STA 371G Outline Fall 2018

Transcription

1 STA 371G Outline Fall 2018 Instruct: Mingyuan Zhou, Ph.D., Assistant Profess of Statistics Office: CBA Phone: Website: Office Hours: Monday & Wednesday 5:00-6:00 PM. You are welcome to come by my office at other times. Wednesday, August 29 Topics: Introduction Probability Random variables You are recommended to read: Chapter 1 of OpenIntro Statistics, 3rd edition Wednesday, September 5 Topics: Probability distributions Mean, variance and standard deviation of a random variable If you are not familiar with the topics discussed in class, you are recommended to read: pp , Business Analytics: Business Analytics: Data analysis and decision making, 6th edition pp , , of Data analysis and decision making, 4th edition pp , of Data analysis and decision making, 3rd edition You are also recommended to read: pp of 1TopicSummary ProbabilityConceptsAndNmalDistributions.pdf (available in Canvas/files) 1

2 To learn me about these topics, you may further read: Chapters 2.1, 2.2, 2.4, and 2.5 of OpenIntro Statistics, 3rd edition Monday, September 10 Add a constant to a random variable Multiply a random variable by a constant Independent random variables, sum of independent random variables Continuous random variables Probability density function: area under the curve represents probability Standard nmal distribution Z N (0, 1) Nmal distribution X N (µ, σ 2 ) To get familiar with the nmal distribution, you are recommended to read: pp , of Business Analytics: Data analysis and decision making, 6th edition pp , of Data analysis and decision making, 4th edition pp , of Data analysis and decision making, 3rd edition You are also recommended to read: pp of 1TopicSummary ProbabilityConceptsAndNmalDistributions.pdf (available in Canvas/files) You may further read: Chapters 3.1.1, 3.1.2, and of OpenIntro Statistics, 3rd edition Wednesday, September 12 If X N (µ, σ 2 ), then P (X < x) = P ( X u σ < x u σ Standard nmal calculations in Excel: NORMSDIST, in R: pnm (type?pnm in R f help). x u ) = P (Z < σ ). Understand the meaning of the standard deviation σ in a nmal distribution: P (µ σ < X < µ + σ) =? and P (µ 2σ < X < µ + 2σ) =? Nmal calculations in Excel: NORMSDIST, NORMDIST NORMSINV, NORMINV in R: pnm, qnm (type?pnm and?qnm in R f help). 2

3 Standardizing a nmal random variable Z = X µ σ N (0, 1) Interpretation: the value of Z is the number of standard deviations that X deviates towards the left (if Z < 0) the right (if Z > 0) of the mean. Plot a nmal distribution in Excel and R Monday, September 17 Example: Testing at ZTel, we will make an Excel spreadsheet f calculations Case study, Texas BBA Salary Statistics Expectation of a continuous random variable Population mean, variance, standard deviation Sample mean, sample variance, standard err of the sample mean Sampling distribution of the sample mean To learn me about estimation and sampling distribution, please read: pp , , 299, of Business Analytics: Data analysis and decision making, 6th edition pp , , 374, of Data analysis and decision making, 4th edition pp , , , of Data analysis and decision making, 3rd edition You are also recommended to read: 2TopicSummary EstimationAndSamplingDistributions.pdf (available in Canvas/files) F this topic, you may further read: Chapters 4.1, 4.2, 4.4 and 5.3 of OpenIntro Statistics, 3rd edition Wednesday, September 19 Sampling distribution of the sample mean Confidence interval Simple linear regression Linear prediction: Y = b 0 + b 1 X 3

4 Chapters 7.1 and 7.2 of OpenIntro Statistics, 3rd edition pp of Business Analytics: Data analysis and decision making, 6th edition pp of Data analysis and decision making, 4th edition pp of Data analysis and decision making, 3rd edition Monday, September 24 Least squares estimation of b 0 and b 1 Examples: predict house price, baseball runs per game Using Excel and R to do the calculation Excel add-in: Palisade Decision Tools (including StatTools) f Windows, StatPlus:mac LE f Mac. Sample mean, variance, and standard deviation Sample covariance, sample crelation PDF Simple Linear Regression posted in Canvas/files Wednesday, September 26 Linear relationship between X and Y b 0 = ȳ b 1 x, b 1 = r xy sy s x mean(e)=0, Cr(e, X)=0, Cr(e, Ŷ )=0, Cr(Ŷ, X)=1 SST, SSR, SSE Coefficient of determination: R 2 = SSR SST = 1 SSE SST R 2 = r 2 xy measures the proption of variation in Y explained by X. Statistical model f simple linear regression Statistical model f simple linear regression: Y = β 0 + β 1 X + ɛ, ɛ N (0, σ 2 ) Y N (β 0 + β 1 X, σ 2 ) Conditional distribution of Y given X 4

5 95% prediction interval of Y given X: β 0 + β 1 X ± 2σ 3TopicSummary RegressionModelAndEstimation.pdf (available in Canvas/files) 5TopicSummary CrelationAndCovariance.pdf (available in Canvas/files) 6TopicSummary ComputingAndInterpretingRSquare.pdf (available in Canvas/files) 7TopicSummary InterpretingAndEstimatingVarianceOfEpsilon.pdf (available in Canvas/files) Monday, October 1 Conditional and marginal distributions of Y Interpretation of ɛ and σ The err terms ɛ i are independent, and identically distributed Least squares estimation and Gaussian maximum likelihood (optional) True line β 0 + β 1 X and least squares line b 0 + b 1 X Case study: A stock s beta coefficient Wednesday, October 3 Case study: Milk and Money Degrees of freedom In SLR, σ 2 is estimated with s 2 = n i=1 e2 i n 2 = SSE n 2. SLR regression standard err: s = SSE/(n 2) Sampling distributions of regression parameters Confidence intervals of regression parameters Monday, October 8 Hypothesis testing in SLR: t-statistic and p-value Discuss Practice Exam #1 Common problems in homewk assignments Topic summary f Midterm #1 Wednesday, October 10 5

6 Multiple regression T-test Examples: Auto MPG, Baseball Midterm Exam #1, 6:45-9:00 pm Monday October 15 Example: Supervis perfmance data F-test Understanding multiple regression Crelation and causation Wednesday, October 17 Multicollinearity Example: Number of beer and weight & height Monday, October 22 Dummy variables and interactions Example: Gender Discrimination in Salary at Fifth National Bank Case study: Orion Bus Industries Contract Bidding Strategy Chapters 10, , and of Business Analytics: Data analysis and decision making, 6th edition Chapters 10, , and of Data analysis and decision making, 4th edition Chapters 11, , and of Data analysis and decision making, 3rd edition 4TopicSummary NonlinearRelationships.pdf (available in Canvas/files) Wednesday, October 24 Example: MidCity House Price 6

7 Diagnostics Polynomial regression 9TopicSummary MeasuringTheQualityOfTheEstimateOfBeta.pdf (available in Canvas/files) 10TopicSummary HypothesisTestingInRegression.pdf (available in Canvas/files) Monday, October 29 Slides 3.3 pages Variable interaction Log transfmation Case Study, Oakland A s (A) Case Study, Oakland A s (B) Slides 4.1, Slides 4.2 pages 1-15 Time series: fitting a trend Autocrelation Time series regression, Hotel Occupancy Case Chapter 12 of Business Analytics: Data analysis and decision making, 6th edition Chapter 12 of Data analysis and decision making, 4th edition Chapter 13 of Data analysis and decision making, 3rd edition Wednesday, October 31 Slides 4.2 pages 16-end, Slides 4.3 pages 1-15 Random walk models Autegressive models Example: Monthly stock closing prices Example: Daily/Monthly temperature Example: Monthly Boston Armed Robberies Jan.1966-Oct

8 Seasonal models Example: Fisher river daily temperatures 8TopicSummary FecastingModelFSPSSSales.pdf (available in Canvas/files) Monday, November 5 Slides 4.3 pages 16-end Example: Monthly airline passengers Case study: Nthern Napa Valley Winery, Inc. Example: Monthly liqu sales Wednesday, November 7 Slides 5, Slides 6.1 pages 1-3 Outliers Moving averages, exponential smoothing and ARMA Hypothesis testing: Type I Err, Type II Err, significant level, and power Understanding prediction errs in linear regression Model selection Monday, November 12 Model selection Slides 6.1 pages 1-16, Slides 6.2 pages 1-21 Measure uncertainty with probability Frequency probability and subjective probability Probability, lotteries and betting odds Payoff tables Payoffs and Losses Nonprobabilistic criteria f decision making: maximin, maximax, and minimax loss 8

9 Wednesday, November 14 Slides 6.2 pages 22-end, Slides 6.1 pages 17-end, Slides 1.1 pages Probabilistic criteria f decision making: expected payoff, expected loss Utility functions Conditional probability and conditional bets conditional reference contracts Conditional, joint and marginal probabilities Bayes theem Chapter 6 of Business Analytics: Data analysis and decision making, 6th edition Chapter 6 of Data analysis and decision making, 4th edition Chapter 7 of Data analysis and decision making, 3rd edition Monday, November 19 Slides 6.3 pages 1-14, Slides 6.4 pages 1-14 Decision trees, risk profile, sensitivity analysis Risk profile, sensitivity analysis Chapter 6 of Business Analytics: Data analysis and decision making, 6th edition Chapter 6 of Data analysis and decision making, 4th edition Chapter 7 of Data analysis and decision making, 3rd edition Monday, November 26 The value of infmation Expected value of perfect infmation (EVPI) Expected value of sample infmation (EVSI) Expected value of sample infmation (EVSI) Case study: Freemark Abbey Winery 9

10 Wednesday, November 28 Please install R and Rstudio on your laptop and bring it to class Simulation using Excel and R Simulate random numbers from a discrete distribution Find the sample mean and variance, compare them with the true mean and variance Simulate the sampling distribution of the sample mean Unifm random numbers, flip a coin, toss a die, flip two coins, toss two dice, law of large numbers Estimate π with Monte Carlo simulation Simulate nmal random numbers X N (µ, σ 2 ). Find P (X < x) and P (X <?) = p using simulation Demonstrate Central Limit Theem using simulation Simulation of weekly demand Chapters 4.4 ( not found), pp of Business Analytics: Data analysis and decision making, 6th edition Chapters of Data analysis and decision making, 4th edition Chapters of Data analysis and decision making, 3rd edition Monday, December 3 Practice questions f the final exam Wednesday, December 6 Practice questions f the final exam Monday, December 10 (Last class of the semester) Simulation and decision Multivariate distributions, covariance and crelation Sum of crelated random variables Simulate ptfolio return 10

11 Sample from a finite population (with/without replacement) Simulate binomial random variables Simulate student t random variables Simulate a random walk model Simulate an AR+Trend model Simulate prediction intervals f an AR model 11