1 / 13

Statistics for Data Analysis and Inference

Learn descriptive and inferential statistics concepts, graphical analysis, hypothesis testing, regression techniques, and ANOVA. Understand data relationships, distributions, and diagnostic tools. Enhance your statistical skills for analysis and decision-making.

kiayada-shepard
Télécharger la présentation

Statistics for Data Analysis and Inference

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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!

More Related