STAT5044: Regression and ANOVA, Fall 2011 Final Exam on Dec 14. Your Name:
|
|
- Donald Elliott
- 6 years ago
- Views:
Transcription
1 STAT5044: Regression and ANOVA, Fall 2011 Final Exam on Dec 14 Your Name: Please make sure to specify all of your notations in each problem GOOD LUCK! 1
2 Problem# 1. Consider the following model, y i = β 0 + β 1 x 1i + β 2 x 2 1i + β 3 x 2i + σε i, i = 1,...,n where E(ε i ) = 0, Var(ε i ) = 1, Cov(ε i,ε j ) = 0. Parameters (β 0, β 1, β 2, β 3, σ 2 ) are unknown. (a) Under the assumption that ε i are iid and normally distributed, we want to test H 0 : β 0 + β 1 β 2 + β 3 = 0 vs H a : not H 0. What is your test statistic and its distribution? Justify why your test statistic follows this distribution and provide your decision rule. Be sure to define all terms. (b) We found that there is a significant evidence to reject H 01 in (b). We then fit the simple linear model between y and x 1. We found that the p-value obtained from the Shapiro-Wilk test was still smaller than the significant level However, by taking the log transformation of y, we obtained a larger p-value from the Shapiro-Wilk test. Hence we consider the following simple linear regression of log(y) on x 1 log(y i ) = γ 0 + γ 1 x 1i + σε i. From this regression model, we observe that the p-value from Breusch-Pagan test is smaller than the significant level. The scatter plot between abs-residuals and x shows that there is a strong linear relationship between them. Under this situation, we want to obtain a prediction interval of y new for a given new x 1,new. Explain in a step by step manner how to obtain the prediction interval of y new. Be sure to define all terms. 2
3 Problem# 2. An experiment analyzes imperfection rates for two processes used to fabricate silicon wafers for computer chips. For treatment A applied to 10 wafers, the numbers of imperfections are 8, 7, 6,6,3,4,4,7,2,3,4. Treatment B applied to 10 other wafers has 9,9,8,14,8,13,11,5,7,6 imperfections. An experimenter wants to know whether imperfection rates for two treatments are the same or not. (a) Construct generalized linear model (GLM) for this experiment. (b) Based on your GLM in (a), obtain likelihood. (c) Explain in a step by step manner how to estimate parameter. Interpret your parameters. (d) What are the distributions of your parameters? Explain in a step by step manner how to calculate confidence interval for your parameter estimators. (e) Explain in a step by step manner how to use the confidence interval to know whether imperfection rates for two treatments are the same or not. 3
4 Problem# 3. For each problem, identify what analysis or test you can perform. If necessary, give model, null hypothesis, test statistics, and decision rule. Explain how you estimate parameters in your models in detail. (Please make sure to specify all of your notations and index.) (i) The data refer to 10 army corps, each observed for 20 years. In 109 corps-years of exposure, there were no deaths, in 65 corps-years there was one death and so on. We would like to test whether probabilities of occurrences in these five categories follow a Poisson distribution. Number of Number of Deaths Corps-Years (ii) A sample of 100 women suffer from dysmenorrhea. A new analgesic is claimed to provide greater relief than a standard one. After using each analgesic in a crossover experiment, 40 reported greater relief with the standard analgesic and 60 reported greater relief with the new one. (iii) A study of homicides in a given year for a sample of cities might model the homicide rate, defined for a city as its number of homicides that year divided by its population size. We want to know how the rate depends on the city s unemployment rate, its residents median income, and the percentage of residents having completed high school. (iv) The dataset from Dalal, Fowlkes, and Hoadley contains data on O-rings on 23 U.S. space shuttle missions prior to the Challenger disaster of January 20, For each of the previous missions, the temperature at take-off and the pressure of a prelaunch test were recorded, along with the number of O-rings that filed out of six. Use these data to try to understand the probability of failure as a function of temperature, and of temperature and pressure. We want to estimate the probability of failure of an O-ring when the temperature was 31 F, the launch temperature on January 20, We also want to predict the the probability of failure of an O-ring when the temperature is 31 F, the launch temperature on January 20,
5 Some formula Large sample distribution of log of relative risk (r) log(ˆr) N[log( π 1 π 2 ),( 1 π 1 π 1 n 1 π 2 π 2 n 2 )] Large sample distribution of log of odds ratio (θ) log(ˆθ) N[log(θ),( 1 nπ 11 nπ 12 nπ 21 nπ 22 )] where n is the total sample size and π i j is the proportion of cell (i,j) in contingency table 5
STA 4504/5503 Sample Exam 1 Spring 2011 Categorical Data Analysis. 1. Indicate whether each of the following is true (T) or false (F).
STA 4504/5503 Sample Exam 1 Spring 2011 Categorical Data Analysis 1. Indicate whether each of the following is true (T) or false (F). (a) (b) (c) (d) (e) In 2 2 tables, statistical independence is equivalent
More informationSTA 4504/5503 Sample Exam 1 Spring 2011 Categorical Data Analysis. 1. Indicate whether each of the following is true (T) or false (F).
STA 4504/5503 Sample Exam 1 Spring 2011 Categorical Data Analysis 1. Indicate whether each of the following is true (T) or false (F). (a) T In 2 2 tables, statistical independence is equivalent to a population
More informationST3241 Categorical Data Analysis I Generalized Linear Models. Introduction and Some Examples
ST3241 Categorical Data Analysis I Generalized Linear Models Introduction and Some Examples 1 Introduction We have discussed methods for analyzing associations in two-way and three-way tables. Now we will
More information22s:152 Applied Linear Regression. Chapter 2: Regression Analysis. a class of statistical methods for
22s:152 Applied Linear Regression Chapter 2: Regression Analysis Regression analysis a class of statistical methods for studying relationships between variables that can be measured e.g. predicting blood
More informationSTAT5044: Regression and Anova
STAT5044: Regression and Anova Inyoung Kim 1 / 18 Outline 1 Logistic regression for Binary data 2 Poisson regression for Count data 2 / 18 GLM Let Y denote a binary response variable. Each observation
More informationWhat is a Hypothesis?
What is a Hypothesis? A hypothesis is a claim (assumption) about a population parameter: population mean Example: The mean monthly cell phone bill in this city is μ = $42 population proportion Example:
More information12 Modelling Binomial Response Data
c 2005, Anthony C. Brooms Statistical Modelling and Data Analysis 12 Modelling Binomial Response Data 12.1 Examples of Binary Response Data Binary response data arise when an observation on an individual
More informationExam details. Final Review Session. Things to Review
Exam details Final Review Session Short answer, similar to book problems Formulae and tables will be given You CAN use a calculator Date and Time: Dec. 7, 006, 1-1:30 pm Location: Osborne Centre, Unit
More information(c) Interpret the estimated effect of temperature on the odds of thermal distress.
STA 4504/5503 Sample questions for exam 2 1. For the 23 space shuttle flights that occurred before the Challenger mission in 1986, Table 1 shows the temperature ( F) at the time of the flight and whether
More informationSTAT5044: Regression and Anova. Inyoung Kim
STAT5044: Regression and Anova Inyoung Kim 2 / 47 Outline 1 Regression 2 Simple Linear regression 3 Basic concepts in regression 4 How to estimate unknown parameters 5 Properties of Least Squares Estimators:
More informationCorrelation and Simple Linear Regression
Correlation and Simple Linear Regression Sasivimol Rattanasiri, Ph.D Section for Clinical Epidemiology and Biostatistics Ramathibodi Hospital, Mahidol University E-mail: sasivimol.rat@mahidol.ac.th 1 Outline
More informationLinear regression is designed for a quantitative response variable; in the model equation
Logistic Regression ST 370 Linear regression is designed for a quantitative response variable; in the model equation Y = β 0 + β 1 x + ɛ, the random noise term ɛ is usually assumed to be at least approximately
More informationFinal Exam - Solutions
Ecn 102 - Analysis of Economic Data University of California - Davis March 19, 2010 Instructor: John Parman Final Exam - Solutions You have until 5:30pm to complete this exam. Please remember to put your
More informationReview for Final. Chapter 1 Type of studies: anecdotal, observational, experimental Random sampling
Review for Final For a detailed review of Chapters 1 7, please see the review sheets for exam 1 and. The following only briefly covers these sections. The final exam could contain problems that are included
More informationK. Model Diagnostics. residuals ˆɛ ij = Y ij ˆµ i N = Y ij Ȳ i semi-studentized residuals ω ij = ˆɛ ij. studentized deleted residuals ɛ ij =
K. Model Diagnostics We ve already seen how to check model assumptions prior to fitting a one-way ANOVA. Diagnostics carried out after model fitting by using residuals are more informative for assessing
More informationInstitute of Actuaries of India
Institute of Actuaries of India Subject CT3 Probability & Mathematical Statistics May 2011 Examinations INDICATIVE SOLUTION Introduction The indicative solution has been written by the Examiners with the
More informationStatistics Boot Camp. Dr. Stephanie Lane Institute for Defense Analyses DATAWorks 2018
Statistics Boot Camp Dr. Stephanie Lane Institute for Defense Analyses DATAWorks 2018 March 21, 2018 Outline of boot camp Summarizing and simplifying data Point and interval estimation Foundations of statistical
More information(ii) Scan your answer sheets INTO ONE FILE only, and submit it in the drop-box.
FINAL EXAM ** Two different ways to submit your answer sheet (i) Use MS-Word and place it in a drop-box. (ii) Scan your answer sheets INTO ONE FILE only, and submit it in the drop-box. Deadline: December
More informationReview. DS GA 1002 Statistical and Mathematical Models. Carlos Fernandez-Granda
Review DS GA 1002 Statistical and Mathematical Models http://www.cims.nyu.edu/~cfgranda/pages/dsga1002_fall16 Carlos Fernandez-Granda Probability and statistics Probability: Framework for dealing with
More informationPh.D. Preliminary Examination Statistics June 2, 2014
Ph.D. Preliminary Examination Statistics June, 04 NOTES:. The exam is worth 00 points.. Partial credit may be given for partial answers if possible.. There are 5 pages in this exam paper. I have neither
More information2 Prediction and Analysis of Variance
2 Prediction and Analysis of Variance Reading: Chapters and 2 of Kennedy A Guide to Econometrics Achen, Christopher H. Interpreting and Using Regression (London: Sage, 982). Chapter 4 of Andy Field, Discovering
More informationSTAT5044: Regression and Anova
STAT5044: Regression and Anova Inyoung Kim 1 / 49 Outline 1 How to check assumptions 2 / 49 Assumption Linearity: scatter plot, residual plot Randomness: Run test, Durbin-Watson test when the data can
More informationSTAT 512 MidTerm I (2/21/2013) Spring 2013 INSTRUCTIONS
STAT 512 MidTerm I (2/21/2013) Spring 2013 Name: Key INSTRUCTIONS 1. This exam is open book/open notes. All papers (but no electronic devices except for calculators) are allowed. 2. There are 5 pages in
More informationThe Flight of the Space Shuttle Challenger
The Flight of the Space Shuttle Challenger On January 28, 1986, the space shuttle Challenger took off on the 25 th flight in NASA s space shuttle program. Less than 2 minutes into the flight, the spacecraft
More informationFormal Statement of Simple Linear Regression Model
Formal Statement of Simple Linear Regression Model Y i = β 0 + β 1 X i + ɛ i Y i value of the response variable in the i th trial β 0 and β 1 are parameters X i is a known constant, the value of the predictor
More informationStat 500 Midterm 2 8 November 2007 page 0 of 4
Stat 500 Midterm 2 8 November 2007 page 0 of 4 Please put your name on the back of your answer book. Do NOT put it on the front. Thanks. DO NOT START until I tell you to. You are welcome to read this front
More informationTA: Sheng Zhgang (Th 1:20) / 342 (W 1:20) / 343 (W 2:25) / 344 (W 12:05) Haoyang Fan (W 1:20) / 346 (Th 12:05) FINAL EXAM
STAT 301, Fall 2011 Name Lec 4: Ismor Fischer Discussion Section: Please circle one! TA: Sheng Zhgang... 341 (Th 1:20) / 342 (W 1:20) / 343 (W 2:25) / 344 (W 12:05) Haoyang Fan... 345 (W 1:20) / 346 (Th
More informationCh 3: Multiple Linear Regression
Ch 3: Multiple Linear Regression 1. Multiple Linear Regression Model Multiple regression model has more than one regressor. For example, we have one response variable and two regressor variables: 1. delivery
More informationLab 11 - Heteroskedasticity
Lab 11 - Heteroskedasticity Spring 2017 Contents 1 Introduction 2 2 Heteroskedasticity 2 3 Addressing heteroskedasticity in Stata 3 4 Testing for heteroskedasticity 4 5 A simple example 5 1 1 Introduction
More informationHypothesis testing. Data to decisions
Hypothesis testing Data to decisions The idea Null hypothesis: H 0 : the DGP/population has property P Under the null, a sample statistic has a known distribution If, under that that distribution, the
More informationInferences for Regression
Inferences for Regression An Example: Body Fat and Waist Size Looking at the relationship between % body fat and waist size (in inches). Here is a scatterplot of our data set: Remembering Regression In
More informationStat 135 Fall 2013 FINAL EXAM December 18, 2013
Stat 135 Fall 2013 FINAL EXAM December 18, 2013 Name: Person on right SID: Person on left There will be one, double sided, handwritten, 8.5in x 11in page of notes allowed during the exam. The exam is closed
More informationWe know from STAT.1030 that the relevant test statistic for equality of proportions is:
2. Chi 2 -tests for equality of proportions Introduction: Two Samples Consider comparing the sample proportions p 1 and p 2 in independent random samples of size n 1 and n 2 out of two populations which
More information0.3. Proportion failing Temperature
The Flight of the Space Shuttle Challenger On January 28, 1986, the space shuttle Challenger took o on the 25 th ight in NASA's space shuttle program. Less than 2 minutes into the ight, the spacecraft
More informationEcn Analysis of Economic Data University of California - Davis February 23, 2010 Instructor: John Parman. Midterm 2. Name: ID Number: Section:
Ecn 102 - Analysis of Economic Data University of California - Davis February 23, 2010 Instructor: John Parman Midterm 2 You have until 10:20am to complete this exam. Please remember to put your name,
More informationUnit 9: Inferences for Proportions and Count Data
Unit 9: Inferences for Proportions and Count Data Statistics 571: Statistical Methods Ramón V. León 12/15/2008 Unit 9 - Stat 571 - Ramón V. León 1 Large Sample Confidence Interval for Proportion ( pˆ p)
More information(a) (3 points) Construct a 95% confidence interval for β 2 in Equation 1.
Problem 1 (21 points) An economist runs the regression y i = β 0 + x 1i β 1 + x 2i β 2 + x 3i β 3 + ε i (1) The results are summarized in the following table: Equation 1. Variable Coefficient Std. Error
More information2.4.3 Estimatingσ Coefficient of Determination 2.4. ASSESSING THE MODEL 23
2.4. ASSESSING THE MODEL 23 2.4.3 Estimatingσ 2 Note that the sums of squares are functions of the conditional random variables Y i = (Y X = x i ). Hence, the sums of squares are random variables as well.
More informationLecture 14: Introduction to Poisson Regression
Lecture 14: Introduction to Poisson Regression Ani Manichaikul amanicha@jhsph.edu 8 May 2007 1 / 52 Overview Modelling counts Contingency tables Poisson regression models 2 / 52 Modelling counts I Why
More informationModelling counts. Lecture 14: Introduction to Poisson Regression. Overview
Modelling counts I Lecture 14: Introduction to Poisson Regression Ani Manichaikul amanicha@jhsph.edu Why count data? Number of traffic accidents per day Mortality counts in a given neighborhood, per week
More informationTests about a population mean
October 2 nd, 2017 Overview Week 1 Week 2 Week 4 Week 7 Week 10 Week 12 Chapter 1: Descriptive statistics Chapter 6: Statistics and Sampling Distributions Chapter 7: Point Estimation Chapter 8: Confidence
More informationMidterm 2 - Solutions
Ecn 102 - Analysis of Economic Data University of California - Davis February 24, 2010 Instructor: John Parman Midterm 2 - Solutions You have until 10:20am to complete this exam. Please remember to put
More informationCorrelation Analysis
Simple Regression Correlation Analysis Correlation analysis is used to measure strength of the association (linear relationship) between two variables Correlation is only concerned with strength of the
More informationStatistics 5100 Spring 2018 Exam 1
Statistics 5100 Spring 2018 Exam 1 Directions: You have 60 minutes to complete the exam. Be sure to answer every question, and do not spend too much time on any part of any question. Be concise with all
More informationUnit 9: Inferences for Proportions and Count Data
Unit 9: Inferences for Proportions and Count Data Statistics 571: Statistical Methods Ramón V. León 1/15/008 Unit 9 - Stat 571 - Ramón V. León 1 Large Sample Confidence Interval for Proportion ( pˆ p)
More informationMultivariate Regression (Chapter 10)
Multivariate Regression (Chapter 10) This week we ll cover multivariate regression and maybe a bit of canonical correlation. Today we ll mostly review univariate multivariate regression. With multivariate
More informationExercise Sheet 6: Solutions
Exercise Sheet 6: Solutions R.G. Pierse 1. (a) Regression yields: Dependent Variable: LC Date: 10/29/02 Time: 18:37 Sample(adjusted): 1950 1985 Included observations: 36 after adjusting endpoints C 0.244716
More informationORF 245 Fundamentals of Engineering Statistics. Final Exam
Princeton University Department of Operations Research and Financial Engineering ORF 245 Fundamentals of Engineering Statistics Final Exam May 22, 2008 7:30pm-10:30pm PLEASE DO NOT TURN THIS PAGE AND START
More informationTest Yourself! Methodological and Statistical Requirements for M.Sc. Early Childhood Research
Test Yourself! Methodological and Statistical Requirements for M.Sc. Early Childhood Research HOW IT WORKS For the M.Sc. Early Childhood Research, sufficient knowledge in methods and statistics is one
More informationOpen book and notes. 120 minutes. Covers Chapters 8 through 14 of Montgomery and Runger (fourth edition).
IE 330 Seat # Open book and notes 10 minutes Covers Chapters 8 through 14 of Montgomery and Runger (fourth edition) Cover page and eight pages of exam No calculator ( points) I have, or will, complete
More informationMATH 644: Regression Analysis Methods
MATH 644: Regression Analysis Methods FINAL EXAM Fall, 2012 INSTRUCTIONS TO STUDENTS: 1. This test contains SIX questions. It comprises ELEVEN printed pages. 2. Answer ALL questions for a total of 100
More informationLAB 5 INSTRUCTIONS LINEAR REGRESSION AND CORRELATION
LAB 5 INSTRUCTIONS LINEAR REGRESSION AND CORRELATION In this lab you will learn how to use Excel to display the relationship between two quantitative variables, measure the strength and direction of the
More informationOne-Way Tables and Goodness of Fit
Stat 504, Lecture 5 1 One-Way Tables and Goodness of Fit Key concepts: One-way Frequency Table Pearson goodness-of-fit statistic Deviance statistic Pearson residuals Objectives: Learn how to compute the
More informationCHAPTER 10. Regression and Correlation
CHAPTER 10 Regression and Correlation In this Chapter we assess the strength of the linear relationship between two continuous variables. If a significant linear relationship is found, the next step would
More informationConcordia University (5+5)Q 1.
(5+5)Q 1. Concordia University Department of Mathematics and Statistics Course Number Section Statistics 360/1 40 Examination Date Time Pages Mid Term Test May 26, 2004 Two Hours 3 Instructor Course Examiner
More informationChapter 7, continued: MANOVA
Chapter 7, continued: MANOVA The Multivariate Analysis of Variance (MANOVA) technique extends Hotelling T 2 test that compares two mean vectors to the setting in which there are m 2 groups. We wish to
More informationRegression Models - Introduction
Regression Models - Introduction In regression models there are two types of variables that are studied: A dependent variable, Y, also called response variable. It is modeled as random. An independent
More informationSMAM 314 Exam 49 Name. 1.Mark the following statements true or false (10 points-2 each)
SMAM 314 Exam 49 Name 1.Mark the following statements true or false (10 points-2 each) _F A. When fitting a least square equation it is necessary that the observations come from a normal distribution.
More informationMathematical Notation Math Introduction to Applied Statistics
Mathematical Notation Math 113 - Introduction to Applied Statistics Name : Use Word or WordPerfect to recreate the following documents. Each article is worth 10 points and should be emailed to the instructor
More informationBIOS 312: Precision of Statistical Inference
and Power/Sample Size and Standard Errors BIOS 312: of Statistical Inference Chris Slaughter Department of Biostatistics, Vanderbilt University School of Medicine January 3, 2013 Outline Overview and Power/Sample
More informationEcon 583 Final Exam Fall 2008
Econ 583 Final Exam Fall 2008 Eric Zivot December 11, 2008 Exam is due at 9:00 am in my office on Friday, December 12. 1 Maximum Likelihood Estimation and Asymptotic Theory Let X 1,...,X n be iid random
More informationSTAT Final Practice Problems
STAT 48 -- Final Practice Problems.Out of 5 women who had uterine cancer, 0 claimed to have used estrogens. Out of 30 women without uterine cancer 5 claimed to have used estrogens. Exposure Outcome (Cancer)
More informationMidterm 2 - Solutions
Ecn 102 - Analysis of Economic Data University of California - Davis February 23, 2010 Instructor: John Parman Midterm 2 - Solutions You have until 10:20am to complete this exam. Please remember to put
More informationExercise Sheet 5: Solutions
Exercise Sheet 5: Solutions R.G. Pierse 2. Estimation of Model M1 yields the following results: Date: 10/24/02 Time: 18:06 C -1.448432 0.696587-2.079327 0.0395 LPC -0.306051 0.272836-1.121740 0.2640 LPF
More informationexp{ (x i) 2 i=1 n i=1 (x i a) 2 (x i ) 2 = exp{ i=1 n i=1 n 2ax i a 2 i=1
4 Hypothesis testing 4. Simple hypotheses A computer tries to distinguish between two sources of signals. Both sources emit independent signals with normally distributed intensity, the signals of the first
More informationSTAT 7030: Categorical Data Analysis
STAT 7030: Categorical Data Analysis 5. Logistic Regression Peng Zeng Department of Mathematics and Statistics Auburn University Fall 2012 Peng Zeng (Auburn University) STAT 7030 Lecture Notes Fall 2012
More informationEXAM # 2. Total 100. Please show all work! Problem Points Grade. STAT 301, Spring 2013 Name
STAT 301, Spring 2013 Name Lec 1, MWF 9:55 - Ismor Fischer Discussion Section: Please circle one! TA: Shixue Li...... 311 (M 4:35) / 312 (M 12:05) / 315 (T 4:00) Xinyu Song... 313 (M 2:25) / 316 (T 12:05)
More informationSTAT 350 Final (new Material) Review Problems Key Spring 2016
1. The editor of a statistics textbook would like to plan for the next edition. A key variable is the number of pages that will be in the final version. Text files are prepared by the authors using LaTeX,
More informationAnswers: Problem Set 9. Dynamic Models
Answers: Problem Set 9. Dynamic Models 1. Given annual data for the period 1970-1999, you undertake an OLS regression of log Y on a time trend, defined as taking the value 1 in 1970, 2 in 1972 etc. The
More informationChapter 8: Simple Linear Regression
Chapter 8: Simple Linear Regression Shiwen Shen University of South Carolina 2017 Summer 1 / 70 Introduction A problem that arises in engineering, economics, medicine, and other areas is that of investigating
More informationChapters 9 and 10. Review for Exam. Chapter 9. Correlation and Regression. Overview. Paired Data
Chapters 9 and 10 Review for Exam 1 Chapter 9 Correlation and Regression 2 Overview Paired Data is there a relationship if so, what is the equation use the equation for prediction 3 Definition Correlation
More informationSimple Linear Regression
Simple Linear Regression In simple linear regression we are concerned about the relationship between two variables, X and Y. There are two components to such a relationship. 1. The strength of the relationship.
More informationMathematical statistics
November 1 st, 2018 Lecture 18: Tests about a population mean Overview 9.1 Hypotheses and test procedures test procedures errors in hypothesis testing significance level 9.2 Tests about a population mean
More informationSleep data, two drugs Ch13.xls
Model Based Statistics in Biology. Part IV. The General Linear Mixed Model.. Chapter 13.3 Fixed*Random Effects (Paired t-test) ReCap. Part I (Chapters 1,2,3,4), Part II (Ch 5, 6, 7) ReCap Part III (Ch
More informationHypothesis Testing for Var-Cov Components
Hypothesis Testing for Var-Cov Components When the specification of coefficients as fixed, random or non-randomly varying is considered, a null hypothesis of the form is considered, where Additional output
More informationChapter 1 Linear Regression with One Predictor
STAT 525 FALL 2018 Chapter 1 Linear Regression with One Predictor Professor Min Zhang Goals of Regression Analysis Serve three purposes Describes an association between X and Y In some applications, the
More informationChapter 2 Multiple Regression I (Part 1)
Chapter 2 Multiple Regression I (Part 1) 1 Regression several predictor variables The response Y depends on several predictor variables X 1,, X p response {}}{ Y predictor variables {}}{ X 1, X 2,, X p
More informationSTAT 501 EXAM I NAME Spring 1999
STAT 501 EXAM I NAME Spring 1999 Instructions: You may use only your calculator and the attached tables and formula sheet. You can detach the tables and formula sheet from the rest of this exam. Show your
More informationProblem #1 #2 #3 #4 #5 #6 Total Points /6 /8 /14 /10 /8 /10 /56
STAT 391 - Spring Quarter 2017 - Midterm 1 - April 27, 2017 Name: Student ID Number: Problem #1 #2 #3 #4 #5 #6 Total Points /6 /8 /14 /10 /8 /10 /56 Directions. Read directions carefully and show all your
More informationSTAT763: Applied Regression Analysis. Multiple linear regression. 4.4 Hypothesis testing
STAT763: Applied Regression Analysis Multiple linear regression 4.4 Hypothesis testing Chunsheng Ma E-mail: cma@math.wichita.edu 4.4.1 Significance of regression Null hypothesis (Test whether all β j =
More informationa. When a data set is not normally distributed, what should you try in order to appropriately make statistical tests on that data?
1 1. Briefly answer the following: a. When a data set is not normally distributed, what should you try in order to appropriately make statistical tests on that data? transformations b. Why are paired samples
More informationM(t) = 1 t. (1 t), 6 M (0) = 20 P (95. X i 110) i=1
Math 66/566 - Midterm Solutions NOTE: These solutions are for both the 66 and 566 exam. The problems are the same until questions and 5. 1. The moment generating function of a random variable X is M(t)
More informationPoisson Regression. James H. Steiger. Department of Psychology and Human Development Vanderbilt University
Poisson Regression James H. Steiger Department of Psychology and Human Development Vanderbilt University James H. Steiger (Vanderbilt University) Poisson Regression 1 / 49 Poisson Regression 1 Introduction
More informationTextbook Examples of. SPSS Procedure
Textbook s of IBM SPSS Procedures Each SPSS procedure listed below has its own section in the textbook. These sections include a purpose statement that describes the statistical test, identification of
More informationInteractions. Interactions. Lectures 1 & 2. Linear Relationships. y = a + bx. Slope. Intercept
Interactions Lectures 1 & Regression Sometimes two variables appear related: > smoking and lung cancers > height and weight > years of education and income > engine size and gas mileage > GMAT scores and
More informationRef.: Spring SOS3003 Applied data analysis for social science Lecture note
SOS3003 Applied data analysis for social science Lecture note 05-2010 Erling Berge Department of sociology and political science NTNU Spring 2010 Erling Berge 2010 1 Literature Regression criticism I Hamilton
More informationStats Review Chapter 14. Mary Stangler Center for Academic Success Revised 8/16
Stats Review Chapter 14 Revised 8/16 Note: This review is meant to highlight basic concepts from the course. It does not cover all concepts presented by your instructor. Refer back to your notes, unit
More informationTopic 21 Goodness of Fit
Topic 21 Goodness of Fit Contingency Tables 1 / 11 Introduction Two-way Table Smoking Habits The Hypothesis The Test Statistic Degrees of Freedom Outline 2 / 11 Introduction Contingency tables, also known
More informationThis document contains 3 sets of practice problems.
P RACTICE PROBLEMS This document contains 3 sets of practice problems. Correlation: 3 problems Regression: 4 problems ANOVA: 8 problems You should print a copy of these practice problems and bring them
More informationSTAT 526 Spring Midterm 1. Wednesday February 2, 2011
STAT 526 Spring 2011 Midterm 1 Wednesday February 2, 2011 Time: 2 hours Name (please print): Show all your work and calculations. Partial credit will be given for work that is partially correct. Points
More informationIntroduction to the Generalized Linear Model: Logistic regression and Poisson regression
Introduction to the Generalized Linear Model: Logistic regression and Poisson regression Statistical modelling: Theory and practice Gilles Guillot gigu@dtu.dk November 4, 2013 Gilles Guillot (gigu@dtu.dk)
More informationSTAT 461/561- Assignments, Year 2015
STAT 461/561- Assignments, Year 2015 This is the second set of assignment problems. When you hand in any problem, include the problem itself and its number. pdf are welcome. If so, use large fonts and
More information16.400/453J Human Factors Engineering. Design of Experiments II
J Human Factors Engineering Design of Experiments II Review Experiment Design and Descriptive Statistics Research question, independent and dependent variables, histograms, box plots, etc. Inferential
More informationStatistical Inference. Part IV. Statistical Inference
Part IV Statistical Inference As of Oct 5, 2017 Sampling Distributions of the OLS Estimator 1 Statistical Inference Sampling Distributions of the OLS Estimator Testing Against One-Sided Alternatives Two-Sided
More informationIntroduction to statistical modeling
Introduction to statistical modeling Illustrated with XLSTAT Jean Paul Maalouf webinar@xlstat.com linkedin.com/in/jean-paul-maalouf November 30, 2016 www.xlstat.com 1 PLAN XLSTAT: who are we? Statistics:
More informationFinal Exam. Question 1 (20 points) 2 (25 points) 3 (30 points) 4 (25 points) 5 (10 points) 6 (40 points) Total (150 points) Bonus question (10)
Name Economics 170 Spring 2004 Honor pledge: I have neither given nor received aid on this exam including the preparation of my one page formula list and the preparation of the Stata assignment for the
More informationWooldridge, Introductory Econometrics, 2d ed. Chapter 8: Heteroskedasticity In laying out the standard regression model, we made the assumption of
Wooldridge, Introductory Econometrics, d ed. Chapter 8: Heteroskedasticity In laying out the standard regression model, we made the assumption of homoskedasticity of the regression error term: that its
More information4 Hypothesis testing. 4.1 Types of hypothesis and types of error 4 HYPOTHESIS TESTING 49
4 HYPOTHESIS TESTING 49 4 Hypothesis testing In sections 2 and 3 we considered the problem of estimating a single parameter of interest, θ. In this section we consider the related problem of testing whether
More information12.10 (STUDENT CD-ROM TOPIC) CHI-SQUARE GOODNESS- OF-FIT TESTS
CDR4_BERE601_11_SE_C1QXD 1//08 1:0 PM Page 1 110: (Student CD-ROM Topic) Chi-Square Goodness-of-Fit Tests CD1-1 110 (STUDENT CD-ROM TOPIC) CHI-SQUARE GOODNESS- OF-FIT TESTS In this section, χ goodness-of-fit
More informationStat 231 Exam 2 Fall 2013
Stat 231 Exam 2 Fall 2013 I have neither given nor received unauthorized assistance on this exam. Name Signed Date Name Printed 1 1. Some IE 361 students worked with a manufacturer on quantifying the capability
More information