文档介绍：第12章简单线性回归与相关
The Simple Linear Regression and Correlation
本章概要
Types of Regression Models
Determining the Simple Linear Regression Equation
Measures of Variation in Regression and Correlation
Assumptions of Regression and Correlation
Residual Analysis and the Durbin-Watson Statistic
Estimation of Predicted Values
Correlation - Measuring the Strength of the Association
Purpose of Regression and Correlation Analysis 回归与相关分析的目的
Regression Analysis is Used Primarily for Prediction(回归主要用于预测)
A statistical model used to predict the values of a dependent or response variable based on values of at least one independent or explanatory variable
Correlation Analysis is Used to Measure Strength of the Association Between Numerical Variables(度量关系密切程度)
The Scatter Diagram 散点图
Plot of all (Xi , Yi) pairs
Types of Regression Models
Positive Linear Relationship
Negative Linear Relationship
Relationship NOT Linear
No Relationship
Simple Linear Regression Model 简单线性回归模型
Y intercept
Slope
The Straight Line that Best Fit the Data
Relationship Between Variables Is a Linear Function
Random Error
Dependent (Response) Variable
Independent (Explanatory) Variable
i
= Random Error
Y
X
Population Linear Regression Model
Observed Value
Observed Value
YX
i
X
0
1
Y
X
i
i
i
0
1
Sample Linear Regression Model 简单线性相关模型
Yi
= Predicted Value of Y for observation i
Xi
= Value of X for observation i
b0
= Sample Y - intercept used as estimate of the population 0
b1
= Sample Slope used as estimate of the population 1
Simple Linear Regression Equation: Example
You wish to examine the relationship between the square footage of produce stores and its annual sales. Sample data for 7 stores were obtained. Find the equation of the straight line that fits the data best
Annual Store Square Sales Feet ($000)
1 1,726 3,681
2 1,542 3,395
3 2,816 6,653
4 5,555 9,543
5 1,292 3,318
6 2,208 5,563
7 1,313 3,760
Scatte