2013 MBA Jump Start Program. Statistics Module Part 3


 Clementine Porter
 2 years ago
 Views:
Transcription
1 2013 MBA Jump Start Program Module 1: Statistics Thomas Gilbert Part 3 Statistics Module Part 3 Hypothesis Testing (Inference) Regressions 2 1
2 Making an Investment Decision A researcher in your firm just invented a new flavor of ice cream Given the short Seattle spring, you only had the opportunity to ask ten people about the taste Six liked it and four hated it After a quick meeting with your co founder, you have decided to abandon the last year of R&D that culminated in this amazingly different ice cream Is this a reasonable decision? 3 The Power of Statistics After sitting down with your consultants, you established that your target market comprises of 25 million DINKS To be profitable, you need to sell your ice cream to 30% of that market over the course of the summer How many people do you need to sample in order to be 95% confident that at least 30% of that market will like the ice cream? This is something you will be able to answer by the end of the winter quarter! 4 2
3 Estimating parameters Goal Parameter: a characteristic of the population (e.g. μ) Feature of the data generating process Statistics: an observed characteristic of a sample (ӯ) To estimate is to use a statistic to approximate a parameter 5 Sampling Variation Sampling variation is the variability in the value of a statistic from sample to sample It is the price we pay for working with a sample rather than the population Example: Average exam class grade 6 3
4 From Data to Probability Over the long run (with enough data), the accumulated relative frequency converges to a constant (probability) The Law of Large Numbers: The relative frequency of an outcome converges to a number, the probability of the outcome, as the number of observed outcomes increases 7 GDP Growth What has been the average annual Gross Domestic Product (GDP) growth in the U.S. since 1947? In Excel, you have annualized quarterly real GDP growth Is this the true average GDP growth? Is this next quarter s expected GDP growth? 8 4
5 Normal Models Sample means are normally distributed (bell shape curve) if the individual values are normally distributed We never have exact normal distributions The Central Limit Theorem shows that the sampling distribution of averages is approximately normal even if the underlying population is not normally distributed Sample size needs to be large enough for averaging to smooth away deviations from normality 9 Standard Error of the Mean The standard error of the mean of a simple random sample of n measurements from a process or population with standard deviation σ is: SE x n The larger the sample size, the smaller the sampling variation from sample to sample What is the standard error in our average GDP growth estimate? 10 5
6 Concept of Statistical Test We estimated the average annualized GDP growth at 3.3%. Is it different from 4%? Use a statistical test to answer this question Consider the plausibility of a specific claim Claims are called hypotheses 11 Concept of Statistical Test Statistical hypothesis: claim about a parameter of a population Null hypothesis (H 0 ): specifies a default course of action, preserves the status quo Alternative hypothesis (H a ): contradicts the assertion of the null hypothesis 12 6
7 Hypotheses Is average GDP growth (3.3%) different from 4%? H 0 : H a : 13 Types of Errors Type I error: Reject H 0 incorrectly Believe that GDP growth is 4% even though it is not False positive Type II error: Accept H 0 incorrectly Believe that GDP growth is not 4% even though it is False negative 14 7
8 Confidence Interval In order to estimate the long term tax revenue from closing a tax loophole, the White House needs to know what future GDP growth will be It can use past GDP growth as a basis for long term planning Use confidence intervals to answer such questions Confidence intervals convey information about the precision of the estimates 15 Ranges for Parameters A confidence interval is a range of plausible values for a parameter based on a sample Constructing confidence intervals relies on the sampling distribution of the statistic We will assume a normal model based on the Central Limit Theorem 16 8
9 Confidence Interval for the Mean We will use the estimated standard error of the mean SE x n Based on the normal distribution, random samples have the following property: The sample statistic in 95% of samples lies within about two standard errors of the population parameter 17 Confidence Interval for the Mean As a result, the confidence interval (at 95% confidence) for the mean is x 2 SE x to x 2 SE x What is your 95% confidence interval on annual GDP growth in the U.S. over the last 65 years? 18 9
10 Interpreting the Confidence Interval What does this mean? We are 95% confident that μ (true GDP growth) lies between 2.75% and 3.78% Might μ be 2%? It could be, but it is unlikely given the sample results 19 Wrong interpretations! Common Confusion 95% of years witness a GDP growth between 2.75% and 3.78% The average GDP growth is between 2.75% and 3.78% 20 10
11 Practice Quiz #5 and Break Please take a few minutes and complete the practice quiz on the next page Hypothesis testing for the mean return of PCAR Then take a 10 min break to stretch your legs! 21 Statistics Module Part 3 Hypothesis Testing (Inference) Regressions 22 11
12 Regression We are interested in understanding how changes in one variable can be explained by movements in one or more other variables A response variable in a dataset measures the outcome of a study An explanatory variable explains or influences changes in a response variable A regression line is a straight line that describes how a response variable y changes as an explanatory variable x changes: y = f(x) 23 Regression We use regression lines to predict y as a function of x: y = a + b*x How do we estimate a and b? How do we find the best line to fit between y and x? A ordinary least squares (OLS) regression line of y on x is the line that minimizes the sum of the squares of the vertical distance between the data points and the line 24 12
13 Graphical Explanation 25 OLS Regression The slope coefficient is given by: bˆ x Covar y, x V ar This is actually an estimated slope b hat and we also have an estimated intercept a hat : aˆ y bˆ x Using these estimates, we can calculate some predicted values of y given the values of x: yˆ aˆ bˆ x 26 13
14 Regression in Excel Let s regress PCAR returns on market returns Go to Data Analysis Select Regression Highlight the y and x variables and press OK Note the many options: Labels No intercepts: y = b*x Confidence intervals Residuals and residual plots 27 Regression Output SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 108 ANOVA df SS MS F Significance F Regression E 15 Residual Total Coefficients Standard Error t Stat P value Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept X Variable E
15 Alternative Visualization Build scatter plot of the returns (need to reverse the columns in order to have PCAR vertically and the market horizontally) Add linear trendline (highlight data on chart and rightclick) Note: Can also use intercept( ) and slope( ) functions 29 Interpreting the Fitted Line Interpreting the slope The slope estimates the marginal PCAR return per unit of market return While tempting, it is not correct to describe the slope as the change in y caused by changing x Question: Is the slope statistically different from 0? 30 15
16 Explaining Variation R squared (R 2 ) It is the squared correlation between x and y It is the fraction of the variation in y accounted by the variation in x In our example, 44% of the variation in PCAR returns can be explained by variation in market returns 31 Regression Example Relationship between age and blood pressure 32 16
17 Regression Example (2) Explaining home selling prices using multiple explanatory variables 33 Caution! Association (or correlation) does not imply causation! Must use common sense! It could be co linearity It could be a missing variable: need to control for it It could be a variable that is not independent Example: Someone says, There is a strong positive correlation between the number of firefighters at a fire and the amount of damage the fire does. So sending lots of firefighters just causes more damage. Explain why this reasoning is wrong 34 17
18 Summary of Part 3 Hypothesis testing is the cornerstone of inference in statistics Attempt to reject (or fail to reject) a null Standard errors of parameter estimates are key to answer Regressions are powerful tools to understand relations between variables Simple regression is very similar to a correlation Multiple right hand side variables allow decomposition of effects (or controls) 35 Part 1 Summary of Statistics Module Review of basic data analysis, such as means and standard deviation Histograms and distributions Part 2 Review of co variation analysis (covariance and correlation) Working with random variables Part 3 Inference and regressions Additional Problem Set at the end contains more problems on (almost) all topics Good statistics and its understanding is too overlooked and leads to poor decision making! 36 18
Chapter 7: Simple linear regression Learning Objectives
Chapter 7: Simple linear regression Learning Objectives Reading: Section 7.1 of OpenIntro Statistics Video: Correlation vs. causation, YouTube (2:19) Video: Intro to Linear Regression, YouTube (5:18) 
More informationLinear Regression. Chapter 5. Prediction via Regression Line Number of new birds and Percent returning. Least Squares
Linear Regression Chapter 5 Regression Objective: To quantify the linear relationship between an explanatory variable (x) and response variable (y). We can then predict the average response for all subjects
More informationRegression Analysis: A Complete Example
Regression Analysis: A Complete Example This section works out an example that includes all the topics we have discussed so far in this chapter. A complete example of regression analysis. PhotoDisc, Inc./Getty
More informationCHAPTER 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
More information2. 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
More informationChapter 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
More information1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96
1 Final Review 2 Review 2.1 CI 1propZint Scenario 1 A TV manufacturer claims in its warranty brochure that in the past not more than 10 percent of its TV sets needed any repair during the first two years
More informationBusiness Statistics. Successful completion of Introductory and/or Intermediate Algebra courses is recommended before taking Business Statistics.
Business Course Text Bowerman, Bruce L., Richard T. O'Connell, J. B. Orris, and Dawn C. Porter. Essentials of Business, 2nd edition, McGrawHill/Irwin, 2008, ISBN: 9780073319889. Required Computing
More informationLAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK DEPARTMENT OF MATHEMATICS, ENGINEERING, AND COMPUTER SCIENCE
LAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK DEPARTMENT OF MATHEMATICS, ENGINEERING, AND COMPUTER SCIENCE MAT 119 STATISTICS AND ELEMENTARY ALGEBRA 5 Lecture Hours, 2 Lab Hours, 3 Credits Pre
More informationLesson 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
More informationSimple Linear Regression Inference
Simple Linear Regression Inference 1 Inference requirements The Normality assumption of the stochastic term e is needed for inference even if it is not a OLS requirement. Therefore we have: Interpretation
More informationRegression stepbystep using Microsoft Excel
Step 1: Regression stepbystep using Microsoft Excel Notes prepared by Pamela Peterson Drake, James Madison University Type the data into the spreadsheet The example used throughout this How to is a regression
More informationSan Jose State University Engineering 10 1
KY San Jose State University Engineering 10 1 Select Insert from the main menu Plotting in Excel Select All Chart Types San Jose State University Engineering 10 2 Definition: A chart that consists of multiple
More informationThe 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 3031, 2008 B. Weaver, NHRC 2008 1 The Objective
More informationExercise 1.12 (Pg. 2223)
Individuals: The objects that are described by a set of data. They may be people, animals, things, etc. (Also referred to as Cases or Records) Variables: The characteristics recorded about each individual.
More informationCourse Text. Required Computing Software. Course Description. Course Objectives. StraighterLine. Business Statistics
Course Text Business Statistics Lind, Douglas A., Marchal, William A. and Samuel A. Wathen. Basic Statistics for Business and Economics, 7th edition, McGrawHill/Irwin, 2010, ISBN: 9780077384470 [This
More informationTechnology StepbyStep Using StatCrunch
Technology StepbyStep 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
More informationIntroduction to Regression and Data Analysis
Statlab Workshop Introduction to Regression and Data Analysis with Dan Campbell and Sherlock Campbell October 28, 2008 I. The basics A. Types of variables Your variables may take several forms, and it
More informationFinal Exam Practice Problem Answers
Final Exam Practice Problem Answers The following data set consists of data gathered from 77 popular breakfast cereals. The variables in the data set are as follows: Brand: The brand name of the cereal
More information, 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 (11/20/0611/24/06) CD Lessons: 69, 70, 1620 Textbook: pp. 520528, 111124, 133141 An SRS of size 100 is taken from a population having proportion 0.8 of successes. An
More informationMultiple Linear Regression
Multiple Linear Regression A regression with two or more explanatory variables is called a multiple regression. Rather than modeling the mean response as a straight line, as in simple regression, it is
More informationA Primer on Forecasting Business Performance
A Primer on Forecasting Business Performance There are two common approaches to forecasting: qualitative and quantitative. Qualitative forecasting methods are important when historical data is not available.
More informationSimple Predictive Analytics Curtis Seare
Using Excel to Solve Business Problems: Simple Predictive Analytics Curtis Seare Copyright: Vault Analytics July 2010 Contents Section I: Background Information Why use Predictive Analytics? How to use
More informationChapter 5 Analysis of variance SPSS Analysis of variance
Chapter 5 Analysis of variance SPSS Analysis of variance Data file used: gss.sav How to get there: Analyze Compare Means Oneway ANOVA To test the null hypothesis that several population means are equal,
More informationChapter 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
More informationSimple Methods and Procedures Used in Forecasting
Simple Methods and Procedures Used in Forecasting The project prepared by : Sven Gingelmaier Michael Richter Under direction of the Maria JadamusHacura What Is Forecasting? Prediction of future events
More informationElementary Statistics Sample Exam #3
Elementary Statistics Sample Exam #3 Instructions. No books or telephones. Only the supplied calculators are allowed. The exam is worth 100 points. 1. A chi square goodness of fit test is considered to
More informationInferential Statistics
Inferential Statistics Sampling and the normal distribution Zscores Confidence levels and intervals Hypothesis testing Commonly used statistical methods Inferential Statistics Descriptive statistics are
More informationSIMPLE 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
More informationChapter 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
More information" Y. Notation and Equations for Regression Lecture 11/4. Notation:
Notation: Notation and Equations for Regression Lecture 11/4 m: The number of predictor variables in a regression Xi: One of multiple predictor variables. The subscript i represents any number from 1 through
More informatione = 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.
More informationData Analysis Tools. Tools for Summarizing Data
Data Analysis Tools This section of the notes is meant to introduce you to many of the tools that are provided by Excel under the Tools/Data Analysis menu item. If your computer does not have that tool
More informationMTH 140 Statistics Videos
MTH 140 Statistics Videos Chapter 1 Picturing Distributions with Graphs Individuals and Variables Categorical Variables: Pie Charts and Bar Graphs Categorical Variables: Pie Charts and Bar Graphs Quantitative
More informationWeek TSX Index 1 8480 2 8470 3 8475 4 8510 5 8500 6 8480
1) The S & P/TSX Composite Index is based on common stock prices of a group of Canadian stocks. The weekly close level of the TSX for 6 weeks are shown: Week TSX Index 1 8480 2 8470 3 8475 4 8510 5 8500
More informationInstitute of Actuaries of India Subject CT3 Probability and Mathematical Statistics
Institute of Actuaries of India Subject CT3 Probability and Mathematical Statistics For 2015 Examinations Aim The aim of the Probability and Mathematical Statistics subject is to provide a grounding in
More informationUnivariate Regression
Univariate Regression Correlation and Regression The regression line summarizes the linear relationship between 2 variables Correlation coefficient, r, measures strength of relationship: the closer r is
More informationRegression. 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
More informationNCSS 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
More informationViolent crime total. Problem Set 1
Problem Set 1 Note: this problem set is primarily intended to get you used to manipulating and presenting data using a spreadsheet program. While subsequent problem sets will be useful indicators of the
More informationX X X a) perfect linear correlation b) no correlation c) positive correlation (r = 1) (r = 0) (0 < r < 1)
CORRELATION AND REGRESSION / 47 CHAPTER EIGHT CORRELATION AND REGRESSION Correlation and regression are statistical methods that are commonly used in the medical literature to compare two or more variables.
More informationFactors affecting online sales
Factors affecting online sales Table of contents Summary... 1 Research questions... 1 The dataset... 2 Descriptive statistics: The exploratory stage... 3 Confidence intervals... 4 Hypothesis tests... 4
More information2. What is the general linear model to be used to model linear trend? (Write out the model) = + + + or
Simple and Multiple Regression Analysis Example: Explore the relationships among Month, Adv.$ and Sales $: 1. Prepare a scatter plot of these data. The scatter plots for Adv.$ versus Sales, and Month versus
More informationBusiness Valuation Review
Business Valuation Review Regression Analysis in Valuation Engagements By: George B. Hawkins, ASA, CFA Introduction Business valuation is as much as art as it is science. Sage advice, however, quantitative
More informationAnswer: C. The strength of a correlation does not change if units change by a linear transformation such as: Fahrenheit = 32 + (5/9) * Centigrade
Statistics Quiz Correlation and Regression  ANSWERS 1. Temperature and air pollution are known to be correlated. We collect data from two laboratories, in Boston and Montreal. Boston makes their measurements
More informationDATA INTERPRETATION AND STATISTICS
PholC60 September 001 DATA INTERPRETATION AND STATISTICS Books A easy and systematic introductory text is Essentials of Medical Statistics by Betty Kirkwood, published by Blackwell at about 14. DESCRIPTIVE
More informationSection 14 Simple Linear Regression: Introduction to Least Squares Regression
Slide 1 Section 14 Simple Linear Regression: Introduction to Least Squares Regression There are several different measures of statistical association used for understanding the quantitative relationship
More informationSimple 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
More informationCourse Objective This course is designed to give you a basic understanding of how to run regressions in SPSS.
SPSS Regressions Social Science Research Lab American University, Washington, D.C. Web. www.american.edu/provost/ctrl/pclabs.cfm Tel. x3862 Email. SSRL@American.edu Course Objective This course is designed
More informationUsing 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
More informationModule 3: Correlation and Covariance
Using Statistical Data to Make Decisions Module 3: Correlation and Covariance Tom Ilvento Dr. Mugdim Pašiƒ University of Delaware Sarajevo Graduate School of Business O ften our interest in data analysis
More informationBill Burton Albert Einstein College of Medicine william.burton@einstein.yu.edu April 28, 2014 EERS: Managing the Tension Between Rigor and Resources 1
Bill Burton Albert Einstein College of Medicine william.burton@einstein.yu.edu April 28, 2014 EERS: Managing the Tension Between Rigor and Resources 1 Calculate counts, means, and standard deviations Produce
More informationUsing 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
More informationHow To Run Statistical Tests in Excel
How To Run Statistical Tests in Excel Microsoft Excel is your best tool for storing and manipulating data, calculating basic descriptive statistics such as means and standard deviations, and conducting
More informationStatistics 151 Practice Midterm 1 Mike Kowalski
Statistics 151 Practice Midterm 1 Mike Kowalski Statistics 151 Practice Midterm 1 Multiple Choice (50 minutes) Instructions: 1. This is a closed book exam. 2. You may use the STAT 151 formula sheets and
More informationStatistics Review PSY379
Statistics Review PSY379 Basic concepts Measurement scales Populations vs. samples Continuous vs. discrete variable Independent vs. dependent variable Descriptive vs. inferential stats Common analyses
More informationSimple linear regression
Simple linear regression Introduction Simple linear regression is a statistical method for obtaining a formula to predict values of one variable from another where there is a causal relationship between
More informationSTAT 360 Probability and Statistics. Fall 2012
STAT 360 Probability and Statistics Fall 2012 1) General information: Crosslisted course offered as STAT 360, MATH 360 Semester: Fall 2012, Aug 20Dec 07 Course name: Probability and Statistics Number
More informationINTRODUCTORY STATISTICS
INTRODUCTORY STATISTICS FIFTH EDITION Thomas H. Wonnacott University of Western Ontario Ronald J. Wonnacott University of Western Ontario WILEY JOHN WILEY & SONS New York Chichester Brisbane Toronto Singapore
More informationCorrelation key concepts:
CORRELATION Correlation key concepts: Types of correlation Methods of studying correlation a) Scatter diagram b) Karl pearson s coefficient of correlation c) Spearman s Rank correlation coefficient d)
More informationCorrelation and Regression
Correlation and Regression Scatterplots Correlation Explanatory and response variables Simple linear regression General Principles of Data Analysis First plot the data, then add numerical summaries Look
More informationUsing 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
More informationUnit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression
Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression Objectives: To perform a hypothesis test concerning the slope of a least squares line To recognize that testing for a
More informationCORRELATED TO THE SOUTH CAROLINA COLLEGE AND CAREERREADY FOUNDATIONS IN ALGEBRA
We Can Early Learning Curriculum PreK Grades 8 12 INSIDE ALGEBRA, GRADES 8 12 CORRELATED TO THE SOUTH CAROLINA COLLEGE AND CAREERREADY FOUNDATIONS IN ALGEBRA April 2016 www.voyagersopris.com Mathematical
More informationAn analysis appropriate for a quantitative outcome and a single quantitative explanatory. 9.1 The model behind linear regression
Chapter 9 Simple Linear Regression An analysis appropriate for a quantitative outcome and a single quantitative explanatory variable. 9.1 The model behind linear regression When we are examining the relationship
More information12: Analysis of Variance. Introduction
1: Analysis of Variance Introduction EDA Hypothesis Test Introduction In Chapter 8 and again in Chapter 11 we compared means from two independent groups. In this chapter we extend the procedure to consider
More informationOutline: Demand Forecasting
Outline: Demand Forecasting Given the limited background from the surveys and that Chapter 7 in the book is complex, we will cover less material. The role of forecasting in the chain Characteristics of
More informationScatter Plot, Correlation, and Regression on the TI83/84
Scatter Plot, Correlation, and Regression on the TI83/84 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
More informationChapter 10. Key Ideas Correlation, Correlation Coefficient (r),
Chapter 0 Key Ideas Correlation, Correlation Coefficient (r), Section 0: Overview We have already explored the basics of describing single variable data sets. However, when two quantitative variables
More informationSimple 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,
More informationChapter 23 Inferences About Means
Chapter 23 Inferences About Means Chapter 23  Inferences About Means 391 Chapter 23 Solutions to Class Examples 1. See Class Example 1. 2. We want to know if the mean battery lifespan exceeds the 300minute
More informationACTM State ExamStatistics
ACTM State ExamStatistics For the 25 multiplechoice questions, make your answer choice and record it on the answer sheet provided. Once you have completed that section of the test, proceed to the tiebreaker
More information1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number
1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number A. 3(x  x) B. x 3 x C. 3x  x D. x  3x 2) Write the following as an algebraic expression
More informationModule 5: Multiple Regression Analysis
Using Statistical Data Using to Make Statistical Decisions: Data Multiple to Make Regression Decisions Analysis Page 1 Module 5: Multiple Regression Analysis Tom Ilvento, University of Delaware, College
More informationseven Statistical Analysis with Excel chapter OVERVIEW CHAPTER
seven Statistical Analysis with Excel CHAPTER chapter OVERVIEW 7.1 Introduction 7.2 Understanding Data 7.3 Relationships in Data 7.4 Distributions 7.5 Summary 7.6 Exercises 147 148 CHAPTER 7 Statistical
More informationName: Date: Use the following to answer questions 23:
Name: Date: 1. A study is conducted on students taking a statistics class. Several variables are recorded in the survey. Identify each variable as categorical or quantitative. A) Type of car the student
More informationSimple Linear Regression
STAT 101 Dr. Kari Lock Morgan Simple Linear Regression SECTIONS 9.3 Confidence and prediction intervals (9.3) Conditions for inference (9.1) Want More Stats??? If you have enjoyed learning how to analyze
More informationInstrumental Variables Regression. Instrumental Variables (IV) estimation is used when the model has endogenous s.
Instrumental Variables Regression Instrumental Variables (IV) estimation is used when the model has endogenous s. IV can thus be used to address the following important threats to internal validity: Omitted
More information17. SIMPLE LINEAR REGRESSION II
17. SIMPLE LINEAR REGRESSION II The Model In linear regression analysis, we assume that the relationship between X and Y is linear. This does not mean, however, that Y can be perfectly predicted from X.
More informationhp 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
More informationChicago Booth BUSINESS STATISTICS 41000 Final Exam Fall 2011
Chicago Booth BUSINESS STATISTICS 41000 Final Exam Fall 2011 Name: Section: I pledge my honor that I have not violated the Honor Code Signature: This exam has 34 pages. You have 3 hours to complete this
More informationSouth Carolina College and CareerReady (SCCCR) Probability and Statistics
South Carolina College and CareerReady (SCCCR) Probability and Statistics South Carolina College and CareerReady Mathematical Process Standards The South Carolina College and CareerReady (SCCCR)
More informationScatter 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
More informationStatTools Assignment #1, Winter 2007 This assignment has three parts.
StatTools Assignment #1, Winter 2007 This assignment has three parts. Before beginning this assignment, be sure to carefully read the General Instructions document that is located on the StatTools Assignments
More informationCalculating the Probability of Returning a Loan with Binary Probability Models
Calculating the Probability of Returning a Loan with Binary Probability Models Associate Professor PhD Julian VASILEV (email: vasilev@uevarna.bg) Varna University of Economics, Bulgaria ABSTRACT The
More informationProblems With Using Microsoft Excel for Statistics
Proceedings of the Annual Meeting of the American Statistical Association, August 59, 2001 Problems With Using Microsoft Excel for Statistics Jonathan D. Cryer (JonCryer@uiowa.edu) Department of Statistics
More informationDESCRIPTIVE STATISTICS. The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses.
DESCRIPTIVE STATISTICS The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses. DESCRIPTIVE VS. INFERENTIAL STATISTICS Descriptive To organize,
More informationANOVA Analysis of Variance
ANOVA Analysis of Variance What is ANOVA and why do we use it? Can test hypotheses about mean differences between more than 2 samples. Can also make inferences about the effects of several different IVs,
More informationRegression Analysis. Data Calculations Output
Regression Analysis In an attempt to find answers to questions such as those posed above, empirical labour economists use a useful tool called regression analysis. Regression analysis is essentially a
More informationCorrelation and Simple Linear Regression
Correlation and Simple Linear Regression We are often interested in studying the relationship among variables to determine whether they are associated with one another. When we think that changes in a
More informationRegression and Correlation
Regression and Correlation Topics Covered: Dependent and independent variables. Scatter diagram. Correlation coefficient. Linear Regression line. by Dr.I.Namestnikova 1 Introduction Regression analysis
More informationSPSS Guide: Regression Analysis
SPSS Guide: Regression Analysis I put this together to give you a stepbystep 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
More informationPremaster Statistics Tutorial 4 Full solutions
Premaster Statistics Tutorial 4 Full solutions Regression analysis Q1 (based on Doane & Seward, 4/E, 12.7) a. Interpret the slope of the fitted regression = 125,000 + 150. b. What is the prediction for
More informationEstimation of σ 2, the variance of ɛ
Estimation of σ 2, the variance of ɛ The variance of the errors σ 2 indicates how much observations deviate from the fitted surface. If σ 2 is small, parameters β 0, β 1,..., β k will be reliably estimated
More information11. Analysis of Casecontrol Studies Logistic Regression
Research methods II 113 11. Analysis of Casecontrol Studies Logistic Regression This chapter builds upon and further develops the concepts and strategies described in Ch.6 of Mother and Child Health:
More informationSection A. Index. Section A. Planning, Budgeting and Forecasting Section A.2 Forecasting techniques... 1. Page 1 of 11. EduPristine CMA  Part I
Index Section A. Planning, Budgeting and Forecasting Section A.2 Forecasting techniques... 1 EduPristine CMA  Part I Page 1 of 11 Section A. Planning, Budgeting and Forecasting Section A.2 Forecasting
More informationAppendix E: Graphing Data
You will often make scatter diagrams and line graphs to illustrate the data that you collect. Scatter diagrams are often used to show the relationship between two variables. For example, in an absorbance
More informationPredictor Coef StDev T P Constant 970667056 616256122 1.58 0.154 X 0.00293 0.06163 0.05 0.963. S = 0.5597 RSq = 0.0% RSq(adj) = 0.
Statistical analysis using Microsoft Excel Microsoft Excel spreadsheets have become somewhat of a standard for data storage, at least for smaller data sets. This, along with the program often being packaged
More information7.1 Inference for comparing means of two populations
Objectives 7.1 Inference for comparing means of two populations Matched pair t confidence interval Matched pair t hypothesis test http://onlinestatbook.com/2/tests_of_means/correlated.html Overview of
More informationFlorida Math for College Readiness
Core Florida Math for College Readiness Florida Math for College Readiness provides a fourthyear math curriculum focused on developing the mastery of skills identified as critical to postsecondary readiness
More information