321w1p1 - 1. Introduction & Review (Appendices...

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Unformatted text preview: 1. Introduction & Review (Appendices & chapter 1) Math, Probability, Stats Review Constant something that does not change Variable something that takes on different values for different observations Parameters constants that define the direction & strength of a relationship between variables. Basic Math summation operator : i = 1 n x i = x 1 x 2 ... x n Properties of Summation Operator For any constant c: i = 1 n c = nc For any constant c: i = 1 n cx i = c i = 1 n x i For any constants a and b, and variables x and y: i = 1 n ax i by i = a i = 1 n x i + b i = 1 n y i be careful! i = 1 n x i y i i = 1 n x i / i = 1 n y i Some Statistics using Basic Math mean of a variable: x = n 1 i = 1 n x i Deviation from the mean: d i = x i x Sum of deviations: i = 1 n d i = i = 1 n x i x = i = 1 n x i i = 1 n x = 0 Variance: 1 n i = 1 n x i x 2 = 1 n i = 1 n x 2 2x i x x 2 = 1 n i = 1 n x i 2 x 2 Linear Functions : y = x y is a linear function of the variable x. The parameters (constants) are and . y y = x slope = = y x y = x y / x = = marginal effect of x on y (constant) x proportional change = relative change = x 1 x / x = x / x precentage change = 100* proportional change =change Properties of the natural log function ln ab = ln a ln b ln a / b = ln a ln b ln a b = b ln a ln b a = ln a / b ln e x = x ln 1 x x forsmallx d [ ln x ]/ dx = 1 / x log b x = ln x / ln b careful! ln a b ln a ln b Properties of the exponents e = 1 e 1 = e e ln x = x b p = e p ln b e x y = e x e y e xy = e x y 1 / e x = 1 / e x = e x a x b x = ab x 1 / a = a 1 d / dx e x = e x d /...
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321w1p1 - 1. Introduction & Review (Appendices...

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