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# 201-Lect 5 - Objectives Week 5 Curve Fitting Interpolation...

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1 Week 5 Week 5 Curve Fitting & Interpolation Week 5 Objectives • Use least-square regression to fit a straight line to measured data • Use polynomial regression to fit polynomials to the measured data Week 5 Curve Fitting • There are two approaches for curve fitting: least-squares regression & interpolation Least-squares regression : When the data exhibits a significant degree of error, then the strategy is to derive a single curve that represents the general trend of the data Interpolation : when the data is known to be very precise, the basic approach is to fit a curve or a series of curves that pass directly through each of the points. Estimation of values between well-known discrete points is called interpolation Week 5 Curve fitting Interpolation

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2 Week 5 Least-squares regression • Least-squares regression uses basic concepts of statistics: mean, standard deviation, residual sum of the squares, and confidence intervals • Arithmetic mean: sum of the individual data points divided by the number of points • Standard deviation: the square root of ratio of total sum of the squares of the residuals and (n-1) n y y i = () 1 2 = n y y s i y Week 5 Least-squares fit of a straight line • A straight line is fitted to a set of observed points ( x 1 , y 1 ), ( x 2 , y 2 ) … , ( x n , y n ) y = a 0 + a 1 x • Let e be the error or residual between the true value of y and approximate value ∑∑ = = = = i i i n n n x a a y e or x a a y e x a a y e x a a y e 1 0 1 0 2 1 0 2 2 1 1 0 1 1 L L L L L L Week 5
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201-Lect 5 - Objectives Week 5 Curve Fitting Interpolation...

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