Regression Analysis Webinar

8/11/2019 Regression Analysis Webinar

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Neil W. Polhemus, CTO, StatPoint Technologies, Inc.

Regression Analysis Using

Statgraphics Centurion

Copyright 2011 by StatPoint Technologies, Inc.

Web site: www.statgraphics.com


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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


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Regression Model Setup

3

Dependent variable: Y

Independent variable(s): X1, X2, , Xk

Error term: e

Model: Y = f (X1, X2, , Xk) + e


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Types of Regression Models (#1)

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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


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5


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


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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


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Example 1: Stability study

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Y: percent of available chlorine

X: number of weeks since production

Lower acceptable limit for Y: 0.40


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X-Y Scatterplot with Smooth

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Simple Regression

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Analysis Options

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Tables and Graphs

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Analysis Window

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Analysis Summary

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Lack-of-Fit Test

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Comparison of Alternative Models

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Fitted Reciprocal-X Model

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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


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Lower 95% Prediction Limit

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Outlier Removal

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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


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Example 2: Nonlinear Regression

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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.


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Data Input Dialog Box

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Initial Parameter Estimates

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Analysis Options

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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))


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Example 3: Calibration

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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.


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Reverse Prediction

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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


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Example 4: Comparison of

Regression Lines

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Y: amount of scrap produced

X: production line speed

Levels: line number


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Analysis Options

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Line1

2


100 140 180 220 260 300 340

Speed

140

240

340

440

540

Scrap


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Significance Tests

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Parallel Slope Model

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Example 5: Multiple Regression

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Stepwise Regression

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Analysis Options

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Selected Variables

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All Possible Regressions

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Analysis Options

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Example 6: Logistic Regression

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Response variable may be in the form of proportions or binary (0/1).


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Logistic Model

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)...(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)


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Data Input - Proportions

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0 20 40 60 80 100

Load


with 95.0% confide nce limits

0

0.2

0.4

0.6

0.8

1

Failures/Spe

cimens


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Statistical Results

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Data Input - Binary

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Analysis Options

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Analysis Summary

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Example 7: Poisson Regression

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Response variable is a count.


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Poisson Model

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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


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Data Input

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Analysis Options

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Statistical Results

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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


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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.

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More Information

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Regression Analysis Webinar