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MER301: Engineering Reliability

This lecture covers multiple regression analysis, equations, precision, and significance in regression models. Learn about confidence limits, standard errors, and correlation coefficients. Understand ANOVA and hypothesis testing for significance determination.

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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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