Lecture_Statistics_Spring_2013b

The sum of squares function is defined as n 2 s y i

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Unformatted text preview: performing a calculation carry an extra nonsignificant digit or two to avoid rounding errors. At the end of the calculation round your number to the appropriate number of significant figures for the lab report. V. Significant Figures Examples: For standard deviation (s) < 1.5 x 10X: 3.54678 ± 0.01438 3.547 ± 0.014 (1.9856 ± 0.1175) x 105 (1.99 ± 0.12) x 105 For standard deviation (s) > 1.5 x 10X: 101.3256 ± 2.654 101 ± 3 14.55567 ± 0.09789 14.6 ± 0.1 V. Significant Figures Examples: For 95% CI < 2.5 x 10X: 101.85678 ± 23.576 102 ± 24 (5.987598 ± 0.0175) x 105 (5.988 ± 0.018) x 105 For 95% CI > 2.5 x 10X: 5679 ± 27.65 5700 ± 30 0.056934 ± 0.00092789 0.0569 ± 0.0009 VI. Linear Regression Linear function y is a linear combination of k independent variables: y = β0 + β1X1 + β 2 X 2 + … + β k X k where β0, β 1, ..., β k are coefficients. * Some equations can be converted into linear equations through simple mathematical transformations. Example: X = 1/x y = A + BX y = A + B/x y = Aexp(Bx) ln y = ln A + Bx * Some equations can not be converted into linear equations through simple mathematical transformations. Example: y = A + Bexp(Cx + D) Non-linear regression is required. VI. Linear Regression Target To determine the values of the βi that will allow us to determine the best fit of a linear equation to a set of observations. The sum of squares function is defined as: N 2 ˆ S = ∑ (y i − y i ) i =1 N ȹ k ȹ ȹ ȹ = ∑ ȹ y i − ȹ β 0 + ∑ β i X i ȹ ȹ ȹ ȹ ȹ ȹ i =1ȹ i =1 ȹ Ⱥ Ⱥ 2 Thu...
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