# RESIDUAL = ACTUAL PREDICTED The following questions refer to this data set:

Save this PDF as:

Size: px
Start display at page:

Download "RESIDUAL = ACTUAL PREDICTED The following questions refer to this data set:"

## Transcription

1 REGRESSION DIAGNOSTICS After fitting a regression line it is important to do some diagnostic checks to verify that regression fit was OK One aspect of diagnostic checking is to find the rms error This is an overall measure of the goodness of fit It measures how close the regression line is to all of the points simultaneously The rms is computed using the residuals from a regression It is also imperative to view residual plots Also, to check another diagnostic: homoscedasticity 11 1 RESIDUAL = ACTUAL PREDICTED The following questions refer to this data set: Point x y A 1 B 3 9 C 4 7 D 1 E 7 13 Average 4 7 SD 2 4 r 2/ y the regression line for y on x E x For point E, the actual value of y is For point E, the predicted value of y using the regression method is : 7 is units, or SDs, average for x Predicted value of y is SDs, or units, average For point E, the error in prediction is Prediction error = actual value predicted value The statistical jargon for prediction error is The residual for point E is What is that saying about the scatter diagram? Point E is vertical units the regression line The residual for point D is 68 What is that saying about the scatter diagram? Point D is vertical units the regression line 11 2

2 THE RMS ERROR OF PREDICTION There is a prediction error for each of the points A, B, C, D, and E How can we measure the overall size of these errors? By the so-called rms error of the regression line, ie, by the root-mean-square of the residuals: Square the residuals, Average the squares, Take the square root of the average square Point x Actual y Predicted y Residual (Residual) 2 A 1 46 B C D E Average (residual) 2 = y rms error = = x = rms error regression line 1 rms error The points on a scatter diagram deviate from the regression line (up or down) by residuals which are similar in size to the rms error The rms error is to the regression line as the SD is to the average 11 3 EXERCISES Below are three scatter diagrams The regression line has been drawn across each one In each case, guess whether the rms error is about 2, 1, or (a) (b) (c) A regression line for predicting test scores has a rms error of 8 points About 68% of the time, the predictions will be right to within points About 9% of the time, the predictions will be right to within points 68% One rms error One rms error 9% 11 4 Two rms errors Two rms errors

3 COMPUTING THE RMS ERROR How is the rms error for the regression line (of y on x) related to the SD of y and the correlation coefficient r? rms error = 1 r 2 (the SD of y) Point x y A 1 B 3 9 C 4 7 D 1 E 7 13 Average 4 7 SD 2 4 r 2/ r = 1 r2 = SD of y = rms error = 1 r 2 SD of y = Does the short-cut formula work for all scatter diagrams? Yes What is the interpretation of the quantity 1 r 2? Predictions based on the regression line are more accurate than predictions using just the average of y, by a factor of 1 r 2 y SD of y Average of y rms error Regression line What are the units for the rms error? The same as for by the SD of y ; that s what reminds you to multiply TWINS In one study of identical male twins, the average height was found to be about 68 inches, with an SD of about 3 inches The correlation between the heights of the twins was about 9, and the scatter diagram was football-shaped (a) You have to guess the height of one of these twins, without any further information What method would you use? method = (b) Find the rms error for the method in (a) rms error = (c) One twin of the pair is standing in front of you You have to guess the height of the other twin What method would you use? (For instance, suppose the twin you see is 6 feet 2 inches) method = height of other twin = 11 x (d) Find the rms error for the method in (c) rms error = 11 6

4 What is a residual plot? RESIDUAL PLOTS A plot of the residuals versus x, or perhaps versus some other relevant variable Point x Residual A 1 4 B 3 28 C 4 D 68 E 7 36 Residual In general, the residuals average out to, and the regression line for the residual plot is All the linear trend in the data is accounted for by the regression line for the data What advantage does a residual plot have over the original scatter diagram? A residual plot lets you use a larger vertical scale, which makes departures from linearity stand out more clearly What do you look for in a residual plot? Outliers Unusual patterns Other signs that it would be a mistake to make predictions using a straight line x Example The math department of a large state university must plan in advance the number of sections and instructors required for elementary courses The department hopes that the number of students in these courses can be predicted from the number of entering freshmen, which is known before the new students actually choose courses The table below contains the data for recent years The explanatory variable x is the number of students in the freshman class, and the response variable y is the number of students who enroll in math courses at the 1 level Year x y Here is the scatter plot and the regression line for elementary mathematics enrollment on number of freshmen How would you describe the nature of the relationship? Elementary math enrollment Number of freshmen

5 Here is the residual plot for the regression of elementary math enrollment on number of freshmen Do you see anything strange? Residuals Number of freshmen rms= What does this plot of the residuals against time reveal? 3 2 LOOKING AT VERTICAL STRIPS Reconsider Pearson s father-son data Son s height (inches) Heights of 1,78 fathers and their full-grown sons Residuals Year Father s height (inches) How does the spread of son s height change as father s height varies?

6 The following plot shows how the conditional quartiles of son s height vary with father s height Son s height (inches) The first, second, and third regression curves Father s height (inches) Reading from left to right, the top curve traces out the third quartile of son s height for fathers who are respectively 61, 62,, 73 inches tall, to the nearest inch The middle curve traces out the corresponding medians, and the bottom curve traces out the corresponding first quartiles What are the conclusions? The variation in son s height, as measured by the interquartile range, is about the same in all the vertical strips The interquartile range doesn t vary much from strip to strip, but the (full) range does Why is that? The full range depends on the extremes, and the extremes depend in part on how many points there are in the strip HOMOGENEITY OF VARIANCE What does it mean to say that a scatter diagram is homoscedastic? All the vertical strips in the diagram show similar amounts of spread (Homo means same, scedastic means scatter ) What bearing does that have on prediction? The prediction errors are similar all along the regression line The spread in each vertical strip is about the rms error How do you recognize homoscedasticity? The residual plot should look football-shaped For a more careful analysis, construct the first and third quartile regression curves and check whether they are roughly parallel (You could also construct the regression curve for the Average + 1SD, and for the Average 1SD, and check whether those two curves are roughly parallel) 11 12

7 HETEROGENEITY OF VARIANCE If you haven t got homoscedasticity, what have you got? Heteroscedasticity That means that the prediction errors are different in different parts of the scatter diagram (hetero means different ) In some vertical strips, the spread is greater than the rms error; in others, the spread is smaller Example Weight (pounds) Percentiles of weight at given ages, for girls aged 2 to Age (years) How does weight vary with respect to age? In regards to location? In regards to spread? Is the distribution of weight at age 18 normal, or nonnormal? USING THE NORMAL CURVE INSIDE A VERTICAL STRIP Reconsider Pearson s father-son data Percent per inch Percent per inch Percent per inch Heights of sons whose fathers are a given height 64 inch fathers Height (inches) 67 inch fathers Height (inches) 7 inch fathers Height (inches) These histograms show the distribution of height among sons whose fathers are respectively 64, 67, and 7 inches tall, to the nearest inch Note that each of these so-called conditional distributions of sons height is approximately normal This will be true for any football-shaped scatter diagram 11 14

8 USING THE NORMAL CURVE INSIDE A VERTICAL STRIP The normal approximation can be used on the points inside a narrow vertical strip on a shaped scatter diagram Think of the y values in this strip as a whole new data set The new average is estimated by the The new SD is about equal to the The normal approximation can be done as usual, based on the average and SD for y, rather than the average and SD for y Regression line Pearson and Lee obtained the following results for about 1, families: average height of husband 68, SD 27 average height of wife 63, SD 2, r 2 The scatter diagram is football shaped What percentage of the women were over feet 8 inches? Average = SD = Overall SD Overall average New SD New average Wife s height Standard units Statisticians often use the terms conditional for New, and unconditional for Overall

9 Pearson and Lee obtained the following results for about 1, families: average height of husband 68, SD 27 average height of wife 63, SD 2, r 2 The scatter diagram is football shaped Of the women who were married to men of height 6 feet, what percentage were over feet 8 inches? Average = (These women are somewhat taller than the overall average) SD = (These women are a more homegeneous group, will less variation in their heights) Percentage = SUMMARY With a regression line the difference between the actual value and the predicted value is called a residual The RMS error measures the overall size of the residuals The RMS error for the regression line of y on x can be figured as 1 r2 SD of y The residual plot shows the residuals! If a pattern appears then the linear regression may not have captured all the structure in the data set Data sets with similar amounts of spread in all vertical strips are called homoscedastic Those that show different amounts of spread are called heteroscedastic If the scatter diagram is football-shaped, the normal curve can be used inside a vertical strip, using the conditional mean and SD of y for the given value of x Wife s height Standard units

### . 58 58 60 62 64 66 68 70 72 74 76 78 Father s height (inches)

PEARSON S FATHER-SON DATA The following scatter diagram shows the heights of 1,0 fathers and their full-grown sons, in England, circa 1900 There is one dot for each father-son pair Heights of fathers and

### Chapter 11: r.m.s. error for regression

Chapter 11: r.m.s. error for regression Context................................................................... 2 Prediction error 3 r.m.s. error for the regression line...............................................

### Correlation & Regression, II. Residual Plots. What we like to see: no pattern. Steps in regression analysis (so far)

Steps in regression analysis (so far) Correlation & Regression, II 9.07 4/6/2004 Plot a scatter plot Find the parameters of the best fit regression line, y =a+bx Plot the regression line on the scatter

### 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

### 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.

### 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.

### MEASURES OF VARIATION

NORMAL DISTRIBTIONS MEASURES OF VARIATION In statistics, it is important to measure the spread of data. A simple way to measure spread is to find the range. But statisticians want to know if the data are

### 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

### Inferential Statistics

Inferential Statistics Sampling and the normal distribution Z-scores Confidence levels and intervals Hypothesis testing Commonly used statistical methods Inferential Statistics Descriptive statistics are

### 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 Normal Distribution

Chapter 6 The Normal Distribution 6.1 The Normal Distribution 1 6.1.1 Student Learning Objectives By the end of this chapter, the student should be able to: Recognize the normal probability distribution

### Applied Data Analysis. Fall 2015

Applied Data Analysis Fall 2015 Course information: Labs Anna Walsdorff anna.walsdorff@rochester.edu Tues. 9-11 AM Mary Clare Roche maryclare.roche@rochester.edu Mon. 2-4 PM Lecture outline 1. Practice

### Descriptive Statistics

Descriptive Statistics Primer Descriptive statistics Central tendency Variation Relative position Relationships Calculating descriptive statistics Descriptive Statistics Purpose to describe or summarize

### 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

### MULTIPLE REGRESSION EXAMPLE

MULTIPLE REGRESSION EXAMPLE For a sample of n = 166 college students, the following variables were measured: Y = height X 1 = mother s height ( momheight ) X 2 = father s height ( dadheight ) X 3 = 1 if

### 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

### 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

### 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

### 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) -

### 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,

### 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

### 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

### 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

### , 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

### Chapter 5: The normal approximation for data

Chapter 5: The normal approximation for data Context................................................................... 2 Normal curve 3 Normal curve.............................................................

### 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

### 5 Week Modular Course in Statistics & Probability Strand 1. Module 2

5 Week Modular Course in Statistics & Probability Strand 1 Module 2 Analysing Data Numerically Measures of Central Tendency Mean Median Mode Measures of Spread Range Standard Deviation Inter-Quartile Range

### STAT 155 Introductory Statistics. Lecture 5: Density Curves and Normal Distributions (I)

The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL STAT 155 Introductory Statistics Lecture 5: Density Curves and Normal Distributions (I) 9/12/06 Lecture 5 1 A problem about Standard Deviation A variable

### Presentation of Data

ECON 2A: Advanced Macroeconomic Theory I ve put together some pointers when assembling the data analysis portion of your presentation and final paper. These are not all inclusive, but are things to keep

### AP Statistics 2001 Solutions and Scoring Guidelines

AP Statistics 2001 Solutions and Scoring Guidelines The materials included in these files are intended for non-commercial use by AP teachers for course and exam preparation; permission for any other use

### 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

### 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

### CC Investigation 5: Histograms and Box Plots

Content Standards 6.SP.4, 6.SP.5.c CC Investigation 5: Histograms and Box Plots At a Glance PACING 3 days Mathematical Goals DOMAIN: Statistics and Probability Display numerical data in histograms and

### Exam Style Questions. Revision for this topic. Name: Ensure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser

Name: Exam Style Questions Ensure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser You may use tracing paper if needed Guidance 1. Read each question carefully before you begin answering

### 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

### STATS8: Introduction to Biostatistics. Data Exploration. Babak Shahbaba Department of Statistics, UCI

STATS8: Introduction to Biostatistics Data Exploration Babak Shahbaba Department of Statistics, UCI Introduction After clearly defining the scientific problem, selecting a set of representative members

### Chapter 3: Data Description Numerical Methods

Chapter 3: Data Description Numerical Methods Learning Objectives Upon successful completion of Chapter 3, you will be able to: Summarize data using measures of central tendency, such as the mean, median,

### Outline. Correlation & Regression, III. Review. Relationship between r and regression

Outline Correlation & Regression, III 9.07 4/6/004 Relationship between correlation and regression, along with notes on the correlation coefficient Effect size, and the meaning of r Other kinds of correlation

### AP Statistics Solutions to Packet 2

AP Statistics Solutions to Packet 2 The Normal Distributions Density Curves and the Normal Distribution Standard Normal Calculations HW #9 1, 2, 4, 6-8 2.1 DENSITY CURVES (a) Sketch a density curve that

### CORRELATIONAL ANALYSIS: PEARSON S r Purpose of correlational analysis The purpose of performing a correlational analysis: To discover whether there

CORRELATIONAL ANALYSIS: PEARSON S r Purpose of correlational analysis The purpose of performing a correlational analysis: To discover whether there is a relationship between variables, To find out the

### 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

### 4. Introduction to Statistics

Statistics for Engineers 4-1 4. Introduction to Statistics Descriptive Statistics Types of data A variate or random variable is a quantity or attribute whose value may vary from one unit of investigation

### First Midterm Exam (MATH1070 Spring 2012)

First Midterm Exam (MATH1070 Spring 2012) Instructions: This is a one hour exam. You can use a notecard. Calculators are allowed, but other electronics are prohibited. 1. [40pts] Multiple Choice Problems

### Describing, Exploring, and Comparing Data

24 Chapter 2. Describing, Exploring, and Comparing Data Chapter 2. Describing, Exploring, and Comparing Data There are many tools used in Statistics to visualize, summarize, and describe data. This chapter

### 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

### 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

### Chapter 1: Exploring Data

Chapter 1: Exploring Data Chapter 1 Review 1. As part of survey of college students a researcher is interested in the variable class standing. She records a 1 if the student is a freshman, a 2 if the student

### REGRESSION LINES IN STATA

REGRESSION LINES IN STATA THOMAS ELLIOTT 1. Introduction to Regression Regression analysis is about eploring linear relationships between a dependent variable and one or more independent variables. Regression

### Rescaling and shifting

Rescaling and shifting A fancy way of changing one variable to another Main concepts involve: Adding or subtracting a number (shifting) Multiplying or dividing by a number (rescaling) Where have you seen

### College of the Canyons Math 140 Exam 1 Amy Morrow. Name:

Name: Answer the following questions NEATLY. Show all necessary work directly on the exam. Scratch paper will be discarded unread. One point each part unless otherwise marked. 1. Owners of an exercise

### Geostatistics Exploratory Analysis

Instituto Superior de Estatística e Gestão de Informação Universidade Nova de Lisboa Master of Science in Geospatial Technologies Geostatistics Exploratory Analysis Carlos Alberto Felgueiras cfelgueiras@isegi.unl.pt

### 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.

### Exploratory Data Analysis. Psychology 3256

Exploratory Data Analysis Psychology 3256 1 Introduction If you are going to find out anything about a data set you must first understand the data Basically getting a feel for you numbers Easier to find

### Means, standard deviations and. and standard errors

CHAPTER 4 Means, standard deviations and standard errors 4.1 Introduction Change of units 4.2 Mean, median and mode Coefficient of variation 4.3 Measures of variation 4.4 Calculating the mean and standard

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

Open book and note Calculator OK Multiple Choice 1 point each MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the mean for the given sample data.

### Statistiek II. John Nerbonne. March 24, 2010. Information Science, Groningen Slides improved a lot by Harmut Fitz, Groningen!

Information Science, Groningen j.nerbonne@rug.nl Slides improved a lot by Harmut Fitz, Groningen! March 24, 2010 Correlation and regression We often wish to compare two different variables Examples: compare

### Statistics E100 Fall 2013 Practice Midterm I - A Solutions

STATISTICS E100 FALL 2013 PRACTICE MIDTERM I - A SOLUTIONS PAGE 1 OF 5 Statistics E100 Fall 2013 Practice Midterm I - A Solutions 1. (16 points total) Below is the histogram for the number of medals won

### The Big 50 Revision Guidelines for S1

The Big 50 Revision Guidelines for S1 If you can understand all of these you ll do very well 1. Know what is meant by a statistical model and the Modelling cycle of continuous refinement 2. Understand

### 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

### Exploratory data analysis (Chapter 2) Fall 2011

Exploratory data analysis (Chapter 2) Fall 2011 Data Examples Example 1: Survey Data 1 Data collected from a Stat 371 class in Fall 2005 2 They answered questions about their: gender, major, year in school,

### EXAM #1 (Example) Instructor: Ela Jackiewicz. Relax and good luck!

STP 231 EXAM #1 (Example) Instructor: Ela Jackiewicz Honor Statement: I have neither given nor received information regarding this exam, and I will not do so until all exams have been graded and returned.

### 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

### Dimensionality Reduction: Principal Components Analysis

Dimensionality Reduction: Principal Components Analysis In data mining one often encounters situations where there are a large number of variables in the database. In such situations it is very likely

### 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

### Running head: ASSUMPTIONS IN MULTIPLE REGRESSION 1. Assumptions in Multiple Regression: A Tutorial. Dianne L. Ballance ID#

Running head: ASSUMPTIONS IN MULTIPLE REGRESSION 1 Assumptions in Multiple Regression: A Tutorial Dianne L. Ballance ID#00939966 University of Calgary APSY 607 ASSUMPTIONS IN MULTIPLE REGRESSION 2 Assumptions

### MATH 103/GRACEY PRACTICE EXAM/CHAPTERS 2-3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MATH 3/GRACEY PRACTICE EXAM/CHAPTERS 2-3 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) The frequency distribution

### The Correlation Coefficient

The Correlation Coefficient Lelys Bravo de Guenni April 22nd, 2015 Outline The Correlation coefficient Positive Correlation Negative Correlation Properties of the Correlation Coefficient Non-linear association

### Chapter 1: Looking at Data Section 1.1: Displaying Distributions with Graphs

Types of Variables Chapter 1: Looking at Data Section 1.1: Displaying Distributions with Graphs Quantitative (numerical)variables: take numerical values for which arithmetic operations make sense (addition/averaging)

### THE CORRELATION COEFFICIENT

THE CORRELATION COEFFICIENT 1 More Statistical Notation Correlational analysis requires scores from two variables. X stands for the scores on one variable and Y stands for the scores on the other variable.

### 2.0 Lesson Plan. Answer Questions. Summary Statistics. Histograms. The Normal Distribution. Using the Standard Normal Table

2.0 Lesson Plan Answer Questions 1 Summary Statistics Histograms The Normal Distribution Using the Standard Normal Table 2. Summary Statistics Given a collection of data, one needs to find representations

### January 26, 2009 The Faculty Center for Teaching and Learning

THE BASICS OF DATA MANAGEMENT AND ANALYSIS A USER GUIDE January 26, 2009 The Faculty Center for Teaching and Learning THE BASICS OF DATA MANAGEMENT AND ANALYSIS Table of Contents Table of Contents... i

### 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)

### Hints for Success on the AP Statistics Exam. (Compiled by Zack Bigner)

Hints for Success on the AP Statistics Exam. (Compiled by Zack Bigner) The Exam The AP Stat exam has 2 sections that take 90 minutes each. The first section is 40 multiple choice questions, and the second

### 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

### Sample Exam #1 Elementary Statistics

Sample Exam #1 Elementary Statistics Instructions. No books, notes, or calculators are allowed. 1. Some variables that were recorded while studying diets of sharks are given below. Which of the variables

### 1.3 Measuring Center & Spread, The Five Number Summary & Boxplots. Describing Quantitative Data with Numbers

1.3 Measuring Center & Spread, The Five Number Summary & Boxplots Describing Quantitative Data with Numbers 1.3 I can n Calculate and interpret measures of center (mean, median) in context. n Calculate

### Chapter 3. The Normal Distribution

Chapter 3. The Normal Distribution Topics covered in this chapter: Z-scores Normal Probabilities Normal Percentiles Z-scores Example 3.6: The standard normal table The Problem: What proportion of observations

### 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

### 13.2 Measures of Central Tendency

13.2 Measures of Central Tendency Measures of Central Tendency For a given set of numbers, it may be desirable to have a single number to serve as a kind of representative value around which all the numbers

### business statistics using Excel OXFORD UNIVERSITY PRESS Glyn Davis & Branko Pecar

business statistics using Excel Glyn Davis & Branko Pecar OXFORD UNIVERSITY PRESS Detailed contents Introduction to Microsoft Excel 2003 Overview Learning Objectives 1.1 Introduction to Microsoft Excel

### 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

T O P I C 1 2 Techniques and tools for data analysis Preview Introduction In chapter 3 of Statistics In A Day different combinations of numbers and types of variables are presented. We go through these

### 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

### 10-3 Measures of Central Tendency and Variation

10-3 Measures of Central Tendency and Variation So far, we have discussed some graphical methods of data description. Now, we will investigate how statements of central tendency and variation can be used.

### 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

### F. Farrokhyar, MPhil, PhD, PDoc

Learning objectives Descriptive Statistics F. Farrokhyar, MPhil, PhD, PDoc To recognize different types of variables To learn how to appropriately explore your data How to display data using graphs How

### Chapter 15 Multiple Choice Questions (The answers are provided after the last question.)

Chapter 15 Multiple Choice Questions (The answers are provided after the last question.) 1. What is the median of the following set of scores? 18, 6, 12, 10, 14? a. 10 b. 14 c. 18 d. 12 2. Approximately

### 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.

### List of Examples. Examples 319

Examples 319 List of Examples DiMaggio and Mantle. 6 Weed seeds. 6, 23, 37, 38 Vole reproduction. 7, 24, 37 Wooly bear caterpillar cocoons. 7 Homophone confusion and Alzheimer s disease. 8 Gear tooth strength.

### 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

### Introduction to Statistics for Psychology. Quantitative Methods for Human Sciences

Introduction to Statistics for Psychology and Quantitative Methods for Human Sciences Jonathan Marchini Course Information There is website devoted to the course at http://www.stats.ox.ac.uk/ marchini/phs.html

### Descriptive Statistics

Y520 Robert S Michael Goal: Learn to calculate indicators and construct graphs that summarize and describe a large quantity of values. Using the textbook readings and other resources listed on the web

### AP * Statistics Review. Descriptive Statistics

AP * Statistics Review Descriptive Statistics Teacher Packet Advanced Placement and AP are registered trademark of the College Entrance Examination Board. The College Board was not involved in the production

### AP Statistics Semester Exam Review Chapters 1-3

AP Statistics Semester Exam Review Chapters 1-3 1. Here are the IQ test scores of 10 randomly chosen fifth-grade students: 145 139 126 122 125 130 96 110 118 118 To make a stemplot of these scores, you

### Week 4: Standard Error and Confidence Intervals

Health Sciences M.Sc. Programme Applied Biostatistics Week 4: Standard Error and Confidence Intervals Sampling Most research data come from subjects we think of as samples drawn from a larger population.

### Mean = (sum of the values / the number of the value) if probabilities are equal

Population Mean Mean = (sum of the values / the number of the value) if probabilities are equal Compute the population mean Population/Sample mean: 1. Collect the data 2. sum all the values in the population/sample.

### Scatter Plots with Error Bars

Chapter 165 Scatter Plots with Error Bars Introduction The procedure extends the capability of the basic scatter plot by allowing you to plot the variability in Y and X corresponding to each point. Each

### Variables. Exploratory Data Analysis

Exploratory Data Analysis Exploratory Data Analysis involves both graphical displays of data and numerical summaries of data. A common situation is for a data set to be represented as a matrix. There is