Parabolic Path to a Best Best-Fit Line:
|
|
- Kory Daniels
- 6 years ago
- Views:
Transcription
1 Studet Activity : Fidig the Least Squares Regressio Lie By Explorig the Relatioship betwee Slope ad Residuals Objective: How does oe determie a best best-fit lie for a set of data? Eyeballig it may be a good place to start, but there is a more exact way. I this activity, you will ot oly fid a best best-fit lie for a data set, you will discover why it must be the best. What to Do: Figure 1: Fathom Case Table 1. Ope the Fathom file Parabolic_Path_LSRL.ftm. 2. I the Case Table (upper left corer of scree), iput the data set as give i Figure Notice the data poits are displayed i a scatter plot (upper right of scree) as i Figure 2. Also o the scatter plot, a blue horizotal lie has appeared that we ca use to fid a best-fit lie to model the data. Figure 2: Fathom Scatter Plot a. The geeral equatio for this lie ca be foud just below the scatter plot. What is it? Write the equatio usig x for mea(x) ad y for mea(y). b. What specific slope does the iitial horizotal (blue) lie have? c. Based o that slope, simplify the geeral liear equatio for the specific lie graphed.
2 4. Below the Case Table (Figure 1) o the Fathom scree is a slider (Figure 3) that chages the values of parameter b i the liear equatio. Try movig the slider to the left ad right. Figure 3: Slider for Parameter b a. What effect does chagig the value of b have o the blue lie? Why? b. By chagig b, ca the lie be vertically or horizotally traslated? c. By chagig b, what type of trasformatio does occur? 5. I order to fid a equatio for a lie, at least oe poit o the lie must be kow. For a best-fit lie, a reasoable poit to begi with is ( x, y ), also called the ceter of gravity for the data set. a. Why would the ceter of gravity be a good poit to iclude o a best-fit lie? b. Aroud what poit does the lie o the scatter plot appear to rotate whe the slope, b, is chaged with the slider? c. I the Fathom widow, a Summary Table as i Figure 4 displays statistics o the data, icludig the slope (b), x, y, the sum of the residuals, ad the sum of squared residuals. Based o the data s statistics, what are the specific coordiates of the poit of rotatio? Figure 4: Fathom Summary Table d. Lookig at the lie graphed o the scatter plot, do these coordiates appear to be correct? 2003, rev J. Reihardt & J. Simos 2
3 e. Now look closely at the Case Table as i Figure 5 that cotais the data poits. It also icludes other useful iformatio: YFitted values ad Residual values. How are the YFitted values also kow as predicted values determied? Figure 5: Fathom Case Table f. How are the Residuals determied? What is a residual? 6. Kowig oly oe poit (i this case, the ceter of gravity) is ot sufficiet iformatio to determie ay lie, much less a best-fit lie. We also eed to fid the best slope to fit the data. a. Adjust the slope of the lie by usig the slider to chage the value of b. Try to fid a lie that is a good fit to the data. Record the value of the slope (b) for this iitial estimate. b. How did you decide what the slope of the best-fit lie should be? c. Do you thik someoe else would choose the same slope as you? Why or why ot? 7. Is there a more accurate method for determiig the best slope? Go to the Object meu ad select Show Hidde Objects as i Figure 6. A graph of a fuctio appears. a. What is the explaatory (idepedet) variable of this fuctio? [Hit: How are the axes labeled?] Figure 6: Fathom s Object Meu b. What is the respose (depedet) variable? 2003, rev J. Reihardt & J. Simos 3
4 c. What type of fuctio models the relatioship betwee these two variables? d. What is the shape of this fuctio s graph? 8. Try adjustig the slope (b) of the lie oce agai. This time otice how the mysterious poit o the parabola moves i respose. This poit ad the slope of our best-fit lie are coected. a. Adjust the slope to move the mysterious poit closer to the vertex of the parabola. What effect does this have o how well the lie fits the data? b. Use the parabola ad its vertex to determie the best slope for your liear model. Oce you are satisfied with your choice, record the coordiate values of the mysterious poit to the earest 2 decimal places. (Refer to the Summary Table for values.) c. At the vertex poit, otice that the respose variable has a miimum value. Cosiderig the meaig of the respose variable, why is the vertex helpful i determiig the slope of our best-fit lie? 9. Determie a equatio for the best-fit lie for the data set. a. Use the ceter of gravity ad the slope foud with the parabola to write a equatio for the best-fit lie i poit-slope form, that is, y " y 1 = b( x " x 1 ). b. Rewrite your equatio above i slope-itercept form, y = bx + a. c. The type of best-fit lie that foud i this activity is kow as the Least Squares Regressio Lie, or LSRL, for short. Why is it referred to by this ame? 2003, rev J. Reihardt & J. Simos 4
5 10. Now that we have determied the LSRL, we ca check it with the LSRL as computed by Fathom. a. Highlight (click o) the scatter plot. The select Least-Squares Lie from the Graph meu. Fathom graphs the LSRL (gree lie) o the scatter plot with ours (blue lie). Are they close? What is Fathom s LSRL equatio, ad how does it compare to ours? b. Retur to the Graph meu ad select the Show Squares optio. Notice that squares coected to the LSRL appear as i Figure 7. What do these squares represet? Ad what does the total sum of the areas of these squares represet? Figure 7: Fathom Scatter Plot ad LSRL c. Below the equatio for Fathom s LSRL is a value for its Sum of squares. What is this value? Where ca this value be foud o the graph of the parabola? d. Chage the value of the slope (b) of the lie ad otice the effect o the size of the squares. To determie a best best-fit lie for a data set, we foud a special lie through the ceter of gravity that also does what to the sum of the areas of the gree squares? 11. What two primary characteristics must a Least Squares Regressio Lie (a best-fit lie) have to model a set of data, ad why is each characteristic sigificat? 2003, rev J. Reihardt & J. Simos 5
6 Extesios 1. Why is there a quadratic relatioship betwee the slope of a best-fit lie ad the sum of the squared residuals? Ivestigate this relatioship i the followig: a. Use a lie i the form y = b( x! x ) + y that cotais the ceter of gravity, x = 0.8 ad y =1.0. Fid the residual i terms of b for each of the five data poits i the activity. (It may help to orgaize the results i a table, ad you may wat to collaborate with others.) b. Square each residual. The fid the sum of the squared residuals i terms of b (the slope). c. What type of fuctio describes the relatioship betwee the slope ad the sum of squared residuals for a lie that icludes the ceter of gravity? d. Verify that the geeral quadratic fuctio (give i the parabola s widow i Fathom ad also below) works for the data set i the activity.!(residuals) 2 =!(y i " y) 2 " 2b #! y i (x i " x) + b 2 #!(x i " x) 2 e. Show that the above holds true for ay geeral data set. 2. I the activity, we determied a LSRL lie for a data set of five specific poits. What if the data set chaged? a. How does chagig a poit i the data set affect the quadratic relatioship betwee the slope ad the sum of the squared residuals for a possible best-fit lie? Choose ay oe of the five data poits ad drag it aroud to ew locatios. I what ways does this affect the parabola used to determie the LSRL? How ca the effects o the parabola caused by chagig a poit i the data set be explaied i terms of the parabola s equatio? b. How does chagig a poit i the data set affect the Least Squares Regressio Lie? Highlight (click o) the scatter plot. The uder the Graph meu, de-select Show Squares. Choose ay oe of the five data poits ad drag it aroud to ew locatios. I what ways does this affect the LSRL (the gree lie i the Fathom widow)? Specifically, how does chagig a poit i the data set affect each of the two defiig characteristics of the Least Squares Regressio Lie? 2003, rev J. Reihardt & J. Simos 6
EM375 STATISTICS AND MEASUREMENT UNCERTAINTY LEAST SQUARES LINEAR REGRESSION ANALYSIS
EM375 STATISTICS AND MEASUREMENT UNCERTAINTY LEAST SQUARES LINEAR REGRESSION ANALYSIS I this uit of the course we ivestigate fittig a straight lie to measured (x, y) data pairs. The equatio we wat to fit
More informationMath Section 2.2 Polynomial Functions
Math 1330 - Sectio. Polyomial Fuctios Our objectives i workig with polyomial fuctios will be, first, to gather iformatio about the graph of the fuctio ad, secod, to use that iformatio to geerate a reasoably
More informationThe isoperimetric problem on the hypercube
The isoperimetric problem o the hypercube Prepared by: Steve Butler November 2, 2005 1 The isoperimetric problem We will cosider the -dimesioal hypercube Q Recall that the hypercube Q is a graph whose
More informationPattern Recognition Systems Lab 1 Least Mean Squares
Patter Recogitio Systems Lab 1 Least Mea Squares 1. Objectives This laboratory work itroduces the OpeCV-based framework used throughout the course. I this assigmet a lie is fitted to a set of poits usig
More informationThe Closest Line to a Data Set in the Plane. David Gurney Southeastern Louisiana University Hammond, Louisiana
The Closest Lie to a Data Set i the Plae David Gurey Southeaster Louisiaa Uiversity Hammod, Louisiaa ABSTRACT This paper looks at three differet measures of distace betwee a lie ad a data set i the plae:
More informationIntro to Scientific Computing: Solutions
Itro to Scietific Computig: Solutios Dr. David M. Goulet. How may steps does it take to separate 3 objects ito groups of 4? We start with 5 objects ad apply 3 steps of the algorithm to reduce the pile
More informationBezier curves. Figure 2 shows cubic Bezier curves for various control points. In a Bezier curve, only
Edited: Yeh-Liag Hsu (998--; recommeded: Yeh-Liag Hsu (--9; last updated: Yeh-Liag Hsu (9--7. Note: This is the course material for ME55 Geometric modelig ad computer graphics, Yua Ze Uiversity. art of
More informationConsider the following population data for the state of California. Year Population
Assigmets for Bradie Fall 2016 for Chapter 5 Assigmet sheet for Sectios 5.1, 5.3, 5.5, 5.6, 5.7, 5.8 Read Pages 341-349 Exercises for Sectio 5.1 Lagrage Iterpolatio #1, #4, #7, #13, #14 For #1 use MATLAB
More informationArithmetic Sequences
. Arithmetic Sequeces COMMON CORE Learig Stadards HSF-IF.A. HSF-BF.A.1a HSF-BF.A. HSF-LE.A. Essetial Questio How ca you use a arithmetic sequece to describe a patter? A arithmetic sequece is a ordered
More informationSouth Slave Divisional Education Council. Math 10C
South Slave Divisioal Educatio Coucil Math 10C Curriculum Package February 2012 12 Strad: Measuremet Geeral Outcome: Develop spatial sese ad proportioal reasoig It is expected that studets will: 1. Solve
More informationNumerical Methods Lecture 6 - Curve Fitting Techniques
Numerical Methods Lecture 6 - Curve Fittig Techiques Topics motivatio iterpolatio liear regressio higher order polyomial form expoetial form Curve fittig - motivatio For root fidig, we used a give fuctio
More informationThe VSS CCD photometry spreadsheet
The VSS CCD photometry spreadsheet Itroductio This Excel spreadsheet has bee developed ad tested by the BAA VSS for aalysig results files produced by the multi-image CCD photometry procedure i AIP4Wi v2.
More informationThe number n of subintervals times the length h of subintervals gives length of interval (b-a).
Simulator with MadMath Kit: Riema Sums (Teacher s pages) I your kit: 1. GeoGebra file: Ready-to-use projector sized simulator: RiemaSumMM.ggb 2. RiemaSumMM.pdf (this file) ad RiemaSumMMEd.pdf (educator's
More informationMath 10C Long Range Plans
Math 10C Log Rage Plas Uits: Evaluatio: Homework, projects ad assigmets 10% Uit Tests. 70% Fial Examiatio.. 20% Ay Uit Test may be rewritte for a higher mark. If the retest mark is higher, that mark will
More informationSection 7.2: Direction Fields and Euler s Methods
Sectio 7.: Directio ields ad Euler s Methods Practice HW from Stewart Tetbook ot to had i p. 5 # -3 9-3 odd or a give differetial equatio we wat to look at was to fid its solutio. I this chapter we will
More informationEVALUATION OF TRIGONOMETRIC FUNCTIONS
EVALUATION OF TRIGONOMETRIC FUNCTIONS Whe first exposed to trigoometric fuctios i high school studets are expected to memorize the values of the trigoometric fuctios of sie cosie taget for the special
More informationCivil Engineering Computation
Civil Egieerig Computatio Fidig Roots of No-Liear Equatios March 14, 1945 World War II The R.A.F. first operatioal use of the Grad Slam bomb, Bielefeld, Germay. Cotets 2 Root basics Excel solver Newto-Raphso
More informationGlobal Support Guide. Verizon WIreless. For the BlackBerry 8830 World Edition Smartphone and the Motorola Z6c
Verizo WIreless Global Support Guide For the BlackBerry 8830 World Editio Smartphoe ad the Motorola Z6c For complete iformatio o global services, please refer to verizowireless.com/vzglobal. Whether i
More informationIMP: Superposer Integrated Morphometrics Package Superposition Tool
IMP: Superposer Itegrated Morphometrics Package Superpositio Tool Programmig by: David Lieber ( 03) Caisius College 200 Mai St. Buffalo, NY 4208 Cocept by: H. David Sheets, Dept. of Physics, Caisius College
More informationThe Graphs of Polynomial Functions
Sectio 4.3 The Graphs of Polyomial Fuctios Objective 1: Uderstadig the Defiitio of a Polyomial Fuctio Defiitio Polyomial Fuctio 1 2 The fuctio ax a 1x a 2x a1x a0 is a polyomial fuctio of degree where
More informationExamples and Applications of Binary Search
Toy Gog ITEE Uiersity of Queeslad I the secod lecture last week we studied the biary search algorithm that soles the problem of determiig if a particular alue appears i a sorted list of iteger or ot. We
More information9 x and g(x) = 4. x. Find (x) 3.6. I. Combining Functions. A. From Equations. Example: Let f(x) = and its domain. Example: Let f(x) = and g(x) = x x 4
1 3.6 I. Combiig Fuctios A. From Equatios Example: Let f(x) = 9 x ad g(x) = 4 f x. Fid (x) g ad its domai. 4 Example: Let f(x) = ad g(x) = x x 4. Fid (f-g)(x) B. From Graphs: Graphical Additio. Example:
More informationPolynomial Functions and Models. Learning Objectives. Polynomials. P (x) = a n x n + a n 1 x n a 1 x + a 0, a n 0
Polyomial Fuctios ad Models 1 Learig Objectives 1. Idetify polyomial fuctios ad their degree 2. Graph polyomial fuctios usig trasformatios 3. Idetify the real zeros of a polyomial fuctio ad their multiplicity
More informationA Taste of Maya. Character Setup
This tutorial goes through the steps to add aimatio cotrols to a previously modeled character. The character i the scee below is wearig clothes made with Cloth ad the sceery has bee created with Pait Effects.
More informationA Resource for Free-standing Mathematics Qualifications
Ope.ls The first sheet is show elow. It is set up to show graphs with equatios of the form = m + c At preset the values of m ad c are oth zero. You ca chage these values usig the scroll ars. Leave the
More informationOverview Chapter 12 A display model
Overview Chapter 12 A display model Why graphics? A graphics model Examples Bjare Stroustrup www.stroustrup.com/programmig 3 Why bother with graphics ad GUI? Why bother with graphics ad GUI? It s very
More informationOur Learning Problem, Again
Noparametric Desity Estimatio Matthew Stoe CS 520, Sprig 2000 Lecture 6 Our Learig Problem, Agai Use traiig data to estimate ukow probabilities ad probability desity fuctios So far, we have depeded o describig
More informationAlpha Individual Solutions MAΘ National Convention 2013
Alpha Idividual Solutios MAΘ Natioal Covetio 0 Aswers:. D. A. C 4. D 5. C 6. B 7. A 8. C 9. D 0. B. B. A. D 4. C 5. A 6. C 7. B 8. A 9. A 0. C. E. B. D 4. C 5. A 6. D 7. B 8. C 9. D 0. B TB. 570 TB. 5
More informationSharing Collections. Share a Collection via . Share a Collection via Google Classroom. Quick Reference Guide
Quick Referece Guide Share a Collectio via Email Sharig your collectio with others is a great way to collaborate. You ca easily sed a lik to your colleagues, studets, classmates ad frieds. Recipiets do
More informationIt just came to me that I 8.2 GRAPHS AND CONVERGENCE
44 Chapter 8 Discrete Mathematics: Fuctios o the Set of Natural Numbers (a) Take several odd, positive itegers for a ad write out eough terms of the 3N sequece to reach a repeatig loop (b) Show that ot
More information9.1. Sequences and Series. Sequences. What you should learn. Why you should learn it. Definition of Sequence
_9.qxd // : AM Page Chapter 9 Sequeces, Series, ad Probability 9. Sequeces ad Series What you should lear Use sequece otatio to write the terms of sequeces. Use factorial otatio. Use summatio otatio to
More informationLearning to Shoot a Goal Lecture 8: Learning Models and Skills
Learig to Shoot a Goal Lecture 8: Learig Models ad Skills How do we acquire skill at shootig goals? CS 344R/393R: Robotics Bejami Kuipers Learig to Shoot a Goal The robot eeds to shoot the ball i the goal.
More informationMOTIF XF Extension Owner s Manual
MOTIF XF Extesio Ower s Maual Table of Cotets About MOTIF XF Extesio...2 What Extesio ca do...2 Auto settig of Audio Driver... 2 Auto settigs of Remote Device... 2 Project templates with Iput/ Output Bus
More informationChapter 10. Defining Classes. Copyright 2015 Pearson Education, Ltd.. All rights reserved.
Chapter 10 Defiig Classes Copyright 2015 Pearso Educatio, Ltd.. All rights reserved. Overview 10.1 Structures 10.2 Classes 10.3 Abstract Data Types 10.4 Itroductio to Iheritace Copyright 2015 Pearso Educatio,
More informationRecursive Procedures. How can you model the relationship between consecutive terms of a sequence?
6. Recursive Procedures I Sectio 6.1, you used fuctio otatio to write a explicit formula to determie the value of ay term i a Sometimes it is easier to calculate oe term i a sequece usig the previous terms.
More informationPython Programming: An Introduction to Computer Science
Pytho Programmig: A Itroductio to Computer Sciece Chapter 1 Computers ad Programs 1 Objectives To uderstad the respective roles of hardware ad software i a computig system. To lear what computer scietists
More informationPrinceton Instruments Reference Manual
Priceto Istrumets Referece Maual Improvisio, Viscout Cetre II, Uiversity of Warwick Sciece Park, Millbur Hill Road, Covetry. CV4 7HS Tel: 0044 (0) 24 7669 2229 Fax: 0044 (0) 24 7669 0091 e-mail: admi@improvisio.com
More informationPseudocode ( 1.1) Analysis of Algorithms. Primitive Operations. Pseudocode Details. Running Time ( 1.1) Estimating performance
Aalysis of Algorithms Iput Algorithm Output A algorithm is a step-by-step procedure for solvig a problem i a fiite amout of time. Pseudocode ( 1.1) High-level descriptio of a algorithm More structured
More informationCHAPTER IV: GRAPH THEORY. Section 1: Introduction to Graphs
CHAPTER IV: GRAPH THEORY Sectio : Itroductio to Graphs Sice this class is called Number-Theoretic ad Discrete Structures, it would be a crime to oly focus o umber theory regardless how woderful those topics
More informationLecturers: Sanjam Garg and Prasad Raghavendra Feb 21, Midterm 1 Solutions
U.C. Berkeley CS170 : Algorithms Midterm 1 Solutios Lecturers: Sajam Garg ad Prasad Raghavedra Feb 1, 017 Midterm 1 Solutios 1. (4 poits) For the directed graph below, fid all the strogly coected compoets
More informationChapter 1. Introduction to Computers and C++ Programming. Copyright 2015 Pearson Education, Ltd.. All rights reserved.
Chapter 1 Itroductio to Computers ad C++ Programmig Copyright 2015 Pearso Educatio, Ltd.. All rights reserved. Overview 1.1 Computer Systems 1.2 Programmig ad Problem Solvig 1.3 Itroductio to C++ 1.4 Testig
More informationGetting Started. Getting Started - 1
Gettig Started Gettig Started - 1 Issue 1 Overview of Gettig Started Overview of Gettig Started This sectio explais the basic operatios of the AUDIX system. It describes how to: Log i ad log out of the
More informationFundamentals of Media Processing. Shin'ichi Satoh Kazuya Kodama Hiroshi Mo Duy-Dinh Le
Fudametals of Media Processig Shi'ichi Satoh Kazuya Kodama Hiroshi Mo Duy-Dih Le Today's topics Noparametric Methods Parze Widow k-nearest Neighbor Estimatio Clusterig Techiques k-meas Agglomerative Hierarchical
More information. Written in factored form it is easy to see that the roots are 2, 2, i,
CMPS A Itroductio to Programmig Programmig Assigmet 4 I this assigmet you will write a java program that determies the real roots of a polyomial that lie withi a specified rage. Recall that the roots (or
More informationOnes Assignment Method for Solving Traveling Salesman Problem
Joural of mathematics ad computer sciece 0 (0), 58-65 Oes Assigmet Method for Solvig Travelig Salesma Problem Hadi Basirzadeh Departmet of Mathematics, Shahid Chamra Uiversity, Ahvaz, Ira Article history:
More informationIntermediate Statistics
Gait Learig Guides Itermediate Statistics Data processig & display, Cetral tedecy Author: Raghu M.D. STATISTICS DATA PROCESSING AND DISPLAY Statistics is the study of data or umerical facts of differet
More informationWeston Anniversary Fund
Westo Olie Applicatio Guide 2018 1 This guide is desiged to help charities applyig to the Westo to use our olie applicatio form. The Westo is ope to applicatios from 5th Jauary 2018 ad closes o 30th Jue
More informationCOMPOSITE TRANSFORMATIONS. DOES ORDER MATTER Use the composite transformation to plot A B C and A B C. 1a)
U3 L1 HW OMPOSITE TRNSFORMTIONS DOES ORDER MTTER Use the coposite trasforatio to plot ad 1a) T 3,5 ry axis ( ) b) ry axis T 3,5 ( ) c) Did doig the trasforatios i a differet order atter? Explai why? 2a)
More informationSD vs. SD + One of the most important uses of sample statistics is to estimate the corresponding population parameters.
SD vs. SD + Oe of the most importat uses of sample statistics is to estimate the correspodig populatio parameters. The mea of a represetative sample is a good estimate of the mea of the populatio that
More information1.8 What Comes Next? What Comes Later?
35 1.8 What Comes Next? What Comes Later? A Practice Uderstadig Task For each of the followig tables, CC BY Hiroaki Maeda https://flic.kr/p/6r8odk describe how to fid the ext term i the sequece, write
More informationReading. Parametric curves. Mathematical curve representation. Curves before computers. Required: Angel , , , 11.9.
Readig Required: Agel.-.3,.5.,.6-.7,.9. Optioal Parametric curves Bartels, Beatty, ad Barsky. A Itroductio to Splies for use i Computer Graphics ad Geometric Modelig, 987. Fari. Curves ad Surfaces for
More informationDescriptive Statistics Summary Lists
Chapter 209 Descriptive Statistics Summary Lists Itroductio This procedure is used to summarize cotiuous data. Large volumes of such data may be easily summarized i statistical lists of meas, couts, stadard
More informationMATHEMATICAL METHODS OF ANALYSIS AND EXPERIMENTAL DATA PROCESSING (Or Methods of Curve Fitting)
MATHEMATICAL METHODS OF ANALYSIS AND EXPERIMENTAL DATA PROCESSING (Or Methods of Curve Fittig) I this chapter, we will eamie some methods of aalysis ad data processig; data obtaied as a result of a give
More informationAPPLICATION NOTE PACE1750AE BUILT-IN FUNCTIONS
APPLICATION NOTE PACE175AE BUILT-IN UNCTIONS About This Note This applicatio brief is iteded to explai ad demostrate the use of the special fuctios that are built ito the PACE175AE processor. These powerful
More informationTexture Mapping. Jian Huang. This set of slides references the ones used at Ohio State for instruction.
Texture Mappig Jia Huag This set of slides refereces the oes used at Ohio State for istructio. Ca you do this What Dreams May Come Texture Mappig Of course, oe ca model the exact micro-geometry + material
More information6.854J / J Advanced Algorithms Fall 2008
MIT OpeCourseWare http://ocw.mit.edu 6.854J / 18.415J Advaced Algorithms Fall 2008 For iformatio about citig these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 18.415/6.854 Advaced Algorithms
More informationUNIT 4 Section 8 Estimating Population Parameters using Confidence Intervals
UNIT 4 Sectio 8 Estimatig Populatio Parameters usig Cofidece Itervals To make ifereces about a populatio that caot be surveyed etirely, sample statistics ca be take from a SRS of the populatio ad used
More information12-5A. Equivalent Fractions and Decimals. 1 Daily Common Core Review. Common Core. Lesson. Lesson Overview. Math Background
Lesso -A Equivalet Fractios ad Decimals Commo Core Lesso Overview Domai Number ad Operatios Fractios Cluster Uderstad decimal otatio for fractios, ad compare decimal fractios. Stadards.NF. Use decimal
More informationHomework 1 Solutions MA 522 Fall 2017
Homework 1 Solutios MA 5 Fall 017 1. Cosider the searchig problem: Iput A sequece of umbers A = [a 1,..., a ] ad a value v. Output A idex i such that v = A[i] or the special value NIL if v does ot appear
More informationPython Programming: An Introduction to Computer Science
Pytho Programmig: A Itroductio to Computer Sciece Chapter 6 Defiig Fuctios Pytho Programmig, 2/e 1 Objectives To uderstad why programmers divide programs up ito sets of cooperatig fuctios. To be able to
More informationArea As A Limit & Sigma Notation
Area As A Limit & Sigma Notatio SUGGESTED REFERENCE MATERIAL: As you work through the problems listed below, you should referece Chapter 5.4 of the recommeded textbook (or the equivalet chapter i your
More informationUsing the Keyboard. Using the Wireless Keyboard. > Using the Keyboard
1 A wireless keyboard is supplied with your computer. The wireless keyboard uses a stadard key arragemet with additioal keys that perform specific fuctios. Usig the Wireless Keyboard Two AA alkalie batteries
More informationBaan Tools User Management
Baa Tools User Maagemet Module Procedure UP008A US Documetiformatio Documet Documet code : UP008A US Documet group : User Documetatio Documet title : User Maagemet Applicatio/Package : Baa Tools Editio
More informationECE4050 Data Structures and Algorithms. Lecture 6: Searching
ECE4050 Data Structures ad Algorithms Lecture 6: Searchig 1 Search Give: Distict keys k 1, k 2,, k ad collectio L of records of the form (k 1, I 1 ), (k 2, I 2 ),, (k, I ) where I j is the iformatio associated
More informationPLEASURE TEST SERIES (XI) - 04 By O.P. Gupta (For stuffs on Math, click at theopgupta.com)
wwwtheopguptacom wwwimathematiciacom For all the Math-Gya Buy books by OP Gupta A Compilatio By : OP Gupta (WhatsApp @ +9-9650 350 0) For more stuffs o Maths, please visit : wwwtheopguptacom Time Allowed
More informationOCR Statistics 1. Working with data. Section 3: Measures of spread
Notes ad Eamples OCR Statistics 1 Workig with data Sectio 3: Measures of spread Just as there are several differet measures of cetral tedec (averages), there are a variet of statistical measures of spread.
More informationVisualization of Gauss-Bonnet Theorem
Visualizatio of Gauss-Boet Theorem Yoichi Maeda maeda@keyaki.cc.u-tokai.ac.jp Departmet of Mathematics Tokai Uiversity Japa Abstract: The sum of exteral agles of a polygo is always costat, π. There are
More informationMarkov Chain Model of HomePlug CSMA MAC for Determining Optimal Fixed Contention Window Size
Markov Chai Model of HomePlug CSMA MAC for Determiig Optimal Fixed Cotetio Widow Size Eva Krimiger * ad Haiph Latchma Dept. of Electrical ad Computer Egieerig, Uiversity of Florida, Gaiesville, FL, USA
More informationAssignment 5; Due Friday, February 10
Assigmet 5; Due Friday, February 10 17.9b The set X is just two circles joied at a poit, ad the set X is a grid i the plae, without the iteriors of the small squares. The picture below shows that the iteriors
More informationLecture 18. Optimization in n dimensions
Lecture 8 Optimizatio i dimesios Itroductio We ow cosider the problem of miimizig a sigle scalar fuctio of variables, f x, where x=[ x, x,, x ]T. The D case ca be visualized as fidig the lowest poit of
More informationParametric curves. Reading. Parametric polynomial curves. Mathematical curve representation. Brian Curless CSE 457 Spring 2015
Readig Required: Agel 0.-0.3, 0.5., 0.6-0.7, 0.9 Parametric curves Bria Curless CSE 457 Sprig 05 Optioal Bartels, Beatty, ad Barsy. A Itroductio to Splies for use i Computer Graphics ad Geometric Modelig,
More informationComputational Geometry
Computatioal Geometry Chapter 4 Liear programmig Duality Smallest eclosig disk O the Ageda Liear Programmig Slides courtesy of Craig Gotsma 4. 4. Liear Programmig - Example Defie: (amout amout cosumed
More information( n+1 2 ) , position=(7+1)/2 =4,(median is observation #4) Median=10lb
Chapter 3 Descriptive Measures Measures of Ceter (Cetral Tedecy) These measures will tell us where is the ceter of our data or where most typical value of a data set lies Mode the value that occurs most
More informationMath 167 Review for Test 4 Chapters 7, 8 & 9
Math 167 Review for Tet 4 Chapter 7, 8 & 9 Vocabulary 1. A ordered pair (a, b) i a of a equatio i term of x ad y if the equatio become a true tatemet whe a i ubtituted for x ad b i ubtituted for y. 2.
More informationChapter 5. Functions for All Subtasks. Copyright 2015 Pearson Education, Ltd.. All rights reserved.
Chapter 5 Fuctios for All Subtasks Copyright 2015 Pearso Educatio, Ltd.. All rights reserved. Overview 5.1 void Fuctios 5.2 Call-By-Referece Parameters 5.3 Usig Procedural Abstractio 5.4 Testig ad Debuggig
More informationName Date Hr. ALGEBRA 1-2 SPRING FINAL MULTIPLE CHOICE REVIEW #2
Name Date Hr. ALGEBRA - SPRING FINAL MULTIPLE CHOICE REVIEW # 5. Which measure of ceter is most appropriate for the followig data set? {7, 7, 75, 77,, 9, 9, 90} Mea Media Stadard Deviatio Rage 5. The umber
More information1.2 Binomial Coefficients and Subsets
1.2. BINOMIAL COEFFICIENTS AND SUBSETS 13 1.2 Biomial Coefficiets ad Subsets 1.2-1 The loop below is part of a program to determie the umber of triagles formed by poits i the plae. for i =1 to for j =
More informationChapter 11. Friends, Overloaded Operators, and Arrays in Classes. Copyright 2014 Pearson Addison-Wesley. All rights reserved.
Chapter 11 Frieds, Overloaded Operators, ad Arrays i Classes Copyright 2014 Pearso Addiso-Wesley. All rights reserved. Overview 11.1 Fried Fuctios 11.2 Overloadig Operators 11.3 Arrays ad Classes 11.4
More informationBAAN IVc/BaanERP. Conversion Guide Oracle7 to Oracle8
BAAN IVc/BaaERP A publicatio of: Baa Developmet B.V. P.O.Box 143 3770 AC Bareveld The Netherlads Prited i the Netherlads Baa Developmet B.V. 1999. All rights reserved. The iformatio i this documet is subject
More informationcondition w i B i S maximum u i
ecture 10 Dyamic Programmig 10.1 Kapsack Problem November 1, 2004 ecturer: Kamal Jai Notes: Tobias Holgers We are give a set of items U = {a 1, a 2,..., a }. Each item has a weight w i Z + ad a utility
More informationChapter 9. Pointers and Dynamic Arrays. Copyright 2015 Pearson Education, Ltd.. All rights reserved.
Chapter 9 Poiters ad Dyamic Arrays Copyright 2015 Pearso Educatio, Ltd.. All rights reserved. Overview 9.1 Poiters 9.2 Dyamic Arrays Copyright 2015 Pearso Educatio, Ltd.. All rights reserved. Slide 9-3
More informationAvid Interplay Bundle
Avid Iterplay Budle Versio 2.5 Cofigurator ReadMe Overview This documet provides a overview of Iterplay Budle v2.5 ad describes how to ru the Iterplay Budle cofiguratio tool. Iterplay Budle v2.5 refers
More informationLecture 5. Counting Sort / Radix Sort
Lecture 5. Coutig Sort / Radix Sort T. H. Corme, C. E. Leiserso ad R. L. Rivest Itroductio to Algorithms, 3rd Editio, MIT Press, 2009 Sugkyukwa Uiversity Hyuseug Choo choo@skku.edu Copyright 2000-2018
More informationCSC 220: Computer Organization Unit 11 Basic Computer Organization and Design
College of Computer ad Iformatio Scieces Departmet of Computer Sciece CSC 220: Computer Orgaizatio Uit 11 Basic Computer Orgaizatio ad Desig 1 For the rest of the semester, we ll focus o computer architecture:
More informationCS 683: Advanced Design and Analysis of Algorithms
CS 683: Advaced Desig ad Aalysis of Algorithms Lecture 6, February 1, 2008 Lecturer: Joh Hopcroft Scribes: Shaomei Wu, Etha Feldma February 7, 2008 1 Threshold for k CNF Satisfiability I the previous lecture,
More informationc) Did doing the transformations in a different order matter? Explain why?
G.O..5 WORKSHEET #8 geoetrycoocore NME: 1 OMPOSITE TRNSFORMTIONS DOES ORDER MTTER Use the coposite trasforatio to plot ad 1a) T 3,5 r ( ) y axis b) y axis T 3,5 (6,-1) (6,-1) (3,-4) (3,-4) (5,-7) (5,-7)
More informationENGR Spring Exam 1
ENGR 300 Sprig 03 Exam INSTRUCTIONS: Duratio: 60 miutes Keep your eyes o your ow work! Keep your work covered at all times!. Each studet is resposible for followig directios. Read carefully.. MATLAB ad
More informationName Date Hr. ALGEBRA 1-2 SPRING FINAL MULTIPLE CHOICE REVIEW #1
Name Date Hr. ALGEBRA - SPRING FINAL MULTIPLE CHOICE REVIEW #. The high temperatures for Phoeix i October of 009 are listed below. Which measure of ceter will provide the most accurate estimatio of the
More informationHP Media Center PC Getting Started Guide
HP Media Ceter PC Gettig Started Guide The oly warraties for Hewlett-Packard products ad services are set forth i the express statemets accompayig such products ad services. Nothig herei should be costrued
More information2) Give an example of a polynomial function of degree 4 with leading coefficient of -6
Math 165 Read ahead some cocepts from sectios 4.1 Read the book or the power poit presetatios for this sectio to complete pages 1 ad 2 Please, do ot complete the other pages of the hadout If you wat to
More informationK-NET bus. When several turrets are connected to the K-Bus, the structure of the system is as showns
K-NET bus The K-Net bus is based o the SPI bus but it allows to addressig may differet turrets like the I 2 C bus. The K-Net is 6 a wires bus (4 for SPI wires ad 2 additioal wires for request ad ackowledge
More informationCMPT 125 Assignment 2 Solutions
CMPT 25 Assigmet 2 Solutios Questio (20 marks total) a) Let s cosider a iteger array of size 0. (0 marks, each part is 2 marks) it a[0]; I. How would you assig a poiter, called pa, to store the address
More informationCopyright Hewlett-Packard Development Company, L.P.
Media Ceter Software Guide The oly warraties for HP products ad services are set forth i the express warraty statemets accompayig such products ad services. Nothig herei should be costrued as costitutig
More informationA SOFTWARE MODEL FOR THE MULTILAYER PERCEPTRON
A SOFTWARE MODEL FOR THE MULTILAYER PERCEPTRON Roberto Lopez ad Eugeio Oñate Iteratioal Ceter for Numerical Methods i Egieerig (CIMNE) Edificio C1, Gra Capitá s/, 08034 Barceloa, Spai ABSTRACT I this work
More informationInvestigation Monitoring Inventory
Ivestigatio Moitorig Ivetory Name Period Date Art Smith has bee providig the prits of a egravig to FieArt Gallery. He plas to make just 2000 more prits. FieArt has already received 70 of Art s prits. The
More informationImproving Template Based Spike Detection
Improvig Template Based Spike Detectio Kirk Smith, Member - IEEE Portlad State Uiversity petra@ee.pdx.edu Abstract Template matchig algorithms like SSE, Covolutio ad Maximum Likelihood are well kow for
More informationCIS 121 Data Structures and Algorithms with Java Spring Stacks, Queues, and Heaps Monday, February 18 / Tuesday, February 19
CIS Data Structures ad Algorithms with Java Sprig 09 Stacks, Queues, ad Heaps Moday, February 8 / Tuesday, February 9 Stacks ad Queues Recall the stack ad queue ADTs (abstract data types from lecture.
More informationANN WHICH COVERS MLP AND RBF
ANN WHICH COVERS MLP AND RBF Josef Boští, Jaromír Kual Faculty of Nuclear Scieces ad Physical Egieerig, CTU i Prague Departmet of Software Egieerig Abstract Two basic types of artificial eural etwors Multi
More informationReading. Subdivision curves and surfaces. Subdivision curves. Chaikin s algorithm. Recommended:
Readig Recommeded: Stollitz, DeRose, ad Salesi. Wavelets for Computer Graphics: Theory ad Applicatios, 996, sectio 6.-6.3, 0., A.5. Subdivisio curves ad surfaces Note: there is a error i Stollitz, et al.,
More informationPerformance Plus Software Parameter Definitions
Performace Plus+ Software Parameter Defiitios/ Performace Plus Software Parameter Defiitios Chapma Techical Note-TG-5 paramete.doc ev-0-03 Performace Plus+ Software Parameter Defiitios/2 Backgroud ad Defiitios
More information