Class Lectures & Homeworks
EMSE 6765 - Data Analysis for Engineering & Science
Course Description (3 credits)
Probability and Statistical review is provided in the first three to three lectures. Statistical Inference topics that will be discussed include estimation, confidence intervals, hypothesis testing and goodness-of-fit testing. These methods perform statistical inference in a single dimension (also known as univariate data analysis).
Discussions of multivariate data analysis utilize matrices and vectors. One class will review rules of matrix-vector algebra and provides some intuitive geographical interpretations of these operations. Multivariate data analysis will be introduced by first discussing the classical Hotelling T2 hypothesis test, which is a natural extension of the univariate T test.
Next, the class introduces regression nalysis (in matrix-vector format) and principal component analysis. The introduction of these topics will be cursory and their application will be facilitated by the use of the MINITAB software program. Discussion of these multivariate techniques will concentrate on intuition, not a rigorous derivation of their methodologies.
Part 1: Prob and Stats Review
Session 1
Lecture Description
• Probability Calculus • Discrete and Continuous Random Variables
Chapter 1: Why Probability and Statistics?
Chapter 2: Outcomes, Events, and Probability
Chapter 3: Conditional Probability and Independence
Chapter 4: Discrete Random Variables
Chapter 5: Continuous Random Variables
Session 2
Lecture Description
• Expectation, Variance and Covariance • Exploratory Data Analysis • Graphical Summaries
Chapter 7: Expectation and Variance
Chapter 10: Covariance and Correlation
Chapter 15: Exploratory Data Analysis: Graphical Summaries
Session 3
Lecture Description
• Exploratory Data Analysis: • Numerical Summaries • Basic Statistical Models • Confidence Intervals
Chapter 16: Exploratory Data Analysis: Numerical Summaries
Chapter 17: Basic statistical models
Chapter 23: Confidence Intervals for the Mean
Part 2: Statistical Inference
Session 4
Lecture Description
• Estimator Distributions • Confidence Intervals for the Mean and Variance Hypothesis Testing • P-Values • Type I and Type II Errors
Lecture Note
Session 5
Lecture Description
• Method-of-Moments • Maximul Likelihood Estimation • Goodness-of-Fit • Credibility Intervals
Lecture Note
Part 3: Multivariate Estimation
Session 6
Textbook Chapter - Matrix Algebra
Lecture Description
• Two Sample Hypothesis-Testing • Review Matrix Algebra • Multivariate Point Estimation
Lecture Note
Homework Problem
Session 7
Lecture Description
• One sample Hotelling T^2 Test • Two Sample Hotelling T^2 Test • Hypothesis-Test on equality of covariance matrices • Mutlivariate Box’s M-Test for equality of Covariance Matrices
Lecture Note
Session 8
Lecture Description
• Practice Mid-term Exam
Exam Note
Part 4: Regression Analysis
Session 9
Lecture Description
• Simple Linear Regression • Model Testing • Parameter Inference
Lecture Note
Session 10
Lecture Description
• Multiple Linear Regression • Residual Diagnostics • Outliers
Lecture Note
Session 11
Lecture Description
• Multiple Linear Regression • Comparing Models • Forecasting
Lecture Note
Part 5: ANOVA Analysis
Session 12
Lecture Description
• One-Way ANOVA
Lecture Note
Session 13
Lecture Description
• Two-Way ANOVA and 2^k ANOVA • 2 -Factorial Analysis of Variance (ANOVA)
Lecture Note
Session 14 - Final Reports
Final Project Reports
• Regression Analysis Final Report • Two-Way ANOVA Final Report
