1. © 2001 Prentice-Hall, Inc.Chap 9-1 BA 201 Lecture 22 Estimation of Predicted Values

2. © 2001 Prentice-Hall, Inc. Chap 9-2 Topics Estimation of Mean Values and Prediction of Individual Values Pitfalls in Regression and Ethical Issues

3. © 2001 Prentice-Hall, Inc. Chap 9-3 Sample Linear Regression (continued) Y X Observed Value p.462

4. © 2001 Prentice-Hall, Inc. Chap 9-4 Estimation of Mean Values Confidence Interval Estimate for : The Mean of Y given a particular X i t value from table with df=n-2 Standard error of the estimate Size of interval vary according to distance away from mean, p.488

5. © 2001 Prentice-Hall, Inc. Chap 9-5 Prediction of Individual Values Prediction Interval for Individual Response Y i at a Particular X i Addition of 1 increases width of interval from that for the mean of Y p.490

6. © 2001 Prentice-Hall, Inc. Chap 9-6 Interval Estimates for Different Values of X Y X Prediction Interval for a individual Y i A given X Confidence Interval for the mean of Y Y i = b 0 + b 1 X i  p.???

7. © 2001 Prentice-Hall, Inc. Chap 9-7 Example: Produce Stores Data for 7 Stores: Regression Model Obtained: Predict the annual sales for a store with 2000 square feet. Annual Store Square Sales Feet($000) 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

8. © 2001 Prentice-Hall, Inc. Chap 9-8 Estimation of Mean Values: Example Find the 95% confidence interval for the average annual sales for stores of 2,000 square feet Predicted Sales Y i = 1636.415 +1.487X i = 4610.45 ($000)  X = 2350.29S YX = 611.75 t n-2 = t 5 = 2.5706 Confidence Interval Estimate for

9. © 2001 Prentice-Hall, Inc. Chap 9-9 Prediction Interval for Y : Example Find the 95% prediction interval for annual sales of one particular store of 2,000 square feet Predicted Sales Y i = 1636.415 +1.487X i = 4610.45 ($000)  X = 2350.29S YX = 611.75 t n-2 = t 5 = 2.5706 Prediction Interval for Individual Y

10. © 2001 Prentice-Hall, Inc. Chap 9-10 Estimation of Mean Values and Prediction of Individual Values in PHStat In Excel, use PHStat | Regression | Simple Linear Regression … Check the “Confidence and Prediction Interval for X=” box EXCEL Spreadsheet of Regression Sales on Footage

11. © 2001 Prentice-Hall, Inc. Chap 9-11 Pitfalls of Regression Analysis Lacking an Awareness of the Assumptions Underlining Least-squares Regression Not Knowing How to Evaluate the Assumptions Not Knowing What the Alternatives to Least- squares Regression are if a Particular Assumption is Violated Using a Regression Model Without Knowledge of the Subject Matter pp.493-497

12. © 2001 Prentice-Hall, Inc. Chap 9-12 Strategy for Avoiding the Pitfalls of Regression Start with a scatter plot of Y on X to observe possible relationship Perform residual analysis to check the assumptions Use a histogram, stem-and-leaf display, box- and-whisker plot, or normal probability plot of the residuals to uncover possible non- normality pp.493-497

13. © 2001 Prentice-Hall, Inc. Chap 9-13 Strategy for Avoiding the Pitfalls of Regression If there is violation of any assumption, use alternative methods (e.g. least absolute deviation regression or least median of squares regression) to least-squares regression or alternative least-squares models (e.g. curvilinear or multiple regression) If there is no evidence of assumption violation, then test for the significance of the regression coefficients and construct confidence intervals and prediction intervals (continued) pp.493-497

14. © 2001 Prentice-Hall, Inc. Chap 9-14 Summary Addressed Estimation of Mean Values and Prediction of Individual Values Discussed Pitfalls in Regression and Ethical Issues