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 Q Cuyahoga 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: