We would need to know what are feasible values for

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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 Pearson-Tukey three-point 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 cause-and-effect 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.

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