Linear Regression. use waist
|
|
- Alan Small
- 7 years ago
- Views:
Transcription
1 Linear Regression In this tutorial we will explore fitting linear regression models using STATA. We will also cover ways of re-expressing variables in a data set if the conditions for linear regression aren t satisfied. We will be working with the data set discussed in examples on page 210 of the textbook. The data set consists of three variables waist (waist size in inches), weight (weight in pounds) and fat (body fat in %) measured on 20 male subjects. To access the data type: use in the command window. To create a scatter plot for the variables fat and waist type: scatter fat waist This gives rise to the following plot: fat waist Studying the plot, the association between the variables appears to be strong, linear and positive. As the scatter plot indicates a linear relationship between the variables we decide to find the least-squares regression line. We do this by typing the command: regress fat waist In this notation the first variable, fat, is the response variable and the second variable, waist, is the explanatory variable.
2 This command gives rise to the following output in the results window: The output indicates that the least-square regression line is given by. fat ˆ = waist This implies that for each additional inch in waist size, the model predicts an increase of 2.22% body fat. The fraction of the variability in fat that is explained by the least squares line of fat on waist is equal to Next, we want to calculate the predicted values from the regression. We can do this by typing: predict yhat, xb This command is solely used to create a new variable, yhat, and there will be no output in the results window. However, if you look in the variables window a new variable yhat is now present. To plot the regression line together with the data type: scatter fat waist line yhat waist A vertical line can be obtained by simultaneously pressing the shift and the backslash (\) button on your keyboard. This button is located directly above the enter key. To obtain two vertical lines, repeat this procedure twice.
3 The command above tells STATA to create a scatterplot of fat against waist and superimpose the line given by yhat created in the previous command. This command gives the following plot: fat/linear prediction waist fat Linear prediction The line appears to fit the data well. However, it is important to make residual plots when performing regression. We can calculate the residuals by typing the command: predict r, resid Again, note that other than creating a new variable, r, there will be no additional output. The new variable consists of the set of residuals, and a residual plot can be created by typing: scatter r waist This gives rise to the following plot: Residuals waist The residual plot shows no apparent pattern. The residual plot and the relatively 2 high value of R indicate that the linear model we fit is appropriate.
4 Re-expressing Data Often the conditions necessary for performing linear regression aren t satisfied in a data set. However, it may still be possible to use these methods if we reexpress one or both of the variables. To re-express data we need be able to create new variables using STATA. We can do this using the generate command. For example to create a new variable named logx which is the logarithm of an already existing variable x, we type: generate logx = log(x) If we instead wanted to create a variable that is the square root of x, we could type generate sqx = sqrt(x) In general, the command is on the format: generate new_variable = expression(old_variable) where expression is the mathematical function applied to the old variable. Note that by default STATA uses log base e. Linear regression using re-expressed data In this portion of the tutorial we will be working with the data set discussed in example on page 256 of the textbook. The data set gives information on the highest paid baseball players in the period spanning The data set consists of 3 variables player, and salary. To access the data type: use in the command window. We begin by making a scatter plot of salary and. scatter salary
5 This gives rise to the following plot: salary The relationship between and highest salary is moderately strong, positive and curved. Since the scatter plot shows a curved relationship, a linear model is not appropriate. However, it appears that taking the logarithm of salary may help straighten the plot. We can generate a new variable named logsalary, which is the logarithm of the variable salary, by typing: generate logsalary = log(salary) We can make a scatter plot of this new variable against by typing scatter logsalary This gives rise to the following plot: logsalary It appears that the transformation has significantly straightened the scatter plot. We can now proceed with fitting a linear regression model to the transformed data by typing: regress logsalary Note that now the response variable is logsalary instead of salary.
6 This gives rise to the following output: The output indicates that the least-square regression line is given by. log( salary ˆ ) = The fraction of the variability in log(salary) that is explained by the least squares line of log(salary) on is equal to Next, we want to calculate the predicted values from our regression. We can do this by typing: predict yhat, xb Note that other than creating a new variable, yhat, there will be no additional output. To plot the regression line together with the data type: scatter logsalary line yhat The command above tells STATA to create a scatterplot of logsalary against and to superimpose the line given by yhat. This command gives the following output logsalary/linear prediction logsalary Linear prediction
7 The line appears to fit the data well. However, we always want to make sure to check the residual plots. We can calculate the residuals by typing the command: predict r, resid Again, note that other than creating a new variable named r there will be no additional output. We can use this new variable to create a residual plot by typing: scatter r This gives rise to the following output: Residuals e The residual plot shows no apparent pattern. Homework: Do problems RII.8 and 10.9 from the textbook. Solve both of these problems using STATA. For each questions make sure to hand in (a) your log file, (b) a scatter plot with a regression line superimposed, (c) a residual plot, and (d) answers to all the questions in the text.
Descriptive Statistics
Descriptive Statistics Descriptive statistics consist of methods for organizing and summarizing data. It includes the construction of graphs, charts and tables, as well various descriptive measures such
More informationStraightening Data in a Scatterplot Selecting a Good Re-Expression Model
Straightening Data in a Scatterplot Selecting a Good Re-Expression What Is All This Stuff? Here s what is included: Page 3: Graphs of the three main patterns of data points that the student is likely to
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) All but one of these statements contain a mistake. Which could be true? A) There is a correlation
More 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 informationTransforming Bivariate Data
Math Objectives Students will recognize that bivariate data can be transformed to reduce the curvature in the graph of a relationship between two variables. Students will use scatterplots, residual plots,
More 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 informationExercise 1.12 (Pg. 22-23)
Individuals: The objects that are described by a set of data. They may be people, animals, things, etc. (Also referred to as Cases or Records) Variables: The characteristics recorded about each individual.
More informationMATH 4470/5470 EXPLORATORY DATA ANALYSIS ONLINE COURSE SYLLABUS
MATH 4470/5470 EXPLORATORY DATA ANALYSIS ONLINE COURSE SYLLABUS COURSE DESCRIPTION Introduction to modern techniques in data analysis, including stem-and-leafs, box plots, resistant lines, smoothing and
More informationStata Tutorial. 1 Introduction. 1.1 Stata Windows and toolbar. Econometrics676, Spring2008
1 Introduction Stata Tutorial Econometrics676, Spring2008 1.1 Stata Windows and toolbar Review : past commands appear here Variables : variables list Command : where you type your commands Results : results
More informationMULTIPLE 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
More informationHomework 8 Solutions
Math 17, Section 2 Spring 2011 Homework 8 Solutions Assignment Chapter 7: 7.36, 7.40 Chapter 8: 8.14, 8.16, 8.28, 8.36 (a-d), 8.38, 8.62 Chapter 9: 9.4, 9.14 Chapter 7 7.36] a) A scatterplot is given below.
More informationLecture 11: Chapter 5, Section 3 Relationships between Two Quantitative Variables; Correlation
Lecture 11: Chapter 5, Section 3 Relationships between Two Quantitative Variables; Correlation Display and Summarize Correlation for Direction and Strength Properties of Correlation Regression Line Cengage
More 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 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 informationGetting started with the Stata
Getting started with the Stata 1. Begin by going to a Columbia Computer Labs. 2. Getting started Your first Stata session. Begin by starting Stata on your computer. Using a PC: 1. Click on start menu 2.
More informationData analysis and regression in Stata
Data analysis and regression in Stata This handout shows how the weekly beer sales series might be analyzed with Stata (the software package now used for teaching stats at Kellogg), for purposes of comparing
More informationRegression III: Advanced Methods
Lecture 4: Transformations Regression III: Advanced Methods William G. Jacoby Michigan State University Goals of the lecture The Ladder of Roots and Powers Changing the shape of distributions Transforming
More 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 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 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 informationch12 practice test SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
ch12 practice test 1) The null hypothesis that x and y are is H0: = 0. 1) 2) When a two-sided significance test about a population slope has a P-value below 0.05, the 95% confidence interval for A) does
More informationCurve Fitting with Maple
Curve Fitting with Maple Maplesoft, a division of Waterloo Maple Inc., 2007 Introduction Maple includes a number of assistants that allows a user to experiment and easily perform key tasks. This Tips and
More informationCorrelation Coefficient The correlation coefficient is a summary statistic that describes the linear relationship between two numerical variables 2
Lesson 4 Part 1 Relationships between two numerical variables 1 Correlation Coefficient The correlation coefficient is a summary statistic that describes the linear relationship between two numerical variables
More informationDetermine If An Equation Represents a Function
Question : What is a linear function? The term linear function consists of two parts: linear and function. To understand what these terms mean together, we must first understand what a function is. The
More informationSection 3 Part 1. Relationships between two numerical variables
Section 3 Part 1 Relationships between two numerical variables 1 Relationship between two variables The summary statistics covered in the previous lessons are appropriate for describing a single variable.
More informationDoing Multiple Regression with SPSS. In this case, we are interested in the Analyze options so we choose that menu. If gives us a number of choices:
Doing Multiple Regression with SPSS Multiple Regression for Data Already in Data Editor Next we want to specify a multiple regression analysis for these data. The menu bar for SPSS offers several options:
More informationChapter 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 informationDescribing, 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
More informationRegression III: Advanced Methods
Lecture 16: Generalized Additive Models Regression III: Advanced Methods Bill Jacoby Michigan State University http://polisci.msu.edu/jacoby/icpsr/regress3 Goals of the Lecture Introduce Additive Models
More informationSession 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
More information1 Review of Least Squares Solutions to Overdetermined Systems
cs4: introduction to numerical analysis /9/0 Lecture 7: Rectangular Systems and Numerical Integration Instructor: Professor Amos Ron Scribes: Mark Cowlishaw, Nathanael Fillmore Review of Least Squares
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 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 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 informationName: Date: Use the following to answer questions 2-3:
Name: Date: 1. A study is conducted on students taking a statistics class. Several variables are recorded in the survey. Identify each variable as categorical or quantitative. A) Type of car the student
More informationScatter Plot, Correlation, and Regression on the TI-83/84
Scatter Plot, Correlation, and Regression on the TI-83/84 Summary: When you have a set of (x,y) data points and want to find the best equation to describe them, you are performing a regression. This page
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 informationLecture 2 Mathcad Basics
Operators Lecture 2 Mathcad Basics + Addition, - Subtraction, * Multiplication, / Division, ^ Power ( ) Specify evaluation order Order of Operations ( ) ^ highest level, first priority * / next priority
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 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 informationAP Statistics. Chapter 4 Review
Name AP Statistics Chapter 4 Review 1. In a study of the link between high blood pressure and cardiovascular disease, a group of white males aged 35 to 64 was followed for 5 years. At the beginning of
More informationTutorial for the TI-89 Titanium Calculator
SI Physics Tutorial for the TI-89 Titanium Calculator Using Scientific Notation on a TI-89 Titanium calculator From Home, press the Mode button, then scroll down to Exponential Format. Select Scientific.
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 informationLeast Squares Regression. Alan T. Arnholt Department of Mathematical Sciences Appalachian State University arnholt@math.appstate.
Least Squares Regression Alan T. Arnholt Department of Mathematical Sciences Appalachian State University arnholt@math.appstate.edu Spring 2006 R Notes 1 Copyright c 2006 Alan T. Arnholt 2 Least Squares
More informationMultiple Regression: What Is It?
Multiple Regression Multiple Regression: What Is It? Multiple regression is a collection of techniques in which there are multiple predictors of varying kinds and a single outcome We are interested in
More informationNonlinear Regression Functions. SW Ch 8 1/54/
Nonlinear Regression Functions SW Ch 8 1/54/ The TestScore STR relation looks linear (maybe) SW Ch 8 2/54/ But the TestScore Income relation looks nonlinear... SW Ch 8 3/54/ Nonlinear Regression General
More information2. Here is a small part of a data set that describes the fuel economy (in miles per gallon) of 2006 model motor vehicles.
Math 1530-017 Exam 1 February 19, 2009 Name Student Number E There are five possible responses to each of the following multiple choice questions. There is only on BEST answer. Be sure to read all possible
More informationRelationships Between Two Variables: Scatterplots and Correlation
Relationships Between Two Variables: Scatterplots and Correlation Example: Consider the population of cars manufactured in the U.S. What is the relationship (1) between engine size and horsepower? (2)
More informationC 5 - COST BEHAVIOR: ANALYSIS AND USE notes-c5.doc Written by Professor Gregory M. Burbage, MBA, CPA, CMA, CFM
C 5 - COST BEHAVIOR: ANALYSIS AND USE notes-c5.doc CHAPTER LEARNING OBJECTIVES: MAJOR: - Use the High-Low method to determine and calculate the structure of a cost. - Define, explain and use variable,
More informationLecture 13/Chapter 10 Relationships between Measurement (Quantitative) Variables
Lecture 13/Chapter 10 Relationships between Measurement (Quantitative) Variables Scatterplot; Roles of Variables 3 Features of Relationship Correlation Regression Definition Scatterplot displays relationship
More informationTutorial Customer Lifetime Value
MARKETING ENGINEERING FOR EXCEL TUTORIAL VERSION 150211 Tutorial Customer Lifetime Value Marketing Engineering for Excel is a Microsoft Excel add-in. The software runs from within Microsoft Excel and only
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 informationALGEBRA 2/TRIGONOMETRY
ALGEBRA /TRIGONOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA /TRIGONOMETRY Tuesday, June 1, 011 1:15 to 4:15 p.m., only Student Name: School Name: Print your name
More informationCurve Fitting in Microsoft Excel By William Lee
Curve Fitting in Microsoft Excel By William Lee This document is here to guide you through the steps needed to do curve fitting in Microsoft Excel using the least-squares method. In mathematical equations
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 informationCURVE FITTING LEAST SQUARES APPROXIMATION
CURVE FITTING LEAST SQUARES APPROXIMATION Data analysis and curve fitting: Imagine that we are studying a physical system involving two quantities: x and y Also suppose that we expect a linear relationship
More informationStata Walkthrough 4: Regression, Prediction, and Forecasting
Stata Walkthrough 4: Regression, Prediction, and Forecasting Over drinks the other evening, my neighbor told me about his 25-year-old nephew, who is dating a 35-year-old woman. God, I can t see them getting
More informationA Primer on Mathematical Statistics and Univariate Distributions; The Normal Distribution; The GLM with the Normal Distribution
A Primer on Mathematical Statistics and Univariate Distributions; The Normal Distribution; The GLM with the Normal Distribution PSYC 943 (930): Fundamentals of Multivariate Modeling Lecture 4: September
More informationThe KaleidaGraph Guide to Curve Fitting
The KaleidaGraph Guide to Curve Fitting Contents Chapter 1 Curve Fitting Overview 1.1 Purpose of Curve Fitting... 5 1.2 Types of Curve Fits... 5 Least Squares Curve Fits... 5 Nonlinear Curve Fits... 6
More information3.2. Solving quadratic equations. Introduction. Prerequisites. Learning Outcomes. Learning Style
Solving quadratic equations 3.2 Introduction A quadratic equation is one which can be written in the form ax 2 + bx + c = 0 where a, b and c are numbers and x is the unknown whose value(s) we wish to find.
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 informationStatistics 2014 Scoring Guidelines
AP Statistics 2014 Scoring Guidelines College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. AP Central is the official online home
More informationUsing R for Linear Regression
Using R for Linear Regression In the following handout words and symbols in bold are R functions and words and symbols in italics are entries supplied by the user; underlined words and symbols are optional
More informationQuickstart for Desktop Version
Quickstart for Desktop Version What is GeoGebra? Dynamic Mathematics Software in one easy-to-use package For learning and teaching at all levels of education Joins interactive 2D and 3D geometry, algebra,
More informationEXCEL Tutorial: How to use EXCEL for Graphs and Calculations.
EXCEL Tutorial: How to use EXCEL for Graphs and Calculations. Excel is powerful tool and can make your life easier if you are proficient in using it. You will need to use Excel to complete most of your
More informationBinary Logistic Regression
Binary Logistic Regression Main Effects Model Logistic regression will accept quantitative, binary or categorical predictors and will code the latter two in various ways. Here s a simple model including
More informationBasics of STATA. 1 Data les. 2 Loading data into STATA
Basics of STATA This handout is intended as an introduction to STATA. STATA is available on the PCs in the computer lab as well as on the Unix system. Throughout, bold type will refer to STATA commands,
More informationComputer exercise 4 Poisson Regression
Chalmers-University of Gothenburg Department of Mathematical Sciences Probability, Statistics and Risk MVE300 Computer exercise 4 Poisson Regression When dealing with two or more variables, the functional
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 information8.1. Cramer s Rule for Solving Simultaneous Linear Equations. Introduction. Prerequisites. Learning Outcomes. Learning Style
Cramer s Rule for Solving Simultaneous Linear Equations 8.1 Introduction The need to solve systems of linear equations arises frequently in engineering. The analysis of electric circuits and the control
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 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 informationSPSS Tutorial, Feb. 7, 2003 Prof. Scott Allard
p. 1 SPSS Tutorial, Feb. 7, 2003 Prof. Scott Allard The following tutorial is a guide to some basic procedures in SPSS that will be useful as you complete your data assignments for PPA 722. The purpose
More informationPrentice Hall Mathematics: Algebra 2 2007 Correlated to: Utah Core Curriculum for Math, Intermediate Algebra (Secondary)
Core Standards of the Course Standard 1 Students will acquire number sense and perform operations with real and complex numbers. Objective 1.1 Compute fluently and make reasonable estimates. 1. Simplify
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 informationThere are six different windows that can be opened when using SPSS. The following will give a description of each of them.
SPSS Basics Tutorial 1: SPSS Windows There are six different windows that can be opened when using SPSS. The following will give a description of each of them. The Data Editor The Data Editor is a spreadsheet
More information0 Introduction to Data Analysis Using an Excel Spreadsheet
Experiment 0 Introduction to Data Analysis Using an Excel Spreadsheet I. Purpose The purpose of this introductory lab is to teach you a few basic things about how to use an EXCEL 2010 spreadsheet to do
More informationActivity 5. Two Hot, Two Cold. Introduction. Equipment Required. Collecting the Data
. Activity 5 Two Hot, Two Cold How do we measure temperatures? In almost all countries of the world, the Celsius scale (formerly called the centigrade scale) is used in everyday life and in science and
More informationMeans, 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
More informationCHAPTER 2 Estimating Probabilities
CHAPTER 2 Estimating Probabilities Machine Learning Copyright c 2016. Tom M. Mitchell. All rights reserved. *DRAFT OF January 24, 2016* *PLEASE DO NOT DISTRIBUTE WITHOUT AUTHOR S PERMISSION* This is a
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS B. Thursday, January 29, 2004 9:15 a.m. to 12:15 p.m.
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS B Thursday, January 9, 004 9:15 a.m. to 1:15 p.m., only Print Your Name: Print Your School s Name: Print your name and
More informationy = a + bx Chapter 10: Horngren 13e The Dependent Variable: The cost that is being predicted The Independent Variable: The cost driver
Chapter 10: Dt Determining ii How Costs Behave Bh Horngren 13e 1 The Linear Cost Function y = a + bx The Dependent Variable: The cost that is being predicted The Independent Variable: The cost driver The
More informationThe right edge of the box is the third quartile, Q 3, which is the median of the data values above the median. Maximum Median
CONDENSED LESSON 2.1 Box Plots In this lesson you will create and interpret box plots for sets of data use the interquartile range (IQR) to identify potential outliers and graph them on a modified box
More informationA Short Guide to R with RStudio
Short Guides to Microeconometrics Fall 2013 Prof. Dr. Kurt Schmidheiny Universität Basel A Short Guide to R with RStudio 1 Introduction 2 2 Installing R and RStudio 2 3 The RStudio Environment 2 4 Additions
More informationFactorizations: Searching for Factor Strings
" 1 Factorizations: Searching for Factor Strings Some numbers can be written as the product of several different pairs of factors. For example, can be written as 1, 0,, 0, and. It is also possible to write
More informationEngineering Problem Solving and Excel. EGN 1006 Introduction to Engineering
Engineering Problem Solving and Excel EGN 1006 Introduction to Engineering Mathematical Solution Procedures Commonly Used in Engineering Analysis Data Analysis Techniques (Statistics) Curve Fitting techniques
More informationIrrational Numbers. A. Rational Numbers 1. Before we discuss irrational numbers, it would probably be a good idea to define rational numbers.
Irrational Numbers A. Rational Numbers 1. Before we discuss irrational numbers, it would probably be a good idea to define rational numbers. Definition: Rational Number A rational number is a number that
More informationA Short Introduction to Eviews
A Short Introduction to Eviews Note You are responsible to get familiar with Eviews as soon as possible. All homeworks are likely to contain questions for which you will need to use this software package.
More informationLinear Models in STATA and ANOVA
Session 4 Linear Models in STATA and ANOVA Page Strengths of Linear Relationships 4-2 A Note on Non-Linear Relationships 4-4 Multiple Linear Regression 4-5 Removal of Variables 4-8 Independent Samples
More informationStatistics courses often teach the two-sample t-test, linear regression, and analysis of variance
2 Making Connections: The Two-Sample t-test, Regression, and ANOVA In theory, there s no difference between theory and practice. In practice, there is. Yogi Berra 1 Statistics courses often teach the two-sample
More informationChapter Seven. Multiple regression An introduction to multiple regression Performing a multiple regression on SPSS
Chapter Seven Multiple regression An introduction to multiple regression Performing a multiple regression on SPSS Section : An introduction to multiple regression WHAT IS MULTIPLE REGRESSION? Multiple
More informationGeneralized Linear Models
Generalized Linear Models We have previously worked with regression models where the response variable is quantitative and normally distributed. Now we turn our attention to two types of models where the
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 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 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 informationMEASURES 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
More informationECONOMICS 351* -- Stata 10 Tutorial 2. Stata 10 Tutorial 2
Stata 10 Tutorial 2 TOPIC: Introduction to Selected Stata Commands DATA: auto1.dta (the Stata-format data file you created in Stata Tutorial 1) or auto1.raw (the original text-format data file) TASKS:
More informationMethod To Solve Linear, Polynomial, or Absolute Value Inequalities:
Solving Inequalities An inequality is the result of replacing the = sign in an equation with ,, or. For example, 3x 2 < 7 is a linear inequality. We call it linear because if the < were replaced with
More informationIn this chapter, you will learn to use cost-volume-profit analysis.
2.0 Chapter Introduction In this chapter, you will learn to use cost-volume-profit analysis. Assumptions. When you acquire supplies or services, you normally expect to pay a smaller price per unit as the
More informationSummary of important mathematical operations and formulas (from first tutorial):
EXCEL Intermediate Tutorial Summary of important mathematical operations and formulas (from first tutorial): Operation Key Addition + Subtraction - Multiplication * Division / Exponential ^ To enter a
More information