(Approximately) Bivariate Normal Data and Inference Based on Hotelling’s T2 WNBA Regular Season Home Point Spread and Over/Under Differentials 2010-2018.

Slides:

Advertisements

Similar presentations

STATISTICS Joint and Conditional Distributions

Advertisements

Regression of NFL Scores on Vegas Line – 2007 Regular Season.

STATISTICAL INFERENCE PART V CONFIDENCE INTERVALS 1.

Ka-fu Wong © 2003 Chap 8- 1 Dr. Ka-fu Wong ECON1003 Analysis of Economic Data.

Correlation. Introduction Two meanings of correlation –Research design –Statistical Relationship –Scatterplots.

Chapter 13 Conducting & Reading Research Baumgartner et al Data Analysis.

Correlation and Simple Regression Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing.

GRA 6020 Multivariate Statistics Ulf H. Olsson Professor of Statistics.

Multivariate Distance and Similarity Robert F. Murphy Cytometry Development Workshop 2000.

Sampling Distributions

The General LISREL MODEL and Non-normality Ulf H. Olsson Professor of Statistics.

Analysis of Research Data

The General LISREL MODEL and Non-normality Ulf H. Olsson Professor of Statistics.

The General LISREL MODEL and Non-normality Ulf H. Olsson Professor of Statistics.

The Multivariate Normal Distribution, Part 2 BMTRY 726 1/14/2014.

1 Multivariate Normal Distribution Shyh-Kang Jeng Department of Electrical Engineering/ Graduate Institute of Communication/ Graduate Institute of Networking.

Normal and Sampling Distributions A normal distribution is uniquely determined by its mean, , and variance,  2 The random variable Z = (X-  /  is.

Things that I think are important Chapter 1 Bar graphs, histograms Outliers Mean, median, mode, quartiles of data Variance and standard deviation of.

MathematicalMarketing Slide 2.1 Descriptive Statistics Chapter 2: Descriptive Statistics We will be comparing the univariate and matrix formulae for common.

6.1 What is Statistics? Definition: Statistics – science of collecting, analyzing, and interpreting data in such a way that the conclusions can be objectively.

Ch2: Probability Theory Some basics Definition of Probability Characteristics of Probability Distributions Descriptive statistics.

7.4 – Sampling Distribution Statistic: a numerical descriptive measure of a sample Parameter: a numerical descriptive measure of a population.

Using the Empirical Rule. Normal Distributions These are special density curves. They have the same overall shape  Symmetric  Single-Peaked  Bell-Shaped.

Chapter 3 Descriptive Statistics II: Additional Descriptive Measures and Data Displays.

Problem: 1) Show that is a set of sufficient statistics 2) Being location and scale parameters, take as (improper) prior and show that inferences on ……

Appendix B: Statistical Methods. Statistical Methods: Graphing Data Frequency distribution Histogram Frequency polygon.

Estimation of covariance matrix under informative sampling Julia Aru University of Tartu and Statistics Estonia Tartu, June 25-29, 2007.

University of Colorado Boulder ASEN 5070: Statistical Orbit Determination I Fall 2015 Professor Brandon A. Jones Lecture 14: Probability and Statistics.

Inference for the mean vector. Univariate Inference Let x 1, x 2, …, x n denote a sample of n from the normal distribution with mean  and variance 

© 2010 Pearson Prentice Hall. All rights reserved 7-1.

Beginning Statistics Table of Contents HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2008 by Hawkes Learning Systems/Quant Systems, Inc.

Chapter 12: Correlation and Linear Regression 1.

Statistics and probability Dr. Khaled Ismael Almghari Phone No:

Welcome to MM305 Unit 2 Seminar Dr. Bob Statistical Foundations for Quantitative Analysis.

Lecture 8 Data Analysis: Univariate Analysis and Data Description Research Methods and Statistics 1.

Thursday, May 12, 2016 Report at 11:30 to Prairieview

Ch5.4 Central Limit Theorem

Statistical Methods Michael J. Watts

Chapter 1 A Review of Basic Concepts (Optional).

Review 1. Describing variables.

Statistical Methods Michael J. Watts

Basic simulation methodology

Figure Legend: From: Bayesian inference for psychometric functions

STATISTICS Joint and Conditional Distributions

Inference for the mean vector

Module 6: Descriptive Statistics

1-Way Random Effects Model

Math 4030 – 12a Correlation.

Chapter 4 – Numerical Descriptive Techniques

AP Statistics: Chapter 7

Using the Empirical Rule

Statistical Evaluation

Statistical Inference for the Mean Confidence Interval

Inference about the Slope and Intercept

Sampling Distribution Models

Inference about the Slope and Intercept

Statistical Inference for Managers

Sampling Distribution of Pearson Correlation

Regression with Random Predictor(s)

The Multivariate Normal Distribution, Part 2

Confidence Ellipse for Bivariate Normal Data

Ch11 Curve Fitting II.

数据的矩阵描述.

1-Way Random Effects Model

Control Charts Johnson, R.A. and D.W. Wichern (2007). Applied Multivariate Statistical Analysis, 6th. Ed. Pearson, Upper Saddle River, N.J. Montgomery,

The two sample problem.

Principal Component Analysis

Professor Ke-sheng Cheng

Introductory Statistics

What’s your New Year’s Resolution?

Presentation transcript:

(Approximately) Bivariate Normal Data and Inference Based on Hotelling’s T2 WNBA Regular Season Home Point Spread and Over/Under Differentials 2010-2018

Description of Population Units: N=1833 WNBA Regular Season Games with Home Team Point Spread and Over/Under Total Lines During 2010-2018 Regular Seasons Home Point Spread Line (X1) : The Number of Points the Home Teams “Starts Up” by at Game Begin (Negative Spread Implies Home Team is Favored – Starts Behind) Over/Under Total Line (X2) : Expected Total Points by Both Teams in a Game Home Team Score (X3) Away Team Score (X4)

Population Data

Sampling Distributions of Mean Vector and Variance-Covariance Matrix

Hotelling’s T2

Sampling from the Population Number of Random Samples: 100000 Sample Size: n = 50 For each Sample: Save: Mean Vector and Variance-Covariance Matrix Test H0: d = 0 Obtain 95% CIs for d1, d2 Compare Univariate Distributions of Mean Differences with Theoretical Distributions Plot Mean Differences with Superimposed Bivariate Normal Ellipsoid Graph Histogram of Scaled T2 Statistics with Superimposed F-distribution Compare Mean and Variance of Sample Variances and Covariance with Theoretical Values Graph Histogram of Scaled Correlation Coefficients with t-density (r ≈ 0)

Empirical Results

Empirical Distributions of Means and Normal Densities

Bivariate Empirical Distributions and Normal Ellipsoid