Statistics in WR: Lecture 11

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Presentation transcript:

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

Regression Assumptions

Formulas used in the derivation of the normal equations

(1) Plot the data: TDS vs Q Cuyahoga River

(1a) Plot the Data: TDS vs LogQ

(2) Interpret Regression Statistics

A good set of Residuals

Residuals for TDS vs LogQ relationship

Durbin-Watson Statistic for testing autocorrelation of the residuals

Multiple Linear Regression

Simple vs Complex regression models

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/section3/eda3673.htm