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Chapter 12:

Chapter 12:. Linear Regression. Introduction. Regression analysis and Analysis of variance are the two most widely used statistical procedures. Regression analysis: Description Prediction Estimation. 12.1 Simple Linear Regression. (12.1 ). (12.2). 12.1 Simple Linear Regression.

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Chapter 12:

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  1. Chapter 12: Linear Regression

  2. Introduction • Regression analysis and Analysis of variance are the two most widely used statistical procedures. • Regression analysis: • Description • Prediction • Estimation

  3. 12.1 Simple Linear Regression (12.1) (12.2)

  4. 12.1 Simple Linear Regression

  5. Table 12.1 Quality Improvement Data

  6. Figure 12.1 Scatter Plot

  7. Figure 12.1a Scatter Plot

  8. 12.1 Simple Linear Regression

  9. 12.1 Simple Linear Regression The regression equation is Y = 55.9 - 0.641 X Predictor Coef SE Coef T P Constant 55.923 2.824 19.80 0.000 X -0.64067 0.04332 -14.79 0.000 S = 0.888854 R-Sq = 95.6% R-Sq(adj) = 95.2% Analysis of Variance Source DF SS MS F P Regression 1 172.77 172.77 218.67 0.000 Residual Error 10 7.90 0.79 Total 11 180.67

  10. 12.1 Simple Linear Regression

  11. 12.2 Worth of the Prediction Equation

  12. 12.2 Worth of the Prediction Equation (12.4)

  13. 12.3 Assumptions (12.1)

  14. 12.4 Checking Assumptions through Residual Plots

  15. 12.4 Checking Assumptions through Residual Plots

  16. 12.5 Confidence Intervals

  17. 12.5 Hypothesis Test

  18. 12.6 Prediction Interval for Y

  19. 12.6 Prediction Interval for Y

  20. 12.7 Regression Control Chart (12.5) (12.6)

  21. 12.8 Cause-Selecting Control Chart • The general idea is to try to distinguish between quality problems that occur at one stage in a process from problems that occur at a previous processing step. • Let Y be the output from the second step and let X denote the output from the first step. The relationship between X and Y would be modeled.

  22. 12.9 Linear, Nonlinear, and Nonparametric Profiles • Profile refers to the quality of a process or product being characterized by a (Linear, Nonlinear, or Nonparametric) relationship between a response variable and one or more explanatory variables. • A possible way is to monitor each parameter in the model with a Shewhart chart. • The independent variables must be fixed • Control chart for R2

  23. 12.10 Inverse Regression • An important application of simple linear regression for quality improvement is in the area of calibration. • Assume two measuring tools are available – One is quite accurate but expensive to use and the other is not as expensive but also not as accurate. If the measurements obtained from the two devices are highly correlated, then the measurement that would have been made using the expensive measuring device could be predicted fairly from the measurement using the less expensive device. • Let Y = measurement from the less expensive device X = measurement from the accurate device

  24. 12.10 Inverse Regression

  25. 12.10 Inverse RegressionExample Y X 2.3 2.4 2.5 2.6 2.4 2.5 2.8 2.9 2.9 3.0 2.6 2.7 2.4 2.5 2.2 2.3 2.1 2.2 2.7 2.7

  26. 12.11 Multiple Linear Regression

  27. 12.12 Issues in Multiple Regression12.12.1 Variable Selection

  28. 12.12.3 Multicollinear Data • Problems occur when at least two of the regressors are related in some manner. • Solutions: • Discard one or more variables causing the multicollinearity • Use ridge regression

  29. 12.12.4 Residual Plots

  30. 12.12.6 Transformations

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