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# Mba512 Simple Linear Regression Notes

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### Mba512 Simple Linear Regression Notes

1. 1. Learning Objectives Statistics for Managers In this chapter, you learn: Using Microsoft® Excel  To use regression analysis to predict the value of a dependent variable based on an independent variable 5th Edition  The meaning of the regression coefficients b0 and b1  To evaluate the assumptions of regression analysis and know what to do if the assumptions are violated Chapter 13  To make inferences about the slope and correlation Simple Linear Regression coefficient  To estimate mean values and predict individual values Some revisions/omissions made by Jennifer J. Edmonds, PhD @ Wilkes University Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc. Chap 13-1 Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc. Chap 13-2 Regression Analysis Simple Linear Regression Model Regression analysis is used to:  Only one independent variable, X  Explain the impact of changes in an independent variable on the dependent variable  Relationship between X and Y is described by a linear function  Predict the value of a dependent variable based on the  Changes in Y are related to changes in X value of at least one independent variable Dependent variable: the variable you wish to explain Independent variable: the variable used to explain the dependent variable Some revisions/omissions made by Jennifer J. Edmonds, PhD @ Wilkes University Some revisions made by Jennifer J. Edmonds, PhD Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc. Chap 13-3 Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc. Chap 13-4 1
2. 2. Types of Relationships Types of Relationships Linear relationships Curvilinear relationships Strong relationships Weak relationships Y Y Y Y X X X X Y Y Y Y Some revisions made by Jennifer J. Edmonds, PhD Some revisions made by Jennifer J. Edmonds, PhD X X X X Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc. Chap 13-5 Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc. Chap 13-6 Types of Relationships The Linear Regression Model Relationship between X and Y is described by a linear function Y Y Yi β 0 β1 X i εi Observed Value of Y for Xi εi Slope = β1 No relationship X Predicted Value Random Error of Y for Xi for this Xi value Y Intercept = β0 Some revisions made by Jennifer J. Edmonds, PhD X Xi X Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc. Chap 13-7 Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc. Chap 13-8 2
3. 3. The Linear Regression Model Linear Regression Equation The simple linear regression equation provides an estimate of the Population Random population regression line Population Independent Error Slope Y intercept Variable term Coefficient Estimated (or Dependent Variable predicted) Y Estimate of the Estimate of the β 0 β1 X i εi value for regression regression slope Yi observation i intercept Value of X for Linear component Random Error How do we calculate ˆ Yi b0 b1X i observation i component The population regression model these estimates? Some revisions made by Jennifer J. Edmonds, PhD Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc. Chap 13-9 Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc. Chap 13-10 Finding the Least Squares The Least Squares Method Equation Y b0 and b1 are obtained by finding the values of b0 and b1 that minimize the sum of εi Slope = β1  The coefficients b0 and b1 , and other regression results the squared differences between Y Random Error for this Xi value in this chapter, will be found using Excel and : Yˆ Intercept = β0 (between the data and the line) Xi X Chap 13-11 Our estimate Formulas are shown in the text for ˆ Yi b0 b1X i of the line Yi the data those who are interested Minimize min ˆ (Yi Yi )2 min (Yi (b0 b1Xi ))2 this equation… Some revisions made by Jennifer J. Edmonds, PhD Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc. Chap 13-11 Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc. Chap 13-12 3
4. 4. Interpretation of the Intercept and the Slope LEAST SQUARES REGRESSION ESTIMATES  b0 is the estimated mean value of Y when the value of X is zero =INTERCEPT(y-range, x-range)  b1 is the estimated change in the mean value of Y for every one-unit change in X =SLOPE(y-range, x-range) ˆ Yi b0 b1X i Some revisions made by Jennifer J. Edmonds, PhD Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc. Chap 13-13 4