Multiple Regression Analysis in Ecology: UCSB ESM 206B Course Outline, Study notes of Environmental Science

Download Multiple Regression Analysis in Ecology: UCSB ESM 206B Course Outline and more Study notes Environmental Science in PDF only on Docsity! 30 March 2009 UCSB ESM 206B Stephanie Hampton National Center for Ecological Analysis & Synthesis Contact for appointment – [email protected] Lectures & labs Readings posted to website Lab assignments & take-home “micro-exam” 30 March Review Multiple Regression 1 April Model Selection in Multiple Regression 6-8 April Nonlinear Regression 13-15 April Logistic Regression 20-22 April Bootstrapping & Monte Carlo 27-29 April Similarity Metrics for Multivariate Stats Suggestions? 1. Simple regression Yi = β0 + β1 Xi +εi e.g. Log(Biomass, mg/L) = -41.49+ 9.02(temperature, C) R2 = 0.52 P < 0.001 1. Simple regression Yi = β0 + β1 Xi +εi e.g. Log(Biomass, mg/L) = -41.49+ 9.02(temperature, C) R2 = 0.52 P < 0.001 1a. Bad residuals? Biomass 2507 200 6 7 8 9 101112131415 1617 Temp 1b. Where do parameters come from? Yi = β0 + β1 Xi +εi 1b. Where do parameters come from? Yi = β0 + β1 Xi +εi SS = Σ(Yi – β0 - β1 Xi) Neter et al 1996 Applied Linear Statistics. McGraw-Hill 1b. Where do parameters come from? Yi = β0 + β1 Xi +εi SS = Σ(Yi – β0 - β1 Xi) Minimize this number = “least squares” method Neter et al 1996 Applied Linear Statistics. McGraw-Hill 1b. Least squares Yi = β0 + β1 Xi +εi e.g. Log(Biomass, mg/L) = -41.49+ 9.02(temperature, C) 2. Multiple regression (1st order = no interactions) Yi = β0 + β1 X1,i + β2 X2,i +εi 2. Multiple regression (1st order = no interactions) Yi = β0 + β1 X1,i + β2 X2,i +εi e.g. Log(Biomass, mg/L) = -41.49+ 9.02(temperature, C) + 7.10(Phosphorus, ug/L Parameters differ from simple regression Log(Biomass, mg/L) = 60.72 + 9.49(temperature, C) Log(Biomass, mg/L) = 56.44 + 8.14(Phosporus, ug/L) 2. Multiple regression (1st order = no interactions) Yi = β0 + β1,i X1 + β2,i X2 +εi Log(Biomass, mg/L) = -41.49+ 9.02(temperature, C) + 7.10(Phosphorus, ug/L Partial Regression Parameters -41.49+ 9.02(temperature, C) + 7.10(Phosphorus, ug/L) Log(Biomass, mg/L) = 60.72 + 9.49(temperature, C) Log(Biomass, mg/L) = 56.44 + 8.14(Phosporus, ug/L) 3. Multicollinearity – correlated Xn variables Yi = β0 + β1 X1,i + β2 X2,i +εi 3. Multicollinearity – correlated Xn variables Cyanobacteria = β1 Phosphorus + β2 Caffeine 3. Multicollinearity – correlated Xn variables Cyanobacteria = β1 Phosphorus + β2 Caffeine 3. Multicollinearity – correlated Xn variables Cyanobacteria = β1 Phosphorus + β2 Caffeine Generally increases parameter estimates Confounds interpretation