Chapter 4 Exam. A scatterplot of a response variable Y versus an explanatory variable X is given below.

Size: px
Start display at page:

Download "Chapter 4 Exam. A scatterplot of a response variable Y versus an explanatory variable X is given below."

Transcription

1 Chapter 4 Exam A scatterplot of a response variable Y versus an explanatory variable X is given below. 1 Which of the following is true? A) There is a nonlinear relationship between Y and X. B) There is a very strong positive correlation between Y and X because there is an obvious relationship between these variables. C) There is a monotonic relationship between Y and X. D) There is a strong quadratic relationship between Y and X Suppose we measure a response variable Y at each of several times. A scatterplot of log Y versus time of measurement looks approximately like a positively sloping straight line. We may conclude that A) the correlation between time of measurement and Y is negative, since logarithms of positive fractions (such as correlations) are negative. B) the rate of growth of Y is positive, but slowing down over time. C) a logarithmic growth model would approximately describe the relationship between Y and the time of measurement. D) a mistake has been made. It would have been better to plot Y versus the logarithm of the time of measurement. E) an exponential growth model would approximately describe the relationship between Y and time of measurement. Suppose the relationship between a response variable y and a predictor variable x is approximately y = x Which of the following plots would approximately follow a straight line? A) A plot of y against x. D) A plot of 10 y against x. B) A plot of y against log x. E) A plot of log y against log x. C) A plot of log y against x. When possible, the best way to establish that an observed association is the result of a cause-and-effect relation is by means of A) the least-squares regression line. B) the correlation coefficient. C) randomization to select the data variables. D) a well-designed experiment. E) examining z-scores rather than the original variables.

2 Which of the following scatterplots would indicate that Y is growing exponentially over time? A) C) B) D) 5 E) 6 The owner of a chain of supermarkets notices that there is a positive correlation between the sales of beer and the sales of ice cream over the course of the previous year. During seasons when sales of beer were above average, sales of ice cream also tended to be above average. Likewise, during seasons when sales of beer were below average, sales of ice cream also tended to be below average. Which of the following would be a valid conclusion from these facts? A) The sales records must be in error. There should be no association between beer and ice cream sales. B) Temperature is clearly a lurking variable when considering sales of beer and ice cream. C) A scatterplot of monthly ice cream sales versus monthly beer sales would show that a straight line describes the pattern in the plot, but it would have to be a horizontal line. D) Evidently, for a significant proportion of customers of these supermarkets, drinking beer causes a desire for ice cream or eating ice cream causes a thirst for beer. E) None of the above.

3 7 Two variables, an explanatory variable x and a response variable y, are measured on each of several individuals. The correlation between these variables is found to be To help us interpret this correlation, we should do which of the following? A) Compute the least-squares regression line of y on x and consider whether the slope is positive or negative. B) Interchange the roles of x and y (i.e., treat x as the response variable and y as the explanatory variable) and recompute the correlation. C) Plot the data. D) Determine whether x or y has larger values before computing the residuals. 8 According to the 1990 census, those states that had an above-average number X of people who failed to complete high school tended to have an above-average number Y of infant deaths. In other words, there was a positive association between X and Y. The most plausible explanation for this association is that A) populations were used instead of rates. B) Y causes X. Therefore, programs that reduce infant deaths will ultimately reduce the number of high school dropouts. C) changes in X and Y are due to a common response to other variables. For example, states with large populations will have both larger numbers of people who fail to complete high school and larger numbers of infant deaths. D) the association between X and Y is purely coincidental. It is implausible to believe the observed association could be anything other than accidental. E) X causes Y. Therefore, programs to keep teens in school will help reduce the number of infant deaths Which of the following would be necessary to establish a cause-and-effect relation between two variables? A) Strong association between the variables. B) A well-designed experiment. C) Plausibility of the alleged cause. D) An association between the variables observed in many different settings A researcher notices that in a sample of adults, those that take larger amounts of vitamin C have fewer illnesses. However, those that take larger amounts of vitamin C also tend to exercise more. As explanations for having fewer illnesses, the variables amount of vitamin C taken and amount of exercise are A) skewed. B) confounded. C) common responses. D) symmetric. E) linked.

4 In 1982 Kennesaw, Georgia, passed a law requiring all citizens to own at least one gun. Although the law was never enforced, six months after the law was passed the number of burglaries in that month was less than in the month prior to passage of the law. We may conclude which of the following? A) Gun ownership and burglary rates are negatively associated. B) Gun ownership causes a reduction in crime. This is because there is a negative association between gun ownership and burglary rates and because there is a plausible explanation for this association (gun ownership acts as a deterrent to crime). C) Criminals are more likely to avoid homes in towns where guns are more prevalent. D) All of the above. E) None of the above. 33. The reversal of the direction of an association when lurking variables are taken into account is called A) Simpson s paradox. D) a residual plot. B) least-squares regression. E) negative association. C) confounding. 34. The two-way table below categorizes suicides committed in 1983 by the sex of the victim and the method used. Method Male Female Firearms 13,959 2,641 Poison 3,148 2,469 Hanging 3, Other 1, Which of the following statements is consistent with the table? A) There is absolutely no evidence of a relation between the sex of the victim and the method of suicide used. B) More women commit suicide than men. C) Men display a greater tendency to use firearms to commit suicide than do women. D) The correlation between method of suicide and sex of the victim is clearly positive. E) The proportion of men who use poison to commit suicide is higher than the proportion of women who use poison to commit suicide. 36. X and Y are two categorical variables. The best way to determine whether there is a relationship between them is to A) compute the least-squares regression line between X and Y. B) draw a scatterplot of the X and Y values. C) make a two-way table of the X and Y values. D) calculate the correlation between X and Y. E) do all of the above.

5 Researchers studied a sample of 100 adults between the ages of 25 and 35 and found a strong negative correlation between the amount of vitamin C an individual consumed and the number of pounds the individual was overweight. Which of the following may we conclude? A) This is strong, but not conclusive, evidence that large amounts of vitamin C inhibit weight gain. B) If the amount of vitamin C consumed and the number of pounds overweight for each individual in this study were plotted on a scatterplot, the points would lie close to a negatively sloping straight line. C) If a larger sample of adults between the ages of 25 and 35 had been studied, the correlation would have been even stronger. D) If people consumed more vitamin C, they would likely lose more weight. FREE RESPONSE 16. What does the dotted line represent in the figure below? X Y 17. Over the past 30 years in the United States there has been a strong positive correlation between cigarette sales and the number of high school graduates. Is the association between these two variables most likely due to causation, confounding, or common response? Justify your answer 18. If someone suspects a relationship between two quantitative variables to follow the equation y = ax 2, what transformation could be performed without using logarithms to achieve linearity?

6 19. A company decided to expand, so it opened a new factory with 455 available jobs. The following tables summarize the hiring decisions made by the company. Workers Managers Male Female Male Female Applied Applied Hired Hired (a) Calculate the percent of male and female workers that are hired. Then do likewise for male and female managers. (b) Use the tables above to create a two-way table that shows the relationship between gender and hiring decision. (c) Calculate the percent of male and female applicants that were hired. (d) Explain your findings in (a) and (c). (explain why it is happening not just what it is)

7 20. Cell phones, a fairly recent innovation, have become increasingly popular with all segments of our society. According to the Strategis Group, the number of cellular and personal communications systems subscribers in the United States increased dramatically beginning in 1990, as shown in the following table. No. of subscribers Year (millions) (a) Describe the relationship between year and number of subscribers. (b) What type of relationship appears to be present? Justify your answer. (c) Perform an appropriate transformation to linearize the data. Find the equation of the leastsquares line for the transformed data. Write the equation below. Be sure to define any variables you use. (d) How well does the linear model you calculated in (c) fit the transformed data? Justify your answer with graphical and numerical evidence. (e) The Strategis Group predicts 70.8 million subscribers in 1998, and 99.2 million in the year How many subscribers does your model predict for these years? Show your method.

Linear Regression. Chapter 5. Prediction via Regression Line Number of new birds and Percent returning. Least Squares

Linear Regression. Chapter 5. Prediction via Regression Line Number of new birds and Percent returning. Least Squares Linear Regression Chapter 5 Regression Objective: To quantify the linear relationship between an explanatory variable (x) and response variable (y). We can then predict the average response for all subjects

More information

AP Statistics. Chapter 4 Review

AP Statistics. Chapter 4 Review Name AP Statistics Chapter 4 Review 1. In a study of the link between high blood pressure and cardiovascular disease, a group of white males aged 35 to 64 was followed for 5 years. At the beginning of

More information

Name: Date: Use the following to answer questions 2-3:

Name: Date: Use the following to answer questions 2-3: Name: Date: 1. A study is conducted on students taking a statistics class. Several variables are recorded in the survey. Identify each variable as categorical or quantitative. A) Type of car the student

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) All but one of these statements contain a mistake. Which could be true? A) There is a correlation

More information

Lecture 11: Chapter 5, Section 3 Relationships between Two Quantitative Variables; Correlation

Lecture 11: Chapter 5, Section 3 Relationships between Two Quantitative Variables; Correlation Lecture 11: Chapter 5, Section 3 Relationships between Two Quantitative Variables; Correlation Display and Summarize Correlation for Direction and Strength Properties of Correlation Regression Line Cengage

More information

2. Here is a small part of a data set that describes the fuel economy (in miles per gallon) of 2006 model motor vehicles.

2. Here is a small part of a data set that describes the fuel economy (in miles per gallon) of 2006 model motor vehicles. Math 1530-017 Exam 1 February 19, 2009 Name Student Number E There are five possible responses to each of the following multiple choice questions. There is only on BEST answer. Be sure to read all possible

More information

Statistics 151 Practice Midterm 1 Mike Kowalski

Statistics 151 Practice Midterm 1 Mike Kowalski Statistics 151 Practice Midterm 1 Mike Kowalski Statistics 151 Practice Midterm 1 Multiple Choice (50 minutes) Instructions: 1. This is a closed book exam. 2. You may use the STAT 151 formula sheets and

More information

Chapter 10. Key Ideas Correlation, Correlation Coefficient (r),

Chapter 10. Key Ideas Correlation, Correlation Coefficient (r), Chapter 0 Key Ideas Correlation, Correlation Coefficient (r), Section 0-: Overview We have already explored the basics of describing single variable data sets. However, when two quantitative variables

More information

a) Find the five point summary for the home runs of the National League teams. b) What is the mean number of home runs by the American League teams?

a) Find the five point summary for the home runs of the National League teams. b) What is the mean number of home runs by the American League teams? 1. Phone surveys are sometimes used to rate TV shows. Such a survey records several variables listed below. Which ones of them are categorical and which are quantitative? - the number of people watching

More information

Chapter 7: Simple linear regression Learning Objectives

Chapter 7: Simple linear regression Learning Objectives Chapter 7: Simple linear regression Learning Objectives Reading: Section 7.1 of OpenIntro Statistics Video: Correlation vs. causation, YouTube (2:19) Video: Intro to Linear Regression, YouTube (5:18) -

More information

Section 14 Simple Linear Regression: Introduction to Least Squares Regression

Section 14 Simple Linear Regression: Introduction to Least Squares Regression Slide 1 Section 14 Simple Linear Regression: Introduction to Least Squares Regression There are several different measures of statistical association used for understanding the quantitative relationship

More information

Statistics 2014 Scoring Guidelines

Statistics 2014 Scoring Guidelines AP Statistics 2014 Scoring Guidelines College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. AP Central is the official online home

More information

Relationships Between Two Variables: Scatterplots and Correlation

Relationships Between Two Variables: Scatterplots and Correlation Relationships Between Two Variables: Scatterplots and Correlation Example: Consider the population of cars manufactured in the U.S. What is the relationship (1) between engine size and horsepower? (2)

More information

Describing Relationships between Two Variables

Describing Relationships between Two Variables Describing Relationships between Two Variables Up until now, we have dealt, for the most part, with just one variable at a time. This variable, when measured on many different subjects or objects, took

More information

Regression III: Advanced Methods

Regression III: Advanced Methods Lecture 4: Transformations Regression III: Advanced Methods William G. Jacoby Michigan State University Goals of the lecture The Ladder of Roots and Powers Changing the shape of distributions Transforming

More information

Straightening Data in a Scatterplot Selecting a Good Re-Expression Model

Straightening Data in a Scatterplot Selecting a Good Re-Expression Model Straightening Data in a Scatterplot Selecting a Good Re-Expression What Is All This Stuff? Here s what is included: Page 3: Graphs of the three main patterns of data points that the student is likely to

More information

Outline: Demand Forecasting

Outline: Demand Forecasting Outline: Demand Forecasting Given the limited background from the surveys and that Chapter 7 in the book is complex, we will cover less material. The role of forecasting in the chain Characteristics of

More information

1. The parameters to be estimated in the simple linear regression model Y=α+βx+ε ε~n(0,σ) are: a) α, β, σ b) α, β, ε c) a, b, s d) ε, 0, σ

1. The parameters to be estimated in the simple linear regression model Y=α+βx+ε ε~n(0,σ) are: a) α, β, σ b) α, β, ε c) a, b, s d) ε, 0, σ STA 3024 Practice Problems Exam 2 NOTE: These are just Practice Problems. This is NOT meant to look just like the test, and it is NOT the only thing that you should study. Make sure you know all the material

More information

AP STATISTICS REVIEW (YMS Chapters 1-8)

AP STATISTICS REVIEW (YMS Chapters 1-8) AP STATISTICS REVIEW (YMS Chapters 1-8) Exploring Data (Chapter 1) Categorical Data nominal scale, names e.g. male/female or eye color or breeds of dogs Quantitative Data rational scale (can +,,, with

More information

Univariate Regression

Univariate Regression Univariate Regression Correlation and Regression The regression line summarizes the linear relationship between 2 variables Correlation coefficient, r, measures strength of relationship: the closer r is

More information

Simple Predictive Analytics Curtis Seare

Simple Predictive Analytics Curtis Seare Using Excel to Solve Business Problems: Simple Predictive Analytics Curtis Seare Copyright: Vault Analytics July 2010 Contents Section I: Background Information Why use Predictive Analytics? How to use

More information

Mind on Statistics. Chapter 12

Mind on Statistics. Chapter 12 Mind on Statistics Chapter 12 Sections 12.1 Questions 1 to 6: For each statement, determine if the statement is a typical null hypothesis (H 0 ) or alternative hypothesis (H a ). 1. There is no difference

More information

STAT 350 Practice Final Exam Solution (Spring 2015)

STAT 350 Practice Final Exam Solution (Spring 2015) PART 1: Multiple Choice Questions: 1) A study was conducted to compare five different training programs for improving endurance. Forty subjects were randomly divided into five groups of eight subjects

More information

Lecture 13/Chapter 10 Relationships between Measurement (Quantitative) Variables

Lecture 13/Chapter 10 Relationships between Measurement (Quantitative) Variables Lecture 13/Chapter 10 Relationships between Measurement (Quantitative) Variables Scatterplot; Roles of Variables 3 Features of Relationship Correlation Regression Definition Scatterplot displays relationship

More information

This unit will lay the groundwork for later units where the students will extend this knowledge to quadratic and exponential functions.

This unit will lay the groundwork for later units where the students will extend this knowledge to quadratic and exponential functions. Algebra I Overview View unit yearlong overview here Many of the concepts presented in Algebra I are progressions of concepts that were introduced in grades 6 through 8. The content presented in this course

More information

Statistics. Measurement. Scales of Measurement 7/18/2012

Statistics. Measurement. Scales of Measurement 7/18/2012 Statistics Measurement Measurement is defined as a set of rules for assigning numbers to represent objects, traits, attributes, or behaviors A variableis something that varies (eye color), a constant does

More information

We are often interested in the relationship between two variables. Do people with more years of full-time education earn higher salaries?

We are often interested in the relationship between two variables. Do people with more years of full-time education earn higher salaries? Statistics: Correlation Richard Buxton. 2008. 1 Introduction We are often interested in the relationship between two variables. Do people with more years of full-time education earn higher salaries? Do

More information

Diagrams and Graphs of Statistical Data

Diagrams and Graphs of Statistical Data Diagrams and Graphs of Statistical Data One of the most effective and interesting alternative way in which a statistical data may be presented is through diagrams and graphs. There are several ways in

More information

Module 3: Correlation and Covariance

Module 3: Correlation and Covariance Using Statistical Data to Make Decisions Module 3: Correlation and Covariance Tom Ilvento Dr. Mugdim Pašiƒ University of Delaware Sarajevo Graduate School of Business O ften our interest in data analysis

More information

Homework 8 Solutions

Homework 8 Solutions Math 17, Section 2 Spring 2011 Homework 8 Solutions Assignment Chapter 7: 7.36, 7.40 Chapter 8: 8.14, 8.16, 8.28, 8.36 (a-d), 8.38, 8.62 Chapter 9: 9.4, 9.14 Chapter 7 7.36] a) A scatterplot is given below.

More information

The Importance of Statistics Education

The Importance of Statistics Education The Importance of Statistics Education Professor Jessica Utts Department of Statistics University of California, Irvine http://www.ics.uci.edu/~jutts jutts@uci.edu Outline of Talk What is Statistics? Four

More information

Section 3 Part 1. Relationships between two numerical variables

Section 3 Part 1. Relationships between two numerical variables Section 3 Part 1 Relationships between two numerical variables 1 Relationship between two variables The summary statistics covered in the previous lessons are appropriate for describing a single variable.

More information

Transforming Bivariate Data

Transforming Bivariate Data Math Objectives Students will recognize that bivariate data can be transformed to reduce the curvature in the graph of a relationship between two variables. Students will use scatterplots, residual plots,

More information

Answer: C. The strength of a correlation does not change if units change by a linear transformation such as: Fahrenheit = 32 + (5/9) * Centigrade

Answer: C. The strength of a correlation does not change if units change by a linear transformation such as: Fahrenheit = 32 + (5/9) * Centigrade Statistics Quiz Correlation and Regression -- ANSWERS 1. Temperature and air pollution are known to be correlated. We collect data from two laboratories, in Boston and Montreal. Boston makes their measurements

More information

Georgia Department of Education Common Core Georgia Performance Standards Framework Teacher Edition Coordinate Algebra Unit 4

Georgia Department of Education Common Core Georgia Performance Standards Framework Teacher Edition Coordinate Algebra Unit 4 Equal Salaries for Equal Work? Mathematical Goals Represent data on a scatter plot Describe how two variables are related Informally assess the fit of a function by plotting and analyzing residuals Fit

More information

Mind on Statistics. Chapter 4

Mind on Statistics. Chapter 4 Mind on Statistics Chapter 4 Sections 4.1 Questions 1 to 4: The table below shows the counts by gender and highest degree attained for 498 respondents in the General Social Survey. Highest Degree Gender

More information

Algebra II EOC Practice Test

Algebra II EOC Practice Test Algebra II EOC Practice Test Name Date 1. Suppose point A is on the unit circle shown above. What is the value of sin? (A) 0.736 (B) 0.677 (C) (D) (E) none of these 2. Convert to radians. (A) (B) (C) (D)

More information

MTH 140 Statistics Videos

MTH 140 Statistics Videos MTH 140 Statistics Videos Chapter 1 Picturing Distributions with Graphs Individuals and Variables Categorical Variables: Pie Charts and Bar Graphs Categorical Variables: Pie Charts and Bar Graphs Quantitative

More information

South Carolina College- and Career-Ready (SCCCR) Probability and Statistics

South Carolina College- and Career-Ready (SCCCR) Probability and Statistics South Carolina College- and Career-Ready (SCCCR) Probability and Statistics South Carolina College- and Career-Ready Mathematical Process Standards The South Carolina College- and Career-Ready (SCCCR)

More information

Descriptive statistics; Correlation and regression

Descriptive statistics; Correlation and regression Descriptive statistics; and regression Patrick Breheny September 16 Patrick Breheny STA 580: Biostatistics I 1/59 Tables and figures Descriptive statistics Histograms Numerical summaries Percentiles Human

More information

Correlational Research. Correlational Research. Stephen E. Brock, Ph.D., NCSP EDS 250. Descriptive Research 1. Correlational Research: Scatter Plots

Correlational Research. Correlational Research. Stephen E. Brock, Ph.D., NCSP EDS 250. Descriptive Research 1. Correlational Research: Scatter Plots Correlational Research Stephen E. Brock, Ph.D., NCSP California State University, Sacramento 1 Correlational Research A quantitative methodology used to determine whether, and to what degree, a relationship

More information

The correlation coefficient

The correlation coefficient The correlation coefficient Clinical Biostatistics The correlation coefficient Martin Bland Correlation coefficients are used to measure the of the relationship or association between two quantitative

More information

Correlation Coefficient The correlation coefficient is a summary statistic that describes the linear relationship between two numerical variables 2

Correlation Coefficient The correlation coefficient is a summary statistic that describes the linear relationship between two numerical variables 2 Lesson 4 Part 1 Relationships between two numerical variables 1 Correlation Coefficient The correlation coefficient is a summary statistic that describes the linear relationship between two numerical variables

More information

Simple linear regression

Simple linear regression Simple linear regression Introduction Simple linear regression is a statistical method for obtaining a formula to predict values of one variable from another where there is a causal relationship between

More information

Course Objective This course is designed to give you a basic understanding of how to run regressions in SPSS.

Course Objective This course is designed to give you a basic understanding of how to run regressions in SPSS. SPSS Regressions Social Science Research Lab American University, Washington, D.C. Web. www.american.edu/provost/ctrl/pclabs.cfm Tel. x3862 Email. SSRL@American.edu Course Objective This course is designed

More information

CURVE FITTING LEAST SQUARES APPROXIMATION

CURVE FITTING LEAST SQUARES APPROXIMATION CURVE FITTING LEAST SQUARES APPROXIMATION Data analysis and curve fitting: Imagine that we are studying a physical system involving two quantities: x and y Also suppose that we expect a linear relationship

More information

So, using the new notation, P X,Y (0,1) =.08 This is the value which the joint probability function for X and Y takes when X=0 and Y=1.

So, using the new notation, P X,Y (0,1) =.08 This is the value which the joint probability function for X and Y takes when X=0 and Y=1. Joint probabilit is the probabilit that the RVs & Y take values &. like the PDF of the two events, and. We will denote a joint probabilit function as P,Y (,) = P(= Y=) Marginal probabilit of is the probabilit

More information

The Effect of Dropping a Ball from Different Heights on the Number of Times the Ball Bounces

The Effect of Dropping a Ball from Different Heights on the Number of Times the Ball Bounces The Effect of Dropping a Ball from Different Heights on the Number of Times the Ball Bounces Or: How I Learned to Stop Worrying and Love the Ball Comment [DP1]: Titles, headings, and figure/table captions

More information

Linear Models in STATA and ANOVA

Linear Models in STATA and ANOVA Session 4 Linear Models in STATA and ANOVA Page Strengths of Linear Relationships 4-2 A Note on Non-Linear Relationships 4-4 Multiple Linear Regression 4-5 Removal of Variables 4-8 Independent Samples

More information

Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression

Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression Objectives: To perform a hypothesis test concerning the slope of a least squares line To recognize that testing for a

More information

Fairfield Public Schools

Fairfield Public Schools Mathematics Fairfield Public Schools AP Statistics AP Statistics BOE Approved 04/08/2014 1 AP STATISTICS Critical Areas of Focus AP Statistics is a rigorous course that offers advanced students an opportunity

More information

Chapter 9 Descriptive Statistics for Bivariate Data

Chapter 9 Descriptive Statistics for Bivariate Data 9.1 Introduction 215 Chapter 9 Descriptive Statistics for Bivariate Data 9.1 Introduction We discussed univariate data description (methods used to eplore the distribution of the values of a single variable)

More information

Algebra II End of Course Exam Answer Key Segment I. Scientific Calculator Only

Algebra II End of Course Exam Answer Key Segment I. Scientific Calculator Only Algebra II End of Course Exam Answer Key Segment I Scientific Calculator Only Question 1 Reporting Category: Algebraic Concepts & Procedures Common Core Standard: A-APR.3: Identify zeros of polynomials

More information

X X X a) perfect linear correlation b) no correlation c) positive correlation (r = 1) (r = 0) (0 < r < 1)

X X X a) perfect linear correlation b) no correlation c) positive correlation (r = 1) (r = 0) (0 < r < 1) CORRELATION AND REGRESSION / 47 CHAPTER EIGHT CORRELATION AND REGRESSION Correlation and regression are statistical methods that are commonly used in the medical literature to compare two or more variables.

More information

LOGISTIC REGRESSION ANALYSIS

LOGISTIC REGRESSION ANALYSIS LOGISTIC REGRESSION ANALYSIS C. Mitchell Dayton Department of Measurement, Statistics & Evaluation Room 1230D Benjamin Building University of Maryland September 1992 1. Introduction and Model Logistic

More information

DESCRIPTIVE STATISTICS. The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses.

DESCRIPTIVE STATISTICS. The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses. DESCRIPTIVE STATISTICS The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses. DESCRIPTIVE VS. INFERENTIAL STATISTICS Descriptive To organize,

More information

Lean Six Sigma Analyze Phase Introduction. TECH 50800 QUALITY and PRODUCTIVITY in INDUSTRY and TECHNOLOGY

Lean Six Sigma Analyze Phase Introduction. TECH 50800 QUALITY and PRODUCTIVITY in INDUSTRY and TECHNOLOGY TECH 50800 QUALITY and PRODUCTIVITY in INDUSTRY and TECHNOLOGY Before we begin: Turn on the sound on your computer. There is audio to accompany this presentation. Audio will accompany most of the online

More information

c. Construct a boxplot for the data. Write a one sentence interpretation of your graph.

c. Construct a boxplot for the data. Write a one sentence interpretation of your graph. MBA/MIB 5315 Sample Test Problems Page 1 of 1 1. An English survey of 3000 medical records showed that smokers are more inclined to get depressed than non-smokers. Does this imply that smoking causes depression?

More information

Correlation and Regression

Correlation and Regression Correlation and Regression Scatterplots Correlation Explanatory and response variables Simple linear regression General Principles of Data Analysis First plot the data, then add numerical summaries Look

More information

Example: Boats and Manatees

Example: Boats and Manatees Figure 9-6 Example: Boats and Manatees Slide 1 Given the sample data in Table 9-1, find the value of the linear correlation coefficient r, then refer to Table A-6 to determine whether there is a significant

More information

Exponential Growth and Modeling

Exponential Growth and Modeling Exponential Growth and Modeling Is it Really a Small World After All? I. ASSESSSMENT TASK OVERVIEW & PURPOSE: Students will apply their knowledge of functions and regressions to compare the U.S. population

More information

Exercise 1.12 (Pg. 22-23)

Exercise 1.12 (Pg. 22-23) Individuals: The objects that are described by a set of data. They may be people, animals, things, etc. (Also referred to as Cases or Records) Variables: The characteristics recorded about each individual.

More information

2013 MBA Jump Start Program. Statistics Module Part 3

2013 MBA Jump Start Program. Statistics Module Part 3 2013 MBA Jump Start Program Module 1: Statistics Thomas Gilbert Part 3 Statistics Module Part 3 Hypothesis Testing (Inference) Regressions 2 1 Making an Investment Decision A researcher in your firm just

More information

Basic Statistics and Data Analysis for Health Researchers from Foreign Countries

Basic Statistics and Data Analysis for Health Researchers from Foreign Countries Basic Statistics and Data Analysis for Health Researchers from Foreign Countries Volkert Siersma siersma@sund.ku.dk The Research Unit for General Practice in Copenhagen Dias 1 Content Quantifying association

More information

LAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK DEPARTMENT OF MATHEMATICS, ENGINEERING, AND COMPUTER SCIENCE

LAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK DEPARTMENT OF MATHEMATICS, ENGINEERING, AND COMPUTER SCIENCE LAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK DEPARTMENT OF MATHEMATICS, ENGINEERING, AND COMPUTER SCIENCE MAT 119 STATISTICS AND ELEMENTARY ALGEBRA 5 Lecture Hours, 2 Lab Hours, 3 Credits Pre-

More information

Descriptive Statistics

Descriptive Statistics Descriptive Statistics Descriptive statistics consist of methods for organizing and summarizing data. It includes the construction of graphs, charts and tables, as well various descriptive measures such

More information

1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number

1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number 1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number A. 3(x - x) B. x 3 x C. 3x - x D. x - 3x 2) Write the following as an algebraic expression

More information

Algebra 1 Course Information

Algebra 1 Course Information Course Information Course Description: Students will study patterns, relations, and functions, and focus on the use of mathematical models to understand and analyze quantitative relationships. Through

More information

TIME SERIES ANALYSIS & FORECASTING

TIME SERIES ANALYSIS & FORECASTING CHAPTER 19 TIME SERIES ANALYSIS & FORECASTING Basic Concepts 1. Time Series Analysis BASIC CONCEPTS AND FORMULA The term Time Series means a set of observations concurring any activity against different

More information

A full analysis example Multiple correlations Partial correlations

A full analysis example Multiple correlations Partial correlations A full analysis example Multiple correlations Partial correlations New Dataset: Confidence This is a dataset taken of the confidence scales of 41 employees some years ago using 4 facets of confidence (Physical,

More information

Association Between Variables

Association Between Variables Contents 11 Association Between Variables 767 11.1 Introduction............................ 767 11.1.1 Measure of Association................. 768 11.1.2 Chapter Summary.................... 769 11.2 Chi

More information

The Big Picture. Correlation. Scatter Plots. Data

The Big Picture. Correlation. Scatter Plots. Data The Big Picture Correlation Bret Hanlon and Bret Larget Department of Statistics Universit of Wisconsin Madison December 6, We have just completed a length series of lectures on ANOVA where we considered

More information

Mind on Statistics. Chapter 2

Mind on Statistics. Chapter 2 Mind on Statistics Chapter 2 Sections 2.1 2.3 1. Tallies and cross-tabulations are used to summarize which of these variable types? A. Quantitative B. Mathematical C. Continuous D. Categorical 2. The table

More information

Forecast. Forecast is the linear function with estimated coefficients. Compute with predict command

Forecast. Forecast is the linear function with estimated coefficients. Compute with predict command Forecast Forecast is the linear function with estimated coefficients T T + h = b0 + b1timet + h Compute with predict command Compute residuals Forecast Intervals eˆ t = = y y t+ h t+ h yˆ b t+ h 0 b Time

More information

Assumptions. Assumptions of linear models. Boxplot. Data exploration. Apply to response variable. Apply to error terms from linear model

Assumptions. Assumptions of linear models. Boxplot. Data exploration. Apply to response variable. Apply to error terms from linear model Assumptions Assumptions of linear models Apply to response variable within each group if predictor categorical Apply to error terms from linear model check by analysing residuals Normality Homogeneity

More information

Module 5: Multiple Regression Analysis

Module 5: Multiple Regression Analysis Using Statistical Data Using to Make Statistical Decisions: Data Multiple to Make Regression Decisions Analysis Page 1 Module 5: Multiple Regression Analysis Tom Ilvento, University of Delaware, College

More information

Students summarize a data set using box plots, the median, and the interquartile range. Students use box plots to compare two data distributions.

Students summarize a data set using box plots, the median, and the interquartile range. Students use box plots to compare two data distributions. Student Outcomes Students summarize a data set using box plots, the median, and the interquartile range. Students use box plots to compare two data distributions. Lesson Notes The activities in this lesson

More information

11. Analysis of Case-control Studies Logistic Regression

11. Analysis of Case-control Studies Logistic Regression Research methods II 113 11. Analysis of Case-control Studies Logistic Regression This chapter builds upon and further develops the concepts and strategies described in Ch.6 of Mother and Child Health:

More information

Business Statistics. Successful completion of Introductory and/or Intermediate Algebra courses is recommended before taking Business Statistics.

Business Statistics. Successful completion of Introductory and/or Intermediate Algebra courses is recommended before taking Business Statistics. Business Course Text Bowerman, Bruce L., Richard T. O'Connell, J. B. Orris, and Dawn C. Porter. Essentials of Business, 2nd edition, McGraw-Hill/Irwin, 2008, ISBN: 978-0-07-331988-9. Required Computing

More information

Non-Linear Regression 2006-2008 Samuel L. Baker

Non-Linear Regression 2006-2008 Samuel L. Baker NON-LINEAR REGRESSION 1 Non-Linear Regression 2006-2008 Samuel L. Baker The linear least squares method that you have een using fits a straight line or a flat plane to a unch of data points. Sometimes

More information

Chapter 7 Scatterplots, Association, and Correlation

Chapter 7 Scatterplots, Association, and Correlation 78 Part II Exploring Relationships Between Variables Chapter 7 Scatterplots, Association, and Correlation 1. Association. a) Either weight in grams or weight in ounces could be the explanatory or response

More information

Simple Methods and Procedures Used in Forecasting

Simple Methods and Procedures Used in Forecasting Simple Methods and Procedures Used in Forecasting The project prepared by : Sven Gingelmaier Michael Richter Under direction of the Maria Jadamus-Hacura What Is Forecasting? Prediction of future events

More information

Statistics courses often teach the two-sample t-test, linear regression, and analysis of variance

Statistics courses often teach the two-sample t-test, linear regression, and analysis of variance 2 Making Connections: The Two-Sample t-test, Regression, and ANOVA In theory, there s no difference between theory and practice. In practice, there is. Yogi Berra 1 Statistics courses often teach the two-sample

More information

Introduction to Quantitative Methods

Introduction to Quantitative Methods Introduction to Quantitative Methods October 15, 2009 Contents 1 Definition of Key Terms 2 2 Descriptive Statistics 3 2.1 Frequency Tables......................... 4 2.2 Measures of Central Tendencies.................

More information

1) The table lists the smoking habits of a group of college students. Answer: 0.218

1) The table lists the smoking habits of a group of college students. Answer: 0.218 FINAL EXAM REVIEW Name ) The table lists the smoking habits of a group of college students. Sex Non-smoker Regular Smoker Heavy Smoker Total Man 5 52 5 92 Woman 8 2 2 220 Total 22 2 If a student is chosen

More information

ALGEBRA 2/TRIGONOMETRY

ALGEBRA 2/TRIGONOMETRY ALGEBRA /TRIGONOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA /TRIGONOMETRY Tuesday, June 1, 011 1:15 to 4:15 p.m., only Student Name: School Name: Print your name

More information

Class 19: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.1)

Class 19: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.1) Spring 204 Class 9: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.) Big Picture: More than Two Samples In Chapter 7: We looked at quantitative variables and compared the

More information

NEW YORK STATE TEACHER CERTIFICATION EXAMINATIONS

NEW YORK STATE TEACHER CERTIFICATION EXAMINATIONS NEW YORK STATE TEACHER CERTIFICATION EXAMINATIONS TEST DESIGN AND FRAMEWORK September 2014 Authorized for Distribution by the New York State Education Department This test design and framework document

More information

ANALYSIS OF TREND CHAPTER 5

ANALYSIS OF TREND CHAPTER 5 ANALYSIS OF TREND CHAPTER 5 ERSH 8310 Lecture 7 September 13, 2007 Today s Class Analysis of trends Using contrasts to do something a bit more practical. Linear trends. Quadratic trends. Trends in SPSS.

More information

Chapter 7: Modeling Relationships of Multiple Variables with Linear Regression

Chapter 7: Modeling Relationships of Multiple Variables with Linear Regression Chapter 7: Modeling Relationships of Multiple Variables with Linear Regression Overview Chapters 5 and 6 examined methods to test relationships between two variables. Many research projects, however, require

More information

Linear Regression. use http://www.stat.columbia.edu/~martin/w1111/data/body_fat. 30 35 40 45 waist

Linear Regression. use http://www.stat.columbia.edu/~martin/w1111/data/body_fat. 30 35 40 45 waist Linear Regression In this tutorial we will explore fitting linear regression models using STATA. We will also cover ways of re-expressing variables in a data set if the conditions for linear regression

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Module 7 Test Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. You are given information about a straight line. Use two points to graph the equation.

More information

COMMON CORE STATE STANDARDS FOR

COMMON CORE STATE STANDARDS FOR COMMON CORE STATE STANDARDS FOR Mathematics (CCSSM) High School Statistics and Probability Mathematics High School Statistics and Probability Decisions or predictions are often based on data numbers in

More information

What is the purpose of this document? What is in the document? How do I send Feedback?

What is the purpose of this document? What is in the document? How do I send Feedback? This document is designed to help North Carolina educators teach the Common Core (Standard Course of Study). NCDPI staff are continually updating and improving these tools to better serve teachers. Statistics

More information

Correlation key concepts:

Correlation key concepts: CORRELATION Correlation key concepts: Types of correlation Methods of studying correlation a) Scatter diagram b) Karl pearson s coefficient of correlation c) Spearman s Rank correlation coefficient d)

More information

Eight things you need to know about interpreting correlations:

Eight things you need to know about interpreting correlations: Research Skills One, Correlation interpretation, Graham Hole v.1.0. Page 1 Eight things you need to know about interpreting correlations: A correlation coefficient is a single number that represents the

More information

F.IF.7b: Graph Root, Piecewise, Step, & Absolute Value Functions

F.IF.7b: Graph Root, Piecewise, Step, & Absolute Value Functions F.IF.7b: Graph Root, Piecewise, Step, & Absolute Value Functions F.IF.7b: Graph Root, Piecewise, Step, & Absolute Value Functions Analyze functions using different representations. 7. Graph functions expressed

More information

Pearson Algebra 1 Common Core 2015

Pearson Algebra 1 Common Core 2015 A Correlation of Pearson Algebra 1 Common Core 2015 To the Common Core State Standards for Mathematics Traditional Pathways, Algebra 1 High School Copyright 2015 Pearson Education, Inc. or its affiliate(s).

More information

Introduction to Regression and Data Analysis

Introduction to Regression and Data Analysis Statlab Workshop Introduction to Regression and Data Analysis with Dan Campbell and Sherlock Campbell October 28, 2008 I. The basics A. Types of variables Your variables may take several forms, and it

More information