1. Linear Model

2. Formal Definition

3. General Linear Model

4. 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

5. Polynomial Regression

6. 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

7. GLM

8. Generalized Linear Models

10. 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

11. Normal Distribution WikipediaAKA “Gaussian” Distribution

12. Binomial Number of successes of yes/no experimentsWikipedia

13. Poisson Number of events in time T, k=number of occurrences Wikipedia

14. Gamma Distribution Wait times, seed distribution, etc. Wikipedia

15. Deviance

16. Degrees of Freedom