02 STAT descriptive stats 2-LONG SLIDES(1)

# 02 STAT descriptive stats 2-LONG SLIDES(1) - DESCRIPTIVE...

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1 DESCRIPTIVE STATISTICS Dr. V.R. Bencivenga Economic Statistics Economics 329 DESCRIPTIVE STATISTICS PART 2 Outline I. Covariance II. Correlation III. More on linear transformations IV. Regression V. Correlation and regression: “regression to the mean” VI. A simple model of “regression to the mean” Appendix: Two proofs (OPTIONAL) Objectives: Methods for describing how the distributions of two variables are related What it means for two variables to be more “tightly” associated How is strength of association affected by “stretching/shrinking” and “shifting” the variables? Estimating a line through a cloud of points Relationship between “correlation” and the “best fitting line” (regression line)

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2 DESCRIPTIVE STATISTICS I. COVARIANCE
3 DESCRIPTIVE STATISTICS An important type of question is whether two variables tend to move together or in opposite directions , as we go from observation to observation … Y X Y X Y X Y X

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4 DESCRIPTIVE STATISTICS An important type of question is whether two variables tend to move together or in opposite directions , as we go from observation to observation … … and if so, what is the strength of this tendency. Y X Y X Y X Y X Y X Y X
5 DESCRIPTIVE STATISTICS Examples (weekly data on stock prices, 2000-2010) X = Exxon Y = American Airline X = Exxon Y = Toyota X = Hovnanian Enterprises Y = Marriott Weak negative association Strong positive association Substantial positive association

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6 DESCRIPTIVE STATISTICS How should we measure the strength of association? We should build our measure from deviations . The measure should increase as the observations become more “tightly clustered” around a line. We want a measure of how “tightly clustered” the cloud of points is, relative to S X (dispersion of X) and S Y (dispersion of Y).
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## This note was uploaded on 02/26/2012 for the course ECONOMICS 329 taught by Professor Bencivenga during the Spring '12 term at University of Texas.

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02 STAT descriptive stats 2-LONG SLIDES(1) - DESCRIPTIVE...

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