Example: Body Fat
Yuqing Xu
Department of Statistics
University of WisconsinMadison
March 31, 2017
([email protected])
Chapter 12
March 31, 2017
1 / 67
Outline
1
Data Cleaning
2
Selection Criteria
3
Optimization Methods
([email protected])
Chapter 12
March 3
Weighted Least Squares
Yuqing Xu
Department of Statistics
University of WisconsinMadison
March 17, 2017
([email protected])
WLS
March 17, 2017
1 / 25
Outline
1
Heteroskedasticity
([email protected])
WLS
March 17, 2017
2 / 25
Crab Data
The following dataset i
Chapter 10. Diagnostics abnormal points
Yuqing Xu
Department of Statistics
University of WisconsinMadison
March 3, 2017
([email protected])
Chapter 10
March 3, 2017
1 / 21
Outline
1
Diagnostics Topics
2
Introduction of Outliers
3
Computation and Diagnostic
Ridge Regression and CV
Yuqing Xu
Department of Statistics
University of WisconsinMadison
April 7, 2017
([email protected])
Ridge Regression and CV
April 7, 2017
1 / 11
Outline
1
Ridge Regression
2
Cross Validation
([email protected])
Ridge Regression and CV
Stat 602 Statistical MethodsII
Zhengjun Zhang
Department of Statistics
University of Wisconsin
Madison, WI 53706, USA
beamertulog
Z. Zhang (UWMadison)
Stat 602 Week 11
March 2830, 2017
88 / 198
Why select?
In practice, we never know the underlying tr
Stat 602 Statistical MethodsII
Zhengjun Zhang
Department of Statistics
University of Wisconsin
Madison, WI 53706, USA
beamertulog
Z. Zhang (UWMadison)
Stat 602 Week 12
April, 2017
140 / 198
Cross Validation
Cross validation is a general method for var
Stat 602 Statistical MethodsII
Zhengjun Zhang
Department of Statistics
University of Wisconsin
Madison, WI 53706, USA
beamertulog
Z. Zhang (UWMadison)
Stat 602 Week 56
February 1621, 2017
1 / 200
Outline
1
Week 56: R demo of straight line and polyn
Stat 602 Statistical MethodsII
Zhengjun Zhang
Department of Statistics
University of Wisconsin
Madison, WI 53706, USA
beamertulog
Z. Zhang (UWMadison)
Stat 602 Week 9
March, 2017
61 / 200
Weighted Least Squares
Weighted least squares (when the lineari
Stat 602 Statistical MethodsII
Zhengjun Zhang
Department of Statistics
University of Wisconsin
Madison, WI 53706, USA
beamertulog
Z. Zhang (UWMadison)
Stat 602 Week 6
February, 2017
40 / 200
Consider the concentration of polychlorinated biphenyls (PCB
Introductory Applied Statistics for the Life Sciences
STATISTICS 371

Spring 2014
Statistics 371
Discussion 10: Hypothesis Testing  with Solutions
March 2829, 2017
1. A certain manufactured product is supposed to contain 23% potassium by weight. A random sample of 10
specimens of this product had an average percentage of 23.3 with a
Introductory Applied Statistics for the Life Sciences
STATISTICS 371

Spring 2014
Statistics 371
Discussion 9: Hypothesis Testing  with Solutions
March 1415, 2017
1. The length of time a patient stays in a hospital is a variable of great interest for insurance and resource
allocation purposes. In a given hospital, a simple random sam
Introductory Applied Statistics for the Life Sciences
STATISTICS 371

Spring 2014
Stat 371
Discussion 3: Descriptive Stats / Probability  with Solutions
Spring, 2017
1. A random sample of elementary school students at a particular school was taken. Each selected student
was asked, How many bowls of cereal do you eat in a typical week?
Introductory Applied Statistics for the Life Sciences
STATISTICS 371

Spring 2014
Stat 371
Discussion 2: Descriptive Stats  Solutions
January 2425, 2017
1. The National Hockey League (NHL) consists of 30 teams. Teams earn points during the regular season by
playing 82 games against other teams in the league. If a game is decided in r
Introductory Applied Statistics for the Life Sciences
STATISTICS 371

Spring 2014
Emily Cibulka
Statistics 371
Section 331Tuesdays 4:35
February 3, 2017
Homework 1
1.
a)
b) The mean is 2.609333 cm/s and the standard deviation is 0.6178473 cm/s. The mean is
telling us the average of all of the 15 different data points, and the standard
Data Analysis Course
Two Independent Populations  Summary
Draft: September 9, 2016
Comparing Two Independent Populations
1. To make a boxplot:
Plot a bar at the median, and at the first and third quartiles.
Connect the ends of the bars to make a box wi
STAT 224/324, Lecture 001
Final Exam
May 8th, 2016
Name:
Disc. Session:
For instructors use:
You are allowed three 8.5 by 11 inch piece of paper, both sides, for
notes, and you may use a calculator. Laptops, tablets, and smartphones are not allowed.
To
Data Analysis Course
Goodness of Fit Tests  Summary
Draft: September 12, 2016
Goodness of Fit Tests  Summary
1. Chisquare tests.
Chisquare goodness of fit tests are all based on the chisquare statistic:
2 =
P
cells
(Observed CountsExpected Counts)2
E
Data Analysis Course
Two Paired Populations  Summary
Draft: January 18, 2016
Comparing Two Paired Populations  Summary
1. The Paired TTest (Differences Normal)
The data consists of paired observations. Let:
X1,i = a data point from population 1
1 = tru
1 Introduction
population vs. sample, parameter vs. statistic
mumerical data, discrete vs. continuous
categorical data, ordinal vs. nominal
2 Graphical and Numerical Summaries
= 1 P Xi
X
n
n
n
M = sorted sample midpoint: n odd = at position n+1
2 , n
Difference of two means, X Y
Normal (without assuming X
Welchs t
Normal, X = Y : 2sample t
1
2
s2X
s2Y
(rule of thumb: X = Y plausible if <
q 2
S
S2
(X Y ) tnX +ny 2,/2 nXp + nYp , where
(nX 1)s2X + (nY 1)s2Y
Sp2 =
nX + nY 2
(
x1 x
2 ) 0
T = q 2
tnX +n
Bootstrap for
Inference patterns
Draw simple random sample of size n from the
population. Find x
and s.
Confidence interval for :
(table value for confidence)
Resample x1 , . . . , xn with replacement from
x
x
data. Find x
, s and t = .
s / n
Test
Data Analysis Course
Tests of Location for a Single Population  Summary
Draft: January 13, 2016
Tests of Location for a Single Population
1. When the data is drawn from a population that has a normal distribution and is unknown, use a ttest.
To test:
H0
Statistics 371
Discussion 12  Two Sample Independent/Paired Tests  With Solutions
December 67, 2016
Example Problems
1. Revisit the data from problem 2 from the previous handout. As a reminder, 6 people were randomized to
receive a drug (treatment grou
Stat 371
Assignment #2 Solutions
1. Circuit boards.
(a) The circuit board as a whole is only functional if both resistors are functional. Since the draws out
of each bin are independent, we multiply the probabilities that each resistor is functional and f
Stat 371
First Midterm Exam
October 13, 2016
Name:
For instructors use:
You are allowed on sheet of paper, 8.5in by 11in, for notes, and a
calculator. Laptops, tablets, and smartphones are not allowed.
To receive full credit, you must show your work. Pa
Stat 371
Fall 2016
November 4, 2016
Assignment #6 Solutions
1. A doctor would like to estimate the mean lowdensity lipoprotein (LDL) blood cholesterol level of her large
population of healthy patients, measured in mg/dL. She believes the distribution of
Stat 371
Assignment #3 Due Friday, October 7, by 4pm
*Submit your homework to Bowen Hus mailbox anytime prior to the due date/time. The mailboxes are to
the left as you enter the Medical Science Center (1300 University Ave.) from the main University Ave.