age Z-scoresVariables Model 1 Model 2 t-stat P value t-stat P valueConstant -3.187 0.002 -3.745 0.000EDUCSPOUS 0.661 0.509 1.437 0.152ATTCLINI 2.863* 0.005 2.273** 0.024DRINKDST -0.37 0.712 -0.286 0.775LATERINE 0.375 0.708 0.615 0.539PXFD 1.479 0.141AGEMNTH -2.642* 0.009 -2.78* 0.006AGESQ 1.949** 0.053 2.022** 0.044CLINFEED 3.018* 0.003 3.394* 0.001DIARRHEA -3.171* 0.002 -3.584* 0.00BFEEDNEW 0.489 0.625 0.580 0.563INSECURE 2.977* 0.003HEALTDST -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. Nutritional Status of Children 18
  19. 19. Table 10.10 Part and partial correlation coefficients for weight for age and height for ageVariables Weight for age Height for age Part correlation Partial correlation Part correlation Partial correlationEDUCSPOUS 0.169 0.19 0.042 0.046ATTCLINI 0.172 0.193 0.183 0.197DRINKDST -0.159 -0.179 -0.024 -0.026LATERINE 0.05 0.057 0.024 0.026PXFD 0.067 0.076 0.094 0.103AGEMNTH -0.228 -0.253 -0.168 -0.182AGESQ 0.175 0.196 0.124 0.136CLINFEED 0.224 0.248 0.192 0.207DIARRHEA -0.17 -0.192 -0.202 -0.217BFEEDNEW 0.166 0.187 0.031 0.034HEALTDST -0.075 -0.085 -0.073 -0.08 Nutritional Status of Children 19
  20. 20. Figure 10.1 Histogram of standardized residuals of weight for age Nutritional Status of Children 20
  21. 21. Figure 10.2 Normal P-P plot of regression standardized residuals Nutritional Status of Children 21
  22. 22. Figure 10.3 Residuals plotted against predicted values for weight for age Nutritional Status of Children 22
  23. 23. Figure 10.4 Residuals plotted against predicted values for height for age Nutritional Status of Children 23

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