1. Claire Ferguson 1, Adrian Bowman 1, Marian Scott 1 and Laurence Carvalho 2 1 University of Glasgow 2 Centre for Ecology & Hydrology A Case Study of Loch Leven http://www.tulbol.demon.co.uk/art/banatvewe.jpg Regression Case Study Additive and Varying-Coefficient Models

2. Dataset: 1968 - 2002 150 variables measured, covering… Physics Lake chemistry Lake biology Weather Loch Leven (LL)

3. Loch Leven – The Data

4. The EC Water Framework Directive (WFD) 2000 states that there should be good status in all shallow waters by 2016. Research: Investigating statistical techniques to explore the combined impacts of climate and nutrients on water quality. Motivation

5. chlorophyll a Response year, month, SRP, Daphnia, water temp, NO 3 -N Covariates Additive Model 1988 - 2002

6. Chlorophyll

7. Mainly linear relationships between variables. Little evidence of trend and seasonality. Important ecological relationships identified. The nature of trends and relationships can be explored simultaneously. For chlorophyll a (in this time period)- Summary of Additive Models

8. Linear Regression Model Varying-coefficient Model (VCM) Varying-coefficient Model m = month Do relationships change throughout the year?

9. VCM LL Case Study 1988-2007