概率与统计（英文）chapter 12 Simple Linear Regression.ppt

Simple Linear Regression
and Correlation
Introduction
Regression analysis is the part of statistics that deals with investigation of the relationship between two or more variables relation in a nondeterministic fashion. In this chapter, we generalize the linear relation y= β0+β1x to a linear probabilistic relationship, develop procedures for making inferences about the parameters of the model, and obtain a quantitative measure of the extent to which the two variables are related.
The Simple Linear Regression Model
Whose value is fixed by the experimenter will be denote by x.
x may called Independent variable, Predictor variable, Explanatory variable
For fixed x, the second variable y will be random, we called it Dependent variable, Response variable, Explained variable
The correlation relationship between variables
x=the age of child
y=the size of vocabulary
x=5
y=100,200,300,400,500,…,1000
OR
Example : Visual and musculoskeletal problems associated with the use of visual display terminals (VDTs) have become rather common in recent years. Some researchers have focused on vertical gaze direction as a source of eye strain and irritation. This direction is known to be closely related to ocular surface area (OSA), so a method of measuring OSA is needed. The accompanying representative data on y=OSA (cm2) and x=width of the palprebal fissure is from the article “Analysis of Ocular Surface Area for Comfortable VDT Workstation Layout”. The order in which observations were obtained was not given, so for convenience they are listed in increasing order of x values.
The first step in regression analysis----Scatter plot
Example Forest growth and decline phenomena throughout the world have attracted considerable public and scientific interest. The article “ Relationship among crown condition, growth, and stand nutrition in seven northern sugarbushes” included a scatter plot y= mean crown dieback(%), one indicator