商务与经济统计ppt第14章A
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Statistics for Business and Economics
Anderson Sweeney Williams
Slides by
John Loucks
St. Edward’s University
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 2
Simple Linear Regression
Managerial decisions often are based on the relationship between two or more variables.
Regression analysis can be used to develop an equation showing how the variables are related.
y = b0 + b1x +e where:
b0 and b1 are called parameters of the model, e is a random variable called the error term.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
b0 and b1
Estimated
Regression Equation
yˆ b0 b1x
Sample Statistics
b0, b1
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 6
Simple Linear Regression Equation
Positive Linear Relationship E(y)
Regression line
Intercept
b0
Slope b1
is positive
x
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 3
Simple Linear Regression
Simple linear regression involves one independent variable and one dependent variable.
The relationship between the two variables is approximated by a straight line.
Slide 7
Simple Linear Regression Equation
Negative Linear Relationship
E(y)
Intercept
b0
Regression line
Slope b1
is negative
x
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 10
Estimation Process
Regression Model
y = b0 + b1x +e
Regression Equation
E(y) = b0 + b1x
Unknown Parameters
b0, b1
Sample Data: xy
x1 y1 .. .. xn yn
b0 and b1 provide estimates of
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 9
Estimated Simple Linear Regression Equation
The estimated simple linear regression equation
yˆ b0 b1x
• The graph is called the estimated regression line. • b0 is the y intercept of the line. • b1 is the slope of the line. • yˆ is the estimated value of y for a given x value.
Regression analysis involving two or more independent variables is called multiple regression.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 5
Simple Linear Regression Equation
The simple linear regression equation is:
E(y) = b0 + b1x
• Graph of the regression equation is a straight line. • b0 is the y intercept of the regression line. • b1 is the slope of the regression line. • E(y) is the expected value of y for a given x value.
The variable being predicted is called the dependent variable and is denoted by y.
The variables being used to predict the value of the dependent variable are called the independent variables and are denoted by x.
Slide 8
Simple Linear Regression Equation
No Relationship E(y)
Intercept
b0
Regression line
Slope b1
is 0
x
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 4ຫໍສະໝຸດ Baidu
Simple Linear Regression Model
The equation that describes how y is related to x and an error term is called the regression model.
The simple linear regression model is:
Slide 13
Least Squares Method
yi = value of dependent variable for ith _ observation x_ = mean value for independent variable y = mean value for dependent variable
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 1
Chapter 14, Part A Simple Linear Regression
Simple Linear Regression Model Least Squares Method Coefficient of Determination Model Assumptions Testing for Significance
Slide 11
Least Squares Method
Least Squares Criterion
min (yi y i )2
where: yi = observed value of the dependent variable for the ith observation y^i = estimated value of the dependent variable for the ith observation
Slide 12
Least Squares Method
Slope for the Estimated Regression Equation
b1
(xi x )(yi y ) (xi x )2
where:
xi = value of independent variable for ith observation
Anderson Sweeney Williams
Slides by
John Loucks
St. Edward’s University
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 2
Simple Linear Regression
Managerial decisions often are based on the relationship between two or more variables.
Regression analysis can be used to develop an equation showing how the variables are related.
y = b0 + b1x +e where:
b0 and b1 are called parameters of the model, e is a random variable called the error term.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
b0 and b1
Estimated
Regression Equation
yˆ b0 b1x
Sample Statistics
b0, b1
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 6
Simple Linear Regression Equation
Positive Linear Relationship E(y)
Regression line
Intercept
b0
Slope b1
is positive
x
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 3
Simple Linear Regression
Simple linear regression involves one independent variable and one dependent variable.
The relationship between the two variables is approximated by a straight line.
Slide 7
Simple Linear Regression Equation
Negative Linear Relationship
E(y)
Intercept
b0
Regression line
Slope b1
is negative
x
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 10
Estimation Process
Regression Model
y = b0 + b1x +e
Regression Equation
E(y) = b0 + b1x
Unknown Parameters
b0, b1
Sample Data: xy
x1 y1 .. .. xn yn
b0 and b1 provide estimates of
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 9
Estimated Simple Linear Regression Equation
The estimated simple linear regression equation
yˆ b0 b1x
• The graph is called the estimated regression line. • b0 is the y intercept of the line. • b1 is the slope of the line. • yˆ is the estimated value of y for a given x value.
Regression analysis involving two or more independent variables is called multiple regression.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 5
Simple Linear Regression Equation
The simple linear regression equation is:
E(y) = b0 + b1x
• Graph of the regression equation is a straight line. • b0 is the y intercept of the regression line. • b1 is the slope of the regression line. • E(y) is the expected value of y for a given x value.
The variable being predicted is called the dependent variable and is denoted by y.
The variables being used to predict the value of the dependent variable are called the independent variables and are denoted by x.
Slide 8
Simple Linear Regression Equation
No Relationship E(y)
Intercept
b0
Regression line
Slope b1
is 0
x
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 4ຫໍສະໝຸດ Baidu
Simple Linear Regression Model
The equation that describes how y is related to x and an error term is called the regression model.
The simple linear regression model is:
Slide 13
Least Squares Method
yi = value of dependent variable for ith _ observation x_ = mean value for independent variable y = mean value for dependent variable
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 1
Chapter 14, Part A Simple Linear Regression
Simple Linear Regression Model Least Squares Method Coefficient of Determination Model Assumptions Testing for Significance
Slide 11
Least Squares Method
Least Squares Criterion
min (yi y i )2
where: yi = observed value of the dependent variable for the ith observation y^i = estimated value of the dependent variable for the ith observation
Slide 12
Least Squares Method
Slope for the Estimated Regression Equation
b1
(xi x )(yi y ) (xi x )2
where:
xi = value of independent variable for ith observation