Exam I: Information and Practice Problems
with Solutions
Statistics 509 Winter 2018
February 19, 2018
Information: The Midterm Exam will be Thursday, February 22, from 6:008:00pm in
Chem 1800. It wil
Problem Set 2  Solutions
Statistics 509 Winter 2018
Instructions. You may work in teams, but you must turn in your own work/code/results.
Also for the problems requiring use of the Rpackage, you nee
Problem Set 3  Solutions
Statistics 509 Winter 2018
Instructions. You may work in teams, but you must turn in your own work/code/results.
Also for the problems requiring use of the Rpackage, you nee
Problem Set 4
Statistics 509 Winter 2018
Due by Wednesday, February 7 in class
Instructions. You may work in teams, but you must turn in your own work/code/results.
Also for the problems requiring use
Exam I: Information and Practice Problems
Statistics 509 Winter 2018
February 14, 2018
Information: The Midterm Exam will be Thursday, February 22, from 6:008:00pm in
Chem 1800. It will cover the mat
Problem Set 5
Statistics 509 Winter 2018
Due by Wednesday, February 14 in class
Instructions. You may work in teams, but you must turn in your own work/code/results.
Also for the problems requiring us
STATS 250 Midterm Study Guide
Lesson 1: Summarizing Data
Raw Data numbers and category labels that have been collected or measured but have
not yet been processed in any way
Variable characteristic
_
_
Practice Problems 1
Name:
1) Let X he a random variable with mean 10 and variance 1. Let a
constants.
a) Calculate EaX
b) Calculate Var(aX
b
*
/
Vv
H
( 1)<H
b).
:
V
)
=
2 and b
o be

2) )dultipl
Factor Analysis
Stats 503
Instructor: Prof. Long Nguyen
Stats 503
Factor Analysis
1 / 29
Introduction to factor analysis (FA)
Modelbased dimension reduction technique
Aims to relate a given set of va
Classification, Part II
Parametric model based classifiers:
LDA, QDA and Logistic Regression
Stats 503
Intructor: Prof. Long Nguyen
Stats 503
Classification, Part II
1 / 38
Generative models
Discrimin
Classification, Part VI
Ensemble Classifiers
Stats 503
Winter 2017
Stats 503
Classification VI: Ensemble classifiers
1 / 25
Ensemble Classifiers
Classification trees are simple but often unstable. Sol
Categorical Data Analysis
2way contingency tables and loglinear models
Stats 503
Winter 2017
Stats 503
Categorical data I: 2way
1 / 39
Categorical Data Analysis
All variables involved are categoric
Classification, Part I
Introduction and the DecisionTheoretic Framework
Stats 503
Instructor: Prof. Long Nguyen
Stats 503
Classification, Part I
1 / 26
Setup and Objectives
Given: a collection of da
From clustering algorithms to
hierarchical models to Bayesian inference and beyond
Long Nguyen
STATS 503
Department of Statistics
University of Michigan
April 11, 2017
Long Nguyen (UMich)
From cluster
Principal Component Analysis
Stats 503
Stats 503
Principal Component Analysis
1 / 57
Motivation
The main objective: reduce dimensionality of the data set.
Replaces the original p variables with k < p
Introduction and overview
Stats 503
Instructor: Prof. Long Nguyen
Stats 503
Introduction and overview
1 / 25
Learning from Data
Fact: The amount of data and information collected and stored is
constan
Stochastic Processes
Homework No. 12
1. Find the distribution of the sum of 3 i.i.d. uniform variables over (0,1).
2. Find the distribution of the sum of 4 i.i.d. uniform variables over (0,1).
3. Pro
STATS 500  Lecture 4
1 / 19
Simple Linear Regression
Estimation
2 / 19
The Model
3 / 19
Simple Linear Regression Model
Assume the linear model
yi = + xi + i
i
indep
N(0, 2 )
i = 1, . . . , n
yi is t
STATS 500  Lecture 5
1 / 28
Hypothesis Testing
2 / 28
The Four Steps in Hypothesis Testing
Model
Hypothesis
Test Statistic
Decision Rule
3 / 28
Example
Model:
yi = + xi + i
Hypothesis:
Test statistic
STATS 500
1 / 10
The Bivariate Normal Distribution
2 / 10
The Bivariate Normal Distribution
Random variables X and Y have a bivariate normal distribution if, and
only if, there exist constants (a11 ,
STATS 500  Lecture 1
1 / 11
Introduction to Class
2 / 11
Introduction to STATS 500
This class is about linear models and statistical inference
There is one response (outcome) variable y (n 1 vector)
STATS 500  Lecture 2
1 / 31
Brief Introduction to R
2 / 31
Some Information About R
R is free software
Runs on UNIX platforms, Windows, and MacOS
Freeware version of S (Splus) developed at Bell Labs
STATS 500  Lecture 8
1 / 16
Hypothesis Testing
2 / 16
The Four Steps in Hypothesis Testing
Model
Hypothesis
Test statistic
Decision rule
3 / 16
Example
Model:
Y
Nn (X , 2 I )
Hypothesis:
H0 : 1 = =
STATS 500 Winter 2018
Homework 2 (Due 124)
Instructions: Turn in at the beginning of class. Include all relevant R commands and
output (including the plot) in your homework. Try to keep it 34 pages
STATS 500  Lecture 7
1 / 14
Linear Regression  Estimation
2 / 14
The Normal Linear Model
Assume the linear model
y
y
X
= X +
Nn (0, 2 I n )
is the n 1 random response vector (observed)
is the fixe
STATS 500 Winter 2018
Homework 1 (Due 117)
Instructions: Turn in at the beginning of class. Include all relevant R code and
output (including plots) in your homework. The document Courseinfo.pdf prov
Statistics 500 (Winter 2018)
Course Information
Instructor:
Paul E. Green
270 West Hall
7645493
[email protected]
Office Hours
Tue 1:00pm 2:00pm
GSI:
Yifan Jin
2165 USB
SLC Annex
[email protected]
Of