Statistics in WR: Lecture 11

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Statistics in WR Lecture 11

• Key Themes
• Simple Linear Regression
• Derivation of the normal equations
• Multiple Linear Regression
• Reading Helsel and Hirsch Chapter 7 Comparing
  several independent groups
• Reading Barnett, Environmental Statistics
  Chapter 10 Time series methods
• Slides are from Helsel and Hirsch, Chapter 9

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Regression Assumptions
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Formulas used in the derivation of the normal
equations
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(1) Plot the data TDS vs QCuyahoga River
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(1a) Plot the Data TDS vs LogQ
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(2) Interpret Regression Statistics
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A good set of Residuals
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Residuals for TDS vs LogQ relationship
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Durbin-Watson Statistic for testing
autocorrelation of the residuals
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Multiple Linear Regression
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Simple vs Complex regression models
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F-distribution
http//en.wikipedia.org/wiki/F-test
If U is a Chisquare random variable with m
degrees of freedom, V is a Chisquare random
variable with n degrees of freedom, and if U and
V are independent, then the ratio (U/m)/V/n)
has an F-distribution with (m, n) degrees of
freedom. Haan, Statistical Methods in
Hydrology, p.122 The values of the
F-statistic are tabulated at
http//www.itl.nist.gov/div898/handbook/eda/sectio
n3/eda3673.htm