6.1.2. Durbin-Watson Statistics (Dr. Frank Dieterle)

Frank Dieterle

Ph. D. Thesis

6. Results – Multivariate Calibrations

6.1. PLS Calibration

6.1.2. 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:

(26)

Thereby e_i is the residual corresponding to the observation i and e_i-1 is the residual of the preceding observation. The d value is compared to the lower and upper critical values d_L and d_U proposed by Durbin and Watson [236]. If the calculated d is smaller than the tabulated lower critical value d_L, the null hypothesis is rejected meaning that the residuals are correlated. If the calculated d is bigger than the tabulated upper critical value d_U, 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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