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

2. 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

3. 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

4. 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):

5. 7.2 Linear models in R > Y<-c(0,1,2,4,7,10) > X<-1:6
> plot(Y~X)

6. 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)