Now here is the important step


 Ambrose Bradford
 4 years ago
 Views:
Transcription
1 LINEST i Excel The Excel spreadsheet fuctio "liest" is a complete liear least squares curve fittig routie that produces ucertaity estimates for the fit values. There are two ways to access the "liest" fuctioality; through the fuctio directly ad through the "aalysis tools" set of macros. These istructios cover usig "liest" as a spreadsheet fuctio. Usig liest i your spreadsheets is very easy, after you master the cocept of a array fuctio. Array fuctios are fuctios that while etered ito a sigle spreadsheet cell produce results that fill several cells. The steps outlied below take you setbystep through the process of liear curve fittig. Step 1. Type i your data i two colums, oe for the x variables ad oe for the y. You ca use ay labels you would like. "x" ad "y" are used i the example at right for coveiece. Step 2. Select the area that will hold the output of the array formula. For "liest" you should drag to form a 5 row by 2 colum data array. Step 3. Click i the formula bar at the top of the scree. Now press the fuctio wizard butto. This butto is i the formula bar ad is labeled "fx". A twopart scroll box will appear; i the left scroll box click o "Statistical" ad i the right click o "LINEST". Next click o "Next>." The widow show below will appear. O your spreadsheet select the cells cotaiig the y values by
2 draggig i the origial spreadsheet usig the mouse. Click i the "kow_x's" dialog box, ad select the cells cotaig the x values. Type i "TRUE" i the last two dialog boxes. The first TRUE idicates that you wish the lie to be i the form y=mx+b with a ozero itercept. The secod TRUE specifies that you wish the error estimates to be listed. The Fuctio Wizard dialog box should the appear as below. Step 4. Click o "Fiish." The formula bar should the appear as below, although your y ad x cell rages may be differet, of course. If the values are icorrect, you ca edit them as you would ormally. Step 5. Now here is the importat step. LINEST is a array fuctio, which meas that whe you eter the formula i oe cell, multiple cells will be used for the output of the fuctio. To specify that LINEST is a array fuctio do the followig. Highlight the etire formula, icludig the "=" sig, as show above. O the Macitosh, ext, hold dow the apple key ad press "retur." O the PC hold dow the Ctrl ad Shift keys ad press Eter. Excel adds "{ }" brackets aroud the formula, to show that it is a array. Note that you caot type i the "{ }" characters yourself; if you do Excel will treat the cell cotets as characters ad ot a formula. Highlightig the full formula ad typig the apple key or Ctrl + Shift ad "retur" is the oly way to eter a array formula. The least squares results should be prited as show below. The labels i the first ad last colum are't provided by the LINEST fuctio. We've added them to show the meaig of each cell. For example, the slope is 2.629±0.085 ad the itercept is ± 0.41.
3 x y slope itercept ± ± r s(y) F degrees of freedom regressio ss residual ss Step 6: You should ow evaluate the model that you have built. The r 2 value is ofte used for this purpose, but it is oly a rough idicator of the goodess of fit. The r 2 value is calculated from the total sum of squares, which is the sum of the squared deviatios of the origial data from the mea: total ss = (yi yav) 2 ) ad the regressio sum of squares, which is the sum of the squared deviatios of the fit values from the mea: regressio ss = (y^i y av ) 2 Givig: r 2 = regressio ss total ss = (y^ y av ) 2 ( y i y av ) 2 Values close to oe are good. The ucertaities i the slope ad itercept are much better for judgig the quality of the fit. I the example the ucertaity i the slope is 0.085/2.629*100 = 3% ad the ucertaity i the itercept is 12%, which is oly about two sigificat figures i each. The ucertaities i the slope ad itercept are ot as good as the r 2 of might have idicated! A eve better statistical test of the goodess of fit is to use the Fisher Fstatistic. The Fstatistic is the ratio of the variace i the data explaied by the liear model divided by the variace uexplaied by the model. The Fstatistic is calculated from the regressio sum of squares ad the residual sum of squares. The residual sum of squares is the sum of the squared residuals: residual ss = (y i y^i) 2 = r 2 i Dividig by the degrees of freedom, gives the variace of the y values
4 r 2 i s 2 y = 2 The regressio sum of squares, the residual sum of squares, ad the stadard deviatio of the y values, s(y) are all listed i the liest output. The Fstatistic is the the ratio of the variaces: F= variace explaied variace uexplaied = regressio ss/v ( (y^i y av ) 2 ) 1 /v1 residual ss/v = 2 ( (y i y^i) 2 ) /v2 You use the Fstatistic uder the ull hypothesis that the data is a radom scatter of poits with zero slope. Critical values of the F statistic are listed i stadard statistics texts, the CRC Hadbook, ad Quatitative Aalysis texts. If the Fstatistic is greater tha the Fcritical value, the ull hypothesis fails ad the liear model is sigificat. For the degrees of freedom, which are abbreviated i most tables as v 1 ad v 2,usev 1 =1adv 2 =k,wherekis the umber of variables i the regressio aalysis icludig the itercept ad is the umber of data poits. The value for v 2 is listed as the degrees of freedom i the liest output. A small part of the Ftable is show at right for a α value of 0.05, that is, 95% cofidece. For the example above, v 1 =1adv 2 =6 2=4.The Fcritical value is The Fstatistic for our example is , which is much greater tha the Fcritical value. You are 95% sure that your data is ot a radom scatter of poits ad that the regressio is justified. Fcritical values at α=0.05 v 2 F(v 1 =1) Step 7. You will ow eed to calculate the fit y values, y^ i, which are the values that lie o the lie at the give x values. You ca use the TREND array fuctio for this, but it is just as easy to simply calculate the fit y values directly. Start a ew colum ext to the y values. I this ew colum eter the formula that gives y^ i =mx i + b, with the slope ad itercept from the LINEST output:
5 Step 8. You ca ow use the "Chart Wizard" to help graph the results: first select the three colums i your spreadsheet. Iclude the colum labels. Click o the Chart Wizard ico: The cursor will chage shape idicatig that you are to drag o your spreadsheet where you wat the plot to appear. Remember for lab reports that charts should be at least half a page. The Wizard will the take you through settig up your graph. Do a scatter graph, ad choose the format that has plot symbols, but ot coectig lies. Step 9. You ow eed to replace the plottig symbols for the fit y values poits with coectig lies. Double click o oe of the fit y value data poits. The "Format Data Series" dialog box will appear. Chage the default settigs to o plot symbol (marker) ad coectig lies as show below: The plot should ow appear as at right. Charts ad spreadsheet cells ca easily be copied ad pasted ito Word documets LINEST Tutorial Plot y fit y x (uits?)
6 Addig Error Bars to Plots After you have your graph displayed you ca easily add error bars. Double click o oe of the plottig symbols for your data. The dialog box show below will appear. Click o the "Y Error Bars" tab. Click o the "Both" ico. Next click o the "Custom" butto. Next click i the "+" box ad the select the cell i your spreadsheet that cotais the s(y) value. Repeat this last step i the "" box. Click o "OK" ad the error bars should appear o your plot. The fial chart, i all its glory looks like this: 16 LINEST Tutorial Plot y fit y x (uits?)
Desktop Management. Desktop Management Tools
Desktop Maagemet 9 Desktop Maagemet Tools Mac OS X icludes three desktop maagemet tools that you might fid helpful to work more efficietly ad productively: u Stacks puts expadable folders i the Dock. Clickig
More informationConfidence Intervals for One Mean
Chapter 420 Cofidece Itervals for Oe Mea Itroductio This routie calculates the sample size ecessary to achieve a specified distace from the mea to the cofidece limit(s) at a stated cofidece level for a
More informationI. Chisquared Distributions
1 M 358K Supplemet to Chapter 23: CHISQUARED DISTRIBUTIONS, TDISTRIBUTIONS, AND DEGREES OF FREEDOM To uderstad tdistributios, we first eed to look at aother family of distributios, the chisquared distributios.
More informationLesson 15 ANOVA (analysis of variance)
Outlie Variability betwee group variability withi group variability total variability Fratio Computatio sums of squares (betwee/withi/total degrees of freedom (betwee/withi/total mea square (betwee/withi
More informationLesson 17 Pearson s Correlation Coefficient
Outlie Measures of Relatioships Pearso s Correlatio Coefficiet (r) types of data scatter plots measure of directio measure of stregth Computatio covariatio of X ad Y uique variatio i X ad Y measurig
More informationConfidence Intervals for Linear Regression Slope
Chapter 856 Cofidece Iterval for Liear Regreio Slope Itroductio Thi routie calculate the ample ize eceary to achieve a pecified ditace from the lope to the cofidece limit at a tated cofidece level for
More informationGCSE STATISTICS. 4) How to calculate the range: The difference between the biggest number and the smallest number.
GCSE STATISTICS You should kow: 1) How to draw a frequecy diagram: e.g. NUMBER TALLY FREQUENCY 1 3 5 ) How to draw a bar chart, a pictogram, ad a pie chart. 3) How to use averages: a) Mea  add up all
More information1 Correlation and Regression Analysis
1 Correlatio ad Regressio Aalysis I this sectio we will be ivestigatig the relatioship betwee two cotiuous variable, such as height ad weight, the cocetratio of a ijected drug ad heart rate, or the cosumptio
More informationOutput Analysis (2, Chapters 10 &11 Law)
B. Maddah ENMG 6 Simulatio 05/0/07 Output Aalysis (, Chapters 10 &11 Law) Comparig alterative system cofiguratio Sice the output of a simulatio is radom, the comparig differet systems via simulatio should
More informationDefinition. A variable X that takes on values X 1, X 2, X 3,...X k with respective frequencies f 1, f 2, f 3,...f k has mean
1 Social Studies 201 October 13, 2004 Note: The examples i these otes may be differet tha used i class. However, the examples are similar ad the methods used are idetical to what was preseted i class.
More informationCase Study. Normal and t Distributions. Density Plot. Normal Distributions
Case Study Normal ad t Distributios Bret Halo ad Bret Larget Departmet of Statistics Uiversity of Wiscosi Madiso October 11 13, 2011 Case Study Body temperature varies withi idividuals over time (it ca
More informationTime Value of Money, NPV and IRR equation solving with the TI86
Time Value of Moey NPV ad IRR Equatio Solvig with the TI86 (may work with TI85) (similar process works with TI83, TI83 Plus ad may work with TI82) Time Value of Moey, NPV ad IRR equatio solvig with
More informationMeasures of Spread and Boxplots Discrete Math, Section 9.4
Measures of Spread ad Boxplots Discrete Math, Sectio 9.4 We start with a example: Example 1: Comparig Mea ad Media Compute the mea ad media of each data set: S 1 = {4, 6, 8, 10, 1, 14, 16} S = {4, 7, 9,
More informationTHE REGRESSION MODEL IN MATRIX FORM. For simple linear regression, meaning one predictor, the model is. for i = 1, 2, 3,, n
We will cosider the liear regressio model i matrix form. For simple liear regressio, meaig oe predictor, the model is i = + x i + ε i for i =,,,, This model icludes the assumptio that the ε i s are a sample
More informationOnesample test of proportions
Oesample test of proportios The Settig: Idividuals i some populatio ca be classified ito oe of two categories. You wat to make iferece about the proportio i each category, so you draw a sample. Examples:
More informationPSYCHOLOGICAL STATISTICS
UNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATION B Sc. Cousellig Psychology (0 Adm.) IV SEMESTER COMPLEMENTARY COURSE PSYCHOLOGICAL STATISTICS QUESTION BANK. Iferetial statistics is the brach of statistics
More information15.075 Exam 3. Instructor: Cynthia Rudin TA: Dimitrios Bisias. November 22, 2011
15.075 Exam 3 Istructor: Cythia Rudi TA: Dimitrios Bisias November 22, 2011 Gradig is based o demostratio of coceptual uderstadig, so you eed to show all of your work. Problem 1 A compay makes highdefiitio
More informationMathematical goals. Starting points. Materials required. Time needed
Level A1 of challege: C A1 Mathematical goals Startig poits Materials required Time eeded Iterpretig algebraic expressios To help learers to: traslate betwee words, symbols, tables, ad area represetatios
More informationCenter, Spread, and Shape in Inference: Claims, Caveats, and Insights
Ceter, Spread, ad Shape i Iferece: Claims, Caveats, ad Isights Dr. Nacy Pfeig (Uiversity of Pittsburgh) AMATYC November 2008 Prelimiary Activities 1. I would like to produce a iterval estimate for the
More informationNonlife insurance mathematics. Nils F. Haavardsson, University of Oslo and DNB Skadeforsikring
Nolife isurace mathematics Nils F. Haavardsso, Uiversity of Oslo ad DNB Skadeforsikrig Mai issues so far Why does isurace work? How is risk premium defied ad why is it importat? How ca claim frequecy
More informationhp calculators HP 12C Statistics  average and standard deviation Average and standard deviation concepts HP12C average and standard deviation
HP 1C Statistics  average ad stadard deviatio Average ad stadard deviatio cocepts HP1C average ad stadard deviatio Practice calculatig averages ad stadard deviatios with oe or two variables HP 1C Statistics
More informationODBC. Getting Started With Sage Timberline Office ODBC
ODBC Gettig Started With Sage Timberlie Office ODBC NOTICE This documet ad the Sage Timberlie Office software may be used oly i accordace with the accompayig Sage Timberlie Office Ed User Licese Agreemet.
More informationChapter 7: Confidence Interval and Sample Size
Chapter 7: Cofidece Iterval ad Sample Size Learig Objectives Upo successful completio of Chapter 7, you will be able to: Fid the cofidece iterval for the mea, proportio, ad variace. Determie the miimum
More informationI. Why is there a time value to money (TVM)?
Itroductio to the Time Value of Moey Lecture Outlie I. Why is there the cocept of time value? II. Sigle cash flows over multiple periods III. Groups of cash flows IV. Warigs o doig time value calculatios
More information5: Introduction to Estimation
5: Itroductio to Estimatio Cotets Acroyms ad symbols... 1 Statistical iferece... Estimatig µ with cofidece... 3 Samplig distributio of the mea... 3 Cofidece Iterval for μ whe σ is kow before had... 4 Sample
More informationTime Value of Money. First some technical stuff. HP10B II users
Time Value of Moey Basis for the course Power of compoud iterest $3,600 each year ito a 401(k) pla yields $2,390,000 i 40 years First some techical stuff You will use your fiacial calculator i every sigle
More informationRepeating Decimals are decimal numbers that have number(s) after the decimal point that repeat in a pattern.
5.5 Fractios ad Decimals Steps for Chagig a Fractio to a Decimal. Simplify the fractio, if possible. 2. Divide the umerator by the deomiator. d d Repeatig Decimals Repeatig Decimals are decimal umbers
More informationCHAPTER 3 THE TIME VALUE OF MONEY
CHAPTER 3 THE TIME VALUE OF MONEY OVERVIEW A dollar i the had today is worth more tha a dollar to be received i the future because, if you had it ow, you could ivest that dollar ad ear iterest. Of all
More informationThis document contains a collection of formulas and constants useful for SPC chart construction. It assumes you are already familiar with SPC.
SPC Formulas ad Tables 1 This documet cotais a collectio of formulas ad costats useful for SPC chart costructio. It assumes you are already familiar with SPC. Termiology Geerally, a bar draw over a symbol
More informationZTEST / ZSTATISTIC: used to test hypotheses about. µ when the population standard deviation is unknown
ZTEST / ZSTATISTIC: used to test hypotheses about µ whe the populatio stadard deviatio is kow ad populatio distributio is ormal or sample size is large TTEST / TSTATISTIC: used to test hypotheses about
More informationHow to set up your GMC Online account
How to set up your GMC Olie accout Mai title Itroductio GMC Olie is a secure part of our website that allows you to maage your registratio with us. Over 100,000 doctors already use GMC Olie. We wat every
More informationMannWhitney U 2 Sample Test (a.k.a. Wilcoxon Rank Sum Test)
NoParametric ivariate Statistics: WilcoxoMaWhitey 2 Sample Test 1 MaWhitey 2 Sample Test (a.k.a. Wilcoxo Rak Sum Test) The (Wilcoxo) MaWhitey (WMW) test is the oparametric equivalet of a pooled
More informationIncremental calculation of weighted mean and variance
Icremetal calculatio of weighted mea ad variace Toy Fich faf@cam.ac.uk dot@dotat.at Uiversity of Cambridge Computig Service February 009 Abstract I these otes I eplai how to derive formulae for umerically
More informationHypothesis testing. Null and alternative hypotheses
Hypothesis testig Aother importat use of samplig distributios is to test hypotheses about populatio parameters, e.g. mea, proportio, regressio coefficiets, etc. For example, it is possible to stipulate
More informationConfidence Intervals. CI for a population mean (σ is known and n > 30 or the variable is normally distributed in the.
Cofidece Itervals A cofidece iterval is a iterval whose purpose is to estimate a parameter (a umber that could, i theory, be calculated from the populatio, if measuremets were available for the whole populatio).
More informationDetermining the sample size
Determiig the sample size Oe of the most commo questios ay statisticia gets asked is How large a sample size do I eed? Researchers are ofte surprised to fid out that the aswer depeds o a umber of factors
More informationChapter 14 Nonparametric Statistics
Chapter 14 Noparametric Statistics A.K.A. distributiofree statistics! Does ot deped o the populatio fittig ay particular type of distributio (e.g, ormal). Sice these methods make fewer assumptios, they
More informationConfidence Intervals
Cofidece Itervals Cofidece Itervals are a extesio of the cocept of Margi of Error which we met earlier i this course. Remember we saw: The sample proportio will differ from the populatio proportio by more
More informationSoving Recurrence Relations
Sovig Recurrece Relatios Part 1. Homogeeous liear 2d degree relatios with costat coefficiets. Cosider the recurrece relatio ( ) T () + at ( 1) + bt ( 2) = 0 This is called a homogeeous liear 2d degree
More informationExploratory Data Analysis
1 Exploratory Data Aalysis Exploratory data aalysis is ofte the rst step i a statistical aalysis, for it helps uderstadig the mai features of the particular sample that a aalyst is usig. Itelliget descriptios
More informationCS103X: Discrete Structures Homework 4 Solutions
CS103X: Discrete Structures Homewor 4 Solutios Due February 22, 2008 Exercise 1 10 poits. Silico Valley questios: a How may possible sixfigure salaries i whole dollar amouts are there that cotai at least
More informationTHE ARITHMETIC OF INTEGERS.  multiplication, exponentiation, division, addition, and subtraction
THE ARITHMETIC OF INTEGERS  multiplicatio, expoetiatio, divisio, additio, ad subtractio What to do ad what ot to do. THE INTEGERS Recall that a iteger is oe of the whole umbers, which may be either positive,
More informationHCL Dynamic Spiking Protocol
ELI LILLY AND COMPANY TIPPECANOE LABORATORIES LAFAYETTE, IN Revisio 2.0 TABLE OF CONTENTS REVISION HISTORY... 2. REVISION.0... 2.2 REVISION 2.0... 2 2 OVERVIEW... 3 3 DEFINITIONS... 5 4 EQUIPMENT... 7
More information.04. This means $1000 is multiplied by 1.02 five times, once for each of the remaining sixmonth
Questio 1: What is a ordiary auity? Let s look at a ordiary auity that is certai ad simple. By this, we mea a auity over a fixed term whose paymet period matches the iterest coversio period. Additioally,
More informationNormal Distribution.
Normal Distributio www.icrf.l Normal distributio I probability theory, the ormal or Gaussia distributio, is a cotiuous probability distributio that is ofte used as a first approimatio to describe realvalued
More informationBiology 171L Environment and Ecology Lab Lab 2: Descriptive Statistics, Presenting Data and Graphing Relationships
Biology 171L Eviromet ad Ecology Lab Lab : Descriptive Statistics, Presetig Data ad Graphig Relatioships Itroductio Log lists of data are ofte ot very useful for idetifyig geeral treds i the data or the
More information5.4 Amortization. Question 1: How do you find the present value of an annuity? Question 2: How is a loan amortized?
5.4 Amortizatio Questio 1: How do you fid the preset value of a auity? Questio 2: How is a loa amortized? Questio 3: How do you make a amortizatio table? Oe of the most commo fiacial istrumets a perso
More informationIn order to print in ESC/P mode, the serial connection should be activated.
Appedix: Serial Port Settigs Serial Port Settigs (RS232C) The pi assigmets for the serial cables (RS232C cables) which ca be used with this priter are show i the table below. You ca purchase the cables
More informationMaximum Likelihood Estimators.
Lecture 2 Maximum Likelihood Estimators. Matlab example. As a motivatio, let us look at oe Matlab example. Let us geerate a radom sample of size 00 from beta distributio Beta(5, 2). We will lear the defiitio
More information1. C. The formula for the confidence interval for a population mean is: x t, which was
s 1. C. The formula for the cofidece iterval for a populatio mea is: x t, which was based o the sample Mea. So, x is guarateed to be i the iterval you form.. D. Use the rule : pvalue
More informationAP Calculus AB 2006 Scoring Guidelines Form B
AP Calculus AB 6 Scorig Guidelies Form B The College Board: Coectig Studets to College Success The College Board is a otforprofit membership associatio whose missio is to coect studets to college success
More informationTrigonometric Form of a Complex Number. The Complex Plane. axis. ( 2, 1) or 2 i FIGURE 6.44. The absolute value of the complex number z a bi is
0_0605.qxd /5/05 0:45 AM Page 470 470 Chapter 6 Additioal Topics i Trigoometry 6.5 Trigoometric Form of a Complex Number What you should lear Plot complex umbers i the complex plae ad fid absolute values
More information, a Wishart distribution with n 1 degrees of freedom and scale matrix.
UMEÅ UNIVERSITET Matematiskstatistiska istitutioe Multivariat dataaalys D MSTD79 PA TENTAMEN 00409 LÖSNINGSFÖRSLAG TILL TENTAMEN I MATEMATISK STATISTIK Multivariat dataaalys D, 5 poäg.. Assume that
More informationEngineering Data Management
BaaERP 5.0c Maufacturig Egieerig Data Maagemet Module Procedure UP128A US Documetiformatio Documet Documet code : UP128A US Documet group : User Documetatio Documet title : Egieerig Data Maagemet Applicatio/Package
More informationHere are a couple of warnings to my students who may be here to get a copy of what happened on a day that you missed.
This documet was writte ad copyrighted by Paul Dawkis. Use of this documet ad its olie versio is govered by the Terms ad Coditios of Use located at http://tutorial.math.lamar.edu/terms.asp. The olie versio
More informationAnnuities Under Random Rates of Interest II By Abraham Zaks. Technion I.I.T. Haifa ISRAEL and Haifa University Haifa ISRAEL.
Auities Uder Radom Rates of Iterest II By Abraham Zas Techio I.I.T. Haifa ISRAEL ad Haifa Uiversity Haifa ISRAEL Departmet of Mathematics, Techio  Israel Istitute of Techology, 3000, Haifa, Israel I memory
More informationOverview of some probability distributions.
Lecture Overview of some probability distributios. I this lecture we will review several commo distributios that will be used ofte throughtout the class. Each distributio is usually described by its probability
More informationBioPlex Manager Software
Multiplex Suspesio Array BioPlex Maager Software Extract Kowledge Faster Move Your Research Forward BioRad cotiues to iovate where it matters most. With BioPlex Maager 5.0 software, we offer valuable
More informationUniversity of California, Los Angeles Department of Statistics. Distributions related to the normal distribution
Uiversity of Califoria, Los Ageles Departmet of Statistics Statistics 100B Istructor: Nicolas Christou Three importat distributios: Distributios related to the ormal distributio Chisquare (χ ) distributio.
More informationSECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES
SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES Read Sectio 1.5 (pages 5 9) Overview I Sectio 1.5 we lear to work with summatio otatio ad formulas. We will also itroduce a brief overview of sequeces,
More information0.7 0.6 0.2 0 0 96 96.5 97 97.5 98 98.5 99 99.5 100 100.5 96.5 97 97.5 98 98.5 99 99.5 100 100.5
Sectio 13 KolmogorovSmirov test. Suppose that we have a i.i.d. sample X 1,..., X with some ukow distributio P ad we would like to test the hypothesis that P is equal to a particular distributio P 0, i.e.
More informationProperties of MLE: consistency, asymptotic normality. Fisher information.
Lecture 3 Properties of MLE: cosistecy, asymptotic ormality. Fisher iformatio. I this sectio we will try to uderstad why MLEs are good. Let us recall two facts from probability that we be used ofte throughout
More informationiprox sensors iprox inductive sensors iprox programming tools ProxView programming software iprox the world s most versatile proximity sensor
iprox sesors iprox iductive sesors iprox programmig tools ProxView programmig software iprox the world s most versatile proximity sesor The world s most versatile proximity sesor Eato s iproxe is syoymous
More informationNeolane Reporting. Neolane v6.1
Neolae Reportig Neolae v6.1 This documet, ad the software it describes, are provided subject to a Licese Agreemet ad may ot be used or copied outside of the provisios of the Licese Agreemet. No part of
More informationUnit 8: Inference for Proportions. Chapters 8 & 9 in IPS
Uit 8: Iferece for Proortios Chaters 8 & 9 i IPS Lecture Outlie Iferece for a Proortio (oe samle) Iferece for Two Proortios (two samles) Cotigecy Tables ad the χ test Iferece for Proortios IPS, Chater
More informationBaanERP. BaanERP Windows Client Installation Guide
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 to
More informationLECTURE 13: Crossvalidation
LECTURE 3: Crossvalidatio Resampli methods Cross Validatio Bootstrap Bias ad variace estimatio with the Bootstrap Threeway data partitioi Itroductio to Patter Aalysis Ricardo GutierrezOsua Texas A&M
More informationBaan Service Master Data Management
Baa Service Master Data Maagemet Module Procedure UP069A US Documetiformatio Documet Documet code : UP069A US Documet group : User Documetatio Documet title : Master Data Maagemet Applicatio/Package :
More informationChapter 5 Unit 1. IET 350 Engineering Economics. Learning Objectives Chapter 5. Learning Objectives Unit 1. Annual Amount and Gradient Functions
Chapter 5 Uit Aual Amout ad Gradiet Fuctios IET 350 Egieerig Ecoomics Learig Objectives Chapter 5 Upo completio of this chapter you should uderstad: Calculatig future values from aual amouts. Calculatig
More informationDomain 1: Configuring Domain Name System (DNS) for Active Directory
Maual Widows Domai 1: Cofigurig Domai Name System (DNS) for Active Directory Cofigure zoes I Domai Name System (DNS), a DNS amespace ca be divided ito zoes. The zoes store ame iformatio about oe or more
More informationChapter 6: Variance, the law of large numbers and the MonteCarlo method
Chapter 6: Variace, the law of large umbers ad the MoteCarlo method Expected value, variace, ad Chebyshev iequality. If X is a radom variable recall that the expected value of X, E[X] is the average value
More informationApproximating Area under a curve with rectangles. To find the area under a curve we approximate the area using rectangles and then use limits to find
1.8 Approximatig Area uder a curve with rectagles 1.6 To fid the area uder a curve we approximate the area usig rectagles ad the use limits to fid 1.4 the area. Example 1 Suppose we wat to estimate 1.
More informationMEI Structured Mathematics. Module Summary Sheets. Statistics 2 (Version B: reference to new book)
MEI Mathematics i Educatio ad Idustry MEI Structured Mathematics Module Summary Sheets Statistics (Versio B: referece to ew book) Topic : The Poisso Distributio Topic : The Normal Distributio Topic 3:
More information1 Computing the Standard Deviation of Sample Means
Computig the Stadard Deviatio of Sample Meas Quality cotrol charts are based o sample meas ot o idividual values withi a sample. A sample is a group of items, which are cosidered all together for our aalysis.
More informationDepartment of Computer Science, University of Otago
Departmet of Computer Sciece, Uiversity of Otago Techical Report OUCS200609 Permutatios Cotaiig May Patters Authors: M.H. Albert Departmet of Computer Sciece, Uiversity of Otago Micah Colema, Rya Fly
More information*The most important feature of MRP as compared with ordinary inventory control analysis is its time phasing feature.
Itegrated Productio ad Ivetory Cotrol System MRP ad MRP II Framework of Maufacturig System Ivetory cotrol, productio schedulig, capacity plaig ad fiacial ad busiess decisios i a productio system are iterrelated.
More informationPractice Problems for Test 3
Practice Problems for Test 3 Note: these problems oly cover CIs ad hypothesis testig You are also resposible for kowig the samplig distributio of the sample meas, ad the Cetral Limit Theorem Review all
More informationIn nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008
I ite Sequeces Dr. Philippe B. Laval Keesaw State Uiversity October 9, 2008 Abstract This had out is a itroductio to i ite sequeces. mai de itios ad presets some elemetary results. It gives the I ite Sequeces
More informationDomain 1: Designing a SQL Server Instance and a Database Solution
Maual SQL Server 2008 Desig, Optimize ad Maitai (70450) 18004186789 Domai 1: Desigig a SQL Server Istace ad a Database Solutio Desigig for CPU, Memory ad Storage Capacity Requiremets Whe desigig a
More informationInference on Proportion. Chapter 8 Tests of Statistical Hypotheses. Sampling Distribution of Sample Proportion. Confidence Interval
Chapter 8 Tests of Statistical Hypotheses 8. Tests about Proportios HT  Iferece o Proportio Parameter: Populatio Proportio p (or π) (Percetage of people has o health isurace) x Statistic: Sample Proportio
More information3. Greatest Common Divisor  Least Common Multiple
3 Greatest Commo Divisor  Least Commo Multiple Defiitio 31: The greatest commo divisor of two atural umbers a ad b is the largest atural umber c which divides both a ad b We deote the greatest commo gcd
More informationDomain 1: Identifying Cause of and Resolving Desktop Application Issues Identifying and Resolving New Software Installation Issues
Maual Widows 7 Eterprise Desktop Support Techicia (70685) 18004186789 Domai 1: Idetifyig Cause of ad Resolvig Desktop Applicatio Issues Idetifyig ad Resolvig New Software Istallatio Issues This sectio
More informationwhere: T = number of years of cash flow in investment's life n = the year in which the cash flow X n i = IRR = the internal rate of return
EVALUATING ALTERNATIVE CAPITAL INVESTMENT PROGRAMS By Ke D. Duft, Extesio Ecoomist I the March 98 issue of this publicatio we reviewed the procedure by which a capital ivestmet project was assessed. The
More informationQuadrat Sampling in Population Ecology
Quadrat Samplig i Populatio Ecology Backgroud Estimatig the abudace of orgaisms. Ecology is ofte referred to as the "study of distributio ad abudace". This beig true, we would ofte like to kow how may
More informationCHAPTER 7: Central Limit Theorem: CLT for Averages (Means)
CHAPTER 7: Cetral Limit Theorem: CLT for Averages (Meas) X = the umber obtaied whe rollig oe six sided die oce. If we roll a six sided die oce, the mea of the probability distributio is X P(X = x) Simulatio:
More informationNATIONAL SENIOR CERTIFICATE GRADE 12
NATIONAL SENIOR CERTIFICATE GRADE MATHEMATICS P EXEMPLAR 04 MARKS: 50 TIME: 3 hours This questio paper cosists of 8 pages ad iformatio sheet. Please tur over Mathematics/P DBE/04 NSC Grade Eemplar INSTRUCTIONS
More informationThe following example will help us understand The Sampling Distribution of the Mean. C1 C2 C3 C4 C5 50 miles 84 miles 38 miles 120 miles 48 miles
The followig eample will help us uderstad The Samplig Distributio of the Mea Review: The populatio is the etire collectio of all idividuals or objects of iterest The sample is the portio of the populatio
More informationCS100: Introduction to Computer Science
Review: History of Computers CS100: Itroductio to Computer Sciece Maiframes Miicomputers Lecture 2: Data Storage  Bits, their storage ad mai memory Persoal Computers & Workstatios Review: The Role of
More informationHypergeometric Distributions
7.4 Hypergeometric Distributios Whe choosig the startig lieup for a game, a coach obviously has to choose a differet player for each positio. Similarly, whe a uio elects delegates for a covetio or you
More informationMath C067 Sampling Distributions
Math C067 Samplig Distributios Sample Mea ad Sample Proportio Richard Beigel Some time betwee April 16, 2007 ad April 16, 2007 Examples of Samplig A pollster may try to estimate the proportio of voters
More informationExample 2 Find the square root of 0. The only square root of 0 is 0 (since 0 is not positive or negative, so those choices don t exist here).
BEGINNING ALGEBRA Roots ad Radicals (revised summer, 00 Olso) Packet to Supplemet the Curret Textbook  Part Review of Square Roots & Irratioals (This portio ca be ay time before Part ad should mostly
More informationSimple Annuities Present Value.
Simple Auities Preset Value. OBJECTIVES (i) To uderstad the uderlyig priciple of a preset value auity. (ii) To use a CASIO CFX9850GB PLUS to efficietly compute values associated with preset value auities.
More informationConvexity, Inequalities, and Norms
Covexity, Iequalities, ad Norms Covex Fuctios You are probably familiar with the otio of cocavity of fuctios. Give a twicedifferetiable fuctio ϕ: R R, We say that ϕ is covex (or cocave up) if ϕ (x) 0 for
More informationA GUIDE TO LEVEL 3 VALUE ADDED IN 2013 SCHOOL AND COLLEGE PERFORMANCE TABLES
A GUIDE TO LEVEL 3 VALUE ADDED IN 2013 SCHOOL AND COLLEGE PERFORMANCE TABLES Cotets Page No. Summary Iterpretig School ad College Value Added Scores 2 What is Value Added? 3 The Learer Achievemet Tracker
More informationBENEFITCOST ANALYSIS Financial and Economic Appraisal using Spreadsheets
BENEITCST ANALYSIS iacial ad Ecoomic Appraisal usig Spreadsheets Ch. 2: Ivestmet Appraisal  Priciples Harry Campbell & Richard Brow School of Ecoomics The Uiversity of Queeslad Review of basic cocepts
More informationNATIONAL SENIOR CERTIFICATE GRADE 11
NATIONAL SENIOR CERTIFICATE GRADE MATHEMATICS P NOVEMBER 007 MARKS: 50 TIME: 3 hours This questio paper cosists of 9 pages, diagram sheet ad a page formula sheet. Please tur over Mathematics/P DoE/November
More informationDAME  Microsoft Excel addin for solving multicriteria decision problems with scenarios Radomir Perzina 1, Jaroslav Ramik 2
Itroductio DAME  Microsoft Excel addi for solvig multicriteria decisio problems with scearios Radomir Perzia, Jaroslav Ramik 2 Abstract. The mai goal of every ecoomic aget is to make a good decisio,
More informationSequences and Series Using the TI89 Calculator
RIT Calculator Site Sequeces ad Series Usig the TI89 Calculator Norecursively Defied Sequeces A orecursively defied sequece is oe i which the formula for the terms of the sequece is give explicitly. For
More informationSerial ATA PCI Host Adapter AEC6290/6295
Serial ATA PCI Host Adapter AEC6290/6295 User s Maual Versio:1.0 Copyright 2003 ACARD Techology Corp. Release: April 2003 Copyright ad Trademarks The iformatio of the product i this maual is subject to
More information