第12章简单线性回归与相关 The Simple linear regression and correlation
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 orrelation- Measuring the Strength of the Association
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)
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, y) pairs Y 60 40 20 0 + X 0 20 40 60
The Scatter Diagram 散点图 0 20 40 60 0 20 40 60 X Y Plot of all (Xi , Yi ) pairs
Types of Regression Models Positive Linear relationship Relationship not linear 3.5 2.5 3 5150 15 10 15 Negative Linear Relationship No Relationship 864202 76543 2 10
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 Relationship between Variables Is a Linear Function The Straight Line that Best Fit the Data Y intercept Random Error Yi=Bo+B,Xi+8 Dependent (Response) Independent Slope Variable (Explanatory) Variable
Simple Linear Regression Model 简单线性回归模型 Yi Xi i = + + 0 1 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
Population Linear regression Model Y=阝0+β1X1+ i Observed Value 8,=Random Error 阝0+β1X X Observed Value
i = Random Error Y X Population Linear Regression Model Observed Value Observed Value YX = 0 + 1Xi Yi = + Xi + i 0 1
Sample linear regression model 简单线性相关模型 bo+bX Predicted Value of y for observation i X = Value of X for observation i bo =Sample y-intercept used as estimate of the population Bo b,=Sample Slope used as estimate of the population BI
Sample Linear Regression Model 简单线性相关模型 Y i = b 0 + b 1 X i 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 Annual Store Square Sales Feet ($000) ou wish to exarate 1726 3.681 relationship bet eesthe 1,542 3.395 square Footage o 3 2,816 6.653 produce stores and its 5555 9,543 annual sales. Sample 5 1.292 data for 7 stores were 3,318 obtained. Find the 6 2,208 5563 equation of the straight 7 1.313 3,760 line that fits the data best
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
Scatter Diagram Example 12000 10000 8000 s6000 4000 2000 0 100020003000400050006000 square Feet
Scatter Diagram Example 0 2000 4000 6000 8000 10000 12000 0 1000 2000 3000 4000 5000 6000 S q u a re F e e t Annual Sales ($000)