Results and Analysis 10/4/2012. EE145L Lab 1, Linear Regression
|
|
- Gregory Berry
- 5 years ago
- Views:
Transcription
1 EE145L Lab 1, Linear Regression 10/4/2012 Abstract We examined multiple sets of data to assess the relationship between the variables, linear or non-linear, in addition to studying ways of transforming data to make it linear. Then, we compared the linear relation between variables for one data set using both estimation and linear regression techniques, to conclude that linear regression was a more accurate way of determining a linear fit to the data. Introduction We used the linear regression technique to analyze different sets of data. This technique is based off finding the best-fit line to data to see if it can be called linear. The premise is that a best-fit line should be one that is the least distant from all of the individual data points, but we do not actually try and minimize the distance itself. We actually minimize the square of the distance, since the distance itself can be positive or negative, and if added together would cancel to be a lesser total distance. So, the theory of linear regression is that we will find the best fit line to the data by minimizing the distance-squared from the line. We expect to use this technique to find best-fit lines to data that fit much better than hand-drawn lines, and to experiment with transformations of non-linear data sets to make them linear. We start with the definition of a line being y = mx+b, writing it as y i = a 0 +a 1 x i +e i ; e i = y i (a 0 +a 1 x i ) We also use the quantity S, where S = Σe 2 i = Σ[y i -(a 0 +a 1 x i )] 2 is a function of a 1 and a 0. This is the square of the difference between the individual data points and the linear regression line, so this is the quantity we are minimizing. To minimize an equation, you take the first derivative and set it equal to zero; since this is a multi-variable equation, we will take the partial derivatives ds/da 0 and ds/da 1 and set them both equal to zero, and solve the 2 equations simultaneously to find the 2 variables. We find that ds/da 0 = Σ(2)[y i (a 0 +a 1 x i )](-1) na 0 + a 1 Σx i = Σy i, where n is the number of total data points. We also find ds/da 1 = Σ(2)[y i (a 0 +a 1 x i )](-x i ) 2 Σx i y i = a 0 Σx i +a 1 Σx i From these 2 equations, we can find values for the a 1 and a 0 in our predicted line; we find a 1 = a 0 = Thus, to find our best-fit line of y = a 0 + a 1 x i, we simply plug in our x- and y- values to find a 0 and a 1, and that will give us the equation of the best-fit line. Results and Analysis
2 Exercise 0 In this exercise, we considered different given sets of data, and assessed characteristics of the data such as variable dependence/independence, expected linearity and options of transforming the data to make it linear. The independent variable has values that the experimenter can set, and the values of the independent variable depend on the choices for the independent one. We had 3 different sets of data, labeled in the charts below as part 1 for the first set, part 2 for the second set, and part 3 for the third set. For the first set of data, contained in Figure 1 below labeled Exercise 0 Part 1, we found the independent variable to be the as a quadratic or cubic. Figure 1, Exercise 0 Part 1 For the second set of data, seen in Figure 2 below labeled Exercise 0 Part 2, we found the independent variable to be the data was graphed, it did indeed to appear to be linearly related without any transformations necessary.
3 Figure 2, Exercise 0 Part 2 For the third set of data, seen below in Figure 3 labeled Exercise 0 Part 3, we found the dependent variable to be the Figure 3, Exercise 0 Part 3 not appear to be linear. However, we hypothesized that transforming the data correctly would yield a linear relationship.
4 Figure 4, Exercise 0 Part 4 Exercise 1 In this part of the lab, we analyzed a new set of given data, specific heat of a chemical vs. its temperature. We were first asked to plot the data on a scatter plot, as seen in Figure 5 below. We determined that it appeared a general linear relationship existed between the variables. Figure 5, Scatterplot of data from Exercise 1 We then fit a straight line to the data, and found the slope (m) to be approximately This appeared to fit in well with the linear appearance of this data set.. Exercise 2 In this exercise, we were asked to perform a linear regression on the same data set
5 as in exercise 1. We wanted to find a linear relationship y = a o + a 1 x, and used the derivation given in the introduction to find that a 1 = a 0 =. We then did the appropriate sums with our x- and y-values, noting that n was 12 since we had 12 data points, and found: 0. Plugging these into the equations for a o and a 1, we found a 1 = , and a 0 = Thus, our line would be y =. We were then asked to estimate the specific heat of this chemical (y) when the temperature (x) was 75 degrees Celsius, as we did in exercise 1. Using our new line equation and plugging in 75 for x yielded y =. The percent difference between this value and the value found in exercise 1 was, using this value as the actual and the value from part 1 as experimental, = We believe that the value found in exercise 2 is more accurate, since it was found using a line obtained from performing a linear regression, and the value from exercise 1 was found based off an equation of a line that was hand-drawn to fit the data. Conclusion This experiment was a success, we found all of the conclusions to match our expectations in the introduction. We explored linear versus non-linear data sets, and transformations from non-linear to linear. We also compared data analyzed using both linear regression and simple hand-drawn techniques, and found that the linear regression, as expected, made a more accurate fit to our data. We also saw that further data concluded from these lines varied between the linear regression and estimation models by 1.2%, and thus, values based off the estimated line would not be as accurate as those based on the linear regression line. Linear regression is a valuable technique to check the relationship between variables in an experiment, and is only the beginning of a wide variety of statistical analytical techniques to check correlation between variables.
Approximate Linear Relationships
Approximate Linear Relationships In the real world, rarely do things follow trends perfectly. When the trend is expected to behave linearly, or when inspection suggests the trend is behaving linearly,
More informationChapter 5: Data Transformation
Chapter 5: Data Transformation The circle of transformations The x-squared transformation The log transformation The reciprocal transformation Regression analysis choosing the best transformation TEXT:
More informationregression analysis is a type of inferential statistics which tells us whether relationships between two or more variables exist
regression analysis is a type of inferential statistics which tells us whether relationships between two or more variables exist sales $ (y - dependent variable) advertising $ (x - independent variable)
More informationSolutions to Problems and
Solutions to Problems 1.2.24 and 1.2.27 Will Johnson September 6, 2014 Since people asked me about these problems, I said I d write up some solutions. (27) A general power function looks like f(x) = cx
More information5-Sep-15 PHYS101-2 GRAPHING
GRAPHING Objectives 1- To plot and analyze a graph manually and using Microsoft Excel. 2- To find constants from a nonlinear relation. Exercise 1 - Using Excel to plot a graph Suppose you have measured
More informationContents. 9. Fractional and Quadratic Equations 2 Example Example Example
Contents 9. Fractional and Quadratic Equations 2 Example 9.52................................ 2 Example 9.54................................ 3 Example 9.55................................ 4 1 Peterson,
More informationLearning Goals. 2. To be able to distinguish between a dependent and independent variable.
Learning Goals 1. To understand what a linear regression is. 2. To be able to distinguish between a dependent and independent variable. 3. To understand what the correlation coefficient measures. 4. To
More informationCorrelation and Regression Theory 1) Multivariate Statistics
Correlation and Regression Theory 1) Multivariate Statistics What is a multivariate data set? How to statistically analyze this data set? Is there any kind of relationship between different variables in
More informationBIOSTATISTICS NURS 3324
Simple Linear Regression and Correlation Introduction Previously, our attention has been focused on one variable which we designated by x. Frequently, it is desirable to learn something about the relationship
More informationRegression Models. Chapter 4
Chapter 4 Regression Models To accompany Quantitative Analysis for Management, Eleventh Edition, by Render, Stair, and Hanna Power Point slides created by Brian Peterson Introduction Regression analysis
More informationPredicted Y Scores. The symbol stands for a predicted Y score
REGRESSION 1 Linear Regression Linear regression is a statistical procedure that uses relationships to predict unknown Y scores based on the X scores from a correlated variable. 2 Predicted Y Scores Y
More informationNon-Linear Regression
Non-Linear Regression Recall that linear regression is a technique for finding the equation of the line of best fit (LOBF) when two variables have a linear association (i.e. changes in one variable tend
More informationChapter 3: Examining Relationships
Chapter 3: Examining Relationships Most statistical studies involve more than one variable. Often in the AP Statistics exam, you will be asked to compare two data sets by using side by side boxplots or
More informationUpon completion of this chapter, you should be able to:
1 Chaptter 7:: CORRELATIION Upon completion of this chapter, you should be able to: Explain the concept of relationship between variables Discuss the use of the statistical tests to determine correlation
More informationPHYSICS LAB: CONSTANT MOTION
PHYSICS LAB: CONSTANT MOTION Introduction Experimentation is fundamental to physics (and all science, for that matter) because it allows us to prove or disprove our hypotheses about how the physical world
More informationMeasurement: The Basics
I. Introduction Measurement: The Basics Physics is first and foremost an experimental science, meaning that its accumulated body of knowledge is due to the meticulous experiments performed by teams of
More information1. In Activity 1-1, part 3, how do you think graph a will differ from graph b? 3. Draw your graph for Prediction 2-1 below:
PRE-LAB PREPARATION SHEET FOR LAB 1: INTRODUCTION TO MOTION (Due at the beginning of Lab 1) Directions: Read over Lab 1 and then answer the following questions about the procedures. 1. In Activity 1-1,
More informationMotion II. Goals and Introduction
Motion II Goals and Introduction As you have probably already seen in lecture or homework, and if you ve performed the experiment Motion I, it is important to develop a strong understanding of how to model
More information3 Non-linearities and Dummy Variables
3 Non-linearities and Dummy Variables Reading: Kennedy (1998) A Guide to Econometrics, Chapters 3, 5 and 6 Aim: The aim of this section is to introduce students to ways of dealing with non-linearities
More informationIntermediate Algebra Summary - Part I
Intermediate Algebra Summary - Part I This is an overview of the key ideas we have discussed during the first part of this course. You may find this summary useful as a study aid, but remember that the
More informationCurve Fitting. Objectives
Curve Fitting Objectives Understanding the difference between regression and interpolation. Knowing how to fit curve of discrete with least-squares regression. Knowing how to compute and understand the
More informationCorrelation and Regression
Correlation and Regression 8 9 Copyright Cengage Learning. All rights reserved. Section 9.2 Linear Regression and the Coefficient of Determination Copyright Cengage Learning. All rights reserved. Focus
More informationChapter 12 Summarizing Bivariate Data Linear Regression and Correlation
Chapter 1 Summarizing Bivariate Data Linear Regression and Correlation This chapter introduces an important method for making inferences about a linear correlation (or relationship) between two variables,
More informationA Cubic Regression Group Activity 4 STEM Project Week #7
A Cubic Regression Group Activity 4 STEM Project Week #7 In the first activity we looked at a set of data that was modeled by a line (a linear regression). In the second and third activities we looked
More information23. Inference for regression
23. Inference for regression The Practice of Statistics in the Life Sciences Third Edition 2014 W. H. Freeman and Company Objectives (PSLS Chapter 23) Inference for regression The regression model Confidence
More information1 Measurement Uncertainties
1 Measurement Uncertainties (Adapted stolen, really from work by Amin Jaziri) 1.1 Introduction No measurement can be perfectly certain. No measuring device is infinitely sensitive or infinitely precise.
More informationASSIGNMENT 3 SIMPLE LINEAR REGRESSION. Old Faithful
ASSIGNMENT 3 SIMPLE LINEAR REGRESSION In the simple linear regression model, the mean of a response variable is a linear function of an explanatory variable. The model and associated inferential tools
More informationScatter plot of data from the study. Linear Regression
1 2 Linear Regression Scatter plot of data from the study. Consider a study to relate birthweight to the estriol level of pregnant women. The data is below. i Weight (g / 100) i Weight (g / 100) 1 7 25
More informationUnit 1 Science Models & Graphing
Name: Date: 9/18 Period: Unit 1 Science Models & Graphing Essential Questions: What do scientists mean when they talk about models? How can we get equations from graphs? Objectives Explain why models are
More informationScatterplots and Correlation
Bivariate Data Page 1 Scatterplots and Correlation Essential Question: What is the correlation coefficient and what does it tell you? Most statistical studies examine data on more than one variable. Fortunately,
More informationProb and Stats, Sep 23
Prob and Stats, Sep 23 Calculator Scatter Plots and Equations of Lines of Fit Book Sections: 4.1 Essential Questions: How can the calculator help me to produce a scatter plot, and also the equation of
More informationChapter 4. Regression Models. Learning Objectives
Chapter 4 Regression Models To accompany Quantitative Analysis for Management, Eleventh Edition, by Render, Stair, and Hanna Power Point slides created by Brian Peterson Learning Objectives After completing
More informationMAT 171. August 22, S1.4 Equations of Lines and Modeling. Section 1.4 Equations of Lines and Modeling
MAT 171 WebAdvisor: http://reg.cfcc.edu Dr. Claude Moore, CFCC Session 1 introduces the Course, CourseCompass, and Chapter 1: Graphs, Functions, and Models. This session is available in CourseCompass.
More informationSect Polynomial and Rational Inequalities
158 Sect 10.2 - Polynomial and Rational Inequalities Concept #1 Solving Inequalities Graphically Definition A Quadratic Inequality is an inequality that can be written in one of the following forms: ax
More informationElliptic Curves. Dr. Carmen Bruni. November 4th, University of Waterloo
University of Waterloo November 4th, 2015 Revisit the Congruent Number Problem Congruent Number Problem Determine which positive integers N can be expressed as the area of a right angled triangle with
More informationChapte The McGraw-Hill Companies, Inc. All rights reserved.
12er12 Chapte Bivariate i Regression (Part 1) Bivariate Regression Visual Displays Begin the analysis of bivariate data (i.e., two variables) with a scatter plot. A scatter plot - displays each observed
More informationName. The data below are airfares to various cities from Baltimore, MD (including the descriptive statistics).
Name The data below are airfares to various cities from Baltimore, MD (including the descriptive statistics). 178 138 94 278 158 258 198 188 98 179 138 98 N Mean Std. Dev. Min Q 1 Median Q 3 Max 12 166.92
More informationScatter plot of data from the study. Linear Regression
1 2 Linear Regression Scatter plot of data from the study. Consider a study to relate birthweight to the estriol level of pregnant women. The data is below. i Weight (g / 100) i Weight (g / 100) 1 7 25
More informationInference for Regression Inference about the Regression Model and Using the Regression Line, with Details. Section 10.1, 2, 3
Inference for Regression Inference about the Regression Model and Using the Regression Line, with Details Section 10.1, 2, 3 Basic components of regression setup Target of inference: linear dependency
More informationIT 403 Practice Problems (2-2) Answers
IT 403 Practice Problems (2-2) Answers #1. Which of the following is correct with respect to the correlation coefficient (r) and the slope of the leastsquares regression line (Choose one)? a. They will
More informationLecture 12. Functional form
Lecture 12. Functional form Multiple linear regression model β1 + β2 2 + L+ β K K + u Interpretation of regression coefficient k Change in if k is changed by 1 unit and the other variables are held constant.
More informationLab 1 Uniform Motion - Graphing and Analyzing Motion
Lab 1 Uniform Motion - Graphing and Analyzing Motion Objectives: < To observe the distance-time relation for motion at constant velocity. < To make a straight line fit to the distance-time data. < To interpret
More informationChesapeake Campus Chemistry 111 Laboratory
Chesapeake Campus Chemistry 111 Laboratory Objectives Calculate the density of a sugar solution. Evaluate lab sources of error and their effect on an experiment. Introduction The density of an object is
More informationISP 207L Supplementary Information
ISP 207L Supplementary Information Scientific Notation Numbers written in Scientific Notation are composed of two numbers. 1) Digit term A number between 1 and 10 2) Exponential term Integer power of 10
More informationChapter 10. Correlation and Regression. McGraw-Hill, Bluman, 7th ed., Chapter 10 1
Chapter 10 Correlation and Regression McGraw-Hill, Bluman, 7th ed., Chapter 10 1 Chapter 10 Overview Introduction 10-1 Scatter Plots and Correlation 10- Regression 10-3 Coefficient of Determination and
More informationCorrelation and Regression (Excel 2007)
Correlation and Regression (Excel 2007) (See Also Scatterplots, Regression Lines, and Time Series Charts With Excel 2007 for instructions on making a scatterplot of the data and an alternate method of
More informationWhen a function is defined by a fraction, the denominator of that fraction cannot be equal to zero
As stated in the previous lesson, when changing from a function to its inverse the inputs and outputs of the original function are switched, because we take the original function and solve for x. This
More informationDescribing the Relationship between Two Variables
1 Describing the Relationship between Two Variables Key Definitions Scatter : A graph made to show the relationship between two different variables (each pair of x s and y s) measured from the same equation.
More informationGravity: How fast do objects fall? Student Advanced Version
Gravity: How fast do objects fall? Student Advanced Version Kinematics is the study of how things move their position, velocity, and acceleration. Acceleration is always due to some force acting on an
More informationChapter 10. Correlation and Regression. McGraw-Hill, Bluman, 7th ed., Chapter 10 1
Chapter 10 Correlation and Regression McGraw-Hill, Bluman, 7th ed., Chapter 10 1 Example 10-2: Absences/Final Grades Please enter the data below in L1 and L2. The data appears on page 537 of your textbook.
More informationNotes: Unit 1: Math and Measurement
Name: Regents Chemistry: Notes: Unit 1: Math and Measurement www.chempride.weebly.com Key Ideas Major Understandings: o Chemistry is the study of matter: Matter takes up space and has mass. (K- 4, 3.1a)
More informationNotes: Unit 1: Math and Measurement
Name: Regents Chemistry: Notes: Unit 1: Math and Measurement www.chempride.weebly.com Key Ideas Major Understandings: o Chemistry is the study of matter: Matter takes up space and has mass. (K- 4, 3.1a)
More informationSection 2.5 from Precalculus was developed by OpenStax College, licensed by Rice University, and is available on the Connexions website.
Section 2.5 from Precalculus was developed by OpenStax College, licensed by Rice University, and is available on the Connexions website. It is used under a Creative Commons Attribution-NonCommercial- ShareAlike
More information3.7 Linear and Quadratic Models
3.7. Linear and Quadratic Models www.ck12.org 3.7 Linear and Quadratic Models Learning Objectives Identif functions using differences and ratios. Write equations for functions. Perform eponential and quadratic
More informationPreparation for Physics. Mathematical Graphs Equations of a Line
III-1 Mathematical Graphs and Scientific Graphs Mathematical Graphs Equations of a Line In mathematics, graphs are made while studying functions to give a feel for the shape of the graph of a function.
More informationRegression Models. Chapter 4. Introduction. Introduction. Introduction
Chapter 4 Regression Models Quantitative Analysis for Management, Tenth Edition, by Render, Stair, and Hanna 008 Prentice-Hall, Inc. Introduction Regression analysis is a very valuable tool for a manager
More information371 Lab Rybolt Data Analysis Assignment Name
Data Analysis Assignment 1 371 Lab Rybolt Data Analysis Assignment Name You wake up one morning and feel you may have a fever. You have an oral thermometer marked in Celsius degrees and find your temperature
More informationTalking feet: Scatterplots and lines of best fit
Talking feet: Scatterplots and lines of best fit Student worksheet What does your foot say about your height? Can you predict people s height by how long their feet are? If a Grade 10 student s foot is
More informationI. Pre-Lab Introduction
I. Pre-Lab Introduction Please complete the following pages before the lab by filling in the requested items. A. Atomic notation: Atoms are composed of a nucleus containing neutrons and protons surrounded
More informationSNAP Centre Workshop. Solving Systems of Equations
SNAP Centre Workshop Solving Systems of Equations 35 Introduction When presented with an equation containing one variable, finding a solution is usually done using basic algebraic manipulation. Example
More informationLesson Mathematical Linear Models
STATWAY STUDENT HANDOUT STUDENT NAME DATE INTRODUCTION Jean needs to buy some meat for her housing co-operative. She can go to the Fresh-Plus store to buy it for $3.50 per pound. Or she can go to the warehouse
More informationExperiment 2. F r e e F a l l
Suggested Reading for this Lab Experiment F r e e F a l l Taylor, Section.6, and standard deviation rule in Taylor handout. Review Chapters 3 & 4, Read Sections 8.1-8.6. You will also need some procedures
More informationLinear Equations. Find the domain and the range of the following set. {(4,5), (7,8), (-1,3), (3,3), (2,-3)}
Linear Equations Domain and Range Domain refers to the set of possible values of the x-component of a point in the form (x,y). Range refers to the set of possible values of the y-component of a point in
More informationGraphs. 1. Graph paper 2. Ruler
Graphs Objective The purpose of this activity is to learn and develop some of the necessary techniques to graphically analyze data and extract relevant relationships between independent and dependent phenomena,
More informationCORRELATION AND REGRESSION
CORRELATION AND REGRESSION CORRELATION The correlation coefficient is a number, between -1 and +1, which measures the strength of the relationship between two sets of data. The closer the correlation coefficient
More informationCORRELATION AND REGRESSION
CORRELATION AND REGRESSION CORRELATION Introduction CORRELATION problems which involve measuring the strength of a relationship. Correlation Analysis involves various methods and techniques used for studying
More informationIn chemistry we use metric units (called SI units after the French term for Systeme internationale.
Metric system / SI units: In chemistry we use metric units (called SI units after the French term for Systeme internationale. SI units: The SI units we ll be primarily concerned with are shown here: Base
More informationOne Solution Two Solutions Three Solutions Four Solutions. Since both equations equal y we can set them equal Combine like terms Factor Solve for x
Algebra Notes Quadratic Systems Name: Block: Date: Last class we discussed linear systems. The only possibilities we had we 1 solution, no solution or infinite solutions. With quadratic systems we have
More informationUnit 6 - Introduction to linear regression
Unit 6 - Introduction to linear regression Suggested reading: OpenIntro Statistics, Chapter 7 Suggested exercises: Part 1 - Relationship between two numerical variables: 7.7, 7.9, 7.11, 7.13, 7.15, 7.25,
More informationLab 6 Forces Part 2. Physics 225 Lab
b Lab 6 Forces Part 2 Introduction This is the second part of the lab that you started last week. If you happen to have missed that lab then you should go back and read it first since this lab will assume
More informationMath 120 Winter Handout 3: Finding a Formula for a Polynomial Using Roots and Multiplicities
Math 120 Winter 2009 Handout 3: Finding a Formula for a Polynomial Using Roots and Multiplicities 1 A polynomial function is any function of the form: y = c 0 + c 1 x + c 2 x 2 +... + c n x n where the
More informationGrade 11/12 Math Circles Elliptic Curves Dr. Carmen Bruni November 4, 2015
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 11/12 Math Circles Elliptic Curves Dr. Carmen Bruni November 4, 2015 Revisit the Congruent Number
More informationTake-home Final. The questions you are expected to answer for this project are numbered and italicized. There is one bonus question. Good luck!
Take-home Final The data for our final project come from a study initiated by the Tasmanian Aquaculture and Fisheries Institute to investigate the growth patterns of abalone living along the Tasmanian
More informationAlgebra Review. Finding Zeros (Roots) of Quadratics, Cubics, and Quartics. Kasten, Algebra 2. Algebra Review
Kasten, Algebra 2 Finding Zeros (Roots) of Quadratics, Cubics, and Quartics A zero of a polynomial equation is the value of the independent variable (typically x) that, when plugged-in to the equation,
More informationEXPERIMENT 4: UNIFORM CIRCULAR MOTION
LAB SECTION: NAME: EXPERIMENT 4: UNIFORM CIRCULAR MOTION Introduction: In this lab, you will calculate the force on an object moving in a circle at approximately constant speed. To calculate the force
More information( ) 0. Section 3.3 Graphs of Polynomial Functions. Chapter 3
76 Chapter 3 Section 3.3 Graphs of Polynomial Functions In the previous section we explored the short run behavior of quadratics, a special case of polynomials. In this section we will explore the short
More informationCorrelation and Regression Analysis. Linear Regression and Correlation. Correlation and Linear Regression. Three Questions.
10/8/18 Correlation and Regression Analysis Correlation Analysis is the study of the relationship between variables. It is also defined as group of techniques to measure the association between two variables.
More informationPrecalculus Chapter 7 Page 1
Section 7.1 Polynomial Functions 1. To evaluate polynomial functions.. To identify general shapes of the graphs of polynomial functions. I. Terminology A. Polynomials in one variable B. Examples: Determine
More informationFree-Fall Acceleration
Objective To determine the acceleration due to gravity. Introduction Free-Fall Acceleration The position y of a particle moving along a straight line with a constant acceleration a is given by the following
More informationScatterplots. 3.1: Scatterplots & Correlation. Scatterplots. Explanatory & Response Variables. Section 3.1 Scatterplots and Correlation
3.1: Scatterplots & Correlation Scatterplots A scatterplot shows the relationship between two quantitative variables measured on the same individuals. The values of one variable appear on the horizontal
More informationPrinciples and Problems. Chapter 1: A Physics Toolkit
PHYSICS Principles and Problems Chapter 1: A Physics Toolkit CHAPTER 1 A Physics Toolkit BIG IDEA Physicists use scientific methods to investigate energy and matter. CHAPTER 1 Table Of Contents Section
More informationGraphical Analysis and Errors - MBL
I. Graphical Analysis Graphical Analysis and Errors - MBL Graphs are vital tools for analyzing and displaying data throughout the natural sciences and in a wide variety of other fields. It is imperative
More informationLAB 5 INSTRUCTIONS LINEAR REGRESSION AND CORRELATION
LAB 5 INSTRUCTIONS LINEAR REGRESSION AND CORRELATION In this lab you will learn how to use Excel to display the relationship between two quantitative variables, measure the strength and direction of the
More informationMATH 1150 Chapter 2 Notation and Terminology
MATH 1150 Chapter 2 Notation and Terminology Categorical Data The following is a dataset for 30 randomly selected adults in the U.S., showing the values of two categorical variables: whether or not the
More information[ ESS ESS ] / 2 [ ] / ,019.6 / Lab 10 Key. Regression Analysis: wage versus yrsed, ex
Lab 1 Key Regression Analysis: wage versus yrsed, ex wage = - 4.78 + 1.46 yrsed +.126 ex Constant -4.78 2.146-2.23.26 yrsed 1.4623.153 9.73. ex.12635.2739 4.61. S = 8.9851 R-Sq = 11.9% R-Sq(adj) = 11.7%
More informationLinear Kinematics John Smith Kathy Hernandez (partner) Physics 1 Lab (Friday) Mr. Kiledjian 02/24/2006
Linear Kinematics John Smith Kathy Hernandez (partner) Physics 1 Lab (Friday) Mr. Kiledjian 02/24/2006 Purpose: In this lab, we will investigate the relationship between displacements, velocity, and acceleration.
More informationh h h b b Where B is the area of the base and h is the height. . Multiply this by the height to get 20(81 ) 1620 The base is a circle of area (9)
Area and Volume Area Formulas: A bh 1 A bh A r C r h b b b h h h b b b r Volume: Prisms and Cylinders. V Bh Where B is the area of the base and h is the height. 10ft 9in 4ft 5ft 0in The base can be any
More informationInferences for Regression
Inferences for Regression An Example: Body Fat and Waist Size Looking at the relationship between % body fat and waist size (in inches). Here is a scatterplot of our data set: Remembering Regression In
More informationEXPERIMENT 4 ONE DIMENSIONAL MOTION
EXPERIMENT 4 ONE DIMENSIONAL MOTION INTRODUCTION This experiment explores the meaning of displacement; velocity, acceleration and the relationship that exist between them. An understanding of these concepts
More informationMEASUREMENT VARIATION
Name Partner(s) Section Date MEASUREMENT VARIATION OBJECT This activity focuses on the variability in measurements of a property and explores methods of expressing the variation. Let's explore! PROCEDURE.
More information4.5 linear regression ink.notebook. November 29, page 159. page 160. page Linear Regression. Standards. Lesson Objectives Standards
4.5 linear regression ink.notebook page 159 page 160 page 158 4.5 Linear Regression Lesson Objectives Lesson Objectives Standards Standards Lesson Notes Lesson Notes 4.5 Linear Regression F.BF.1 I will
More informationLESSON #1: VARIABLES, TERMS, AND EXPRESSIONS COMMON CORE ALGEBRA II
1 LESSON #1: VARIABLES, TERMS, AND EXPRESSIONS COMMON CORE ALGEBRA II Mathematics has developed a language all to itself in order to clarify concepts and remove ambiguity from the analysis of problems.
More informationSimple Harmonic Motion
Simple Harmonic Motion Introduction A primary motivation for studying simple harmonic motion is its general applicability to a variety of diverse branches of physics. An example of an elementary system
More informationChapter 2: Looking at Data Relationships (Part 3)
Chapter 2: Looking at Data Relationships (Part 3) Dr. Nahid Sultana Chapter 2: Looking at Data Relationships 2.1: Scatterplots 2.2: Correlation 2.3: Least-Squares Regression 2.5: Data Analysis for Two-Way
More informationLinear Motion with Constant Acceleration
Linear Motion 1 Linear Motion with Constant Acceleration Overview: First you will attempt to walk backward with a constant acceleration, monitoring your motion with the ultrasonic motion detector. Then
More informationGuidelines for Graphing Calculator Use at the Commencement Level
Guidelines for Graphing Calculator Use at the Commencement Level Introduction Graphing calculators are instrumental in the teaching and learning of mathematics. The use of this technology should be encouraged
More informationMath 2 Variable Manipulation Part 6 System of Equations
Name: Date: 1 Math 2 Variable Manipulation Part 6 System of Equations SYSTEM OF EQUATIONS INTRODUCTION A "system" of equations is a set or collection of equations that you deal with all together at once.
More informationLecture Slides. Elementary Statistics Tenth Edition. by Mario F. Triola. and the Triola Statistics Series. Slide 1
Lecture Slides Elementary Statistics Tenth Edition and the Triola Statistics Series by Mario F. Triola Slide 1 Chapter 10 Correlation and Regression 10-1 Overview 10-2 Correlation 10-3 Regression 10-4
More informationMATH 115: Review for Chapter 5
MATH 5: Review for Chapter 5 Can you find the real zeros of a polynomial function and identify the behavior of the graph of the function at its zeros? For each polynomial function, identify the zeros of
More information1) A residual plot: A)
1) A residual plot: A) B) C) D) E) displays residuals of the response variable versus the independent variable. displays residuals of the independent variable versus the response variable. displays residuals
More information