# Chapter 4 Describing the Relation between Two Variables

Save this PDF as:

Size: px
Start display at page:

Download "Chapter 4 Describing the Relation between Two Variables"

## Transcription

1 Chapter 4 Describing the Relation between Two Variables 4.1 Scatter Diagrams and Correlation The response variable is the variable whose value can be explained by the value of the explanatory or predictor variable. A scatter diagram is a graph that shows the relationship between two quantitative variables measured on the same individual. Each individual in the data set is represented by a point in the scatter diagram. I. Scatter plot (x) # hour of sleep (y) performance

2 II. Linear Correlation coefficient (r) The linear correlation coefficient or Pearson product moment correlation coefficient is a measure of the strength and direction of the linear relation between two quantitative variables. The Greek letter ρ (rho) represents the population correlation coefficient, and r represents the sample correlation coefficient. We present only the formula for the sample correlation coefficient. Sample Linear Correlation Coefficient r i x x y i y sx sy n 1 where x is the sample mean of the explanatory variable s x is the sample standard deviation of the explanatory variable y is the sample mean of the response variable s y is the sample standard deviation of the response variable n is the number of individuals in the sample Properties of the Linear Correlation Coefficient 1. The linear correlation coefficient is always between 1 and 1, inclusive. That is, 1 r If r = + 1, then a perfect positive linear relation exists between the two variables. 3. If r = 1, then a perfect negative linear relation exists between the two variables. 4. The closer r is to +1, the stronger is the evidence of positive association between the two variables. 5. The closer r is to 1, the stronger is the evidence of negative association between the two variables. 6. If r is close to 0, then little or no evidence exists of a linear relation between the two variables. So r close to 0 does not imply a relation, just no linear relation. 7. The linear correlation coefficient is a unitless measure of association. So the unit of measure for x and y plays no role in the interpretation of r. 8. The correlation coefficient is not resistant. Therefore, an observation that does not follow the overall pattern of the data could affect the value of the linear correlation coefficient. 2

3 EXAMPLE Determining the Linear Correlation Coefficient Use StatCrunch to determine the linear correlation coefficient of the drilling data. Open StatCrunch Input Data Stat Summary stats Correlation select column(s) Click the 1st variable, and click the 2nd variable while holding the ctrl key compute. Testing for a Linear Relation Step 1 Determine the absolute value of the correlation coefficient Step 2 Find the critical value in Table II from Appendix A for the given sample size Step 3 If the absolute value of the correlation coefficient is greater than the critical value, we say a linear relation exists between the two variables. Otherwise, no linear relation exists. 3

4 EXAMPLE Does a Linear Relation Exist? The correlation between drilling depth and time to drill is The critical value for n = 12 observations is Since > 0.576, there is a positive linear relation between time to drill five feet and depth at which drilling begins. 4.2 Least-Squares Regression EXAMPLE Finding an Equation that Describes Linearly Related Data Using the following sample data: (a) Find a linear equation that relates x (the explanatory variable) and y (the response variable) by selecting two points and finding the equation of the line containing the points. Using (2, 5.7) and (6, 1.9) m = =

5 (b) Graph the equation on the scatter diagram. (c) Use the equation to predict y if x = 3. The difference between the observed value of y and the predicted value of y is the error, or residual. Using the line from the last example, and the predicted value at x = 3: residual = observed y predicted y Least-Squares Regression Criterion If there is positive / negative correlation between x and y; find the best fitted line for the data. The least-squares regression line is the line that minimizes the sum of the squared errors (or residuals). This line minimizes the sum of the squared vertical distance between the observed values of y and those predicted by the line ŷ, ( y-hat ). We represent this as minimize Σresiduals 2 (minimizes the sum of the squared errors). The Least-Squares Regression Line The equation of the least-squares regression line is given by where b 1 = r * S y S x is the slope of the least-squares regression line and b 0 = y - b 1 x is the y-intercept of the least-squares regression line. 5

6 The Least-Squares Regression Line Note: x is the sample mean and s x is the sample standard deviation of the explanatory variable x; y is the sample mean and s y is the sample standard deviation of the response variable y. EXAMPLE Finding the Least-squares Regression Line Using the drilling data (a) Find the least-squares regression line using StatCrunch Open StatCrunch Input Data Stat Regression Simple linear Select 1st variable for x variable, and select 2nd variable for y variable Compute (b) Predict the drilling time if drilling starts at 130 feet. (c) Is the observed drilling time at 130 feet above, or below, average. The observed drilling time is 6.93 seconds. The predicted drilling time is seconds. The drilling time of 6.93 seconds is below average. (d) Draw the least-squares regression line on the scatter diagram of the data. 6

7 Interpretation of Slope: The slope of the regression line is For each additional foot of depth we start drilling, the time to drill five feet increases by minutes, on average. Interpretation of the y-intercept: The y-intercept of the regression line is To interpret the y-intercept, we must first ask two questions: 1. Is 0 a reasonable value for the explanatory variable? 2. Do any observations near x = 0 exist in the data set? A value of 0 is reasonable for the drilling data (this indicates that drilling begins at the surface of Earth. The smallest observation in the data set is x = 35 feet, which is reasonably close to 0. So, interpretation of the y-intercept is reasonable. The time to drill five feet when we begin drilling at the surface of Earth is minutes. Caution: If the least-squares regression line is used to make predictions based on values of the explanatory variable that are much larger or much smaller than the observed values, we say the researcher is working outside the scope of the model. Never use a least-squares regression line to make predictions outside the scope of the model because we can t be sure the linear relation continues to exist. Predictions When There is No Linear Relation: When the correlation coefficient indicates no linear relation between the explanatory and response variables, and the scatter diagram indicates no relation at all between the variables, then we use the mean value of the response variables, then we use the mean value of the response variable as the predicted value so that ŷ y Summary 1. Use StatCrunch to plot a scatter plot 2. Use StatCrunch to calculate r 3. Determine whether there is a positive/negative linear correlation between X and Y. 4. If there is a linear correlation between X and Y, use StatCrunch to find the least squares regression line. Otherwise, do not find the least squares regression line. 7

8 5. When a value is assigned to X if there is a correlation between X and Y, use the least squares regression line to find the best predicted Y. 6. When a value is assigned to X if there is no correlation between X and Y, use StatCrunch to find y and the best predicted Y is y for any X. 8

### Chapter 9. Section Correlation

Chapter 9 Section 9.1 - Correlation Objectives: Introduce linear correlation, independent and dependent variables, and the types of correlation Find a correlation coefficient Test a population correlation

Using Your TI-NSpire Calculator: Linear Correlation and Regression Dr. Laura Schultz Statistics I This handout describes how to use your calculator for various linear correlation and regression applications.

### Correlation. What Is Correlation? Perfect Correlation. Perfect Correlation. Greg C Elvers

Correlation Greg C Elvers What Is Correlation? Correlation is a descriptive statistic that tells you if two variables are related to each other E.g. Is your related to how much you study? When two variables

### Chapter 13 Introduction to Linear Regression and Correlation Analysis

Chapter 3 Student Lecture Notes 3- Chapter 3 Introduction to Linear Regression and Correlation Analsis Fall 2006 Fundamentals of Business Statistics Chapter Goals To understand the methods for displaing

### Using Minitab for Regression Analysis: An extended example

Using Minitab for Regression Analysis: An extended example The following example uses data from another text on fertilizer application and crop yield, and is intended to show how Minitab can be used to

### , has mean A) 0.3. B) the smaller of 0.8 and 0.5. C) 0.15. D) which cannot be determined without knowing the sample results.

BA 275 Review Problems - Week 9 (11/20/06-11/24/06) CD Lessons: 69, 70, 16-20 Textbook: pp. 520-528, 111-124, 133-141 An SRS of size 100 is taken from a population having proportion 0.8 of successes. An

### 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

### table to see that the probability is 0.8413. (b) What is the probability that x is between 16 and 60? The z-scores for 16 and 60 are: 60 38 = 1.

Review Problems for Exam 3 Math 1040 1 1. Find the probability that a standard normal random variable is less than 2.37. Looking up 2.37 on the normal table, we see that the probability is 0.9911. 2. Find

### 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

### 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.

### Sydney Roberts Predicting Age Group Swimmers 50 Freestyle Time 1. 1. Introduction p. 2. 2. Statistical Methods Used p. 5. 3. 10 and under Males p.

Sydney Roberts Predicting Age Group Swimmers 50 Freestyle Time 1 Table of Contents 1. Introduction p. 2 2. Statistical Methods Used p. 5 3. 10 and under Males p. 8 4. 11 and up Males p. 10 5. 10 and under

### 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

### The aspect of the data that we want to describe/measure is the degree of linear relationship between and The statistic r describes/measures the degree

PS 511: Advanced Statistics for Psychological and Behavioral Research 1 Both examine linear (straight line) relationships Correlation works with a pair of scores One score on each of two variables ( and

### Using Excel for Statistical Analysis

Using Excel for Statistical Analysis You don t have to have a fancy pants statistics package to do many statistical functions. Excel can perform several statistical tests and analyses. First, make sure

### 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)

### Regents Exam Questions A2.S.8: Correlation Coefficient

A2.S.8: Correlation Coefficient: Interpret within the linear regression model the value of the correlation coefficient as a measure of the strength of the relationship 1 Which statement regarding correlation

### 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) -

### 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

### WEB APPENDIX. Calculating Beta Coefficients. b Beta Rise Run Y 7.1 1 8.92 X 10.0 0.0 16.0 10.0 1.6

WEB APPENDIX 8A Calculating Beta Coefficients The CAPM is an ex ante model, which means that all of the variables represent before-thefact, expected values. In particular, the beta coefficient used in

### 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

### Regression III: Advanced Methods

Lecture 5: Linear least-squares Regression III: Advanced Methods William G. Jacoby Department of Political Science Michigan State University http://polisci.msu.edu/jacoby/icpsr/regress3 Simple Linear 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

### SIMPLE REGRESSION ANALYSIS

SIMPLE REGRESSION ANALYSIS Introduction. Regression analysis is used when two or more variables are thought to be systematically connected by a linear relationship. In simple regression, we have only two

### 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

### Scatter Plot, Correlation, and Regression on the TI-83/84

Scatter Plot, Correlation, and Regression on the TI-83/84 Summary: When you have a set of (x,y) data points and want to find the best equation to describe them, you are performing a regression. This page

### Yiming Peng, Department of Statistics. February 12, 2013

Regression Analysis Using JMP Yiming Peng, Department of Statistics February 12, 2013 2 Presentation and Data http://www.lisa.stat.vt.edu Short Courses Regression Analysis Using JMP Download Data to Desktop

### Technology Step-by-Step Using StatCrunch

Technology Step-by-Step Using StatCrunch Section 1.3 Simple Random Sampling 1. Select Data, highlight Simulate Data, then highlight Discrete Uniform. 2. Fill in the following window with the appropriate

### Plot the following two points on a graph and draw the line that passes through those two points. Find the rise, run and slope of that line.

Objective # 6 Finding the slope of a line Material: page 117 to 121 Homework: worksheet NOTE: When we say line... we mean straight line! Slope of a line: It is a number that represents the slant of a line

### Session 7 Bivariate Data and Analysis

Session 7 Bivariate Data and Analysis Key Terms for This Session Previously Introduced mean standard deviation New in This Session association bivariate analysis contingency table co-variation least squares

### Stats Review Chapters 3-4

Stats Review Chapters 3-4 Created by Teri Johnson Math Coordinator, Mary Stangler Center for Academic Success Examples are taken from Statistics 4 E by Michael Sullivan, III And the corresponding Test

### Simple Regression Theory I 2010 Samuel L. Baker

SIMPLE REGRESSION THEORY I 1 Simple Regression Theory I 2010 Samuel L. Baker Regression analysis lets you use data to explain and predict. A simple regression line drawn through data points In Assignment

### Chapter 10 - Practice Problems 1

Chapter 10 - Practice Problems 1 1. A researcher is interested in determining if one could predict the score on a statistics exam from the amount of time spent studying for the exam. In this study, the

### 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

### e = random error, assumed to be normally distributed with mean 0 and standard deviation σ

1 Linear Regression 1.1 Simple Linear Regression Model The linear regression model is applied if we want to model a numeric response variable and its dependency on at least one numeric factor variable.

### Elementary Statistics. Scatter Plot, Regression Line, Linear Correlation Coefficient, and Coefficient of Determination

Scatter Plot, Regression Line, Linear Correlation Coefficient, and Coefficient of Determination What is a Scatter Plot? A Scatter Plot is a plot of ordered pairs (x, y) where the horizontal axis is used

### Lesson Lesson Outline Outline

Lesson 15 Linear Regression Lesson 15 Outline Review correlation analysis Dependent and Independent variables Least Squares Regression line Calculating l the slope Calculating the Intercept Residuals and

### Unit 11: Fitting Lines to Data

Unit 11: Fitting Lines to Data Summary of Video Scatterplots are a great way to visualize the relationship between two quantitative variables. For example, the scatterplot of temperatures and coral reef

### Algebra Cheat Sheets

Sheets Algebra Cheat Sheets provide you with a tool for teaching your students note-taking, problem-solving, and organizational skills in the context of algebra lessons. These sheets teach the concepts

### Chapter 5. Regression

Topics covered in this chapter: Chapter 5. Regression Adding a Regression Line to a Scatterplot Regression Lines and Influential Observations Finding the Least Squares Regression Model Adding a Regression

### Pearson s correlation

Pearson s correlation Introduction Often several quantitative variables are measured on each member of a sample. If we consider a pair of such variables, it is frequently of interest to establish if there

### Correlation A relationship between two variables As one goes up, the other changes in a predictable way (either mostly goes up or mostly goes down)

Two-Variable Statistics Correlation A relationship between two variables As one goes up, the other changes in a predictable way (either mostly goes up or mostly goes down) Positive Correlation As one variable

### Monopoly and Regression

Math Objectives Students will analyze the linear association between two variables and interpret the association in the context of a given scenario. Students will calculate a least-squares regression line

### 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)

### Chapter 23. Inferences for Regression

Chapter 23. Inferences for Regression Topics covered in this chapter: Simple Linear Regression Simple Linear Regression Example 23.1: Crying and IQ The Problem: Infants who cry easily may be more easily

### Mind on Statistics. Chapter 3

Mind on Statistics Chapter 3 Section 3.1 1. Which one of the following is not appropriate for studying the relationship between two quantitative variables? A. Scatterplot B. Bar chart C. Correlation D.

### 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.

### 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

### 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

### The importance of graphing the data: Anscombe s regression examples

The importance of graphing the data: Anscombe s regression examples Bruce Weaver Northern Health Research Conference Nipissing University, North Bay May 30-31, 2008 B. Weaver, NHRC 2008 1 The Objective

### Practice Test - Chapter 4. y = 2x 3. The slope-intercept form of a line is y = mx + b, where m is the slope, and b is the y-intercept.

y = 2x 3. The slope-intercept form of a line is y = mx + b, where m is the slope, and b is the y-intercept. Plot the y-intercept (0, 3). The slope is. From (0, 3), move up 2 units and right 1 unit. Plot

### 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

### the Median-Medi Graphing bivariate data in a scatter plot

the Median-Medi Students use movie sales data to estimate and draw lines of best fit, bridging technology and mathematical understanding. david c. Wilson Graphing bivariate data in a scatter plot and drawing

### Dealing with Data in Excel 2010

Dealing with Data in Excel 2010 Excel provides the ability to do computations and graphing of data. Here we provide the basics and some advanced capabilities available in Excel that are useful for dealing

### When it is not in our power to determine what is true, we ought to follow what is most probable.

10 10.1 Scatter Diagrams and Linear Correlation 10.2 Linear Regression and the Coefficient of Determination 10.3 Inferences for Correlation and Regression 10.4 Multiple Regression When it is not in our

### 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

### Regression III: Advanced Methods

Lecture 16: Generalized Additive Models Regression III: Advanced Methods Bill Jacoby Michigan State University http://polisci.msu.edu/jacoby/icpsr/regress3 Goals of the Lecture Introduce Additive Models

Using Your TI-83/84 Calculator: Linear Correlation and Regression Elementary Statistics Dr. Laura Schultz This handout describes how to use your calculator for various linear correlation and regression

### Regression. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

Class: Date: Regression Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Given the least squares regression line y8 = 5 2x: a. the relationship between

### Simple Linear Regression in SPSS STAT 314

Simple Linear Regression in SPSS STAT 314 1. Ten Corvettes between 1 and 6 years old were randomly selected from last year s sales records in Virginia Beach, Virginia. The following data were obtained,

### NCSS Statistical Software Principal Components Regression. In ordinary least squares, the regression coefficients are estimated using the formula ( )

Chapter 340 Principal Components Regression Introduction is a technique for analyzing multiple regression data that suffer from multicollinearity. When multicollinearity occurs, least squares estimates

### 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

### 2. Simple Linear Regression

Research methods - II 3 2. Simple Linear Regression Simple linear regression is a technique in parametric statistics that is commonly used for analyzing mean response of a variable Y which changes according

### 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.

### Chapter 14: Analyzing Relationships Between Variables

Chapter Outlines for: Frey, L., Botan, C., & Kreps, G. (1999). Investigating communication: An introduction to research methods. (2nd ed.) Boston: Allyn & Bacon. Chapter 14: Analyzing Relationships Between

### The Dummy s Guide to Data Analysis Using SPSS

The Dummy s Guide to Data Analysis Using SPSS Mathematics 57 Scripps College Amy Gamble April, 2001 Amy Gamble 4/30/01 All Rights Rerserved TABLE OF CONTENTS PAGE Helpful Hints for All Tests...1 Tests

### 04 Paired Data and Scatter Diagrams

Paired Data and Scatter Diagrams Best Fit Lines: Linear Regressions A runner runs from the College of Micronesia- FSM National campus to PICS via the powerplant/nahnpohnmal back road The runner tracks

### 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

### Simple Regression and Correlation

Simple Regression and Correlation Today, we are going to discuss a powerful statistical technique for examining whether or not two variables are related. Specifically, we are going to talk about the ideas

### Linear Regression and Correlation

Chapter 12 Linear Regression and Correlation 12.1 Linear Regression and Correlation 1 12.1.1 Student Learning Objectives By the end of this chapter, the student should be able to: Discuss basic ideas of

### SPSS Guide: Regression Analysis

SPSS Guide: Regression Analysis I put this together to give you a step-by-step guide for replicating what we did in the computer lab. It should help you run the tests we covered. The best way to get familiar

### 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

### 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

### 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)

### Simple Regression Theory II 2010 Samuel L. Baker

SIMPLE REGRESSION THEORY II 1 Simple Regression Theory II 2010 Samuel L. Baker Assessing how good the regression equation is likely to be Assignment 1A gets into drawing inferences about how close the

### 4. Describing Bivariate Data

4. Describing Bivariate Data A. Introduction to Bivariate Data B. Values of the Pearson Correlation C. Properties of Pearson's r D. Computing Pearson's r E. Variance Sum Law II F. Exercises A dataset with

### Curve Fitting in Microsoft Excel By William Lee

Curve Fitting in Microsoft Excel By William Lee This document is here to guide you through the steps needed to do curve fitting in Microsoft Excel using the least-squares method. In mathematical equations

### Population Prediction Project Demonstration Writeup

Dylan Zwick Math 2280 Spring, 2008 University of Utah Population Prediction Project Demonstration Writeup In this project we will investigate how well a logistic population model predicts actual human

### Coefficient of Determination

Coefficient of Determination The coefficient of determination R 2 (or sometimes r 2 ) is another measure of how well the least squares equation ŷ = b 0 + b 1 x performs as a predictor of y. R 2 is computed

### CHAPTER 13 SIMPLE LINEAR REGRESSION. Opening Example. Simple Regression. Linear Regression

Opening Example CHAPTER 13 SIMPLE LINEAR REGREION SIMPLE LINEAR REGREION! Simple Regression! Linear Regression Simple Regression Definition A regression model is a mathematical equation that descries the

### Calculate Confidence Intervals Using the TI Graphing Calculator

Calculate Confidence Intervals Using the TI Graphing Calculator Confidence Interval for Population Proportion p Confidence Interval for Population μ (σ is known 1 Select: STAT / TESTS / 1-PropZInt x: number

### Regression, least squares

Regression, least squares Joe Felsenstein Department of Genome Sciences and Department of Biology Regression, least squares p.1/24 Fitting a straight line X Two distinct cases: The X values are chosen

### Mathematics Online Instructional Materials Correlation to the 2009 Algebra I Standards of Learning and Curriculum Framework

Provider York County School Division Course Syllabus URL http://yorkcountyschools.org/virtuallearning/coursecatalog.aspx Course Title Algebra I AB Last Updated 2010 - A.1 The student will represent verbal

### 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

### Activity 10 Regression Lines

Activity 10 Regression Lines Topic Area: Data Analysis and Probability NCTM Standard: Select and use appropriate statistical methods to analyze data. Objective: The student will be able to utilize the

### Data Mining Part 5. Prediction

Data Mining Part 5. Prediction 5.7 Spring 2010 Instructor: Dr. Masoud Yaghini Outline Introduction Linear Regression Other Regression Models References Introduction Introduction Numerical prediction is

### CHAPTER 10 REGRESSION AND CORRELATION

CHAPTER 10 REGRESSION AND CORRELATION LINEAR REGRESSION (SECTION 10.1 10.3 OF UNDERSTANDABLE STATISTICS) Important Note: Before beginning this chapter, press y[catalog] (above Ê) and scroll down to the

### hp calculators HP 50g Trend Lines The STAT menu Trend Lines Practice predicting the future using trend lines

The STAT menu Trend Lines Practice predicting the future using trend lines The STAT menu The Statistics menu is accessed from the ORANGE shifted function of the 5 key by pressing Ù. When pressed, a CHOOSE

### SIMPLE LINEAR CORRELATION. r can range from -1 to 1, and is independent of units of measurement. Correlation can be done on two dependent variables.

SIMPLE LINEAR CORRELATION Simple linear correlation is a measure of the degree to which two variables vary together, or a measure of the intensity of the association between two variables. Correlation

### 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

### (Least Squares Investigation)

(Least Squares Investigation) o Open a new sketch. Select Preferences under the Edit menu. Select the Text Tab at the top. Uncheck both boxes under the title Show Labels Automatically o Create two points

### Using Excel (Microsoft Office 2007 Version) for Graphical Analysis of Data

Using Excel (Microsoft Office 2007 Version) for Graphical Analysis of Data Introduction In several upcoming labs, a primary goal will be to determine the mathematical relationship between two variable

### CORRELATION ANALYSIS

CORRELATION ANALYSIS Learning Objectives Understand how correlation can be used to demonstrate a relationship between two factors. Know how to perform a correlation analysis and calculate the coefficient

### Tutorial for the TI-89 Titanium Calculator

SI Physics Tutorial for the TI-89 Titanium Calculator Using Scientific Notation on a TI-89 Titanium calculator From Home, press the Mode button, then scroll down to Exponential Format. Select Scientific.

### Least Squares Regression. Alan T. Arnholt Department of Mathematical Sciences Appalachian State University arnholt@math.appstate.

Least Squares Regression Alan T. Arnholt Department of Mathematical Sciences Appalachian State University arnholt@math.appstate.edu Spring 2006 R Notes 1 Copyright c 2006 Alan T. Arnholt 2 Least Squares

### AP Statistics Section :12.2 Transforming to Achieve Linearity

AP Statistics Section :12.2 Transforming to Achieve Linearity In Chapter 3, we learned how to analyze relationships between two quantitative variables that showed a linear pattern. When two-variable data

### 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.

### 17.0 Linear Regression

17.0 Linear Regression 1 Answer Questions Lines Correlation Regression 17.1 Lines The algebraic equation for a line is Y = β 0 + β 1 X 2 The use of coordinate axes to show functional relationships was

### Experiment #1, Analyze Data using Excel, Calculator and Graphs.

Physics 182 - Fall 2014 - Experiment #1 1 Experiment #1, Analyze Data using Excel, Calculator and Graphs. 1 Purpose (5 Points, Including Title. Points apply to your lab report.) Before we start measuring