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Statistics in WR: Lecture 11

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

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Statistics in WR: Lecture 11

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  1. 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

  2. Regression Assumptions

  3. Formulas used in the derivation of the normal equations

  4. (1) Plot the data: TDS vs QCuyahoga River

  5. (1a) Plot the Data: TDS vs LogQ

  6. (2) Interpret Regression Statistics

  7. A good set of Residuals

  8. Residuals for TDS vs LogQ relationship

  9. Durbin-Watson Statistic for testing autocorrelation of the residuals

  10. Multiple Linear Regression

  11. Simple vs Complex regression models

  12. 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

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