Chapter 8 Regression and Correlation Analyses

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Chapter 8Regression and Correlation Analyses
CIVL 181 Modelling Systems with Uncertainties

• Instructor Prof. Wilson Tang

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Soil Strength Example
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Previous Model
Alternate Model
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A General Formulation
Y is the r.v. of interest where x is the
independent variable.
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Method of Least Square
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Example
0 to 100
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Assume Y is Normal at given x ? e.g. at 24
? E(Y? x 24) 0.018 0.0516 ? 24 1.26
Var(Y? x 24) 0.0368 ? s 0.19
? N(1.26, 0.19)
Read E 8.2
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Advanced topics 1. Non-constant variance,
Var(Y?x) 2. Multiple linear regression 3.
Non-linear regression
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In general, there are 2 different lines except
when X and Y are perfectly dependent. The angle
between 2 lines depend on scatter of data. ? A
measure of scatter.
Application of Regression Analysis in
Engineering 1. Determining empirical relationship
from observed data 2. Checking or verifying
proposed model 3. Economics of indirect
measurements 4. Obtaining preliminary information
(to save time)
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Correlation Analysis
To estimate r, the correlation coefficient
between X and Y
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? dependent ? complete reduction of uncertainty
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Confidence interval on regression line
Due to possible variations in both a (intercept)
and b (slope) more accurate around the middle.