1. © 2001 Prentice-Hall, Inc.Chap 13-1 BA 201 Lecture 18 Introduction to Simple Linear Regression (Data)Data

2. © 2001 Prentice-Hall, Inc. Chap 13-2 Topics Types of Regression Models Determining the Simple Linear Regression Equation

3. © 2001 Prentice-Hall, Inc. Chap 13-3 Purpose of Regression Analysis Regression Analysis is Used Primarily to Model Causality and Provide Prediction Predict the values of a dependent (response) variable based on values of at least one independent (explanatory) variable Explain the effect of the independent variables on the dependent variable p.456

4. © 2001 Prentice-Hall, Inc. Chap 13-4 Types of Regression Models Positive Linear Relationship Negative Linear Relationship Relationship NOT Linear No Relationship p.458

5. © 2001 Prentice-Hall, Inc. Chap 13-5 Simple Linear Regression Model Relationship Between Variables is Described by a Linear Function The Change of One Variable Causes the Other Variable to Change A Dependency of One Variable on the Other p.457

6. © 2001 Prentice-Hall, Inc. Chap 13-6 Population Regression Line (conditional mean) Population Linear Regression average value (conditional mean) Population regression line is a straight line that describes the dependence of the average value (conditional mean) of one variable on the other Population Y intercept Population Slope Coefficient Random Error Dependent (Response) Variable Independent (Explanatory) Variable p.467

7. © 2001 Prentice-Hall, Inc. Chap 13-7 Population Linear Regression (continued) = Random Error Y X (Observed Value of Y) = Observed Value of Y (Conditional Mean) p.??

8. © 2001 Prentice-Hall, Inc. Chap 13-8 estimate Sample regression line provides an estimate of the population regression line as well as a predicted value of Y Sample Linear Regression Sample Y Intercept Sample Slope Coefficient Residual Sample Regression Line (Fitted Regression Line, Predicted Value) p.460

9. © 2001 Prentice-Hall, Inc. Chap 13-9 Sample Linear Regression and are obtained by finding the values of and that minimizes the sum of the squared residuals estimate provides an estimate of estimate provides and estimate of (continued) p.460

10. © 2001 Prentice-Hall, Inc. Chap 13-10 Sample Linear Regression (continued) Y X Observed Value p.462

11. © 2001 Prentice-Hall, Inc. Chap 13-11 Interpretation of the Slope and Intercept is the average value of Y when the value of X is zero. measures the change in the average value of Y as a result of a one-unit change in X. p.??

12. © 2001 Prentice-Hall, Inc. Chap 13-12 Interpretation of the Slope and Intercept estimated is the estimated average value of Y when the value of X is zero. estimated is the estimated change in the average value of Y as a result of a one- unit change in X. (continued) pp.461-463

13. © 2001 Prentice-Hall, Inc. Chap 13-13 Simple Linear Regression: Example You wish to examine the linear dependency of the annual sales of produce stores on their sizes in square footage. Sample data for 7 stores were obtained. Find the equation of the straight line that fits the data best. Annual Store Square Sales Feet($1000) 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

14. © 2001 Prentice-Hall, Inc. Chap 13-14 Scatter Diagram: Example Excel Output

15. © 2001 Prentice-Hall, Inc. Chap 13-15 Equation for the Sample Regression Line: Example From Excel Printout:

16. © 2001 Prentice-Hall, Inc. Chap 13-16 Graph of the Sample Regression Line: Example Y i = 1636.415 +1.487X i 

17. © 2001 Prentice-Hall, Inc. Chap 13-17 Interpretation of Results: Example The slope of 1.487 means that each increase of one unit in X, we predict the average of Y to increase by an estimated 1.487 units. The model estimates that for each increase of 1 square foot in the size of the store, the expected annual sales are predicted to increase by $1487.

18. © 2001 Prentice-Hall, Inc. Chap 13-18 Simple Linear Regression in PHStat In Excel, use PHStat | Regression | Simple Linear Regression … EXCEL Spreadsheet of Regression Sales on Footage p.520

19. © 2001 Prentice-Hall, Inc. Chap 13-19 Summary Introduced Types of Regression Models Discussed Determining the Simple Linear Regression Equation