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Lecture_04_Curve_Fitting_Linear_Regressi-1

# Lecture_04_Curve_Fitting_Linear_Regressi-1 - EGR 102...

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EGR 102 Introduction to Engineering Modeling Curve Fitting Linear Regression Chapter 14.1-14.3 EGR 102 Lecture 4 1 Figures from: “Applied Numerical Methods with MATLAB,” Steven Chapra, McGraw Hill

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Objectives Become familiar with basic statistics and the normal distribution. Learn how to compute the slope and intercept of a best-fit straight line with linear regression. Learn how to compute and understand the meaning of the Learn how to compute and understand the meaning of the coefficient of determination and the standard error of the estimate. Learn how to use transformations to linearize nonlinear Learn how to use transformations to linearize nonlinear equations so that they can be fit with linear regression. EGR 102 Lecture 4 2
The Need to Account for The Need to Account for Variability in Engineering Material Properties Stiffness, strength, conductivity, density Manufacturing Materials processing ency Materials processing, machining tolerances, weld and fastener l ti Freque locations Loading Magnitude, direction, Value EGR 102 Lecture 4 3 Magnitude, direction, distribution

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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 4 4 most frequently in a group of data.
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 . Variance : 2 2 ( ) 2 s y 2 = y i y ( ) n 1 = y i y i / n n 1 EGR 102 Lecture 4 5 Coefficient of variation : c.v. = s y y × 100%

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Histogram For large data sets, the histogram can be approximated by a smooth curve EGR 102 Lecture 4 6
Normal Distribution EGR 102 Lecture 4 7

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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)
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Lecture_04_Curve_Fitting_Linear_Regressi-1 - EGR 102...

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