regression analysis webinar
TRANSCRIPT
-
8/11/2019 Regression Analysis Webinar
1/58
Neil W. Polhemus, CTO, StatPoint Technologies, Inc.
Regression Analysis Using
Statgraphics Centurion
Copyright 2011 by StatPoint Technologies, Inc.
Web site: www.statgraphics.com
-
8/11/2019 Regression Analysis Webinar
2/58
Outline
Regression Models
ExamplesSingle X
Simple regression
Nonlinear models
Calibration
Comparison of regression lines
ExamplesMultiple X
Regression model selection (stepwise, all possible) Logistic regression
Poisson regression
2
-
8/11/2019 Regression Analysis Webinar
3/58
Regression Model Setup
3
Dependent variable: Y
Independent variable(s): X1, X2, , Xk
Error term: e
Model: Y = f (X1, X2, , Xk) + e
-
8/11/2019 Regression Analysis Webinar
4/58
Types of Regression Models (#1)
4
Procedure Dependent variable Independent variables
Simple Regression continuous 1 continuous
Polynomial Regression continuous 1 continuous
Box-Cox Transformations continuous 1 continuous
Calibration Models continuous 1 continuous
Comparison of RegressionLines
continuous 1 continuous and 1categorical
-
8/11/2019 Regression Analysis Webinar
5/58
Types of Regression Models (#2)
5
Procedure Dependent variable Independent variables
Multiple Regression continuous 2+ continuous
Regression Model Selection continuous 2+ continuous
Nonlinear Regression continuous 1+ continuous
Ridge Regression continuous 2+ continuous
Partial Least Squares continuous 2+ continuous
General Linear Models 1+ continuous 2+ continuous or categoricalvariables
-
8/11/2019 Regression Analysis Webinar
6/58
Types of Regression Models (#3)
6
Procedure Dependent variable Independent variables
Logistic Regression proportions 1+ continuous or categorical
Probit Analysis proportions 1+ continuous or categorical
Poisson Regression counts 1+ continuous or categorical
Negative BinomialRegression
counts 1+ continuous or categorical
Life Data - ParametricModels
failure times 1+ continuous or categorical
-
8/11/2019 Regression Analysis Webinar
7/58
Example 1: Stability study
7
Y: percent of available chlorine
X: number of weeks since production
Lower acceptable limit for Y: 0.40
-
8/11/2019 Regression Analysis Webinar
8/58
X-Y Scatterplot with Smooth
8
-
8/11/2019 Regression Analysis Webinar
9/58
Simple Regression
9
-
8/11/2019 Regression Analysis Webinar
10/58
Analysis Options
10
-
8/11/2019 Regression Analysis Webinar
11/58
Tables and Graphs
11
-
8/11/2019 Regression Analysis Webinar
12/58
Analysis Window
12
-
8/11/2019 Regression Analysis Webinar
13/58
Analysis Summary
13
-
8/11/2019 Regression Analysis Webinar
14/58
Lack-of-Fit Test
14
-
8/11/2019 Regression Analysis Webinar
15/58
Comparison of Alternative Models
15
-
8/11/2019 Regression Analysis Webinar
16/58
Fitted Reciprocal-X Model
16
Plot of Fitted Modelchlorine = 0.368053 + 1.02553/weeks
0 10 20 30 40 50
weeks
0.38
0.4
0.42
0.44
0.46
0.48
0.5
chlorine
-
8/11/2019 Regression Analysis Webinar
17/58
Lower 95% Prediction Limit
17
-
8/11/2019 Regression Analysis Webinar
18/58
Outlier Removal
18
Plot of Fitted Model
chlorine = 0.366628 + 1.02548/weeks
0 10 20 30 40 50
weeks
0.38
0.4
0.42
0.44
0.46
0.48
0.5
chlorin
e
-
8/11/2019 Regression Analysis Webinar
19/58
Example 2: Nonlinear Regression
19
Draper and Smith in Applied Regression Analysis suggest fittinga model of the form
Y = a + (0.49-a)exp[-b(x-8)]
Since the model is nonlinear in the parameters, it requires asearch procedure to find the best solution.
-
8/11/2019 Regression Analysis Webinar
20/58
Data Input Dialog Box
20
-
8/11/2019 Regression Analysis Webinar
21/58
Initial Parameter Estimates
21
-
8/11/2019 Regression Analysis Webinar
22/58
Analysis Options
22
-
8/11/2019 Regression Analysis Webinar
23/58
Plot of Fitted Model
23
Plot of Fitted Model
0 10 20 30 40 50
weeks
0.38
0.4
0.42
0.44
0.46
0.48
0.5
chlorin
e
chlorine = 0.390144+(0.49-0.390144)*exp(-0.101644*(weeks-8))
-
8/11/2019 Regression Analysis Webinar
24/58
Example 3: Calibration
24
The general calibration problem is thatof determining the likely value of Xgiven an observed value of Y.
Typically: X = item characteristic, Y =measured value
Step 1: Build a regression model usingsamples with known values of X
(golden samples).Step 2: For another sample with
unknown X, predict X from Y.
-
8/11/2019 Regression Analysis Webinar
25/58
Data Input Dialog Box
25
-
8/11/2019 Regression Analysis Webinar
26/58
Reverse Prediction
26
-
8/11/2019 Regression Analysis Webinar
27/58
Plot of Fitted Model
27
Plot of Fitted Model
measured = -0.0896667 + 1.01433*known
0 2 4 6 8 10known
0
2
4
6
8
10
12
measur
ed
5.85573 (5.59032,6.1215)
5.85
-
8/11/2019 Regression Analysis Webinar
28/58
Example 4: Comparison of
Regression Lines
28
Y: amount of scrap produced
X: production line speed
Levels: line number
-
8/11/2019 Regression Analysis Webinar
29/58
Data Input Dialog Box
29
-
8/11/2019 Regression Analysis Webinar
30/58
Analysis Options
30
-
8/11/2019 Regression Analysis Webinar
31/58
Plot of Fitted Model
31
Line1
2
Plot of Fitted Model
100 140 180 220 260 300 340
Speed
140
240
340
440
540
Scrap
-
8/11/2019 Regression Analysis Webinar
32/58
Significance Tests
32
-
8/11/2019 Regression Analysis Webinar
33/58
Parallel Slope Model
33
-
8/11/2019 Regression Analysis Webinar
34/58
Example 5: Multiple Regression
34
-
8/11/2019 Regression Analysis Webinar
35/58
Stepwise Regression
35
-
8/11/2019 Regression Analysis Webinar
36/58
Analysis Options
36
-
8/11/2019 Regression Analysis Webinar
37/58
Selected Variables
37
-
8/11/2019 Regression Analysis Webinar
38/58
-
8/11/2019 Regression Analysis Webinar
39/58
All Possible Regressions
39
-
8/11/2019 Regression Analysis Webinar
40/58
Analysis Options
40
-
8/11/2019 Regression Analysis Webinar
41/58
-
8/11/2019 Regression Analysis Webinar
42/58
Example 6: Logistic Regression
42
Response variable may be in the form of proportions or binary (0/1).
-
8/11/2019 Regression Analysis Webinar
43/58
Logistic Model
43
)...(exp1
1)(
22110 kkXXX
EventP
kkXXXEventP
EventP
...
)(1
)(log 22110
Let P(Event) be the probability an event occurs at specified values of
the independent variables X.
(1)
(2)
-
8/11/2019 Regression Analysis Webinar
44/58
Data Input - Proportions
44
-
8/11/2019 Regression Analysis Webinar
45/58
-
8/11/2019 Regression Analysis Webinar
46/58
Plot of Fitted Model
46
0 20 40 60 80 100
Load
Plot of Fitted Model
with 95.0% confide nce limits
0
0.2
0.4
0.6
0.8
1
Failures/Spe
cimens
-
8/11/2019 Regression Analysis Webinar
47/58
Statistical Results
47
-
8/11/2019 Regression Analysis Webinar
48/58
Data Input - Binary
48
-
8/11/2019 Regression Analysis Webinar
49/58
Analysis Options
49
-
8/11/2019 Regression Analysis Webinar
50/58
Analysis Summary
50
-
8/11/2019 Regression Analysis Webinar
51/58
Example 7: Poisson Regression
51
Response variable is a count.
-
8/11/2019 Regression Analysis Webinar
52/58
Poisson Model
52
Values of the response variable are assumed to follow a Poisson
distribution:
kkXXX ...log 22110
The rate parameter is related to the predictor variables through a log-
linear link function:
!Y
eYp
Y
-
8/11/2019 Regression Analysis Webinar
53/58
Data Input
53
-
8/11/2019 Regression Analysis Webinar
54/58
Analysis Options
54
-
8/11/2019 Regression Analysis Webinar
55/58
Statistical Results
55
-
8/11/2019 Regression Analysis Webinar
56/58
Plot of Fitted Model
56
Thickness=170.0Extraction=75.0Height=55.0
0 10 20 30 40
Years
Plot of Fitted Mode lwith 95.0% confidence limits
0
1
2
3
4
5
Injuries
-
8/11/2019 Regression Analysis Webinar
57/58
References
Applied Logistic Regression (second edition)Hosmer andLemeshow, Wiley, 2000.
Applied Regression Analysis (third edition)Draper andSmith, Wiley, 1998.
Applied Linear Statistical Models (fifth edition)Kutner etal., McGraw-Hill, 2004.
Classical and Modern Regression with Applications (secondedition)Myers, Brookes-Cole, 1990.
57
-
8/11/2019 Regression Analysis Webinar
58/58
More Information
Go to www.statgraphics.com
Or send e-mail to [email protected]
http://www.statgraphics.com/mailto:[email protected]:[email protected]://www.statgraphics.com/