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Lecture_05_Polynomial_Regression-1

# Lecture_05_Polynomial_Regression-1 - EGR 102 Introduction...

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EGR 102 Introduction to Engineering Modeling i i Curve Fitting Polynomial Regression Chapter 15.1-15.3 EGR 102 Lecture 5 1 Figures from: “Applied Numerical Methods with MATLAB,” Steven Chapra, McGraw Hill

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A Few Words about A Few Words about Academic Dishonesty What it is: Submitting work as your own that you did not do, or aiding someone else to do so Receiving or providing unauthorized assistance on any assignment or exam What it is not: Helping someone else to understand a concept or how to work a problem, when such help is authorized Working together on assignments, when allowed to do so Level of tolerance in engineering: ZERO Level of tolerance in engineering: Must be able to make good decisions under pressure Must act with integrity in all cases The health and safety of others depends upon complete honesty EGR 102 Lecture 5 2
Homework Assignments Should be completed by hand Helps in understanding the theory and the procedure Solutions should be validated, if at all possible Numerical solutions (e.g., Excel or MATLAB) can be used for validation Reading the textbook sections is very important Understanding the background, term definitions, assumptions, formulations and theory is necessary for proper application of methods Getting multiple points of view (e.g., lecture versus text) promotes a d d d deeper understanding Working together is encouraged to aid in understanding, but l f d k EGR 102 Lecture 5 3 always perform and turn in your own work

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Curve Fitting Method(s) to fit an equation to discrete data points Two general approaches: Data exhibit a significant degree of scatter Derive a single line (curve) that represents the general trend of the data Data is very precise Pass a single curve through the points (interpolation) Three general applications in engineering: Trend analysis Predicting values between data points or beyond data range Hypothesis testing Comparing existing mathematical model with measured data Simplified modeling EGR 102 Lecture 5 4 Developing simple math models to represent complex phenomenon
Statistics Review Measures of Central Tendency Arithmetic mean : the sum of the individual data points ( x i ) divided by the number of points n : x x i = Median : the midpoint of a n group of data. Mode : the value that occurs most frequently in a group of EGR 102 Lecture 5 5 most frequently in a group of data.

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Statistics Review Measures of Spread Standard deviation : s y = S t n 1 where S t is the sum of the squares of the data residuals: and n -1 is referred to as the degrees of freedom S t = y i y ( ) 2 and n 1 is referred to as the .
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Lecture_05_Polynomial_Regression-1 - EGR 102 Introduction...

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