Lecture 9_Simple Linear Regression 第九章 简单线性回归分析.ppt

Chapter 12 Simple Linear Regression Learning Objectives In this chapter, you learn: How to use regression analysis to predict the value of a dependent variable based on an independent variable The meaning of the regression coefficients b0 and b1 How to evaluate the assumptions of regression analysis and know what to do if the assumptions are violated To make inferences about the slope and correlation coefficient To estimate mean values and predict individual values Correlation vs. Regression A scatter plot can be used to show the relationship between two variables Correlation analysis is used to measure the strength of the association (linear relationship) between two variables Correlation is only concerned with strength of the relationship No causal effect is implied with correlation Scatter plots were first presented in Ch. 2 Correlation was first presented in Ch. 3 Introduction to Regression Analysis Regression analysis is used to: Predict the value of a dependent variable based on the value of at least one independent variable Explain the impact of changes in an independent variable on the dependent variable Dependent variable: the variable we wish to predict or explain Independent variable: the variable used to predict or explain the dependent variable Simple Linear Regression Model Only one independent variable, X Relationship between X and Y is described by a linear function Changes in Y are assumed to be related to changes in X Types of Relationships Types of Relationships Types of Relationships Simple Linear Regression Model Simple Linear Regression Model Simple Linear Regression Equation (Prediction Line) The Least Squares Method b0 and b1 are obtained by finding the values of that minimize the sum of the squared differences between Y and : Finding the Least Squares Equation The coefficients b0 and b1 , and other regression results in this chapter, will be found using Excel or Minitab Interpretation of th