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2_nonlinear - Assumptions of regression correlation etc...

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Advanced Topics in Forest Biometrics - FOR6934 Non-linear Regression C. Staudhammer, FOR 6934 – fall 2007 Assumptions of regression, correlation, etc. Meeting assumptions is an extremely important prerequisite to data analysis We test if the DEPENDENT data are NORMALLY DISTRIBUTED We test if the variances are HOMOGENOUS BUT what if our data doesn’t meet these assumptions? Do we pretend that they do Or, do we change our data into something else? Or, build a model that looks like our data? C. Staudhammer, FOR 6934 – fall 2007 Building models Models are simplified abstractions of reality Regression, ANOVA, ANCOVA assume linear models In a linear model, all parameters enter the model additively relationships between variables are straight lines when graphed a unit change in a given independent variable has a constant marginal impact on the dependent variable C. Staudhammer, FOR 6934 – fall 2007 Building models – 2 Some models, e.g., Von Bertalanffy growth curve do not assume linearity in the parameters L ( t ) = L 0 *(1- e -k ( t-t 0) ) 0 2 4 6 8 10 12 0 5 10 15 20 t L(t) C. Staudhammer, FOR 6934 – fall 2007 Building models – 3 The goal of modelling is to describe/predict the real world Steps in model building: Selection of model structure that appears most appropriate to the data at hand Selection of appropriate parameters for this model C. Staudhammer, FOR 6934 – fall 2007 Parameter estimation What is a parameter? A parameter is “a quantitative property of a system that is assumed to remain constant over some defined time span of historical data and future prediction” Estimating parameters involves:
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