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MER301: Engineering Reliability

MER301: Engineering Reliability. LECTURE 13 Chapter 6:6.3-6.4 Multiple Linear Regression Models. Summary of Topics. Multiple Regression Analysis Multiple Regression Equation Precision and Significance of a Regression Model Confidence Limits. Summary of Topics.

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MER301: Engineering Reliability

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  1. MER301: Engineering Reliability LECTURE 13 Chapter 6:6.3-6.4 Multiple Linear Regression Models MER301: Engineering Reliability Lecture 13

  2. Summary of Topics • Multiple Regression Analysis • Multiple Regression Equation • Precision and Significance of a Regression Model • Confidence Limits MER301: Engineering Reliability Lecture 13

  3. Summary of Topics Linear Regression Analysis Simple Regression Model Least Squares Estimate of the Coefficients Standard Error of the Coefficients Precision and Significance of a Regression Model Precision Standard Error of the Coefficients R2 - Correlation Coefficient Confidence Limits Significance T-test on Coefficients Analysis of Variance MER301: Engineering Reliability Lecture 12 3

  4. Linear Regression Analysis Simple Regression Model Least Squares Estimate of the Coefficients Standard Error of the Coefficients Precision and Significance of a Regression Model Precision Standard Error of the Coefficients R2 - Correlation Coefficient Confidence Limits Significance T-test on Coefficients Analysis of Variance MER301: Engineering Reliability Lecture 12 4

  5. Regression Analysis • For those cases where there is not a Mechanistic Model of an engineering process, data are used to generate an Empirical Model. A powerful technique for creating such a model doing is called RegressionAnalysis • In Simple Linear Regression, the Dependent Variable Y is a function of one Independent Variable X • Multiple Linear Regression is used when Y is a function of more than one X • The form of regression models is based on the underlying physics as much as possible MER301: Engineering Reliability Lecture 13

  6. Multiple Linear Regression Models • Multiple Regression Models are used when the dependent variable Y is a function of more than one independent variable • Consistent with the physics, the model may include non-linear terms such as • Use as few terms as possible, consistent with the physics.. MER301: Engineering Reliability Lecture 13

  7. General Form of Regression Equation MER301: Engineering Reliability Lecture 13

  8. Forms of Multiple Regression Equations… MER301: Engineering Reliability Lecture 13

  9. Forms of Multiple Regression Equations… • Interaction terms… MER301: Engineering Reliability Lecture 13

  10. Forms of Multiple Regression Equations… • Non-linear terms… MER301: Engineering Reliability Lecture 13

  11. General Form of Regression Equation • The general form of the multiple regression equation for n data points and k independent variables is MER301: Engineering Reliability Lecture 13

  12. Matrix Version of Multi-Linear Regression MER301: Engineering Reliability Lecture 13

  13. Example 13.1 • The pull strength of a wire bond in a semiconductor product is an important characteristic. • We want to investigate the suitability of using a multiple regression model to predict pull strength (Y) as a function of wire length (x1) and die height (x2). • Excel file Example13.1.xls MER301: Engineering Reliability Lecture 13

  14. Example 13.1(page 2) Pull Strength is to be modeled as a function of Wire Length and Die Height Minitab is used to analyze the data set to get values of the MER301: Engineering Reliability Lecture 13

  15. Example 13.1(page 3) Regression Analysis The regression equation is Pull Strength = 2.26 + 2.74 Wire Length + 0.0125 Die Height MER301: Engineering Reliability Lecture 13

  16. Precision and Significance of the Regression… • Dealing with the Precision first…. • Standard Error of the Coefficients • Coefficient of Determination • Confidence Interval on the Mean Response MER301: Engineering Reliability Lecture 13

  17. Example 13.1(page 4) Regression Analysis The regression equation is Pull Strength = 2.26 + 2.74 Wire Length + 0.0125 Die Height (6-46) MER301: Engineering Reliability Lecture 13

  18. Confidence Interval on Mean Response (6-52) MER301: Engineering Reliability Lecture 13

  19. Precision and Significance of the Regression… • And now the Significance…. • Hypothesis Testing • ANOVA MER301: Engineering Reliability Lecture 13

  20. Example 13.1(page 5) Regression Analysis The regression equation is Pull Strength = 2.26 + 2.74 Wire Length + 0.0125 Die Height (6-48) (6-49) MER301: Engineering Reliability Lecture 13

  21. Analysis of Variance(ANOVA) (6-47) (6-45) MER301: Engineering Reliability Lecture 13

  22. Summary of Topics • Multiple Regression Analysis • Multiple Regression Equation • Precision and Significance of a Regression Model • Confidence Limits MER301: Engineering Reliability Lecture 13

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