Teach yourself statistics

## Statistics and Probability

This website provides training and tools to help you solve statistics problems quickly, easily, and accurately - without having to ask anyone for help.

## Online Tutorials

Learn at your own pace. Free online tutorials cover statistics, probability, regression, analysis of variance, survey sampling, and matrix algebra - all explained in plain English.

- Advanced Placement (AP) Statistics . Full coverage of the AP Statistics curriculum.
- Probability . Fundamentals of probability. Clear explanations with pages of solved problems.
- Linear Regression . Regression analysis with one or more independent variables.
- ANOVA . Analysis of variance made easy. How to collect, analyze, and interpret data.
- Survey Sampling . How to conduct a statistical survey and analyze survey data.
- Matrix Algebra . Easy-to-understand introduction to matrix algebra.

Practice and review questions reinforce key points. Online calculators take the drudgery out of computation. Perfect for self-study.

## AP Statistics

Here is your blueprint for test success on the AP Statistics exam.

- AP Tutorial : Study our free, AP statistics tutorial to improve your skills in all test areas.
- Practice exam : Test your understanding of key topics, through sample problems with detailed solutions.

Be prepared. Get the score that you want on the AP Statistics test.

## Random Number Generator

Produce a list of random numbers, based on your specifications.

- Control list size (generate up to 10,000 random numbers).
- Specify the range of values that appear in your list.
- Permit or prevent duplicate entries.

Free and easy to use.

## Sample Size Calculator

Create powerful, cost-effective survey sampling plans.

- Find the optimum design (most precision, least cost).
- See how sample size affects cost and precision.
- Compare different survey sampling methods.
- Assess statistical power and Type II errors.

Tailor your sampling plan to your research needs.

## Stat Toolbox

Check out our statistical tables and online calculators - fast, accurate, and user-friendly.

## Discrete probability distributions

- Hypergeometric
- Multinomial
- Negative binomial
- Poisson distribution

## Continuous probability distributions

- f-Distribution
- Normal distribution
- t-Distribution

## Special-purpose calculators

- Bayes Rule Calculator
- Combination-Permutation
- Event Counter
- Factorial Calculator
- Bartlett's Test Calculator
- Statistics Calculator
- Probability Calculator

Each calculator features clear instructions, answers to frequently-asked questions, and a one or more problems with solutions to illustrate calculator use.

## Synopsis (摘要)

This course is open to graduates and senior undergraduates in applied mathematics, statistics, and engineering who are interested in learning from data. It covers hot topics in statistical learning, also known as machine learning, featured with various in-class projects in computer vision, pattern recognition, computational advertisement, bioinformatics, and social networks, etc. An emphasis this year is on deep learning with convolutional neural networks. Prerequisite: linear algebra, basic probability and multivariate statistics, convex optimization; familiarity with R, Matlab, and/or Python, Torch for deep learning, etc.

## Reference (参考教材)

An Introduction to Statistical Learning, with applications in R. By James, Witten, Hastie, and Tibshirani

ISLR-python, By Jordi Warmenhoven .

ISLR-Python: Labs and Applied, by Matt Caudill .

The Elements of Statistical Learning. 2nd Ed. By Hastie, Tibshirani, and Friedman

statlearning-notebooks , by Sujit Pal, Python implementations of the R labs for the StatLearning: Statistical Learning online course from Stanford taught by Profs Trevor Hastie and Rob Tibshirani.

## Instructors:

Time and venue:.

TuTh 4:30-5:50pm Rm4504 (Lift 25/26), Academic Bldg Piazza discussion forum: sign-up link

## Homework and Projects:

Weekly homeworks, monthly mini-projects, and a final major project. No final exam. For 3-project plan, homework and projects will be counted in grading by 20-20-20-40 in percentage.

Grading scheme: [ description ]

## Teaching Assistant (助教):

Mr. ZHU, Weizhi, Email: statml.hw (add "AT gmail DOT com" afterwards)

Tutorial Material

## Schedule (时间表)

- [ slides in pdf ]
- Homework 1 [pdf] . Deadline: 09/28/2015, Monday. Mark on the head of your homework: Name - Student ID .
- Homework 2 [pdf] . Deadline: 10/12/2015, Monday. Mark on the head of your homework: Name - Student ID .
- Project 1 [pdf] . Deadline: 10/12/2015, Monday. Team work with no more than FIVE (5) collaborators.
- Jiechao XIONG, A Dynamic Approach to Variable Selection
- Homework 3 [pdf] . Deadline: 10/19/2015, Monday. Mark on the head of your homework: Name - Student ID .
- Homework 4 [pdf] . Deadline: 10/26/2015, Monday. Mark on the head of your homework: Name - Student ID .
- Homework 5 [pdf] . Deadline: 11/02/2015, Monday. Mark on the head of your homework: Name - Student ID .
- Xuening ZHU, Network Vector Regression
- Homework 6 [pdf] . Deadline: 11/09/2015, Monday. Mark on the head of your homework: Name - Student ID .

## Datasets (to-be-updated)

- [Animal Sleep Data] Animal species sleeping hours vs. other features
- [Anzhen Heart Data] Heart Operation Effect Prediction , provided by Dr. Jinwen Wang, Anzhen Hospital
- [Beer Data] 877 beers dataset , provided by Mr. Richard Sun, Shanghai
- [Crime Data] Crime rates in 59 US cities during 1970-1992
- [Real-Time-Bidding Algorithm Competition Data] Contest Website
- [红楼梦人物事件矩阵] a 376-by-475 matrix (374-by-475 updated by WAN, Mengting) for character-event appearance in A Dream of Red Mansion (Xueqin Cao) [374 Characters.txt (for R/read.table)] [HongLouMeng374.csv] [HongLouMeng376.xls] [.mat] [readme.m]
- [Keywords Pricing] Keywords and profit index in paid search advertising, by Hansheng Wang (Guanghua, PKU). [readme.txt] [data in csv]
- [Radon Data] Radon measurements of 12,687 houses in US
- [Wells Data] Switch unsafe wells for arsenic pollution in Bangladesh
- to-be-done...

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## High school statistics

Unit 1: displaying a single quantitative variable, unit 2: analyzing a single quantitative variable, unit 3: two-way tables, unit 4: scatterplots, unit 5: study design, unit 6: probability, unit 7: probability distributions & expected value.

## STAT 430: Basics of Statistical Learning

University of illinois at urbana-champaign, fall 2017, dalpiaz, schedule - homework - quizzes - projects, syllabus - compass - r4sl.

- First day of class! Course overview and syllabus discussion.
- Materials : Syllabus Slides , Full Syllabus
- ISL Videos : Opening Remarks and Examples , Supervised and Unsupervised Learning
- Quick probability review. Recapping some R basics.
- Reading : R4SL Chapter 2 , R4SL Chapter 3
- Slides : Probability Recap , R Introduction
- Lab : R Basics , R Basics Solutions
- Introduction to rmarkdown .
- Slides : rmarkdown Introduction
- No class! Labor Day
- More rmarkdown details and practice. What is a model?
- Reading : R4SL Chapter 3
- Lab : rmarkdown , rmarkdown Solutions
- Begin recap of regression basics.
- Reading : ISL 3.1 - 3.4, R4SL Chapter 4
- ISL Slides : Linear Regression
- ISL Videos : Simple Linear Regression , Hypothesis Testing , Interpreting Regression Coefficients , Model Selection and Qualitative Predictors , Interactions and Nonlinearity
- Deadline : Homework 00 Due
- Review using lm() for regression models in R .
- Reading : R4SL Chapter 4
- Introduce the supervised learning, regression, task. Discuss the test-train split and models that generalize to unseen data.
- Reading : ISL 2.1 - 2.2
- ISL Slides : Statistical Learning
- ISL Videos : Statistical Learning and Regression , Assessing Model Accuracy and Bias-Variance Trade-off
- Lab : Test-Train Split , Test-Train Split Solutions
- Continue discussion of regression in the context of statistical learning.
- Slides : Linear Models for Statistical Learning, Regression
- Deadline : Homework 01 Due
- Introduce KNN. Compare non-parametric methods to parametric methods. Discuss tuning parameters versus model parameters.
- Reading : R4SL Chapter 7 (Currently very sparse notes.)
- Continue discussion of KNN. Compare KNN to linear models. Some live coding examples.
- Finish discussion of KNN
- Deadline : Homework 02 Due
- Bias-Variance Tradeoff
- Reading : R4SL Chapter 8
- Slides : Bias-Variance Tradeoff
- Begin classification.
- Reading : ISL 4.1, R4SL Chapter 9
- Slides : Classification Introduction
- More classification. Introduction to logistic regression
- Reading : ISL 4.2 - 4.3, R4SL Chapter 10
- ISL Slides : Classification
- ISL Videos : Introduction to Classification
- Deadline : Homework 03 Due
- Continued discussion of logistic regression.
- Reading : ISL 4.3, R4SL Chapter 10
- ISL Videos : Logistic Regression , Multiple Logistic Regression
- KNN for classification.
- Reading : R4SL Chapter 12
- Generative methods in R .
- Reading : ISL 4.4, R4SL Chapter 11
- Deadline : Homework 04 Due
- Continued discussion of generative methods. Details of univariate LDA.
- ISL Videos : Linear Discriminant Analysis and Bayes Theorem , Univariate Linear Discriminant Analysis
- Continued discussion of generative methods. Multivariate LDA, QDA, Naive Bayes.
- ISL Videos: Multivariate Linear Discriminant Analysis , Quadratic Discriminant Analysis and Naive Bayes
- Some final thoughts on generative methods. Some recap of classification methods. Some R details.
- Deadline : Homework 05 Due
- Begin discussing Statistical Learning in practice.
- Deadline : None. No homework during quiz week.
- Cross-validation and caret .
- Reading: ISL 5.1, R4SL Chapter 20 , R4SL Chapter 21
- ISL Slides: Resampling
- ISL Videos: Validation Set Approach , k-fold Cross-Validation , Cross-Validation: The Right and Wrong Ways
- More cross-validation and caret .
- Deadline : Homework 06 Due
- Some comments on variable selection.
- Reading: ISL 6.1, R4SL Chapter 22
- ISL Slides: Model Selection
- ISL Videos: Best Subset Selection , Forward Stepwise Selection , Backward Stepwise Selection , Estimating Test Error I , Estimating Test Error II
- Entering the modern age. Introducing regularization.
- Reading: ISL 6.2, R4SL Chapter 24 - Regularization
- ISL Videos: Shrinkage Methods and Ridge Regression , The Lasso , Tuning Parameter Selection
- More on ridge and lasso. Using ridge and lasso in R .
- Reading: ISL 6.2, R4SL Chapter 24 - Regularization , R4SL Chapter 25 - Elastic Net
- Deadline : Homework 07 Due
- Elastic net.
- R4SL: Elastic Net
- Overview: Introduction to trees.
- Reading: ISL 8.1
- ISL Slides: Trees
- Additonal Slides: Part II: Tree-based Methods
- ISL Videos: Decision Trees , Pruning a Decision Tree , Classification Trees and Comparison with Linear Models
- Discussed some finer details of R .
- Deadline : Homework 08 Due
- Deadline : Final Project Group Choice
- Continuation of tree discussion. Introduction to ensemble methods, mostly random forests.
- Reading: ISL 8.2
- R4SL: Ensemble Methods
- Additonal Slides: Part I: Pruning, Bagging, Boosting
- ISL Videos: Bootstrap Aggregation (Bagging) and Random Forests , Boosting and Variable Importance
- Continuation of tree discussion. Introduction to ensemble methods, mostly boosting.
- Extensions of random forests and boosting, in R . Some summary of supervised learning.
- Additional Slides: Supervised Learning Review
- Reading: Extremely Randomized Trees, Ranger, XGBoost [ rmarkdown ]
- Reading: Statistical Modeling: The Two Cultures
- Reading: Do we Need Hundreds of Classifiers to Solve Real World Classification Problems?
- No class. Fall break.
- Deadline : Homework 09 Due
- No class . Consider a group meeting.
- Unsupervised learning. Clustering.
- Reading: ISL 10.1 - 10.3
- R4SL: Unsupervised Learning
- ISL Slides: Unsupervised Learning
- Additional Slides: Unsupervised Learning, Part I, Clustering
- ISL Videos: Unsupervised Learning and Principal Components Analysis , Exploring Principal Components Analysis and Proportion of Variance Explained , K-means Clustering , Hierarchical Clustering
- Unsupervised learning. Clustering in R .
- Deadline : Project proposals. No homework is due.
- Unsupervised learning. PCA. Clustering again.
- Additional Slides: Unsupervised Learning, Part II, PCA
- No class. Office hours 8 - 10 at David’s office. Work on projects!
- Discussion of graduate student project results. Thoughts on keeping up to date with data science and machine learning.
- Reading: Some Machine Learning and Data Science Resources
- Deadline : Homework 10 Due
- No class. Finals!
- Deadline : Final Project Report
- Deadline : Final Project Peer Review

## Homework 00

- Due: Friday, September 8
- Assignment: [ html ] [ pdf ] [ zip ]
- Solution: [ zip ]

## Homework 01

- Due: Friday, September 15

## Homework 02

- Due: Friday, September 22

## Homework 03

Homework 04.

- Due: Friday, October 6

## Homework 05

- Due: Friday, October 13

## Homework 06

- Due: Friday, October 27

## Homework 07

- Due: Friday, November 3

## Homework 08

- Due: Friday, November 10

## Homework 09

- Due: Monday, November 20

## Homework 10

- Due: Wednesday, December 13
- Date: Wednesday, October 18
- Review: [ In-Class Practice Probelms ]
- Date: Wednesday, December 6

## Group Final Project

- Group Choice - Friday, November 10, 11:59 PM
- Analysis Proposal - Friday, December 1, 11:59 PM
- Report Template
- Peer Evaluation - Thursday, December 21, 10:00 PM

## Graduate Student Project

- Autograder - Saturday, December 9, 11:59 PM
- Report - Saturday, December 9, 11:59 PM

- Lectures: Mon/Wed 3-4:20pm in Pigott Hall 113
- Sections: Fri 1:30-2:30pm in 200-030
- Osbert Bastani (office hours: Tue 10am-12pm, Thu 10am-12pm in Gates 438)
- Peng Xu (office hours: Mon 10am-12pm, Wed 10am-12pm in Huang Basement)
- Homeworks (40%) : there will be three homeworks (plus a warmup which does not count towards your grade), centered around proving properties of statistical procedures. Each homework must be submitted through Gradescope . Sign up for the course using entry code M4V34N . You are encouraged to use LaTeX to writeup your homeworks (here's a template ), but this is not a requirement. You will receive one (1) bonus point for submitting a typed written assignment (e.g. LaTeX, Microsoft Word). We will accept scanned handwritten assignments but they will not receive the bonus point.
- Exam (25%) : open-book, open-notes. Problems will be like the homeworks, but simpler. You can use laptops as long as you turn off the wireless. Date: Wed Nov 14, 6-10 PM, Bishop Auditorium, Lathrop296
- Paper review (30%) : you will write a 2-4 page review of papers. The goal is to learn to read technically demanding papers critically, and hopefully in the process, generate novel research ideas. Your review should not only summarize the main result of the paper, but critique it, instantiate it on examples, discuss its overall significance, and suggest possible future directions. See this Google doc for detailed guidelines and a list of papers. The paper reviews can be done in pairs. Paper reviews that are done in pairs will be evaluated with a slightly higher bar, and they ideally should contain reviews for two closely-related papers and are allowed two additional pages. Appendix or references beyond the page limit are allowed, but you will not be graded based on them. Instead of doing the paper review, with approval from the course staff on the project topic, you can do a final project. Please come to the Tengyu Ma or Yu Bai's office hours to request the approval by briefly describing the project plan. We don't encourage you to do the project unless you own research area is closely related to machine learning theory. The project can be done in pairs. The page limit for project report is 8 pages, not including reference or appendix. The review and the project should be submitted electronically by 11pm .
- Scribe notes (5%) : Because there is no textbook or set of readings that perfectly fits this course, you will be asked to scribe a note for a lecture in LaTeX. The course staff will select one note for each lecture and share it with other students. 1% bonus credit will be given if your note is selected for posting. See this Google doc for the detailed guidelines. The scribe notes are due 2 days after the lecture (11pm Wed for Mon lecture, and Fri 11pm for Wed lecture). Please sign up here before Sept 29th and plan the time ahead. Extra credits will be given to the notes that are selected for posting. The scribe notes can be done in pairs.

There is no required text for the course. A number of useful references:

Percy Liang's course notes from previous offerings of this course

Peter Bartlett's statistical learning theory course

Boyd and Vandenberghe's Convex Optimization

Sham Kakade's statistical learning theory course

Martin Wainwright's statistical learning theory course

## An Introduction to Statistical Learning

Exercise solutions in r, 1 introduction.

This bookdown document provides solutions for exercises in the book “An Introduction to Statistical Learning” by Gareth James, Daniela Witten, Trevor Hastie and Robert Tibshirani.

## Introduction to Statistics

## Table of Contents

Course contents.

- About This Course
- Course Contents at a Glance
- Learning Outcomes

## Faculty Resources

- OHM Assessments
- I Need Help

## Module 1: Sampling and Data

- Introduction to Sampling and Data
- Definitions of Statistics, Probability, and Key Terms
- Sampling and Data
- Frequency, Frequency Tables, and Levels of Measurement
- Experimental Design and Ethics
- Section Exercises
- Answers to Selected Exercises

## Module 2: Descriptive Statistics

- Introduction to Descriptive Statistics
- Stem-and-Leaf Graphs (Stemplots)
- Histograms, Frequency Polygons, and Time Series Graphs
- Measures of the Location of the Data
- Measures of the Center of the Data
- Skewness and the Mean, Median, and Mode
- Measures of the Spread of Data
- When to use each measure of Central Tendency

## Module 3: Probability

- Introduction to Probability Topics
- The Terminology of Probability
- Independent and Mutually Exclusive Events
- Two Basic Rules of Probability
- Contingency Tables
- Tree and Venn Diagrams

## Module 4: Discrete Random Variables

- Introduction to Discrete Random Variables
- Probability Distribution Function (PDF) for a Discrete Random Variable
- Mean or Expected Value and Standard Deviation
- Binomial Distribution
- Geometric Distribution
- Poisson Distribution

## Module 5: Continuous Random Variables

- Introduction to Continuous Random Variables
- Continuous Probability Functions
- The Uniform Distribution
- The Exponential Distribution

## Module 6: Normal Distribution

- Introduction to the Normal Distribution
- The Standard Normal Distribution
- Using the Normal Distribution

## Module 7: The Central Limit Theorem

- Introduction to the Central Limit Theorem
- The Central Limit Theorem for Sample Means (Averages)
- The Central Limit Theorem for Sums
- Using the Central Limit Theorem

## Module 8: Confidence Intervals

- Introduction to Confidence Intervals
- A Single Population Mean using the Normal Distribution
- A Single Population Mean using Student's t Distribution
- A Population Proportion

## Module 9: Hypothesis Testing With One Sample

- Introduction to Hypothesis Testing with One Sample
- Null and Alternative Hypotheses
- Outcomes and the Type I and Type II Errors
- Distribution Needed for Hypothesis Testing
- Rare Events, the Sample, Decision and Conclusion
- Additional Information and Full Hypothesis Test Examples

## Module 10: Hypothesis Testing With Two Samples

- Introduction to Hypothesis Testing with Two Samples
- Two Population Means with Unknown Standard Deviations
- Two Population Means with Known Standard Deviations
- Comparing Two Independent Population Proportions
- Matched or Paired Samples

## Module 11: The Chi Square Distribution

- Introduction to The Chi-Square Distribution
- Facts About the Chi-Square Distribution
- Goodness-of-Fit Test
- Test of Independence
- Test for Homogeneity
- Comparison of the Chi-Square Tests
- Test of a Single Variance

## Module 12: Linear Regression and Correlation

- Introduction to Linear Regression and Correlation
- Linear Equations
- Scatter Plots
- The Regression Equation
- Testing the Significance of the Correlation Coefficient

## Module 13: F-Distribution and One-Way ANOVA

- Introduction to F Distribution and One-Way ANOVA
- One-Way ANOVA
- The F Distribution and the F-Ratio
- Facts about the F Distribution
- Test of Two Variances
- Relationships in an ANOVA Table

## Module 14: Multiple and Logistic Regression

- Introduction to Multiple and Logistic Regression
- Model Selection
- Checking Model Assumptions Using Graphs
- Introduction to Logistic Regression
- Appendix A: Review Exercises (Ch 3-13)
- Appendix A-1: Solutions to Review Exercises (Ch 3-13)
- Appendix B: Practice Tests (1-4) and Final Exams
- Appendix C: Data Sets
- Appendix D: Group and Partner Projects
- Appendix E: Solution Sheets
- Appendix F: Mathematical Phrases, Symbols, and Formulas
- Appendix G: Notes for the TI-83, 83+, 84, 84+ Calculators
- Appendix H: Tables

This courseware includes resources copyrighted and openly licensed by multiple individuals and organizations. Click the words "Licenses and Attributions" at the bottom of each page for copyright and licensing information specific to the material on that page. If you believe that this courseware violates your copyright, please contact us .

Cover Image: "Ball Pit." Authored by: Greyson Joralemon. Provided by: Unsplash. Located at: https://unsplash.com/photos/9IBqihqhuHc . Content Type: CC Licensed Content, Shared Previously. License: CC0: No Rights Reserved .

## Lumen Learning

Lumen Learning provides a simple, supported path for faculty members to adopt and teach effectively with open educational resources (OER). Read more about what we do.

## 1.1 Definitions of Statistics, Probability, and Key Terms

For each of the following eight exercises, identify: a. the population, b. the sample, c. the parameter, d. the statistic, e. the variable, and f. the data. Give examples where appropriate.

A fitness center is interested in the mean amount of time a client exercises in the center each week.

Ski resorts are interested in the mean age that children take their first ski and snowboard lessons. They need this information to plan their ski classes optimally.

A cardiologist is interested in the mean recovery period of her patients who have had heart attacks.

Insurance companies are interested in the mean health costs each year of their clients, so that they can determine the costs of health insurance.

A politician is interested in the proportion of voters in his district who think he is doing a good job.

A marriage counselor is interested in the proportion of clients she counsels who stay married.

Political pollsters may be interested in the proportion of people who will vote for a particular cause.

A marketing company is interested in the proportion of people who will buy a particular product.

Use the following information to answer the next three exercises: A Lake Tahoe Community College instructor is interested in the mean number of days Lake Tahoe Community College math students are absent from class during a quarter.

What is the population she is interested in?

- all Lake Tahoe Community College students
- all Lake Tahoe Community College English students
- all Lake Tahoe Community College students in her classes
- all Lake Tahoe Community College math students

Consider the following:

X X = number of days a Lake Tahoe Community College math student is absent

In this case, X is an example of a:

- population.

The instructor’s sample produces a mean number of days absent of 3.5 days. This value is an example of a:

## 1.2 Data, Sampling, and Variation in Data and Sampling

For the following exercises, identify the type of data that would be used to describe a response (quantitative discrete, quantitative continuous, or qualitative), and give an example of the data.

number of tickets sold to a concert

percent of body fat

favorite baseball team

time in line to buy groceries

number of students enrolled at Evergreen Valley College

most-watched television show

brand of toothpaste

distance to the closest movie theatre

age of executives in Fortune 500 companies

number of competing computer spreadsheet software packages

Use the following information to answer the next two exercises: A study was done to determine the age, number of times per week, and the duration (amount of time) of resident use of a local park in San Jose. The first house in the neighborhood around the park was selected randomly and then every 8th house in the neighborhood around the park was interviewed.

“Number of times per week” is what type of data?

- qualitative
- quantitative discrete
- quantitative continuous

“Duration (amount of time)” is what type of data?

Airline companies are interested in the consistency of the number of babies on each flight, so that they have adequate safety equipment. Suppose an airline conducts a survey. Over Thanksgiving weekend, it surveys six flights from Boston to Salt Lake City to determine the number of babies on the flights. It determines the amount of safety equipment needed by the result of that study.

- Using complete sentences, list three things wrong with the way the survey was conducted.
- Using complete sentences, list three ways that you would improve the survey if it were to be repeated.

Suppose you want to determine the mean number of students per statistics class in your state. Describe a possible sampling method in three to five complete sentences. Make the description detailed.

Suppose you want to determine the mean number of cans of soda drunk each month by students in their twenties at your school. Describe a possible sampling method in three to five complete sentences. Make the description detailed.

List some practical difficulties involved in getting accurate results from a telephone survey.

List some practical difficulties involved in getting accurate results from a mailed survey.

With your classmates, brainstorm some ways you could overcome these problems if you needed to conduct a phone or mail survey.

The instructor takes her sample by gathering data on five randomly selected students from each Lake Tahoe Community College math class. The type of sampling she used is

- cluster sampling
- stratified sampling
- simple random sampling
- convenience sampling

A study was done to determine the age, number of times per week, and the duration (amount of time) of residents using a local park in San Jose. The first house in the neighborhood around the park was selected randomly and then every eighth house in the neighborhood around the park was interviewed. The sampling method was:

- simple random

Name the sampling method used in each of the following situations:

- A woman in the airport is handing out questionnaires to travelers asking them to evaluate the airport’s service. She does not ask travelers who are hurrying through the airport with their hands full of luggage, but instead asks all travelers who are sitting near gates and not taking naps while they wait.
- A teacher wants to know if her students are doing homework, so she randomly selects rows two and five and then calls on all students in row two and all students in row five to present the solutions to homework problems to the class.
- The marketing manager for an electronics chain store wants information about the ages of its customers. Over the next two weeks, at each store location, 100 randomly selected customers are given questionnaires to fill out asking for information about age, as well as about other variables of interest.
- The librarian at a public library wants to determine what proportion of the library users are children. The librarian has a tally sheet on which she marks whether books are checked out by an adult or a child. She records this data for every fourth patron who checks out books.
- A political party wants to know the reaction of voters to a debate between the candidates. The day after the debate, the party’s polling staff calls 1,200 randomly selected phone numbers. If a registered voter answers the phone or is available to come to the phone, that registered voter is asked whom he or she intends to vote for and whether the debate changed his or her opinion of the candidates.

A “random survey” was conducted of 3,274 people of the “microprocessor generation” (people born since 1971, the year the microprocessor was invented). It was reported that 48% of those individuals surveyed stated that if they had $2,000 to spend, they would use it for computer equipment. Also, 66% of those surveyed considered themselves relatively savvy computer users.

- Do you consider the sample size large enough for a study of this type? Why or why not?
- Based on your “gut feeling,” do you believe the percents accurately reflect the U.S. population for those individuals born since 1971? If not, do you think the percents of the population are actually higher or lower than the sample statistics? Why? Additional information: The survey, reported by Intel Corporation, was filled out by individuals who visited the Los Angeles Convention Center to see the Smithsonian Institute's road show called “America’s Smithsonian.”
- With this additional information, do you feel that all demographic and ethnic groups were equally represented at the event? Why or why not?
- With the additional information, comment on how accurately you think the sample statistics reflect the population parameters.

The Well-Being Index is a survey that follows trends of U.S. residents on a regular basis. There are six areas of health and wellness covered in the survey: Life Evaluation, Emotional Health, Physical Health, Healthy Behavior, Work Environment, and Basic Access. Some of the questions used to measure the Index are listed below.

Identify the type of data obtained from each question used in this survey: qualitative, quantitative discrete, or quantitative continuous.

- Do you have any health problems that prevent you from doing any of the things people your age can normally do?
- During the past 30 days, for about how many days did poor health keep you from doing your usual activities?
- In the last seven days, on how many days did you exercise for 30 minutes or more?
- Do you have health insurance coverage?

In advance of the 1936 Presidential Election, a magazine titled Literary Digest released the results of an opinion poll predicting that the republican candidate Alf Landon would win by a large margin. The magazine sent post cards to approximately 10,000,000 prospective voters. These prospective voters were selected from the subscription list of the magazine, from automobile registration lists, from phone lists, and from club membership lists. Approximately 2,300,000 people returned the postcards.

- Think about the state of the United States in 1936. Explain why a sample chosen from magazine subscription lists, automobile registration lists, phone books, and club membership lists was not representative of the population of the United States at that time.
- What effect does the low response rate have on the reliability of the sample?
- Are these problems examples of sampling error or nonsampling error?
- During the same year, George Gallup conducted his own poll of 30,000 prospective voters. These researchers used a method they called "quota sampling" to obtain survey answers from specific subsets of the population. Quota sampling is an example of which sampling method described in this module?

Crime-related and demographic statistics for 47 US states in 1960 were collected from government agencies, including the FBI's Uniform Crime Report . One analysis of this data found a strong connection between education and crime indicating that higher levels of education in a community correspond to higher crime rates.

Which of the potential problems with samples discussed in 1.2 Data, Sampling, and Variation in Data and Sampling could explain this connection?

YouPolls is a website that allows anyone to create and respond to polls. One question posted April 15 asks:

“Do you feel happy paying your taxes when members of the Obama administration are allowed to ignore their tax liabilities?” (lastbaldeagle. 2013. On Tax Day, House to Call for Firing Federal Workers Who Owe Back Taxes. Opinion poll posted online at: http://www.youpolls.com/details.aspx?id=12328 (accessed May 1, 2013).)

As of April 25, 11 people responded to this question. Each participant answered “NO!”

Which of the potential problems with samples discussed in this module could explain this connection?

A scholarly article about response rates begins with the following quote:

“Declining contact and cooperation rates in random digit dial (RDD) national telephone surveys raise serious concerns about the validity of estimates drawn from such research.”(Scott Keeter et al., “Gauging the Impact of Growing Nonresponse on Estimates from a National RDD Telephone Survey,” Public Opinion Quarterly 70 no. 5 (2006), http://poq.oxfordjournals.org/content/70/5/759.full (accessed May 1, 2013).)

The Pew Research Center for People and the Press admits:

“The percentage of people we interview – out of all we try to interview – has been declining over the past decade or more.” (Frequently Asked Questions, Pew Research Center for the People & the Press, http://www.people-press.org/methodology/frequently-asked-questions/#dont-you-have-trouble-getting-people-to-answer-your-polls (accessed May 1, 2013).)

- What are some reasons for the decline in response rate over the past decade?
- Explain why researchers are concerned with the impact of the declining response rate on public opinion polls.

## 1.3 Frequency, Frequency Tables, and Levels of Measurement

Fifty part-time students were asked how many courses they were taking this term. The (incomplete) results are shown below:

- Fill in the blanks in Table 1.33 .
- What percent of students take exactly two courses?
- What percent of students take one or two courses?

Sixty adults with gum disease were asked the number of times per week they used to floss before their diagnosis. The (incomplete) results are shown in Table 1.34 .

- Fill in the blanks in Table 1.34 .
- What percent of adults flossed six times per week?
- What percent flossed at most three times per week?

Nineteen immigrants to the U.S were asked how many years, to the nearest year, they have lived in the U.S. The data are as follows: 2 ; 5 ; 7 ; 2 ; 2 ; 10 ; 20 ; 15 ; 0 ; 7 ; 0 ; 20 ; 5 ; 12 ; 15 ; 12 ; 4 ; 5 ; 10 .

Table 1.35 was produced.

- Fix the errors in Table 1.35 . Also, explain how someone might have arrived at the incorrect number(s).
- Explain what is wrong with this statement: “47 percent of the people surveyed have lived in the U.S. for 5 years.”
- Fix the statement in b to make it correct.
- What fraction of the people surveyed have lived in the U.S. five or seven years?
- What fraction of the people surveyed have lived in the U.S. at most 12 years?
- What fraction of the people surveyed have lived in the U.S. fewer than 12 years?
- What fraction of the people surveyed have lived in the U.S. from five to 20 years, inclusive?

How much time does it take to travel to work? Table 1.36 shows the mean commute time by state for workers at least 16 years old who are not working at home. Find the mean travel time, and round off the answer properly.

Forbes magazine published data on the best small firms in 2012. These were firms which had been publicly traded for at least a year, have a stock price of at least $5 per share, and have reported annual revenue between $5 million and $1 billion. Table 1.37 shows the ages of the chief executive officers for the first 60 ranked firms.

- What is the frequency for CEO ages between 54 and 65?
- What percentage of CEOs are 65 years or older?
- What is the relative frequency of ages under 50?
- What is the cumulative relative frequency for CEOs younger than 55?
- Which graph shows the relative frequency and which shows the cumulative relative frequency?

Use the following information to answer the next two exercises: Table 1.38 contains data on hurricanes that have made direct hits on the U.S. Between 1851 and 2004. A hurricane is given a strength category rating based on the minimum wind speed generated by the storm.

What is the relative frequency of direct hits that were category 4 hurricanes?

- Not enough information to calculate

What is the relative frequency of direct hits that were AT MOST a category 3 storm?

## 1.4 Experimental Design and Ethics

How does sleep deprivation affect your ability to drive? A recent study measured the effects on 19 professional drivers. Each driver participated in two experimental sessions: one after normal sleep and one after 27 hours of total sleep deprivation. The treatments were assigned in random order. In each session, performance was measured on a variety of tasks including a driving simulation.

Use key terms from this module to describe the design of this experiment.

An advertisement for Acme Investments displays the two graphs in Figure 1.14 to show the value of Acme’s product in comparison with the Other Guy’s product. Describe the potentially misleading visual effect of these comparison graphs. How can this be corrected?

The graph in Figure 1.15 shows the number of complaints for six different airlines as reported to the US Department of Transportation in February 2013. Alaska, Pinnacle, and Airtran Airlines have far fewer complaints reported than American, Delta, and United. Can we conclude that American, Delta, and United are the worst airline carriers since they have the most complaints?

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## Basics of Statistical Learning

Welcome to the Spring 2021 semester of STAT 432, Basics of Statistical Learning, sections 1UG and 1GR, at the University of Illinois at Urbana-Champaign.

STAT 432 provides a broad overview of machine learning, through the eyes of a statistician. As a first course in machine learning, core ideas are stressed, and specific details are de-emphasized. After completing the course, students should be able to train and evaluate statistical models. While we will not discuss an exhaustive list of methods, given the framework developed throughout the course, students should feel comfortable exploring new methods and models on their own. Previous experience with R programming is necessary for success in the course as students will be tested on their ability to use the methods discussed through the use of a statistical computing environment.

Almost all course information can be found on this website. We will use three additional external sites:

- PrairieLearn

Additional information about both resources can be found in the Syllabus ! If this is your first time on this website, that should be the first thing you read. If you’re a student progressing through the course, you’ll find the information for each week in the links to the left or in the burger menu. The numbered links correspond to the weeks of the course.

## Advanced Topics in Statistical Learning: Spring 2024

Other resources.

- Lectures: Mon/Wed 3-4:20pm in Thornt110
- Sections: Fri 1:30-2:30pm in 200-030
- Osbert Bastani (office hours: Tue 10am-12pm, Thu 10am-12pm in Gates 438)
- Peng Xu (office hours: Mon 10am-12pm, Wed 10am-12pm in Huang Basement)
- Homeworks (30%) : there will be three homeworks (plus a warmup which does not count towards your grade), centered around proving properties of statistical procedures. You will also implement and run some of the algorithms as a reality check. Each homework must be turned in at the beginning of class (hard copy), as well as electronically by 11pm . Only the hard copy version will be graded; the electronic copy is just for our records. You are encouraged to use LaTeX to typeset your homeworks; we've provided a template for your convenience.
- Exam (40%) : open-book, open-notes. Problems will be like the homeworks, but simpler. You can use laptops as long as you turn off the wireless. Date: Feb. 25 6-9pm.
- Paper reviews (30%) : you will write two 2-4 page reviews of papers. The goal is to learn to read technically demanding papers critically, and hopefully in the process, generate novel research ideas. Your review should not only summarize the main result of the paper, but critique it, instantiate it on examples, discuss its overall significance, and suggest possible future directions. See this Google doc for detailed guidelines and a list of papers. Each review should be submitted electronically by 11pm . Instead of doing the last paper review, with approval from the course staff on the project topic, you can do a final project, perhaps extending one of the earlier reviews to produce novel results. The project can be done in pairs.

To submit electronically, open up a terminal, (i) copy your submission file(s) (e.g., hw0.pdf ) to cardinal.stanford.edu : scp <your submission file(s)> <your SUNetID>@cardinal.stanford.edu: and (ii) run the submit script: ssh <your SUNetID>cardinal.stanford.edu python /usr/class/cs229t/WWW/submit.py <hw0|hw1|hw2|hw3|p1|p2|p3> . You can submit multiple times; each submission will just replace the previous one.

## IMAGES

## VIDEO

## COMMENTS

An Introduction to Statistical Learning provides a broad and less technical treatment of key topics in statistical learning. This book is appropriate for anyone who wishes to use contemporary tools for data analysis. The first edition of this book, with applications in R (ISLR), was released in 2013. A 2nd Edition of ISLR was published in 2021.

Unit 3: Summarizing quantitative data. 0/1700 Mastery points. Measuring center in quantitative data More on mean and median Interquartile range (IQR) Variance and standard deviation of a population. Variance and standard deviation of a sample More on standard deviation Box and whisker plots Other measures of spread.

Trevor Hastie Trevor Hastie is a professor of statistics at Stanford University. His main research contributions have been in the field of applied nonparametric regression and classification, and he has written two books in this area: "Generalized Additive Models" (with R. Tibshirani, Chapman and Hall, 1991), and "Elements of Statistical Learning" (with R. Tibshirani and J. Friedman, Springer ...

Full coverage of the AP Statistics curriculum. Probability. Fundamentals of probability. Clear explanations with pages of solved problems. Linear Regression. Regression analysis with one or more independent variables. ANOVA. Analysis of variance made easy. How to collect, analyze, and interpret data.

This is an introductory-level course in supervised learning, with a focus on regression and classification methods. The syllabus includes: linear and polynomial regression, logistic regression and linear discriminant analysis; cross-validation and the bootstrap, model selection and regularization methods (ridge and lasso); nonlinear models, splines and generalized additive models; tree-based ...

Statistics 231 / CS229T: Statistical Learning Theory. John Duchi, Stanford University, Spring 2017. Homework questions and problems. We will update the following file with additional questions throughout the quarter. Your homework will always be a selection of questions from the file.

We'll get right to the point: we're asking you to help support Khan Academy. We're a nonprofit that relies on support from people like you. If everyone reading this gives $10 monthly, Khan Academy can continue to thrive for years. Please help keep Khan Academy free, for anyone, anywhere forever. Select gift frequency.

Stat 241B / CS 281B. Instructor: Ryan Tibshirani (ryantibs at berkeley dot edu) GSI: Seunghoon Paik (shpaik at berkeley dot edu) Class times: Tuesdays and Thursdays, 3:30-5pm, Tan 180. Office hours: RT: Wednesdays, 3-4pm, Evans 417. SP: Thursdays, 5-6pm, Evans 444.

Click "ENROLL NOW" to visit Coursera and get more information on course details and enrollment. Stanford's "Introduction to Statistics" teaches you statistical thinking concepts that are essential for learning from data and communicating insights. By the end of the course, you will be able to perform exploratory data analysis, understand ...

Homework 4 Advanced Topics in Statistical Learning, Spring 2023 Due Friday April 14 at 5pm 1 Basic fact about CDFs and quantiles [14 points] Inthisexercise,we ...

It covers hot topics in statistical learning, also known as machine learning, featured with various in-class projects in computer vision, pattern recognition, computational advertisement, bioinformatics, and social networks, etc. An emphasis this year is on deep learning with convolutional neural networks. Prerequisite: linear algebra, basic ...

We'll get right to the point: we're asking you to help support Khan Academy. We're a nonprofit that relies on support from people like you. If everyone reading this gives $10 monthly, Khan Academy can continue to thrive for years. Please help keep Khan Academy free, for anyone, anywhere forever. Select gift frequency. One time. Recurring. Monthly.

STAT 430: Basics of Statistical Learning University of Illinois at Urbana-Champaign Fall 2017, Dalpiaz. Schedule - Homework - Quizzes - Projects Syllabus - Compass - R4SL. Schedule. ... Slides: Linear Models for Statistical Learning, Regression; Deadline: Homework 01 Due; Week 4. Monday | 2017.9.18 Introduce KNN. Compare non-parametric methods ...

ESLThe Elements of Statistical Learning: Data Mining, Inference, and Prediction by Hastie, T., Tibshirani, R. and Friedman, J. ... •We have approximately 12 sets of homework (1 per week), depending on the course progression •Assigned on Monday anddue at Thursday (11:59PM) of the

CS229T/STATS231: Statistical Learning Theory Stanford / Autumn 2018-2019 Announcements. The new version of this course is CS229M / STATS214 (Machien Learning Theory), which can be found ...

1 Introduction. This bookdown document provides solutions for exercises in the book "An Introduction to Statistical Learning" by Gareth James, Daniela Witten, Trevor Hastie and Robert Tibshirani."An Introduction to Statistical Learning" by Gareth James, Daniela Witten, Trevor Hastie and Robert Tibshirani.

Introduction to Descriptive Statistics. Stem-and-Leaf Graphs (Stemplots) Histograms, Frequency Polygons, and Time Series Graphs. Measures of the Location of the Data. Box Plots. Measures of the Center of the Data. Skewness and the Mean, Median, and Mode. Measures of the Spread of Data. When to use each measure of Central Tendency.

Crime-related and demographic statistics for 47 US states in 1960 were collected from government agencies, including the FBI's Uniform Crime Report. One analysis of this data found a strong connection between education and crime indicating that higher levels of education in a community correspond to higher crime rates.

Welcome to the Spring 2021 semester of STAT 432, Basics of Statistical Learning, sections 1UG and 1GR, at the University of Illinois at Urbana-Champaign. STAT 432 provides a broad overview of machine learning, through the eyes of a statistician. As a first course in machine learning, core ideas are stressed, and specific details are de-emphasized.

Class times: Mon, Weds, Fri, 2-3pm, Tan 180. Office hours: RT: Wednesdays, 3-4pm, Evans 417. SP: Thursdays 3:30-5:30pm, Evans 444. Handy links: • Syllabus. • GitHub repo (source files for lectures and homeworks) • Ed discussion (for class discussions and announcements) • bCourses (for grade-keeping and homework solutions)

Coursework: . Homeworks (30%): there will be three homeworks (plus a warmup which does not count towards your grade), centered around proving properties of statistical procedures.You will also implement and run some of the algorithms as a reality check. Each homework must be turned in at the beginning of class (hard copy), as well as electronically by 11pm.

CH4. Problem. 1E. Step-by-step solution. Step 1 of 1. The given question deals with the study of the equivalence of two expressions given in equations and are equivalent. The two equations are, Now the other expression is, Thus the above two are equivalent, since any expression can be obtained from the other one.

Take learning further. MyLab ® Statistics merges dynamic study tools with the content you rely on. Easily customize your course to add a personal touch. With MyLab Statistics, trusted author content and digital tools help you personalize learning experiences and improve results for each student. Channel your teaching style.