Sihua Peng, PhD Shanghai Ocean University 2017.10 Biostatistics 7. Introduction to Linear models Sihua Peng, PhD Shanghai Ocean University 2017.10

Contents Introduction to R Data sets Introductory Statistical Principles Sampling and experimental design with R Graphical data presentation Simple hypothesis testing Introduction to Linear models Correlation and simple linear regression Single factor classification (ANOVA) Nested ANOVA Factorial ANOVA Simple Frequency Analysis

7. Introduction to Linear models A statistical model is an expression that attempts to explain patterns in the observed values of a response variable by relating the response variable to a set of predictor variables and parameters. response variable = model + error

7.1 Linear models An example of a very simple linear model, is the model used to investigate the linear relationship between a continuous response variable (Y and a single continuous predictor variable, X):

7.2 Linear models in R > Y<-c(0,1,2,4,7,10) > X<-1:6 > plot(Y~X)

7.2 Linear models in R > Fictitious.lm <- lm(Y~X) To examine the estimated parameters (and hypothesis tests) from the fitted model, provide the name of the fitted model as an argument to the summary()function. > summary(Fictitious.lm)