Регрессия Excel

08/12/2023
Agenda
Introduction
TGA Example
NLR Basics
Multicollinearity
Prediction
Testing
Bayesian Estimation
Conclusions

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1. Introduction

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Linear and Non-linear Regressions
Close relatives?
2

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2. Thermo Gravimetric Analysis Example
Let’s see it!

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TGA Experiment and Data
TGA Experiment
TGA Data

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TGA Example Variables
Small size
problem!

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Plasticizer Evaporation Model
Diffusion is
not relevant!

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Fitter Worksheet for TGA Example

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Service Life Prediction by TGA Data

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3. NLR Basics

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Data and Errors
Weight is
an effective
instrument!

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Model f(x,a)
Presentation at worksheet

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Data & Model Prepared for Fitter
Apply Fitter!

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Objective Function Q(a)
Parameter estimates
Weighted variance estimate
Objective function Q
is a sum of squares
and may be more…

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Very Important Matrix A
Matrix A is the
cause of troubles..

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Quality of Estimation
Matrix A is the
measure of quality!

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Search by Gradient Method
Matrix A is the
key to search!

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4. Multicollinearity

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Multicollinearity: View
Multicollinearity is degradation of matrix A
Objective function Q(a)
1
N(A) =
2
4
5
6
7

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Multicollinearity: Source

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Data & Model Preprocessing
((a + b) + c) + d ≠ a + (b + (c + d)) as 1+10 –20 = 1

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Example: The Arrhenius Law

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Derivative Calculation and Precision

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5. Prediction

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Reliable Prediction
Forecast should
include uncertainties!

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Nonlinearity and Simulation
Non-linear models call
for special methods of
reliable prediction!

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Prediction: Example
Accelerated aging tests
Upper confidence limits
Model of
rubber aging

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6. Testing

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Hypotheses Testing
Test statistics ξ is compared with critical value t (α)
Test don’t prove a model!
It just shows that
the hypothesis is
accepted or rejected!

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Lack-of-Fit and Variances Tests
These hypotheses are based on variances
and they can’t be tested without replicas!
Lack-of-Fit
is a wily test!

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Outlier and Series Tests
These hypotheses are based on residuals
and they can be tested without replicas
Series test is
very sensitive!

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7. Bayesian Estimation

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Bayesian Estimation
How to eat away
an elephant?
Slice by slice!

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Posterior and Prior Information. Type I
The same error in
each portion of data!

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Posterior and Prior Information. Type II
Different errors in
each portion of data!