Download presentation
Presentation is loading. Please wait.
1
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 1
2
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 2 Regression models are empirical as opposed to mechanistic models Regression modeling is often performed on undesigned or unplanned data Regression modeling is also used extensively to build models to data from designed experiments
3
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 3
4
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 4
5
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 5 L is minimized by taking derivatives with respect to the model parameters and equating to zero
6
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 6 Taking the derivatives and equating to zero results in:
7
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 7
8
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 8
9
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 9
10
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 10 Mean square error
11
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 11
12
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 12
13
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 13
14
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 14
15
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 15
16
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 16
17
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 17
18
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 18
19
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 19
20
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 20
21
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 21
22
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 22
23
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 23
24
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 24
25
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 25
26
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 26
27
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 27
28
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 28
29
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 29 The test uses an ANOVA approach. The regression or model sum of squares is See Table 10.4 for the viscosity regression model
30
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 30
31
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 31
32
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 32 See Table 10.4 for the viscosity regression model
33
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 33
34
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 34
35
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 35
36
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 36
37
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 37
38
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 38
39
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 39 Prediction intervals are useful when running conformation experiments If the new observation falls within the prediction interval that is some evidence that the model is reliable
40
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 40
41
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 41
42
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 42 10.7 Regression Model Diagnostics Scaled residuals and PRESS Standardized residual Studentized residual
43
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 43
44
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 44
45
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 45 Influence Diagnostics
46
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 46
47
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 47 10.8 Testing for Lack of Fit Very important test in both general regression modeling and in analysis of a designed experiment Does the chosen model adequately fit the data, or should higher- order terms be considered? A statistical test can be performed provided that the error term can be decomposed into the two components shown below:
48
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 48
49
Chapter 10Design & Analysis of Experiments 8E 2012 Montgomery 49
Similar presentations
