# Statistics for Environmental Engineers

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Ordinary linear regression is similar to correlation in that there are two variables involved and the relation between them is to be investigated. In regression, the two variables of interest are assigned particular roles. One (x) is treated as the independent (predictor) variable and the other (y) is the dependent (predicted) variable. Regression analysis assumes that only у is affected by measurement error, while x is considered to be controlled or measured without error. Regression of x on у is not strictly valid when there are errors in both variables (although it is often done). The results are useful when the errors in are small relative to the errors in у. As a rule-of-thumb, “small” means sx < 1/3sy. When the errors in x are large relative to those in у, statements about probabilities of confidence intervals on regression coefficients will be wrong. There are special regression methods to deal with the errors-in-variables problem (Mandel, 1964; Fuller, 1987; Helsel and Hirsch, 1992).

### References

Chatfield, C. (1983). Statistics for Technology, 3rd ed., London, Chapman & Hall.

Folks, J. L. (1981). Ideas of Statistics, New York, John Wiley.

Fuller, W. A. (1987). Measurement Error Models, New York, Wiley.

Helsel, D. R. and R. M. Hirsch (1992). Studies in Environmental Science 49: Statistical Models in Water Resources, Amsterdam, Elsevier.

Mandel, J. (1964). The Statistical Analysis of Experimental Data, New York, Interscience Publishers.

Miller, J. C. and J. N. Miller (1984). Statistics for Analytical Chemistry, Chichester, England, Ellis Horwood Ltd.

Siegel, S. and N. J. Castallan (1988). Nonparametric Statistics for the Behavioral Sciences, 2nd ed., New York, McGraw-Hill.

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