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Ph. D. ThesisPh. D. Thesis 6. Results  Multivariate Calibrations6. Results Multivariate Calibrations 6.1. PLS Calibration6.1. PLS Calibration 6.1.2. Durbin-Watson Statistics6.1.2. Durbin-Watson Statistics
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Ph. D. Thesis
  Abstract
  Table of Contents
  1. Introduction
  2. Theory Fundamentals of the Multivariate Data Analysis
  3. Theory Quantification of the Refrigerants R22 and R134a: Part I
  4. Experiments, Setups and Data Sets
  5. Results Kinetic Measurements
  6. Results Multivariate Calibrations
    6.1. PLS Calibration
      6.1.1. Wald-Wolfowitz Runs Test
      6.1.2. Durbin-Watson Statistics
      6.1.3. Results of Statistical Tests
    6.2. Box-Cox Transformation + PLS
    6.3. INLR
    6.4. QPLS
    6.5. CART
    6.6. Model Trees
    6.7. MARS
    6.8. Neural Networks
    6.9. PCA-NN
    6.10. Neural Networks and Pruning
    6.11. Conclusions
  7. Results Genetic Algorithm Framework
  8. Results Growing Neural Network Framework
  9. Results All Data Sets
  10. Results Various Aspects of the Frameworks and Measurements
  11. Summary and Outlook
  12. References
  13. Acknowledgements
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6.1.2.   Durbin-Watson Statistics

The Durbin-Watson statistics can be used to test for a correlation (non-randomness) of the residuals [231],[234],[235]. The null hypothesis that there is no correlation between the successive residuals is evaluated by:

 
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Thereby ei is the residual corresponding to the observation i and ei-1 is the residual of the preceding observation. The d value is compared to the lower and upper critical values dL and dU proposed by Durbin and Watson [236]. If the calculated d is smaller than the tabulated lower critical value dL, the null hypothesis is rejected meaning that the residuals are correlated. If the calculated d is bigger than the tabulated upper critical value dU, the correlation of the residuals is negligible and if the calculated d is between both tabulated critical values, the test is inconclusive.

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