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Linear Model. - residual or error. Formal Definition. , - observed values of predictor variables (i.e. temperature, precipitation) - observed value of the response variable (i.e. tree height) - y intercept:. General Linear Model. General Linear Model.

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## Linear Model

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**Linear Model**- residual or error**Formal Definition**• ,- observed values of predictor variables (i.e. temperature, precipitation) • - observed value of the response variable (i.e. tree height) • - y intercept:**General Linear Model**• Can transform the predictor values to linearize the relationship between the predictors and the response • Also changes the variance so it only should be done if the variance is not uniform and is made uniform by the transform**Need More**• Not all phenomenon follow linear response • Not all residuals are normally distributed • This leads: • GLMs: Single function, specified regression distribution • GAMs: Multiple functions • “Non-parametric” approaches: function is determined by the computer**GLM**• Generalized Linear Model • Not to be confused with a general linear model • Allows a linear model to be related to the response variable via a “Link” function. • Also requires to be from a defined probability distribution**Generalized Linear Models**• - a random variable with some probability distribution • Related to the response values • - error • Residuals • Linear model without the intercept • - Expected value of • Predicted value (no error)**Generalized Linear Models**• Linear model without the error • is a “link” function • = ) • is from a known probability distribution**Common Functions in R**• Probability Distribution (Link Function) • Binomial (link = "logit") • True/false, alive/dead • Gaussian (link = "identity") • Continuous, normal • Gamma (link = "inverse") • Seed distribution, distance from… • Poisson (link = "log") • Counts**Normal Distribution**Wikipedia**Binomial**Number of successes of yes/no experiments**Poisson**Number of events in time T, k=number of occurrences**Gamma Distribution**Wait times, seed distribution, etc.

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