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Lecture_04_Curve_Fitting_Linear_Regressi

# Lecture_04_Curve_Fitting_Linear_Regressi - EGR 102...

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1 EGR 102 Lecture 4 1 EGR 102 Introduction to Engineering Modeling Curve Fitting Linear Regression Chapter 13.1-13.3 Figures from: “Applied Numerical Methods with MATLAB,” Steven Chapra, McGraw Hill EGR 102 Lecture 4 2 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 coefficient of determination and the standard error of the estimate. Learn how to use transformations to linearize nonlinear equations so that they can be fit with linear regression.

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2 EGR 102 Lecture 4 3 The Need to Account for Variability in Engineering Material Properties Stiffness, strength, conductivity, density Manufacturing Materials processing, machining tolerances, weld and fastener locations Loading Magnitude, direction, distribution Frequency Value EGR 102 Lecture 4 4 Statistics Review Measures of Central Tendency Arithmetic mean : the sum of the individual data points ( x i ) divided by the number of points n : Median : the midpoint of a group of data. Mode : the value that occurs most frequently in a group of data. n x x i
3 EGR 102 Lecture 4 5 Statistics Review Measures of Spread Standard deviation : where S t is the sum of the squares of the data residuals: and n -1 is referred to as the degrees of freedom . Variance : Coefficient of variation : s y S t n 1 S t y i y 2 s y 2 y i y 2 n 1 y i 2 y i 2 / n n 1 c.v. s y 100% EGR 102 Lecture 4 6 Histogram For large data sets, the histogram can be approximated by a smooth curve

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4 EGR 102 Lecture 4 7 Normal Distribution EGR 102 Lecture 4 8 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
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Lecture_04_Curve_Fitting_Linear_Regressi - EGR 102...

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