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 inear Regression 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. earn 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. earn 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
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he Need to Account for The Need to Account for Variability in Engineering ± Material Properties ± Stiffness, strength, conductivity, density ± Manufacturing ency ± Materials processing, machining tolerances, weld and fastener Frequ e locations ± Loading agnitude, direction, alue EGR 102 Lecture 4 3 ± Magnitude, direction, distribution Value
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tatistics Review 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 i = ± Median: the midpoint of a n x group of data. ± Mode: the value that occurs ost frequently in a group of EGR 102 Lecture 4 4 most frequently in a group of data.
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tatistics Review 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: nd - is referred to as the S t = y i y () 2 and n 1 is referred to as the degrees of freedom. ± Variance: 2 s y 2 = y i y 2 n 1 = y i 2 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
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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 ±
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Lecture_04_Curve_Fitting_Linear_Regressi-1 - EGR 102...

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