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Econ 240A

Econ 240A. Power 17. Outline. Review Projects. Review: Big Picture 1. #1 Descriptive Statistics Numerical central tendency: mean, median, mode dispersion: std. dev., IQR, max-min skewness kurtosis Graphical Bar plots Histograms Scatter plots: y vs. x

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Econ 240A

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  1. Econ 240A Power 17

  2. Outline • Review • Projects

  3. Review: Big Picture 1 • #1 Descriptive Statistics • Numerical central tendency: mean, median, mode dispersion: std. dev., IQR, max-min skewness kurtosis • Graphical • Bar plots • Histograms • Scatter plots: y vs. x • Plots of a series against time (traces) Question: Is (are) the variable (s) normal?

  4. Review: Big Picture 2 • # 2 Exploratory Data Analysis • Graphical • Stem and leaf diagrams • Box plots • 3-D plots

  5. Review: Big Picture 3 • #3 Inferential statistics • Random variables • Probability • Distributions • Discrete: Equi-probable (uniform), binomial, Poisson • Probability density, Cumulative Distribution Function • Continuous: normal, uniform, exponential • Density, CDF • Standardized Normal, z~N(0,1) • Density and CDF are tabulated • Bivariate normal • Joint density, marginal distributions, conditional distributions • Pearson correlation coefficient, iso-probability contours • Applications: sample proportions from polls

  6. Review: Big Picture 4 • Inferential Statistics, Cont. • The distribution of the sample mean is different than the distribution of the random variable • Central limit theorem • Confidence intervals for the unknown population mean

  7. Review: Big Picture 5 • Inferential Statistics • If population variance is unknown, use sample standard deviation s, and Student’s t-distribution • Hypothesis tests • Decision theory: minimize the expected costs of errors • Type I error, Type II error • Non-parametric statistics • techniques of inference if variable is not normally distributed

  8. Review: Big Picture 6 • Regression, Bivariate and Multivariate • Time series • Linear trend: y(t) = a + b*t +e(t) • Exponential trend: ln y(t) = a +b*t +e(t) • Quadratic trend: y(t) = a + b*t +c*t2 + e(t) • Elasticity estimation: lny(t) = a + b*lnx(t) +e(t) • Returns Generating Process: ri(t) = c + b*rM(t) + e(t) • Problem: autocorrelation • Diagnostic: Durbin-Watson statistic • Diagnostic: inertial pattern in plot(trace) of residual • Fix-up: Cochran-Orcutt • Fix-up: First difference equation

  9. Review: Big Picture 7 • Regression, Bivariate and Multivariate • Cross-section • Linear: y(i) = a + b*x(i) + e(i), i=1,n ; b=dy/dx • Elasticity or log-log: lny(i) = a + b*lnx(i) + e(i); b=(dy/dx)/(y/x) • Linear probability model: y=1 for yes, y=0 for no; y =a + b*x +e • Probit or Logit probability model • Problem: heteroskedasticity • Diagnostic: pattern of residual(or residual squared) with y and/or x • Diagnostic: White heteroskedasticity test • Fix-up: transform equation, for example, divide by x • Table of ANOVA • Source of variation: explained, unexplained, total • Sum of squares, degrees of freedom, mean square, F test

  10. Review: Big Picture 8 • Questions: quantitative dependent, qualitative explanatory variables • Null: No difference in means between two or more populations (groups), One Factor • Graph • Table of ANOVA • Regression Using Dummies • Null: No difference in means between two or more populations (groups), Two Factors • Graph • Table of ANOVA • Comparing Regressions Using Dummies

  11. Review: Big Picture 9 • Cross-classification: nominal categories, e.g. male or female, ordinal categories e.g. better or worse, or quantitative intervals e.g. 13-19, 20-29 • Two Factors mxn; (m-1)x(n-1) degrees of freedom • Null: independence between factors; expected number in cell (i,j) = p(i)*p(j)*n • Pearson Chi- square statistic = sum over all i, j of [observed(i, j) – expected(i, j)]2 /expected(i, j)

  12. Summary • Is there any relationship between 2 or more variables • quantitative y and x: graphs and regression • Qualitative binary y and quantitative x: probability model, linear or non-linear • Quantitative y and qualitative x: graphs and Tables of ANOVA, and regressions with indicator variables • Qualitative y and x: Contingency Tables

  13. That’s all folks!

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