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1、Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 12-1,Chapter 12 Simple Linear Regression,Business Statistics: A First Course Fifth Edition,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc,Chap 12-2,Learning Objectives,In this chapter, you learn: How to use regres
2、sion 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 correlati
3、on coefficient To estimate mean values and predict individual values,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc,Chap 12-3,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
4、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,Business Statistics: A First Course, 5e 2009 P
5、rentice-Hall, Inc,Chap 12-4,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
6、 variable we wish to predict or explain Independent variable: the variable used to predict or explain the dependent variable,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc,Chap 12-5,Simple Linear Regression Model,Only one independent variable, X Relationship between X and Y is descr
7、ibed by a linear function Changes in Y are assumed to be related to changes in X,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc,Chap 12-6,Types of Relationships,Y,X,Y,X,Y,Y,X,X,Linear relationships,Curvilinear relationships,Business Statistics: A First Course, 5e 2009 Prentice-Hall,
8、 Inc,Chap 12-7,Types of Relationships,Y,X,Y,X,Y,Y,X,X,Strong relationships,Weak relationships,(continued),Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc,Chap 12-8,Types of Relationships,Y,X,Y,X,No relationship,(continued),Business Statistics: A First Course, 5e 2009 Prentice-Hall, I
9、nc,Chap 12-9,Linear component,Simple Linear Regression Model,Population Y intercept,Population Slope Coefficient,Random Error term,Dependent Variable,Independent Variable,Random Error component,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc,Chap 12-10,(continued),Random Error for th
10、is Xi value,Y,X,Observed Value of Y for Xi,Predicted Value of Y for Xi,Xi,Slope = 1,Intercept = 0,i,Simple Linear Regression Model,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc,Chap 12-11,The simple linear regression equation provides an estimate of the population regression line,S
11、imple Linear Regression Equation (Prediction Line),Estimate of the regression intercept,Estimate of the regression slope,Estimated (or predicted) Y value for observation i,Value of X for observation i,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc,Chap 12-12,The Least Squares Method
12、,b0 and b1 are obtained by finding the values of that minimize the sum of the squared differences between Y and :,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc,Chap 12-13,Finding the Least Squares Equation,The coefficients b0 and b1 , and other regression results in this chapter, w
13、ill be found using Excel or Minitab,Formulas are shown in the text for those who are interested,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc,Chap 12-14,b0 is the estimated mean value of Y when the value of X is zero b1 is the estimated change in the mean value of Y as a result of
14、a one-unit change in X,Interpretation of the Slope and the Intercept,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc,Chap 12-15,Simple Linear Regression Example,A real estate agent wishes to examine the relationship between the selling price of a home and its size (measured in square
15、 feet) A random sample of 10 houses is selected Dependent variable (Y) = house price in $1000s Independent variable (X) = square feet,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc,Chap 12-16,Simple Linear Regression Example: Data,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc,Chap 12-17,Simple Linear Regression Example: Scatter Plot,House price model: Scatter Plot,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc,Chap 12-18,Simple Linear Regression Example
