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Chapter 8Regression and Correlation Analyses

CIVL 181 Modelling Systems with Uncertainties

- Instructor Prof. Wilson Tang

Soil Strength Example

Previous Model

Alternate Model

A General Formulation

Y is the r.v. of interest where x is the

independent variable.

Method of Least Square

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Example

0 to 100

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

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)

Correlation Analysis

To estimate r, the correlation coefficient

between X and Y

? dependent ? complete reduction of uncertainty

Confidence interval on regression line

Due to possible variations in both a (intercept)

and b (slope) more accurate around the middle.