1 / 54

Final Review

Final Review. Econ 240A. Outline. The Big Picture Processes to remember ( and habits to form) for your quantitative career (FYQC) Concepts to remember FYQC Discrete Distributions Continuous distributions Central Limit Theorem Regression. The Classical Statistical Trail. Rates &

hilde
Download Presentation

Final Review

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. Final Review Econ 240A

  2. Outline • The Big Picture • Processes to remember ( and habits to form) for your quantitative career (FYQC) • Concepts to remember FYQC • Discrete Distributions • Continuous distributions • Central Limit Theorem • Regression

  3. The Classical Statistical Trail Rates & Proportions Inferential Statistics Application Descriptive Statistics Discrete Random Variables Binomial Probability Discrete Probability Distributions; Moments

  4. Where Do We Go From Here? Contingency Tables Regression Properties Assumptions Violations Diagnostics Modeling ANOVA Count Probability

  5. Processes to Remember • Exploratory Data Analysis • Distribution of the random variable • Histogram Lab 1 • Stem and leaf diagram Lab 1 • Box plot Lab 1 • Time Series plot: plot of random variable y(t) Vs. time index t • X-y plots: Y Vs. x1, y Vs. x2 etc. • Diagnostic Plots • Actual, fitted and residual • Cross-section data: heteroskedasticity-White test • Time series data: autocorrelation- Durbin- Watson statistic

  6. Time Series

  7. UCBudsh(t) = a + b*timex(t) + e(t) e(t) = 0.68*e(t-1) + u(t) 0.68*UCbudsh(t-1) = 0.68*a + b*0.68*timex(t-1) + 0.68*e(t-1) [UCbudsh(t) – 0.68*UCbudsh(t-1)] = [(1-0.68)*a] + b*[timex – 0.68*timex(-1)] + u(t) Y(t) = a* + b*x(t) + u(t) Called autoregressive (auto-correlated) error

  8. Concepts to Remember • Random Variable: takes on values with some probability • Flipping a coin • Repeated Independent Bernoulli Trials • Flipping a coin twice or more • Random Sample • Likelihood of a random sample • Prob(e1^e2 …^en) = Prob(e1)*Prob(e2)…*Prob(en)

  9. Discrete Distributions • Discrete Random Variables • Probability density function: Prob(x=x*) • Cumulative distribution function, CDF • Equi-Probable or Uniform • E.g x = 1, 2, 3 Prob(x=1) =1/3 = Prob(x=2) =Prob(x=3)

  10. Discrete Distributions • Binomial: Prob(k) = [n!/k!*(n-k)!]* pk (1-p)n-k • E(k) = n*p, Var(k) = n*p*(1-p) • Simulated sample binomial random variable Lab 2 • Rates and proportions • Poisson

  11. Continuous Distributions • Continuous random variables • Density function, f(x) • Cumulative distribution function • Survivor function S(x*) = 1 – F(x*) • Hazard function h(t) =f(t)/S(t) • Cumulative hazard functin, H(t)

  12. Continuous Distributions • Simple moments • E(x) = mean = expected value • E(x2) • Central Moments • E[x - E(x)] = 0 • E[x – E(x)]2 =Var x • E[x – E(x)]3 , a measure of skewness • E[x – E(x)]4 , a measure of kurtosis

  13. Continuous Distributions • Normal Distribution • Simulated sample random normal variable Lab 3 • Approximation to the binomial, n*p>=5, n*(1-p)>=5 • Standardized normal variate: z = (x-)/ • Exponential Distribution • Weibull Distribution • Cumulative hazard function: H(t) = (1/) t • Logarithmic transform ln H(t) = ln (1/) +  lnt

  14. Central Limit Theorem • Sample mean,

  15. Population Random variable x Distribution f(m, s2) f ? Pop. Sample Sample Statistic Sample Statistic:

  16. The Sample Variance, s2 Is distributed chi square with n-1 degrees of freedom (text, 12.2 “inference about a population variance) (text, pp. 266-270, Chi-Squared distribution)

  17. Regression • Models • Statistical distributions and tests • Student’s t • F • Chi Square • Assumptions • Pathologies

  18. Regression Models • Time Series • Linear trend model: y(t) =a + b*t +e(t) Lab 4 • Exponential trend model: y(t) =exp[a+b*t+e(t)] • Natural logarithmic transformation ln • Ln y(t) = a + b*t + e(t) Lab 4 • Linear rates of change: yi = a + b*xi + ei • dy/dx = b • Returns generating process: • [ri(t) – rf0] =  + *[rM(t) – rf0] + ei(t) Lab 6

  19. Regression Models • Percentage rates of change, elasticities • Cross-section • Ln assetsi =a + b*ln revenuei + ei Lab 5 • dln assets/dlnrevenue = b = [dassets/drevenue]/[assets/revenue] = marginal/average

  20. Linear Trend Model • Linear trend model: y(t) =a + b*t +e(t) Lab 4

  21. Lab 4

  22. Lab Four F-test: F1,36 = [R2/1]/{[1-R2]/36} = 196 = Explained Mean Square/Unexplained mean square t-test: H0: b=0 HA: b≠0 t =[ -0.000915 – 0]/0.0000653 = -14

  23. Lab 4

  24. Lab 4

  25. Lab 4 2.5% -14 -2.03

  26. Lab Four 5% 4.12 196

  27. Exponential Trend Model • Exponential trend model: y(t) =exp[a+b*t+e(t)] • Natural logarithmic transformation ln • Ln y(t) = a + b*t + e(t) Lab 4

  28. Lab Four

  29. Lab Four

  30. Percentage Rates of Change, Elasticities • Percentage rates of change, elasticities • Cross-section • Ln assetsi =a + b*ln revenuei + ei Lab 5 • dln assets/dlnrevenue = b = [dassets/drevenue]/[assets/revenue] = marginal/average

  31. Lab Five Elasticity b = 0.778 H0: b=1 HA: b<1 t25 = [0.778 – 1]/0.148 = - 1.5 t-crit(5%) = -1.71

  32. Linear Rates of Change • Linear rates of change: yi = a + b*xi + ei • dy/dx = b • Returns generating process: • [ri(t) – rf0] =  + *[rM(t) – rf0] + ei(t) Lab 6

  33. Watch Excel on xy plots! True x axis: UC Net

  34. Lab Six rGE = a + b*rSP500 + e

  35. Lab Six

  36. Lab Six

  37. View/Residual tests/Histogram-Normality Test

  38. Linear Multivariate Regression • House Price, # of bedrooms, house size, lot size • Pi = a + b*bedroomsi + c*house_sizei + d*lot_sizei + ei

  39. Lab Six price bedrooms House_size Lot_size

  40. Price = a*dummy2 +b*dummy34 +c*dummy5 +d*house_size01 +e

  41. Lab Six C captures three and four bedroom houses

  42. Regression Models • How to handle zeros? • Labs Six and Seven: Lottery data-file • Linear probability model: dependent variable: zero-one • Logit: dependent variable: zero-one • Probit: dependent variable: zero-one • Tobit: dependent variable: lottery See PowerPoint application to lottery with Bern variable

  43. Regression Models • Failure time models • Exponential • Survivor: S(t) = exp[-*t], ln S(t) = -*t • Hazard rate, h(t) =  • Cumulative hazard function, H(t) = *t • Weibull • Hazard rate, h(t) = f(t)/S(t) = (/)(t/)-1 • Cumulative hazard function: H(t) = (1/) t • Logarithmic transform ln H(t) = ln (1/) +  lnt

  44. Binomial Equi-probable or uniform Poisson Rates & proportions, small samples, ex. Voting polls If I asked a question every day, without replacement, what is the chance I will ask you a question today? Approximate the binomial where p→0 Applications: Discrete Distributions

  45. Multinomial More than two outcomes, ex each face of the die or 6 outcomes Aplications: Discrete Distributions

More Related