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Unformatted text preview: ) for every
possible combination of values for its conditioning
or predecessor variables (X1 and X2).
• We would need to know what are feasible values
for the decision variable (X1), and we would have to
assess a distribution for the possible values for the
uncertain variable (X2).
Note: We would require a lot of data, and even in simple problems this
could be a tedious or infeasible task. 22 Slide No. 44 CHAPTER 10. USING DATA ENCE 627 ©Assakkaf Using Data to Model Relationships
Example: X2 PearsonTukey threepoint
approximation
X1 low, medium, high
Nine different conditional probability
distributions for Y based on the
possible scenarios.
X1 X2 Example: X3 and X4
Three possible
values
Three point
X1 and X2
approximation
We would need to come up with 81
conditional distributions 34 = 81
X1 X2
X3 Y An influence diagram for
modeling relationship among
uncertain quantities X1, X2, and Y. Y X4 An influence diagram relating two
uncertain quantities and two
decision variables to Y. Slide No. 45 CHAPTER 10. USING DATA The Regression Approach ENCE 627 ©Assakkaf One way to model the relationships
between variables
– Determine the conditional expected value
of Y given the X’s, E(Y  X1, . . . , Xk).
– Consider the conditional probability
distribution around that expected value. 23 CHAPTER 10. USING DATA The Regression Approach Slide No. 46
ENCE 627 ©Assakkaf Correlation
– The study of the degree of linear
interrelation between random variables is
called correlation analysis.
– Correlation analysis provides a means of
drawing inferences about the strength of
the relationship between two or more
variables. CHAPTER 10. USING DATA The Regression Approach Slide No. 47
ENCE 627 ©Assakkaf Correlation
– Correlation is a measure of the degree to
which the values of these variables vary in
a systematic manner.
– It provides a quantitative index of the
degree to which one or more variables can
be used to predict the values of another
variable 24 CHAPTER 10. USING DATA Correlation Slide No. 48
ENCE 627 ©Assakkaf Different degrees of
correlation between
variables X and Y .
– High degree of correlation
in Fig. a and e.
– No correlation in Fig. c.
– The degree of correlation is
moderate in Fig’s b and d.
– In Fig. b, exact change in Y
for change in X is difficult to
predict.
– In Fig. f, very predictable
trend, but poor correlation. CHAPTER 10. USING DATA The Regression Approach Slide No. 49
ENCE 627 ©Assakkaf Limitations of Correlation Analysis
– Correlation analysis does not provide an
equation for predicting the value of a
variable..
– Also, it does not indicate whether a
relationship is causal, that is whether there
is a causeandeffect relationship between
the variables. 25 Slide No. 50 CHAPTER 10. USING DATA The Regression Approach ENCE 627 ©Assakkaf Correlation
– Example random variables having causal
relationship and strong correlation:
– The cost of living and wages
– The volumes of rainfall and flood runoff – Example random variables not having causal
relationship and strong correlation:
– The crime rate and the sale of chewing gum la...
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This note was uploaded on 10/24/2012 for the course ESI 6385 taught by Professor Mansoorehmollaghasemi during the Fall '12 term at University of Central Florida.
 Fall '12
 MansoorehMollaghasemi

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