Linear Regression and Correlation. February 11, 2009
|
|
- Jesse O’Brien’
- 5 years ago
- Views:
Transcription
1 Linear Regression and Correlation February 11, 2009
2 The Big Ideas To understand a set of data, start with a graph or graphs.
3 The Big Ideas To understand a set of data, start with a graph or graphs. If the data concern the relationship between two quantitative variables measured on the same individuals, use a scatterplot. If the variables have an explanatory-response relationship, be sure to put the explanatory variable on the horizontal (x) axis of the plot.
4 The Big Ideas When you look at a statistical graph, look for the overall pattern and for striking deviations from that pattern. Thanks to David S. Moore and W.H. Freeman and Company for this summary.
5 The Big Ideas When you look at a statistical graph, look for the overall pattern and for striking deviations from that pattern. When you look at a scatterplot, describe the overall pattern by its form, direction, and strength. Outliers are an important kind of deviation from the pattern. Thanks to David S. Moore and W.H. Freeman and Company for this summary.
6 The Big Ideas When you look at a statistical graph, look for the overall pattern and for striking deviations from that pattern. When you look at a scatterplot, describe the overall pattern by its form, direction, and strength. Outliers are an important kind of deviation from the pattern. If the overall pattern is roughly linear (straight-line), the correlation r measures its direction and strength. Thanks to David S. Moore and W.H. Freeman and Company for this summary.
7 Linear Equations y = a + bx These describe straight lines.
8 Linear Equations y = a + bx These describe straight lines. The constant a is the y-intercept.
9 Linear Equations y = a + bx These describe straight lines. The constant a is the y-intercept. The constant b is the slope.
10 Linear Equations y = a + bx These describe straight lines. The constant a is the y-intercept. The constant b is the slope. The variable x is the independent or explanatory variable.
11 Linear Equations y = a + bx These describe straight lines. The constant a is the y-intercept. The constant b is the slope. The variable x is the independent or explanatory variable. The variable y is the dependent orresponses variable.
12 Example 1 African peoples often eat bushmeat, the meat of wild animals. Thanks to David S. Moore and W.H. Freeman and Company for this example.
13 Example 1 African peoples often eat bushmeat, the meat of wild animals. The explanatory variable is sh supply per person, in kilograms. Thanks to David S. Moore and W.H. Freeman and Company for this example.
14 Example 1 African peoples often eat bushmeat, the meat of wild animals. The explanatory variable is sh supply per person, in kilograms. The response is the percent change in the total biomass (weight in tons). Thanks to David S. Moore and W.H. Freeman and Company for this example.
15 Analyzing Relationships Form: There is a general linear (straight-line) pattern.
16 Analyzing Relationships Form: There is a general linear (straight-line) pattern. Direction: The plot has a clear lower-left to upper-right pattern, so that more positive (or less negative) changes in wildlife go with higher sh supply. This is a positive association between the variables.
17 Analyzing Relationships Form: There is a general linear (straight-line) pattern. Direction: The plot has a clear lower-left to upper-right pattern, so that more positive (or less negative) changes in wildlife go with higher sh supply. This is a positive association between the variables. Strength: The idea of the strength of a relationship is how closely the points follow the overall pattern. A perfectly strong linear relationship means that all points fall exactly on a straight line. The relationship here is moderately strong.
18 Line of Best Fit We can make predictions about the response variable based on the explanatory variable by finding points on a line that best fits the data.
19 Line of Best Fit We can make predictions about the response variable based on the explanatory variable by finding points on a line that best fits the data. We use software to find this line of best fit.
20 Line of Best Fit We can make predictions about the response variable based on the explanatory variable by finding points on a line that best fits the data. We use software to find this line of best fit. Our responsibility is to check to see that the line is sensible and then interpret the value of the predictions.
21 Line of Best Fit The regression equation is the equation of the line of best fit y = a + bx
22 Line of Best Fit The regression equation is the equation of the line of best fit y = a + bx A y values on the line is a predicted value of the response variable for a given explanatory value.
23 Line of Best Fit The regression equation is the equation of the line of best fit y = a + bx A y values on the line is a predicted value of the response variable for a given explanatory value. We use the notation ŷ for predicted values and y for observed values. Thus ŷ 0 = a + bx 0 is the value of the response variable that is predicted by the regression equation for the explanatory value x 0.
24 Errors The error or residual measures the distance between the predicted response to a given explanatory value and the actual response for that explanatory value
25 Errors The error or residual measures the distance between the predicted response to a given explanatory value and the actual response for that explanatory value i.e. the vertical distance between the line and the data. We use the notation ɛ for the error. So, for a data point (x i, y i ) we have ɛ i = y i ŷ i
26 Example 2 Life expectancy and the percent of people who can read.
27 Sum of the Squared Errors SSE stands for the Sum of the Squared Errors.
28 Sum of the Squared Errors SSE stands for the Sum of the Squared Errors. In symbols we have SSE = n ɛ 2 i = i n (y i ŷ) 2 i
29 Sum of the Squared Errors SSE stands for the Sum of the Squared Errors. In symbols we have SSE = n ɛ 2 i = i n (y i ŷ) 2 i The line of best fit is the line that minimizes the SSE.
30 The Correlation Coefficient r The correlation coefficient r measures how strong the relationship is between the the variables.
31 The Correlation Coefficient r The correlation coefficient r measures how strong the relationship is between the the variables. We always have r bounded by ±1. 1 r 1
32 The Correlation Coefficient r The correlation coefficient r measures how strong the relationship is between the the variables. We always have r bounded by ±1. 1 r 1 The bigger the absolute value of r, the stronger the relationship. r = 1 means there is a perfect positive relationship between the variables. r = 0 means there is absolutely no relationship between the variables. r = 1 means there is a perfect negative relationship between the variables.
33 Textbook See page 484 of the text for pictures about positive, negative and zero correlation.
34 Textbook See page 484 of the text for pictures about positive, negative and zero correlation. See page 491 of the text for strength guidelines.
35 Example: Exercise vs. Screen Time What kind of correlation do we expect from the data in our class?
36 Outliers If an error is more than 1.9s than we consider the corresponding data to be a potential outlier. The value of the standard deviation s is s = SSE n 2 = n i ɛ 2 i = n i (y i ŷ) 2 n 2
Chapter 6: Exploring Data: Relationships Lesson Plan
Chapter 6: Exploring Data: Relationships Lesson Plan For All Practical Purposes Displaying Relationships: Scatterplots Mathematical Literacy in Today s World, 9th ed. Making Predictions: Regression Line
More informationChapter 3: Describing Relationships
Chapter 3: Describing Relationships Section 3.2 The Practice of Statistics, 4 th edition For AP* STARNES, YATES, MOORE Chapter 3 Describing Relationships 3.1 Scatterplots and Correlation 3.2 Section 3.2
More informationBIOSTATISTICS NURS 3324
Simple Linear Regression and Correlation Introduction Previously, our attention has been focused on one variable which we designated by x. Frequently, it is desirable to learn something about the relationship
More informationChapter 3: Describing Relationships
Chapter 3: Describing Relationships Section 3.2 The Practice of Statistics, 4 th edition For AP* STARNES, YATES, MOORE Chapter 3 Describing Relationships 3.1 Scatterplots and Correlation 3.2 Section 3.2
More informationDetermine is the equation of the LSRL. Determine is the equation of the LSRL of Customers in line and seconds to check out.. Chapter 3, Section 2
3.2c Computer Output, Regression to the Mean, & AP Formulas Be sure you can locate: the slope, the y intercept and determine the equation of the LSRL. Slope is always in context and context is x value.
More informationAMS 7 Correlation and Regression Lecture 8
AMS 7 Correlation and Regression Lecture 8 Department of Applied Mathematics and Statistics, University of California, Santa Cruz Suumer 2014 1 / 18 Correlation pairs of continuous observations. Correlation
More informationCHAPTER 3 Describing Relationships
CHAPTER 3 Describing Relationships 3.1 Scatterplots and Correlation The Practice of Statistics, 5th Edition Starnes, Tabor, Yates, Moore Bedford Freeman Worth Publishers Scatterplots and Correlation Learning
More informationStat 101: Lecture 6. Summer 2006
Stat 101: Lecture 6 Summer 2006 Outline Review and Questions Example for regression Transformations, Extrapolations, and Residual Review Mathematical model for regression Each point (X i, Y i ) in the
More informationScatterplots and Correlation
Bivariate Data Page 1 Scatterplots and Correlation Essential Question: What is the correlation coefficient and what does it tell you? Most statistical studies examine data on more than one variable. Fortunately,
More informationChapter 7. Scatterplots, Association, and Correlation
Chapter 7 Scatterplots, Association, and Correlation Bin Zou (bzou@ualberta.ca) STAT 141 University of Alberta Winter 2015 1 / 29 Objective In this chapter, we study relationships! Instead, we investigate
More information9. Linear Regression and Correlation
9. Linear Regression and Correlation Data: y a quantitative response variable x a quantitative explanatory variable (Chap. 8: Recall that both variables were categorical) For example, y = annual income,
More informationChapter 4 Describing the Relation between Two Variables
Chapter 4 Describing the Relation between Two Variables 4.1 Scatter Diagrams and Correlation The is the variable whose value can be explained by the value of the or. A is a graph that shows the relationship
More informationImportant note: Transcripts are not substitutes for textbook assignments. 1
In this lesson we will cover correlation and regression, two really common statistical analyses for quantitative (or continuous) data. Specially we will review how to organize the data, the importance
More information7.0 Lesson Plan. Regression. Residuals
7.0 Lesson Plan Regression Residuals 1 7.1 More About Regression Recall the regression assumptions: 1. Each point (X i, Y i ) in the scatterplot satisfies: Y i = ax i + b + ɛ i where the ɛ i have a normal
More informationObjectives. 2.3 Least-squares regression. Regression lines. Prediction and Extrapolation. Correlation and r 2. Transforming relationships
Objectives 2.3 Least-squares regression Regression lines Prediction and Extrapolation Correlation and r 2 Transforming relationships Adapted from authors slides 2012 W.H. Freeman and Company Straight Line
More informationRelationships Regression
Relationships Regression BPS chapter 5 2006 W.H. Freeman and Company Objectives (BPS chapter 5) Regression Regression lines The least-squares regression line Using technology Facts about least-squares
More information3.2: Least Squares Regressions
3.2: Least Squares Regressions Section 3.2 Least-Squares Regression After this section, you should be able to INTERPRET a regression line CALCULATE the equation of the least-squares regression line CALCULATE
More informationLinear Regression. Linear Regression. Linear Regression. Did You Mean Association Or Correlation?
Did You Mean Association Or Correlation? AP Statistics Chapter 8 Be careful not to use the word correlation when you really mean association. Often times people will incorrectly use the word correlation
More informationChapter 5 Friday, May 21st
Chapter 5 Friday, May 21 st Overview In this Chapter we will see three different methods we can use to describe a relationship between two quantitative variables. These methods are: Scatterplot Correlation
More informationStatistical View of Least Squares
Basic Ideas Some Examples Least Squares May 22, 2007 Basic Ideas Simple Linear Regression Basic Ideas Some Examples Least Squares Suppose we have two variables x and y Basic Ideas Simple Linear Regression
More informationDescribing the Relationship between Two Variables
1 Describing the Relationship between Two Variables Key Definitions Scatter : A graph made to show the relationship between two different variables (each pair of x s and y s) measured from the same equation.
More informationChapter 2: Looking at Data Relationships (Part 3)
Chapter 2: Looking at Data Relationships (Part 3) Dr. Nahid Sultana Chapter 2: Looking at Data Relationships 2.1: Scatterplots 2.2: Correlation 2.3: Least-Squares Regression 2.5: Data Analysis for Two-Way
More informationStatistical View of Least Squares
May 23, 2006 Purpose of Regression Some Examples Least Squares Purpose of Regression Purpose of Regression Some Examples Least Squares Suppose we have two variables x and y Purpose of Regression Some Examples
More informationChapter 3: Examining Relationships
Chapter 3: Examining Relationships 3.1 Scatterplots 3.2 Correlation 3.3 Least-Squares Regression Fabric Tenacity, lb/oz/yd^2 26 25 24 23 22 21 20 19 18 y = 3.9951x + 4.5711 R 2 = 0.9454 3.5 4.0 4.5 5.0
More informationAnnouncements: You can turn in homework until 6pm, slot on wall across from 2202 Bren. Make sure you use the correct slot! (Stats 8, closest to wall)
Announcements: You can turn in homework until 6pm, slot on wall across from 2202 Bren. Make sure you use the correct slot! (Stats 8, closest to wall) We will cover Chs. 5 and 6 first, then 3 and 4. Mon,
More informationSTA Module 5 Regression and Correlation. Learning Objectives. Learning Objectives (Cont.) Upon completing this module, you should be able to:
STA 2023 Module 5 Regression and Correlation Learning Objectives Upon completing this module, you should be able to: 1. Define and apply the concepts related to linear equations with one independent variable.
More informationChapter 3: Examining Relationships
Chapter 3: Examining Relationships Most statistical studies involve more than one variable. Often in the AP Statistics exam, you will be asked to compare two data sets by using side by side boxplots or
More informationAP Statistics. Chapter 6 Scatterplots, Association, and Correlation
AP Statistics Chapter 6 Scatterplots, Association, and Correlation Objectives: Scatterplots Association Outliers Response Variable Explanatory Variable Correlation Correlation Coefficient Lurking Variables
More informationChapter 12 Summarizing Bivariate Data Linear Regression and Correlation
Chapter 1 Summarizing Bivariate Data Linear Regression and Correlation This chapter introduces an important method for making inferences about a linear correlation (or relationship) between two variables,
More informationA company recorded the commuting distance in miles and number of absences in days for a group of its employees over the course of a year.
Paired Data(bivariate data) and Scatterplots: When data consists of pairs of values, it s sometimes useful to plot them as points called a scatterplot. A company recorded the commuting distance in miles
More informationBivariate Data Summary
Bivariate Data Summary Bivariate data data that examines the relationship between two variables What individuals to the data describe? What are the variables and how are they measured Are the variables
More informationDr. Allen Back. Sep. 23, 2016
Dr. Allen Back Sep. 23, 2016 Look at All the Data Graphically A Famous Example: The Challenger Tragedy Look at All the Data Graphically A Famous Example: The Challenger Tragedy Type of Data Looked at the
More informationAP Statistics - Chapter 2A Extra Practice
AP Statistics - Chapter 2A Extra Practice 1. A study is conducted to determine if one can predict the yield of a crop based on the amount of yearly rainfall. The response variable in this study is A) yield
More informationappstats8.notebook October 11, 2016
Chapter 8 Linear Regression Objective: Students will construct and analyze a linear model for a given set of data. Fat Versus Protein: An Example pg 168 The following is a scatterplot of total fat versus
More informationChapter 8. Linear Regression. Copyright 2010 Pearson Education, Inc.
Chapter 8 Linear Regression Copyright 2010 Pearson Education, Inc. Fat Versus Protein: An Example The following is a scatterplot of total fat versus protein for 30 items on the Burger King menu: Copyright
More informationLooking at data: relationships
Looking at data: relationships Least-squares regression IPS chapter 2.3 2006 W. H. Freeman and Company Objectives (IPS chapter 2.3) Least-squares regression p p The regression line Making predictions:
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 information23. Inference for regression
23. Inference for regression The Practice of Statistics in the Life Sciences Third Edition 2014 W. H. Freeman and Company Objectives (PSLS Chapter 23) Inference for regression The regression model Confidence
More informationINFERENCE FOR REGRESSION
CHAPTER 3 INFERENCE FOR REGRESSION OVERVIEW In Chapter 5 of the textbook, we first encountered regression. The assumptions that describe the regression model we use in this chapter are the following. We
More informationLeast Squares Regression
Least Squares Regression Sections 5.3 & 5.4 Cathy Poliak, Ph.D. cathy@math.uh.edu Office in Fleming 11c Department of Mathematics University of Houston Lecture 14-2311 Cathy Poliak, Ph.D. cathy@math.uh.edu
More informationMATH 1150 Chapter 2 Notation and Terminology
MATH 1150 Chapter 2 Notation and Terminology Categorical Data The following is a dataset for 30 randomly selected adults in the U.S., showing the values of two categorical variables: whether or not the
More informationPredicted Y Scores. The symbol stands for a predicted Y score
REGRESSION 1 Linear Regression Linear regression is a statistical procedure that uses relationships to predict unknown Y scores based on the X scores from a correlated variable. 2 Predicted Y Scores Y
More informationChi-square tests. Unit 6: Simple Linear Regression Lecture 1: Introduction to SLR. Statistics 101. Poverty vs. HS graduate rate
Review and Comments Chi-square tests Unit : Simple Linear Regression Lecture 1: Introduction to SLR Statistics 1 Monika Jingchen Hu June, 20 Chi-square test of GOF k χ 2 (O E) 2 = E i=1 where k = total
More informationUNIT 12 ~ More About Regression
***SECTION 15.1*** The Regression Model When a scatterplot shows a relationship between a variable x and a y, we can use the fitted to the data to predict y for a given value of x. Now we want to do tests
More informationChapter 6. Exploring Data: Relationships. Solutions. Exercises:
Chapter 6 Exploring Data: Relationships Solutions Exercises: 1. (a) It is more reasonable to explore study time as an explanatory variable and the exam grade as the response variable. (b) It is more reasonable
More informationLecture 4 Scatterplots, Association, and Correlation
Lecture 4 Scatterplots, Association, and Correlation Previously, we looked at Single variables on their own One or more categorical variable In this lecture: We shall look at two quantitative variables.
More informationLecture 4 Scatterplots, Association, and Correlation
Lecture 4 Scatterplots, Association, and Correlation Previously, we looked at Single variables on their own One or more categorical variables In this lecture: We shall look at two quantitative variables.
More informationChapter 5 Least Squares Regression
Chapter 5 Least Squares Regression A Royal Bengal tiger wandered out of a reserve forest. We tranquilized him and want to take him back to the forest. We need an idea of his weight, but have no scale!
More informationBIVARIATE DATA data for two variables
(Chapter 3) BIVARIATE DATA data for two variables INVESTIGATING RELATIONSHIPS We have compared the distributions of the same variable for several groups, using double boxplots and back-to-back stemplots.
More informationAP Statistics Two-Variable Data Analysis
AP Statistics Two-Variable Data Analysis Key Ideas Scatterplots Lines of Best Fit The Correlation Coefficient Least Squares Regression Line Coefficient of Determination Residuals Outliers and Influential
More informationUnit 6 - Introduction to linear regression
Unit 6 - Introduction to linear regression Suggested reading: OpenIntro Statistics, Chapter 7 Suggested exercises: Part 1 - Relationship between two numerical variables: 7.7, 7.9, 7.11, 7.13, 7.15, 7.25,
More informationSimple Linear Regression Using Ordinary Least Squares
Simple Linear Regression Using Ordinary Least Squares Purpose: To approximate a linear relationship with a line. Reason: We want to be able to predict Y using X. Definition: The Least Squares Regression
More informationCREATED BY SHANNON MARTIN GRACEY 146 STATISTICS GUIDED NOTEBOOK/FOR USE WITH MARIO TRIOLA S TEXTBOOK ESSENTIALS OF STATISTICS, 3RD ED.
10.2 CORRELATION A correlation exists between two when the of one variable are somehow with the values of the other variable. EXPLORING THE DATA r = 1.00 r =.85 r = -.54 r = -.94 CREATED BY SHANNON MARTIN
More informationCHAPTER 4 DESCRIPTIVE MEASURES IN REGRESSION AND CORRELATION
STP 226 ELEMENTARY STATISTICS CHAPTER 4 DESCRIPTIVE MEASURES IN REGRESSION AND CORRELATION Linear Regression and correlation allows us to examine the relationship between two or more quantitative variables.
More informationScatterplots and Correlation
Scatterplots and Correlation Al Nosedal University of Toronto Summer 2017 Al Nosedal University of Toronto Scatterplots and Correlation Summer 2017 1 / 65 My momma always said: Life was like a box of chocolates.
More informationAnnouncements. Lecture 10: Relationship between Measurement Variables. Poverty vs. HS graduate rate. Response vs. explanatory
Announcements Announcements Lecture : Relationship between Measurement Variables Statistics Colin Rundel February, 20 In class Quiz #2 at the end of class Midterm #1 on Friday, in class review Wednesday
More informationCorrelation: basic properties.
Correlation: basic properties. 1 r xy 1 for all sets of paired data. The closer r xy is to ±1, the stronger the linear relationship between the x-data and y-data. If r xy = ±1 then there is a perfect linear
More informationTHE PEARSON CORRELATION COEFFICIENT
CORRELATION Two variables are said to have a relation if knowing the value of one variable gives you information about the likely value of the second variable this is known as a bivariate relation There
More informationChapter 3: Examining Relationships
Chapter 3 Review Chapter 3: Examining Relationships 1. A study is conducted to determine if one can predict the yield of a crop based on the amount of yearly rainfall. The response variable in this study
More informationGeneral Least Squares Fitting
Chapter 1 General Least Squares Fitting 1.1 Introduction Previously you have done curve fitting in two dimensions. Now you will learn how to extend that to multiple dimensions. 1.1.1 Non-linear Linearizable
More informationThe response variable depends on the explanatory variable.
A response variable measures an outcome of study. > dependent variables An explanatory variable attempts to explain the observed outcomes. > independent variables The response variable depends on the explanatory
More informationMATH 2560 C F03 Elementary Statistics I Solutions to Assignment N3
MATH 2560 C F03 Elementary Statistics I Solutions to Assignment N3 Total points: 50 (2.5 percents). Question 1: 12 points (1 point is equal to 0.05 percents); Question 2: 20 points; Question 3: 4 points;
More informationAP Statistics Unit 2 (Chapters 7-10) Warm-Ups: Part 1
AP Statistics Unit 2 (Chapters 7-10) Warm-Ups: Part 1 2. 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.
More informationq3_3 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
q3_3 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) In 2007, the number of wins had a mean of 81.79 with a standard
More informationScatterplots. 3.1: Scatterplots & Correlation. Scatterplots. Explanatory & Response Variables. Section 3.1 Scatterplots and Correlation
3.1: Scatterplots & Correlation Scatterplots A scatterplot shows the relationship between two quantitative variables measured on the same individuals. The values of one variable appear on the horizontal
More informationSection 3.3. How Can We Predict the Outcome of a Variable? Agresti/Franklin Statistics, 1of 18
Section 3.3 How Can We Predict the Outcome of a Variable? Agresti/Franklin Statistics, 1of 18 Regression Line Predicts the value for the response variable, y, as a straight-line function of the value of
More informationChapter 10 Correlation and Regression
Chapter 10 Correlation and Regression 10-1 Review and Preview 10-2 Correlation 10-3 Regression 10-4 Variation and Prediction Intervals 10-5 Multiple Regression 10-6 Modeling Copyright 2010, 2007, 2004
More informationChapter 11. Correlation and Regression
Chapter 11 Correlation and Regression Correlation A relationship between two variables. The data can be represented b ordered pairs (, ) is the independent (or eplanator) variable is the dependent (or
More informationRecall, Positive/Negative Association:
ANNOUNCEMENTS: Remember that discussion today is not for credit. Go over R Commander. Go to 192 ICS, except at 4pm, go to 192 or 174 ICS. TODAY: Sections 5.3 to 5.5. Note this is a change made in the daily
More informationObjectives. 2.1 Scatterplots. Scatterplots Explanatory and response variables Interpreting scatterplots Outliers
Objectives 2.1 Scatterplots Scatterplots Explanatory and response variables Interpreting scatterplots Outliers Adapted from authors slides 2012 W.H. Freeman and Company Relationship of two numerical variables
More informationSimple Linear Regression
Simple Linear Regression OI CHAPTER 7 Important Concepts Correlation (r or R) and Coefficient of determination (R 2 ) Interpreting y-intercept and slope coefficients Inference (hypothesis testing and confidence
More informationAP Statistics L I N E A R R E G R E S S I O N C H A P 7
AP Statistics 1 L I N E A R R E G R E S S I O N C H A P 7 The object [of statistics] is to discover methods of condensing information concerning large groups of allied facts into brief and compendious
More informationChapter 8. Linear Regression. The Linear Model. Fat Versus Protein: An Example. The Linear Model (cont.) Residuals
Chapter 8 Linear Regression Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8-1 Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Fat Versus
More informationChapter 10. Regression. Understandable Statistics Ninth Edition By Brase and Brase Prepared by Yixun Shi Bloomsburg University of Pennsylvania
Chapter 10 Regression Understandable Statistics Ninth Edition By Brase and Brase Prepared by Yixun Shi Bloomsburg University of Pennsylvania Scatter Diagrams A graph in which pairs of points, (x, y), are
More informationSTAT Regression Methods
STAT 501 - Regression Methods Unit 9 Examples Example 1: Quake Data Let y t = the annual number of worldwide earthquakes with magnitude greater than 7 on the Richter scale for n = 99 years. Figure 1 gives
More informationLinear Regression Communication, skills, and understanding Calculator Use
Linear Regression Communication, skills, and understanding Title, scale and label the horizontal and vertical axes Comment on the direction, shape (form), and strength of the relationship and unusual features
More informationLooking at Data Relationships. 2.1 Scatterplots W. H. Freeman and Company
Looking at Data Relationships 2.1 Scatterplots 2012 W. H. Freeman and Company Here, we have two quantitative variables for each of 16 students. 1) How many beers they drank, and 2) Their blood alcohol
More informationSimple Linear Regression
9-1 l Chapter 9 l Simple Linear Regression 9.1 Simple Linear Regression 9.2 Scatter Diagram 9.3 Graphical Method for Determining Regression 9.4 Least Square Method 9.5 Correlation Coefficient and Coefficient
More informationTABLES AND FORMULAS FOR MOORE Basic Practice of Statistics
TABLES AND FORMULAS FOR MOORE Basic Practice of Statistics Exploring Data: Distributions Look for overall pattern (shape, center, spread) and deviations (outliers). Mean (use a calculator): x = x 1 + x
More informationHOMEWORK (due Wed, Jan 23): Chapter 3: #42, 48, 74
ANNOUNCEMENTS: Grades available on eee for Week 1 clickers, Quiz and Discussion. If your clicker grade is missing, check next week before contacting me. If any other grades are missing let me know now.
More informationRegression and correlation. Correlation & Regression, I. Regression & correlation. Regression vs. correlation. Involve bivariate, paired data, X & Y
Regression and correlation Correlation & Regression, I 9.07 4/1/004 Involve bivariate, paired data, X & Y Height & weight measured for the same individual IQ & exam scores for each individual Height of
More informationBusiness Statistics. Lecture 10: Correlation and Linear Regression
Business Statistics Lecture 10: Correlation and Linear Regression Scatterplot A scatterplot shows the relationship between two quantitative variables measured on the same individuals. It displays the Form
More informationRelationship Between Interval and/or Ratio Variables: Correlation & Regression. Sorana D. BOLBOACĂ
Relationship Between Interval and/or Ratio Variables: Correlation & Regression Sorana D. BOLBOACĂ OUTLINE Correlation Definition Deviation Score Formula, Z score formula Hypothesis Test Regression - Intercept
More informationInference for Regression Simple Linear Regression
Inference for Regression Simple Linear Regression IPS Chapter 10.1 2009 W.H. Freeman and Company Objectives (IPS Chapter 10.1) Simple linear regression p Statistical model for linear regression p Estimating
More informationMultiple Regression. Inference for Multiple Regression and A Case Study. IPS Chapters 11.1 and W.H. Freeman and Company
Multiple Regression Inference for Multiple Regression and A Case Study IPS Chapters 11.1 and 11.2 2009 W.H. Freeman and Company Objectives (IPS Chapters 11.1 and 11.2) Multiple regression Data for multiple
More informationBusiness Statistics. Lecture 9: Simple Regression
Business Statistics Lecture 9: Simple Regression 1 On to Model Building! Up to now, class was about descriptive and inferential statistics Numerical and graphical summaries of data Confidence intervals
More informationGUIDED NOTES 2.2 LINEAR EQUATIONS IN ONE VARIABLE
GUIDED NOTES 2.2 LINEAR EQUATIONS IN ONE VARIABLE LEARNING OBJECTIVES In this section, you will: Solve equations in one variable algebraically. Solve a rational equation. Find a linear equation. Given
More informationTransforming with Powers and Roots
12.2.1 Transforming with Powers and Roots When you visit a pizza parlor, you order a pizza by its diameter say, 10 inches, 12 inches, or 14 inches. But the amount you get to eat depends on the area of
More informationIntroduction to Simple Linear Regression
Introduction to Simple Linear Regression 1. Regression Equation A simple linear regression (also known as a bivariate regression) is a linear equation describing the relationship between an explanatory
More information6.0 Lesson Plan. Answer Questions. Regression. Transformation. Extrapolation. Residuals
6.0 Lesson Plan Answer Questions Regression Transformation Extrapolation Residuals 1 Information about TAs Lab grader: Pontus, npl@duke.edu Hwk grader: Rachel, rmt6@duke.edu Quiz (Tuesday): Matt, matthew.campbell@duke.edu
More informationObjectives. 2.1 Scatterplots. Scatterplots Explanatory and response variables. Interpreting scatterplots Outliers
Objectives 2.1 Scatterplots Scatterplots Explanatory and response variables Interpreting scatterplots Outliers Adapted from authors slides 2012 W.H. Freeman and Company Relationships A very important aspect
More informationInfluencing Regression
Math Objectives Students will recognize that one point can influence the correlation coefficient and the least-squares regression line. Students will differentiate between an outlier and an influential
More informationSTA 302 H1F / 1001 HF Fall 2007 Test 1 October 24, 2007
STA 302 H1F / 1001 HF Fall 2007 Test 1 October 24, 2007 LAST NAME: SOLUTIONS FIRST NAME: STUDENT NUMBER: ENROLLED IN: (circle one) STA 302 STA 1001 INSTRUCTIONS: Time: 90 minutes Aids allowed: calculator.
More information7. Do not estimate values for y using x-values outside the limits of the data given. This is called extrapolation and is not reliable.
AP Statistics 15 Inference for Regression I. Regression Review a. r à correlation coefficient or Pearson s coefficient: indicates strength and direction of the relationship between the explanatory variables
More informationInference for Regression Inference about the Regression Model and Using the Regression Line
Inference for Regression Inference about the Regression Model and Using the Regression Line PBS Chapter 10.1 and 10.2 2009 W.H. Freeman and Company Objectives (PBS Chapter 10.1 and 10.2) Inference about
More informationSociology 6Z03 Review I
Sociology 6Z03 Review I John Fox McMaster University Fall 2016 John Fox (McMaster University) Sociology 6Z03 Review I Fall 2016 1 / 19 Outline: Review I Introduction Displaying Distributions Describing
More informationMATH 1070 Introductory Statistics Lecture notes Relationships: Correlation and Simple Regression
MATH 1070 Introductory Statistics Lecture notes Relationships: Correlation and Simple Regression Objectives: 1. Learn the concepts of independent and dependent variables 2. Learn the concept of a scatterplot
More informationCorrelation & Simple Regression
Chapter 11 Correlation & Simple Regression The previous chapter dealt with inference for two categorical variables. In this chapter, we would like to examine the relationship between two quantitative variables.
More informationChapter 7. Linear Regression (Pt. 1) 7.1 Introduction. 7.2 The Least-Squares Regression Line
Chapter 7 Linear Regression (Pt. 1) 7.1 Introduction Recall that r, the correlation coefficient, measures the linear association between two quantitative variables. Linear regression is the method of fitting
More informationThe empirical ( ) rule
The empirical (68-95-99.7) rule With a bell shaped distribution, about 68% of the data fall within a distance of 1 standard deviation from the mean. 95% fall within 2 standard deviations of the mean. 99.7%
More information