Polycast Acrylic Sheets.

Size: px
Start display at page:

Download "Polycast Acrylic Sheets."

Transcription

1 ) Introducton: Polycast Acrylc Sheets Davs Earle, Ron Deal and Earl Gaudette SNOSTR3042 revsed and epanded Jan, 4 One hundred and seventy sheets of acrylc have been purchased by SNO from Polycast Polycast has performed varous C measurements on these sheets and n addton * by 4" coupons from each sheet have been shpped to CRL where addtonal C measurements have been performed Polycast has shpped the sheets to Reynolds Polymer Technology (RPT) n Calforna who wll be thermoformng and machnng the sheets pror to shpment to Sudbury for vessel fabrcaton Ths report contans the detals of the measurements performed by Polycast and by CRL on coupons from the sheets and the assumptons made about the sheets from these results Reports of the optcal!) and radoactve 2) qualty of the frst 2% of the sheets have already been dstrbuted In addton most of the contents of ths report have also been reported3) 2) Sheet Inventory: The sheet nventory s summarzed n Table Polycast has cell cast twelve batches of 22" materal and three batches of 4" materal The 22" batches comprsed 4 or 20 sheets and the 4" batches comprsed up to 0 sheets Table lsts only those sheets purchased and shpped to RPT The gaps n the table represent sheets rejected by Polycast as falng to meet the SNO specfcatons Based on sheet qualty, each sheet has been assgned to the vessel (), the qualfcaton program () or as a vessel spare (S) Batches 47 4 and 3 were nferor from an optcal pont of vew and batch 0 from a Th content pont of vew 3) Polycast ualty Control Results Polycast has provded us wth copes of ther test results 3 Thckness They made thckness measurements at 2 postons n each 22" sheet and 2 postons n each 4" sheet The specfcatons requred all measurements to be between 2" and 233" or 47" and 473" Snce

2 Table Sheet Inventory Sheet Batch S 3 4 S S S 7 S S S S 0 S 2 3 S 4 S 7 20 Page

3 Table 2 Mnmum Thckness of each Sheet bat she Page

4 the bucklng forces on the vessel are greater at the top than at the bottom t may be advantageous to placed the thcker panels n the upper hemsphere Table 2 lsts the mnmum thckness measurement of each sheet as reported by Polycast The dstrbuton of these thcknesses are shown graphcally n Fgure 32 Mechancal They have made fve mechancal measurements on one sample from each batch These measurements, summarzed n Table 3, are all better than the specfcatons whch are also ndcated n Table 3 The mechancal propertes measured were tensle strength, tensle elongaton tensle modulus, compressve deformaton under load and resdual monomer Table 3 Mechancal Propertes Batch Ten Str Spec Ten Eton % Ten Mod Def Res Mon % tot ar parts nclus 03 / mcron 2M / K / / 42 3 / / 37 0 / 2 2 / 2 0 / 273 / 2 72 / 7 2 / / 0 0/7 2 / 7 7, / 2 3/4 33 Inclusons They nspected each sheet for fber nclusons and vods and documented the number of each sze from <" to " n fve ncrements The total number of nclusons n each batch s lsted n Table 3 Most batches had no nclusons greater than 0" The detal breakdown of the ncluson data s on fle SNO dd not nsst that Polycast adhere to the ncluson specfcaton, choosng nstead to rely on the radoactvty measurements

5 34 Ar ualty They measured the panculate densty n the ar near the castng machne when t was beng assembled for each batch The densty n partcles per cubc foot above 03 and mcron are lsted n Table 3 where mamum values of 2 0 for 03 mcron and 03 for mcron were the hopedfor lmts These lmts were eceeded for a number of the batches It was not practcal for Polycast to stopped producton durng hgh dust levels and so the batches were made under potentally adverse condtons A correlaton wth the partcle densty and the Th/U content would confrm that dust s the domnate source of radoactvty n the acrylc 3 Optcal Absorpton They measured the optcal absorpton coeffcent as a functon of wavelength of samples from each sheet Measurements were made on as cast materal, on condtoned materal and on materal whch had been heated to thermoformng temperatures and subsequently annealed Smlar measurements were made on samples from every sheet at CRL and the detals of the Polycast results wll be presented below wth the CRL results The optcal qualty of the acrylc deterorates wth every heat treatment but snce the vessel must be made from thermoformed and annealed acrylc t wll be those results whch wll be prmarly of nterest 4) Th and U Content The Th and U content n the acrylc was measured by the three technques 4) reported n SNOSTR20 or AECL074 Prmarly the technque of neutron actvaton followed by gamma ray countng of the Np and Pa was used, as ths technque had been shown to be least susceptble to handlng contamnaton 2) Mass spectrometry measurements ) were also made on samples from all batches and alpha spectroscopy measurements ) were made on a few samples, to check for decay chan dsequlbrum 4 Neutron Actvaton Results Eght hundred gram blocks of acrylc were rradated n the NRU reactor/the nonoptcal or saw cut surfaces were mlled off so as to remove surface handlng contamnaton and the block was vaporzed to a resdue whch was then counted for Np and Pa 2) Typcally four blocks from each batch were measured Table 4 lsts the results and Fg 2 shows them graphcally Table 4 lsts the CRL dentfcaton number (col ), the

6 Table 4Neutron Actvaton Results ID Sample days hours Th n coolnq of count fl done Mar 7 3 to 0 done Dec core core core core pg/g < <00 < <002 <004 < < < U n <0 <03 <0 <03 <03 <03 <03 <3 pg/c <0 <04 <0 < <0 < <03 <03 < <03 <0 <4 < <03 <00 <0 <07 <04 <0 <03 <0 <0 <00

7 Table 4Neutron Actvaton Results R ??0 3 4?4f) 7?0?n??03?04??? ?3 232? C <003 <003 <00 < <007 < < < <004 <00 <0 <00 <03 <03 < <0 < <0 < <0 <04 < <03 <03 <03 < < <04 <007 <00 < < <04 < <4 <03 <0 < < <04 < <0 < <04

8 batch and sheet number (col 2), the duraton between rradaton and countng (col 3) the duraton of the count (col 4), the Th concentraton as a two sgma lmt or wth a one sgma error (col ) and the U concentraton as a two sgma lmt (col ) In col 2 the frst two dgts are the last two dgts of the batch number and the last two dgts are the sheet number In four cases (core) the optcal surfaces were mlled away before vaporzaton The 22 ke Np peak was not seen n any of the spectra and so the U concentratons n the samples are reported as a two sgma upper lmt The lmt vared from 0 pg/g for samples counted wthn a few days of rradaton to pg/g for samples counted several weeks after rradaton The specfcaton s 7 pg/g If there was any suggeston of a 30 ke Pa peak then a Th concentraton was recorded wth a one sgma error If a peak was not dscernble then a two sgma lmt was reported Ecept for batch 0 the Th concentraton of all batches s less than 0 pg/g The specfcaton s 2 pg/g Batch 0 appears to be a sgnfcant ecepton n that the frst four samples were above 0 pg/g Subsequently samples from four other sheets from batch 0 were also hgh confrmng that ths batch s eceptonal The Th concentraton n the frst samples from 702, 402, 20, 30 and 40 were all above 0 pg/g but second samples from the same sheets were all below 0 pg/g, ecept for 30 whch was 04 pg/g Ether there was a local concentraton of Th n these sheets or handlng contamnaton resulted n a readng hgher than the average 42 Mass Spectrometry Results A large quantfy of acrylc has been vaporzed and the resdue analyzed for Th and U by mass Spectrometry The results are lsted n Table and shown n Fg 3 In most cases the acrylc from two coupons (or sheets) was combned so as to get kg samples for analyss These mass Spectrometry results are sgnfcantly hgher than the neutron actvaton results suggestng handlng contamnaton of the mass Spectrometry samples at CRL 2) Even so, almost wthout ecepton, the results are less than the acrylc specfcatons of Th at 2 ppt and U at 7 ppt 43 Alpha Spectroscopy Results Only two dsequlbrum measurements were performed Over 20 kg of acrylc from batch 47 and from batch 7 were vaporzed A porton of the resdue was analyzed by mass Spectrometry and a known amount of Th was added to the remander whch was then separated nto Th, 4

9 Table Mass Spectroscopy Res Batch Sheets 7, 4, 2,2 2,3, 4 4 7, 3,232 4,0 27 3,, , ,3 2 0, ,4,0 2,,3, Weght kg Th oq/q (MS) U pg/g (MS) Page

10 U and Ra usng on echange columns The radosotopes were electroplated out of soluton and the planchettes alpha counted for several weeks There was no evdence for dsequlbrum n the Th/U chans and the levels of Th and U were consstent wth the mass spectrometry results 44 Dscusson of Th/U Results: The mass spectrometry results are well below the specfcatons but they are also sgnfcantly larger than the neutron actvaton results For reasons already reported 2) we should rely on the neutron actvaton results and assume that the saw cuttng at CRL contamnates the cut surfaces We conclude, wth the ecepton of batch 0 that the Th and U n the sheet acrylc s at least an order of magntude better than the specfcatons of 2 and 7 pg/g respectvely Because they contan sgnfcantly hgher levels of Th the sheets from batch 0 have been ecluded from the vessel ) Optcal Absorpton Coeffcents SNO Specfcatons The optcal requrements and specfcatons of the acrylc were detaled n an earler report 7) In that report a weghtng functon was defned whch folded n the Cerenkov spectrum, the transmsson through the DO and H20 and the PMT quantum effcency The lght detected n SNO s the ntegral of the product of the acrylc transmsson tmes the weghtng functon The report also contaned the acrylc optcal absorpton coeffcents requred These coeffcents were based on multple measurements of samples provded by supplers Table lsts the weghtng functon, the absorpton coeffcent specfcaton and the product of the acrylc transmsson for 22" and 4" acrylc tmes the weghtng functon as a functon of wavelength Even though the weghtng functon s sgnfcant at 300 nm, 22" of acrylc attenuates 3% of the lght Whereas at 400 nm only % of the lght s attenuated by the 22" acrylc A fgure of mert s defned as the rato of lght detected wth the acrylc to lght detected wthout acrylc e the sum of column 4 () dvded by the sum of column 2 The specfcatons requre a fgure of mert of 07 for 22" materal (0 for 4" materal)

11 Table Optcal Standards Wavelength Weghtng Abs Coeff trans wegh trans wegh cm 22" materal 4" materal / total 4 4 The C on the optcal absorpton coeffcents showed that the Polycast producton acrylc was not as good as earler samples n that t faled to meet the specfcaton at 300 nm SNO decded to accept ths materal snce most of the lght at ths wavelength was lost anyway but to nsst that the specfcatons be meet at each of the other wavelengths Some materal dd not satsfy the specfcaton at 340 nm n partcular and was rejected 2 Optcal Bulk Absorpton Coeffcents There s a lot of optcal data on fle at CRL but only eamples of t wll be shown n ths report Optcal measurements have been made by Polycast and CRL on over 400 samples Polycast reported the absorpton coeffcent of samples from each sheet at 300 to 440 nm n 20 nm steps and at 00 and 00 nm CRL made measurements n nm steps The Polycast and CRL values for the absorpton coeffcent at 340 nm for all sheets are shown n Fgs 4, & An ndcaton of the measurement uncertanty n the CRL values may be seen from the multple measurements on samples from two sheets one n batch 0 and the other n batch 2 For most of the batches the spread n values wthn the batch s epermental uncertanty The spread between batches, wthn batch 47 4 and 3 and sheet n batch 2 are real Almost all of the 2 2" sheets n batches 47 & 4 and the 4" sheets n batch 3 fal the specfcaton (007) at ths wavelength (340 nm) These sheets wll not be used n the vessel but wll be used by RPT for the fabrcaton qualfcaton process 3 Fgure of Mert Results A plot of the fgure of mert of each sheet may be of more relevance to SNO than the absorpton coeffcents at varous wavelengths and was used to select sheets for the vessel and as nput to the Monte

12 Carlo programs determnng detector response Table 7 lsts the calculated fgure of mert for the 22" and 4" batches Fg 7 and are plots of these values for the two thcknesses In the case of (he 4" materal the fgure of mert was calculated from the absorpton coeffcents as though the materal was 22" thck Ths allows a drect comparson of the qualty of the bulk acrylc Actually, as can be seen from Table 30% of the sgnal s lost by absorpton n 22" acrylc meetng the specfcatons and 42% n the 4" materal Materal for the qualfcaton program should be selected usng these data Batches 47 4 and 4 and sheet n batch 2 are the poorest qualty 22" materal, followed by selected sheets n batches 0 and 7 Batch 3 s the poorest qualty 4" materal Unfortunately the other two batches are not much better Thrteen samples from sheet of batch 0 were measured and the fgure of mert calculated The spread n the absorpton coeffcents at 340 nm s shown n Fg 4 The fgure of mert from batch 0 coupons s shown n Fg The standard devaton of the 3 measurements on sheet s 004 and ths s consstent wth the epected uncertanty n the optcal measurements We conclude that no sgnfcant dfferences between the sheets of batch 0 ests, the spread n Fg s consstent wth epermental uncertantes A detaled eamnaton of the fgure of mert of the varous batches as plotted n Fgs 7 & shows that almost all of the spread wthn batches s epermental Sheet n batch 2 and sheet 7 n batch 3 are clearly worse than the averages of those batches and the spread n the rejected batch 4 s larger than the epermental uncertanty Otherwse less than a dozen sheets are more than 2 standard devatons from the batch average However the dfferences between batches as emphaszed by the averages plotted n Fgs 7 & are real 4 Dscusson of Optcal Results Wth the ecepton of some sheets n the frst two batches of 22" materal (47 & 4) and the frst batch of 4" materal (3) the acrylc satsfes the optcal specfcaton However because of our tests on Polycast materal pror to the purchase order and because of Polycasts assurances n wrtng we epected to get materal 4% better than the specfcatons In fact Polycast epected the materal to have a fgure of mert of 073 but guaranteed 07 Some of ther materal dd sgnfcantly surpass ther epected qualty but many sheets were below that grade and for that reason we have stuck to the letter of the specfcatons and rejected all sheets whch dd not meet the specfcatons at 340 nm even

13 though ntegrated over the frequency spectrum the fgure of mert was not worse than 07 The 4" materal s unformly poor but there are only 0 panels of that materal and they are so thck anyway that much of the sgnal s absorbed The large varablty of the 22" materal may be a problem for the data ftters Ths has yet to be determned Consderaton has to be gven to the dstrbuton of sheets throughout the vessel The current plan s that the good and poor sheets wll be randomly dstrbuted and not be concentrated at specfc locatons RPT are machnng the sheets Acknowledgments: We thank Dr Emmanuel Bonvn for hs contnung nterest n acrylc qualty and n the CRL work All of the fgure of mert values were calculated by hm All of the CRL optcal measurements were made on a spectrophotometer ably operated by Candy Everall The neutron actvaton samples were prepared for rradaton by Roanne Collns and Trsh Robnson and the mllng was done by Carey Grahl The mass spectrometry was performed by Nancy Ellot and Monque Campbell The alpha planchettes were prepared and counted by Shela Kramer Tremblay Wthout ecepton these people worked competently and dlgently for the SNO project We partcular thank John Lee Patty Sheahan and other members of Polycast for ther nterest n our project and ther cooperaton n attemptng to provde SNO wth the best possble acrylc consstent wth ther corporate constrants Polycast shut down for four days to vacuum ther facltes just before our producton runs They purchased a partcle detector and repeatedly measured dust levels They sgnfcantly epanded ther normal C procedures to obtan for us the best possble monomer They ncurred sgnfcant epense n alterng ther procedures so as to provde us wth better acrylc

14 References: ) Optcal ualty of Polycast 27" Acrylc, Batches 47 4 & 4 ED Earle, RJE Deal, E Gaudette CJ Everall & E Bonvn SNOSTR320 2) Th & U levels n Polycast Stage II Acrylc, Batches 47, 4 & 4 ED Earle, RJE Deal, E Gaudette, R Collns N Ellot, S KramerTremblay & E Bonvn SNOSTR30 3) Polycast Acrylc Sheets, a progress report E D Earle, R J Deal and E Gaudette SNOSTR042 4) Measurements of Th and U n Acrylc for the Sudbury Neutrno Observatory E D Earle and E Bonvn AECL074 and SNOSTR20 ) Thermal lonzaton Mass Spectrometrc Analyss for the SNO Project by N L Ellot, General Chemstry Branch SNOSTR20 ) Ultra Trace Analyss of Acrylc for 232Th and 23U Daughters GM Mlton, SJ Kramer, RJE Deal & ED Earle SNOSTR32 & submtted to Appled Radaton & Isotopes 7) Evaluaton of Optcal Propertes of Acrylc Samples from Dfferent Supplers E Bonvn and E D Earle SNOSTR20 Fgures: Mnmum Thckness of Each Sheet 2NAA Results 3MS Results 4,, Absorpton 340 nm 7, Fgure of Mert Fgure of Mert of Batch 0

15 2fc 2 fc U Fg Sheet Thckness at Thnnest Pont a a a D A S s \:r A A *00, t A A,?» * < * *? +, A A o 4 a 7 o A 2 3 A sheet #

16 000 I Fg 2 Th & U cone by NA \ \ : ; ; : ; Th sgma error Th 2 sgma lmt + U 2 sgma lmt ; : I Batch : I ; : : 0) 0) I I + +4 I+,,, f < I I : +! I+ + \! fy A +" ; [ + ; : ; ; ; ; + + ; \ ; r +! :ff! ++ IT +++ * tl IIT rt " ; ; ; :T + + ;: ( :; < on [ <:! n sample # ll ; 00 <l T "< l I I < I 4 + ~

17 < 4 Fg 3 Th & U cone from MS ll ; Ill! h >?! ; I ) 4X I ; v / v /N >$< X r v y\/\ Y >k X k <,,, I*! I IXX X ; : : ;! ; ; ; : th l h " sample #

18 CRL Fg 4 Absorpton Coeffcents for 340 nm Xy X A/\w( Wy \ X X» > X)X» A X A XXy M, Aft I : Polycast v :! Y\ y y! XYN X yy v X y I /<AX~ f\ e \) Sample # 00 20

19 " Fg Absorpton Coeffcents for 340 nm u uv c batch CO ( ) Polycast 007 (0 * C0) l CRL * <D " 04 (0 D (0 nna < y X :: «XX wx Xy X*/ / y «X y A ; X: / y N A / I Sample # 220 0

20 CRL Fg Absorpton Coeffcents for the 4" Batches 00 E c o 00 r CO \ f 007 (A *C<D o 00,? * 0)00 00 c 0 a (0 A (0 003 : XyX XX 200 Sample # batch s s l I rt /? XX Polycast 20

21 0) ) 072 a Fg 7 Fgure of Mert for 2" Batches SsaB ffl a j * a» A,» XX gdf A * * + 0 A 0 s * 0 0 v *» * A y a o 47 4 o 4 A A 3 s 4 a o average 0 20 sheet #

22 Fg Fgure of Mert for the 4" Materal normalzed to 22" o " o 0 o average sheet #

23 Fg Fgure of Mert of Batch D e ' o 072 o o 07 L sheet #

A Robust Method for Calculating the Correlation Coefficient

A Robust Method for Calculating the Correlation Coefficient A Robust Method for Calculatng the Correlaton Coeffcent E.B. Nven and C. V. Deutsch Relatonshps between prmary and secondary data are frequently quantfed usng the correlaton coeffcent; however, the tradtonal

More information

Comparison of Regression Lines

Comparison of Regression Lines STATGRAPHICS Rev. 9/13/2013 Comparson of Regresson Lnes Summary... 1 Data Input... 3 Analyss Summary... 4 Plot of Ftted Model... 6 Condtonal Sums of Squares... 6 Analyss Optons... 7 Forecasts... 8 Confdence

More information

Module 3 LOSSY IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur

Module 3 LOSSY IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur Module 3 LOSSY IMAGE COMPRESSION SYSTEMS Verson ECE IIT, Kharagpur Lesson 6 Theory of Quantzaton Verson ECE IIT, Kharagpur Instructonal Objectves At the end of ths lesson, the students should be able to:

More information

UNIVERSITY OF TORONTO Faculty of Arts and Science. December 2005 Examinations STA437H1F/STA1005HF. Duration - 3 hours

UNIVERSITY OF TORONTO Faculty of Arts and Science. December 2005 Examinations STA437H1F/STA1005HF. Duration - 3 hours UNIVERSITY OF TORONTO Faculty of Arts and Scence December 005 Examnatons STA47HF/STA005HF Duraton - hours AIDS ALLOWED: (to be suppled by the student) Non-programmable calculator One handwrtten 8.5'' x

More information

Copyright 2017 by Taylor Enterprises, Inc., All Rights Reserved. Adjusted Control Limits for P Charts. Dr. Wayne A. Taylor

Copyright 2017 by Taylor Enterprises, Inc., All Rights Reserved. Adjusted Control Limits for P Charts. Dr. Wayne A. Taylor Taylor Enterprses, Inc. Control Lmts for P Charts Copyrght 2017 by Taylor Enterprses, Inc., All Rghts Reserved. Control Lmts for P Charts Dr. Wayne A. Taylor Abstract: P charts are used for count data

More information

An influence line shows how the force in a particular member changes as a concentrated load is moved along the structure.

An influence line shows how the force in a particular member changes as a concentrated load is moved along the structure. CE 331, Fall 2010 Influence Les for Trusses 1 / 7 An fluence le shows how the force a partcular member changes as a concentrated load s moved along the structure. For eample, say we are desgng the seven

More information

THE ROYAL STATISTICAL SOCIETY 2006 EXAMINATIONS SOLUTIONS HIGHER CERTIFICATE

THE ROYAL STATISTICAL SOCIETY 2006 EXAMINATIONS SOLUTIONS HIGHER CERTIFICATE THE ROYAL STATISTICAL SOCIETY 6 EXAMINATIONS SOLUTIONS HIGHER CERTIFICATE PAPER I STATISTICAL THEORY The Socety provdes these solutons to assst canddates preparng for the eamnatons n future years and for

More information

Topic 23 - Randomized Complete Block Designs (RCBD)

Topic 23 - Randomized Complete Block Designs (RCBD) Topc 3 ANOVA (III) 3-1 Topc 3 - Randomzed Complete Block Desgns (RCBD) Defn: A Randomzed Complete Block Desgn s a varant of the completely randomzed desgn (CRD) that we recently learned. In ths desgn,

More information

Economics 130. Lecture 4 Simple Linear Regression Continued

Economics 130. Lecture 4 Simple Linear Regression Continued Economcs 130 Lecture 4 Contnued Readngs for Week 4 Text, Chapter and 3. We contnue wth addressng our second ssue + add n how we evaluate these relatonshps: Where do we get data to do ths analyss? How do

More information

Probability Theory. The nth coefficient of the Taylor series of f(k), expanded around k = 0, gives the nth moment of x as ( ik) n n!

Probability Theory. The nth coefficient of the Taylor series of f(k), expanded around k = 0, gives the nth moment of x as ( ik) n n! 8333: Statstcal Mechancs I Problem Set # 3 Solutons Fall 3 Characterstc Functons: Probablty Theory The characterstc functon s defned by fk ep k = ep kpd The nth coeffcent of the Taylor seres of fk epanded

More information

Polynomial Regression Models

Polynomial Regression Models LINEAR REGRESSION ANALYSIS MODULE XII Lecture - 6 Polynomal Regresson Models Dr. Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur Test of sgnfcance To test the sgnfcance

More information

Topic- 11 The Analysis of Variance

Topic- 11 The Analysis of Variance Topc- 11 The Analyss of Varance Expermental Desgn The samplng plan or expermental desgn determnes the way that a sample s selected. In an observatonal study, the expermenter observes data that already

More information

Statistics II Final Exam 26/6/18

Statistics II Final Exam 26/6/18 Statstcs II Fnal Exam 26/6/18 Academc Year 2017/18 Solutons Exam duraton: 2 h 30 mn 1. (3 ponts) A town hall s conductng a study to determne the amount of leftover food produced by the restaurants n the

More information

Negative Binomial Regression

Negative Binomial Regression STATGRAPHICS Rev. 9/16/2013 Negatve Bnomal Regresson Summary... 1 Data Input... 3 Statstcal Model... 3 Analyss Summary... 4 Analyss Optons... 7 Plot of Ftted Model... 8 Observed Versus Predcted... 10 Predctons...

More information

Econ107 Applied Econometrics Topic 3: Classical Model (Studenmund, Chapter 4)

Econ107 Applied Econometrics Topic 3: Classical Model (Studenmund, Chapter 4) I. Classcal Assumptons Econ7 Appled Econometrcs Topc 3: Classcal Model (Studenmund, Chapter 4) We have defned OLS and studed some algebrac propertes of OLS. In ths topc we wll study statstcal propertes

More information

Lab 2e Thermal System Response and Effective Heat Transfer Coefficient

Lab 2e Thermal System Response and Effective Heat Transfer Coefficient 58:080 Expermental Engneerng 1 OBJECTIVE Lab 2e Thermal System Response and Effectve Heat Transfer Coeffcent Warnng: though the experment has educatonal objectves (to learn about bolng heat transfer, etc.),

More information

BOOTSTRAP METHOD FOR TESTING OF EQUALITY OF SEVERAL MEANS. M. Krishna Reddy, B. Naveen Kumar and Y. Ramu

BOOTSTRAP METHOD FOR TESTING OF EQUALITY OF SEVERAL MEANS. M. Krishna Reddy, B. Naveen Kumar and Y. Ramu BOOTSTRAP METHOD FOR TESTING OF EQUALITY OF SEVERAL MEANS M. Krshna Reddy, B. Naveen Kumar and Y. Ramu Department of Statstcs, Osmana Unversty, Hyderabad -500 007, Inda. nanbyrozu@gmal.com, ramu0@gmal.com

More information

Pop-Click Noise Detection Using Inter-Frame Correlation for Improved Portable Auditory Sensing

Pop-Click Noise Detection Using Inter-Frame Correlation for Improved Portable Auditory Sensing Advanced Scence and Technology Letters, pp.164-168 http://dx.do.org/10.14257/astl.2013 Pop-Clc Nose Detecton Usng Inter-Frame Correlaton for Improved Portable Audtory Sensng Dong Yun Lee, Kwang Myung Jeon,

More information

Reprint (R34) Accurate Transmission Measurements Of Translucent Materials. January 2008

Reprint (R34) Accurate Transmission Measurements Of Translucent Materials. January 2008 Reprnt (R34) Accurate ransmsson Measurements Of ranslucent Materals January 2008 Gooch & Housego 4632 36 th Street, Orlando, FL 32811 el: 1 407 422 3171 Fax: 1 407 648 5412 Emal: sales@goochandhousego.com

More information

Statistics Chapter 4

Statistics Chapter 4 Statstcs Chapter 4 "There are three knds of les: les, damned les, and statstcs." Benjamn Dsrael, 1895 (Brtsh statesman) Gaussan Dstrbuton, 4-1 If a measurement s repeated many tmes a statstcal treatment

More information

Week3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity

Week3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity Week3, Chapter 4 Moton n Two Dmensons Lecture Quz A partcle confned to moton along the x axs moves wth constant acceleraton from x =.0 m to x = 8.0 m durng a 1-s tme nterval. The velocty of the partcle

More information

Quantitative Discrimination of Effective Porosity Using Digital Image Analysis - Implications for Porosity-Permeability Transforms

Quantitative Discrimination of Effective Porosity Using Digital Image Analysis - Implications for Porosity-Permeability Transforms 2004, 66th EAGE Conference, Pars Quanttatve Dscrmnaton of Effectve Porosty Usng Dgtal Image Analyss - Implcatons for Porosty-Permeablty Transforms Gregor P. Eberl 1, Gregor T. Baechle 1, Ralf Weger 1,

More information

CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE

CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE Analytcal soluton s usually not possble when exctaton vares arbtrarly wth tme or f the system s nonlnear. Such problems can be solved by numercal tmesteppng

More information

Lecture 4: November 17, Part 1 Single Buffer Management

Lecture 4: November 17, Part 1 Single Buffer Management Lecturer: Ad Rosén Algorthms for the anagement of Networs Fall 2003-2004 Lecture 4: November 7, 2003 Scrbe: Guy Grebla Part Sngle Buffer anagement In the prevous lecture we taled about the Combned Input

More information

Answers Problem Set 2 Chem 314A Williamsen Spring 2000

Answers Problem Set 2 Chem 314A Williamsen Spring 2000 Answers Problem Set Chem 314A Wllamsen Sprng 000 1) Gve me the followng crtcal values from the statstcal tables. a) z-statstc,-sded test, 99.7% confdence lmt ±3 b) t-statstc (Case I), 1-sded test, 95%

More information

Some Comments on Accelerating Convergence of Iterative Sequences Using Direct Inversion of the Iterative Subspace (DIIS)

Some Comments on Accelerating Convergence of Iterative Sequences Using Direct Inversion of the Iterative Subspace (DIIS) Some Comments on Acceleratng Convergence of Iteratve Sequences Usng Drect Inverson of the Iteratve Subspace (DIIS) C. Davd Sherrll School of Chemstry and Bochemstry Georga Insttute of Technology May 1998

More information

Chapter 2 - The Simple Linear Regression Model S =0. e i is a random error. S β2 β. This is a minimization problem. Solution is a calculus exercise.

Chapter 2 - The Simple Linear Regression Model S =0. e i is a random error. S β2 β. This is a minimization problem. Solution is a calculus exercise. Chapter - The Smple Lnear Regresson Model The lnear regresson equaton s: where y + = β + β e for =,..., y and are observable varables e s a random error How can an estmaton rule be constructed for the

More information

PHYS 450 Spring semester Lecture 02: Dealing with Experimental Uncertainties. Ron Reifenberger Birck Nanotechnology Center Purdue University

PHYS 450 Spring semester Lecture 02: Dealing with Experimental Uncertainties. Ron Reifenberger Birck Nanotechnology Center Purdue University PHYS 45 Sprng semester 7 Lecture : Dealng wth Expermental Uncertantes Ron Refenberger Brck anotechnology Center Purdue Unversty Lecture Introductory Comments Expermental errors (really expermental uncertantes)

More information

A Mechanics-Based Approach for Determining Deflections of Stacked Multi-Storey Wood-Based Shear Walls

A Mechanics-Based Approach for Determining Deflections of Stacked Multi-Storey Wood-Based Shear Walls A Mechancs-Based Approach for Determnng Deflectons of Stacked Mult-Storey Wood-Based Shear Walls FPINNOVATIONS Acknowledgements Ths publcaton was developed by FPInnovatons and the Canadan Wood Councl based

More information

x = , so that calculated

x = , so that calculated Stat 4, secton Sngle Factor ANOVA notes by Tm Plachowsk n chapter 8 we conducted hypothess tests n whch we compared a sngle sample s mean or proporton to some hypotheszed value Chapter 9 expanded ths to

More information

Second Order Analysis

Second Order Analysis Second Order Analyss In the prevous classes we looked at a method that determnes the load correspondng to a state of bfurcaton equlbrum of a perfect frame by egenvalye analyss The system was assumed to

More information

Simultaneous Optimization of Berth Allocation, Quay Crane Assignment and Quay Crane Scheduling Problems in Container Terminals

Simultaneous Optimization of Berth Allocation, Quay Crane Assignment and Quay Crane Scheduling Problems in Container Terminals Smultaneous Optmzaton of Berth Allocaton, Quay Crane Assgnment and Quay Crane Schedulng Problems n Contaner Termnals Necat Aras, Yavuz Türkoğulları, Z. Caner Taşkın, Kuban Altınel Abstract In ths work,

More information

FUZZY FINITE ELEMENT METHOD

FUZZY FINITE ELEMENT METHOD FUZZY FINITE ELEMENT METHOD RELIABILITY TRUCTURE ANALYI UING PROBABILITY 3.. Maxmum Normal tress Internal force s the shear force, V has a magntude equal to the load P and bendng moment, M. Bendng moments

More information

Psychology 282 Lecture #24 Outline Regression Diagnostics: Outliers

Psychology 282 Lecture #24 Outline Regression Diagnostics: Outliers Psychology 282 Lecture #24 Outlne Regresson Dagnostcs: Outlers In an earler lecture we studed the statstcal assumptons underlyng the regresson model, ncludng the followng ponts: Formal statement of assumptons.

More information

NUMERICAL DIFFERENTIATION

NUMERICAL DIFFERENTIATION NUMERICAL DIFFERENTIATION 1 Introducton Dfferentaton s a method to compute the rate at whch a dependent output y changes wth respect to the change n the ndependent nput x. Ths rate of change s called the

More information

Analytical Chemistry Calibration Curve Handout

Analytical Chemistry Calibration Curve Handout I. Quck-and Drty Excel Tutoral Analytcal Chemstry Calbraton Curve Handout For those of you wth lttle experence wth Excel, I ve provded some key technques that should help you use the program both for problem

More information

Markov Chain Monte Carlo Lecture 6

Markov Chain Monte Carlo Lecture 6 where (x 1,..., x N ) X N, N s called the populaton sze, f(x) f (x) for at least one {1, 2,..., N}, and those dfferent from f(x) are called the tral dstrbutons n terms of mportance samplng. Dfferent ways

More information

Chapter 13: Multiple Regression

Chapter 13: Multiple Regression Chapter 13: Multple Regresson 13.1 Developng the multple-regresson Model The general model can be descrbed as: It smplfes for two ndependent varables: The sample ft parameter b 0, b 1, and b are used to

More information

A LINEAR PROGRAM TO COMPARE MULTIPLE GROSS CREDIT LOSS FORECASTS. Dr. Derald E. Wentzien, Wesley College, (302) ,

A LINEAR PROGRAM TO COMPARE MULTIPLE GROSS CREDIT LOSS FORECASTS. Dr. Derald E. Wentzien, Wesley College, (302) , A LINEAR PROGRAM TO COMPARE MULTIPLE GROSS CREDIT LOSS FORECASTS Dr. Derald E. Wentzen, Wesley College, (302) 736-2574, wentzde@wesley.edu ABSTRACT A lnear programmng model s developed and used to compare

More information

29th Monitoring Research Review: Ground-Based Nuclear Explosion Monitoring Technologies

29th Monitoring Research Review: Ground-Based Nuclear Explosion Monitoring Technologies TESTING THE SPECTRAL DECONVOLUTION ALGORITHM TOOL (SDAT) WITH XE SPECTRA Steven R. Begalsk, Kendra M. Foltz Begalsk, and Derek A. Haas The Unversty of Texas at Austn Sponsored by Army Space and Mssle Defense

More information

2010 Black Engineering Building, Department of Mechanical Engineering. Iowa State University, Ames, IA, 50011

2010 Black Engineering Building, Department of Mechanical Engineering. Iowa State University, Ames, IA, 50011 Interface Energy Couplng between -tungsten Nanoflm and Few-layered Graphene Meng Han a, Pengyu Yuan a, Jng Lu a, Shuyao S b, Xaolong Zhao b, Yanan Yue c, Xnwe Wang a,*, Xangheng Xao b,* a 2010 Black Engneerng

More information

Economics 101. Lecture 4 - Equilibrium and Efficiency

Economics 101. Lecture 4 - Equilibrium and Efficiency Economcs 0 Lecture 4 - Equlbrum and Effcency Intro As dscussed n the prevous lecture, we wll now move from an envronment where we looed at consumers mang decsons n solaton to analyzng economes full of

More information

ONE DIMENSIONAL TRIANGULAR FIN EXPERIMENT. Technical Advisor: Dr. D.C. Look, Jr. Version: 11/03/00

ONE DIMENSIONAL TRIANGULAR FIN EXPERIMENT. Technical Advisor: Dr. D.C. Look, Jr. Version: 11/03/00 ONE IMENSIONAL TRIANGULAR FIN EXPERIMENT Techncal Advsor: r..c. Look, Jr. Verson: /3/ 7. GENERAL OJECTIVES a) To understand a one-dmensonal epermental appromaton. b) To understand the art of epermental

More information

3.1 Expectation of Functions of Several Random Variables. )' be a k-dimensional discrete or continuous random vector, with joint PMF p (, E X E X1 E X

3.1 Expectation of Functions of Several Random Variables. )' be a k-dimensional discrete or continuous random vector, with joint PMF p (, E X E X1 E X Statstcs 1: Probablty Theory II 37 3 EPECTATION OF SEVERAL RANDOM VARIABLES As n Probablty Theory I, the nterest n most stuatons les not on the actual dstrbuton of a random vector, but rather on a number

More information

STAT 511 FINAL EXAM NAME Spring 2001

STAT 511 FINAL EXAM NAME Spring 2001 STAT 5 FINAL EXAM NAME Sprng Instructons: Ths s a closed book exam. No notes or books are allowed. ou may use a calculator but you are not allowed to store notes or formulas n the calculator. Please wrte

More information

DUE: WEDS FEB 21ST 2018

DUE: WEDS FEB 21ST 2018 HOMEWORK # 1: FINITE DIFFERENCES IN ONE DIMENSION DUE: WEDS FEB 21ST 2018 1. Theory Beam bendng s a classcal engneerng analyss. The tradtonal soluton technque makes smplfyng assumptons such as a constant

More information

Nice plotting of proteins II

Nice plotting of proteins II Nce plottng of protens II Fnal remark regardng effcency: It s possble to wrte the Newton representaton n a way that can be computed effcently, usng smlar bracketng that we made for the frst representaton

More information

Turbulence classification of load data by the frequency and severity of wind gusts. Oscar Moñux, DEWI GmbH Kevin Bleibler, DEWI GmbH

Turbulence classification of load data by the frequency and severity of wind gusts. Oscar Moñux, DEWI GmbH Kevin Bleibler, DEWI GmbH Turbulence classfcaton of load data by the frequency and severty of wnd gusts Introducton Oscar Moñux, DEWI GmbH Kevn Blebler, DEWI GmbH Durng the wnd turbne developng process, one of the most mportant

More information

5.04, Principles of Inorganic Chemistry II MIT Department of Chemistry Lecture 32: Vibrational Spectroscopy and the IR

5.04, Principles of Inorganic Chemistry II MIT Department of Chemistry Lecture 32: Vibrational Spectroscopy and the IR 5.0, Prncples of Inorganc Chemstry II MIT Department of Chemstry Lecture 3: Vbratonal Spectroscopy and the IR Vbratonal spectroscopy s confned to the 00-5000 cm - spectral regon. The absorpton of a photon

More information

Department of Electrical & Electronic Engineeing Imperial College London. E4.20 Digital IC Design. Median Filter Project Specification

Department of Electrical & Electronic Engineeing Imperial College London. E4.20 Digital IC Design. Median Filter Project Specification Desgn Project Specfcaton Medan Flter Department of Electrcal & Electronc Engneeng Imperal College London E4.20 Dgtal IC Desgn Medan Flter Project Specfcaton A medan flter s used to remove nose from a sampled

More information

Finite Element Modelling of truss/cable structures

Finite Element Modelling of truss/cable structures Pet Schreurs Endhoven Unversty of echnology Department of Mechancal Engneerng Materals echnology November 3, 214 Fnte Element Modellng of truss/cable structures 1 Fnte Element Analyss of prestressed structures

More information

Definition. Measures of Dispersion. Measures of Dispersion. Definition. The Range. Measures of Dispersion 3/24/2014

Definition. Measures of Dispersion. Measures of Dispersion. Definition. The Range. Measures of Dispersion 3/24/2014 Measures of Dsperson Defenton Range Interquartle Range Varance and Standard Devaton Defnton Measures of dsperson are descrptve statstcs that descrbe how smlar a set of scores are to each other The more

More information

This column is a continuation of our previous column

This column is a continuation of our previous column Comparson of Goodness of Ft Statstcs for Lnear Regresson, Part II The authors contnue ther dscusson of the correlaton coeffcent n developng a calbraton for quanttatve analyss. Jerome Workman Jr. and Howard

More information

Number Average Molar Mass. Mass Average Molar Mass. Z-Average Molar Mass

Number Average Molar Mass. Mass Average Molar Mass. Z-Average Molar Mass 17 Molar mass: There are dfferent ways to report a molar mass lke (a) Number average molar mass, (b) mass average molar mass, (c) Vscosty average molar mass, (d) Z- Average molar mass Number Average Molar

More information

The written Master s Examination

The written Master s Examination he wrtten Master s Eamnaton Opton Statstcs and Probablty SPRING 9 Full ponts may be obtaned for correct answers to 8 questons. Each numbered queston (whch may have several parts) s worth the same number

More information

RELIABILITY ASSESSMENT

RELIABILITY ASSESSMENT CHAPTER Rsk Analyss n Engneerng and Economcs RELIABILITY ASSESSMENT A. J. Clark School of Engneerng Department of Cvl and Envronmental Engneerng 4a CHAPMAN HALL/CRC Rsk Analyss for Engneerng Department

More information

Temperature. Chapter Heat Engine

Temperature. Chapter Heat Engine Chapter 3 Temperature In prevous chapters of these notes we ntroduced the Prncple of Maxmum ntropy as a technque for estmatng probablty dstrbutons consstent wth constrants. In Chapter 9 we dscussed the

More information

Correlation and Regression. Correlation 9.1. Correlation. Chapter 9

Correlation and Regression. Correlation 9.1. Correlation. Chapter 9 Chapter 9 Correlaton and Regresson 9. Correlaton Correlaton A correlaton s a relatonshp between two varables. The data can be represented b the ordered pars (, ) where s the ndependent (or eplanator) varable,

More information

Department of Quantitative Methods & Information Systems. Time Series and Their Components QMIS 320. Chapter 6

Department of Quantitative Methods & Information Systems. Time Series and Their Components QMIS 320. Chapter 6 Department of Quanttatve Methods & Informaton Systems Tme Seres and Ther Components QMIS 30 Chapter 6 Fall 00 Dr. Mohammad Zanal These sldes were modfed from ther orgnal source for educatonal purpose only.

More information

Measurement of the Activity Concentration of the Radionuclide Am-241 in a Solution COOMET PROJECT 359/RU/06

Measurement of the Activity Concentration of the Radionuclide Am-241 in a Solution COOMET PROJECT 359/RU/06 Measurement of the Actvty Concentraton of the Radonuclde Am-4 n a Soluton COOMET PROJECT 359/RU/06 I.A. Khartonov, A.V. Zanevsky ), V. Mlevsk, A. Ivanukovch ), P. Oropesa and Y. Moreno 3) ), ) BelGIM,

More information

Uncertainty as the Overlap of Alternate Conditional Distributions

Uncertainty as the Overlap of Alternate Conditional Distributions Uncertanty as the Overlap of Alternate Condtonal Dstrbutons Olena Babak and Clayton V. Deutsch Centre for Computatonal Geostatstcs Department of Cvl & Envronmental Engneerng Unversty of Alberta An mportant

More information

Games of Threats. Elon Kohlberg Abraham Neyman. Working Paper

Games of Threats. Elon Kohlberg Abraham Neyman. Working Paper Games of Threats Elon Kohlberg Abraham Neyman Workng Paper 18-023 Games of Threats Elon Kohlberg Harvard Busness School Abraham Neyman The Hebrew Unversty of Jerusalem Workng Paper 18-023 Copyrght 2017

More information

Chapter 5. Solution of System of Linear Equations. Module No. 6. Solution of Inconsistent and Ill Conditioned Systems

Chapter 5. Solution of System of Linear Equations. Module No. 6. Solution of Inconsistent and Ill Conditioned Systems Numercal Analyss by Dr. Anta Pal Assstant Professor Department of Mathematcs Natonal Insttute of Technology Durgapur Durgapur-713209 emal: anta.bue@gmal.com 1 . Chapter 5 Soluton of System of Lnear Equatons

More information

Uncertainty in measurements of power and energy on power networks

Uncertainty in measurements of power and energy on power networks Uncertanty n measurements of power and energy on power networks E. Manov, N. Kolev Department of Measurement and Instrumentaton, Techncal Unversty Sofa, bul. Klment Ohrdsk No8, bl., 000 Sofa, Bulgara Tel./fax:

More information

/ n ) are compared. The logic is: if the two

/ n ) are compared. The logic is: if the two STAT C141, Sprng 2005 Lecture 13 Two sample tests One sample tests: examples of goodness of ft tests, where we are testng whether our data supports predctons. Two sample tests: called as tests of ndependence

More information

Lecture 3: Probability Distributions

Lecture 3: Probability Distributions Lecture 3: Probablty Dstrbutons Random Varables Let us begn by defnng a sample space as a set of outcomes from an experment. We denote ths by S. A random varable s a functon whch maps outcomes nto the

More information

HMMT February 2016 February 20, 2016

HMMT February 2016 February 20, 2016 HMMT February 016 February 0, 016 Combnatorcs 1. For postve ntegers n, let S n be the set of ntegers x such that n dstnct lnes, no three concurrent, can dvde a plane nto x regons (for example, S = {3,

More information

CHEMICAL ENGINEERING

CHEMICAL ENGINEERING Postal Correspondence GATE & PSUs -MT To Buy Postal Correspondence Packages call at 0-9990657855 1 TABLE OF CONTENT S. No. Ttle Page no. 1. Introducton 3 2. Dffuson 10 3. Dryng and Humdfcaton 24 4. Absorpton

More information

Experiment 1 Mass, volume and density

Experiment 1 Mass, volume and density Experment 1 Mass, volume and densty Purpose 1. Famlarze wth basc measurement tools such as verner calper, mcrometer, and laboratory balance. 2. Learn how to use the concepts of sgnfcant fgures, expermental

More information

AS-Level Maths: Statistics 1 for Edexcel

AS-Level Maths: Statistics 1 for Edexcel 1 of 6 AS-Level Maths: Statstcs 1 for Edecel S1. Calculatng means and standard devatons Ths con ndcates the slde contans actvtes created n Flash. These actvtes are not edtable. For more detaled nstructons,

More information

Week 9 Chapter 10 Section 1-5

Week 9 Chapter 10 Section 1-5 Week 9 Chapter 10 Secton 1-5 Rotaton Rgd Object A rgd object s one that s nondeformable The relatve locatons of all partcles makng up the object reman constant All real objects are deformable to some extent,

More information

Copyright 2017 by Taylor Enterprises, Inc., All Rights Reserved. Adjusted Control Limits for U Charts. Dr. Wayne A. Taylor

Copyright 2017 by Taylor Enterprises, Inc., All Rights Reserved. Adjusted Control Limits for U Charts. Dr. Wayne A. Taylor Taylor Enterprses, Inc. Adjusted Control Lmts for U Charts Copyrght 207 by Taylor Enterprses, Inc., All Rghts Reserved. Adjusted Control Lmts for U Charts Dr. Wayne A. Taylor Abstract: U charts are used

More information

U-Pb Geochronology Practical: Background

U-Pb Geochronology Practical: Background U-Pb Geochronology Practcal: Background Basc Concepts: accuracy: measure of the dfference between an expermental measurement and the true value precson: measure of the reproducblty of the expermental result

More information

Department of Statistics University of Toronto STA305H1S / 1004 HS Design and Analysis of Experiments Term Test - Winter Solution

Department of Statistics University of Toronto STA305H1S / 1004 HS Design and Analysis of Experiments Term Test - Winter Solution Department of Statstcs Unversty of Toronto STA35HS / HS Desgn and Analyss of Experments Term Test - Wnter - Soluton February, Last Name: Frst Name: Student Number: Instructons: Tme: hours. Ads: a non-programmable

More information

One-sided finite-difference approximations suitable for use with Richardson extrapolation

One-sided finite-difference approximations suitable for use with Richardson extrapolation Journal of Computatonal Physcs 219 (2006) 13 20 Short note One-sded fnte-dfference approxmatons sutable for use wth Rchardson extrapolaton Kumar Rahul, S.N. Bhattacharyya * Department of Mechancal Engneerng,

More information

#64. ΔS for Isothermal Mixing of Ideal Gases

#64. ΔS for Isothermal Mixing of Ideal Gases #64 Carnot Heat Engne ΔS for Isothermal Mxng of Ideal Gases ds = S dt + S T V V S = P V T T V PV = nrt, P T ds = v T = nr V dv V nr V V = nrln V V = - nrln V V ΔS ΔS ΔS for Isothermal Mxng for Ideal Gases

More information

Statistics for Economics & Business

Statistics for Economics & Business Statstcs for Economcs & Busness Smple Lnear Regresson Learnng Objectves In ths chapter, you learn: How to use regresson analyss to predct the value of a dependent varable based on an ndependent varable

More information

Final report. Absolute gravimeter Intercomparison

Final report. Absolute gravimeter Intercomparison Federal Department of Justce and Polce FDJP Federal Offce of Metrology METAS Baumann Henr 16.04.010 Fnal report Absolute gravmeter Intercomparson EURAMET Project no. 1093 Coordnator of the comparson Henr

More information

Resource Allocation and Decision Analysis (ECON 8010) Spring 2014 Foundations of Regression Analysis

Resource Allocation and Decision Analysis (ECON 8010) Spring 2014 Foundations of Regression Analysis Resource Allocaton and Decson Analss (ECON 800) Sprng 04 Foundatons of Regresson Analss Readng: Regresson Analss (ECON 800 Coursepak, Page 3) Defntons and Concepts: Regresson Analss statstcal technques

More information

Global Sensitivity. Tuesday 20 th February, 2018

Global Sensitivity. Tuesday 20 th February, 2018 Global Senstvty Tuesday 2 th February, 28 ) Local Senstvty Most senstvty analyses [] are based on local estmates of senstvty, typcally by expandng the response n a Taylor seres about some specfc values

More information

Expectation Maximization Mixture Models HMMs

Expectation Maximization Mixture Models HMMs -755 Machne Learnng for Sgnal Processng Mture Models HMMs Class 9. 2 Sep 200 Learnng Dstrbutons for Data Problem: Gven a collecton of eamples from some data, estmate ts dstrbuton Basc deas of Mamum Lelhood

More information

Report on Image warping

Report on Image warping Report on Image warpng Xuan Ne, Dec. 20, 2004 Ths document summarzed the algorthms of our mage warpng soluton for further study, and there s a detaled descrpton about the mplementaton of these algorthms.

More information

Analysis of Discrete Time Queues (Section 4.6)

Analysis of Discrete Time Queues (Section 4.6) Analyss of Dscrete Tme Queues (Secton 4.6) Copyrght 2002, Sanjay K. Bose Tme axs dvded nto slots slot slot boundares Arrvals can only occur at slot boundares Servce to a job can only start at a slot boundary

More information

STATISTICS QUESTIONS. Step by Step Solutions.

STATISTICS QUESTIONS. Step by Step Solutions. STATISTICS QUESTIONS Step by Step Solutons www.mathcracker.com 9//016 Problem 1: A researcher s nterested n the effects of famly sze on delnquency for a group of offenders and examnes famles wth one to

More information

Inductance Calculation for Conductors of Arbitrary Shape

Inductance Calculation for Conductors of Arbitrary Shape CRYO/02/028 Aprl 5, 2002 Inductance Calculaton for Conductors of Arbtrary Shape L. Bottura Dstrbuton: Internal Summary In ths note we descrbe a method for the numercal calculaton of nductances among conductors

More information

BIPM comparison BIPM.RI(II)-K1.Eu-155 of the activity measurements of the radionuclide 155 Eu. G. Ratel and C. Michotte BIPM

BIPM comparison BIPM.RI(II)-K1.Eu-155 of the activity measurements of the radionuclide 155 Eu. G. Ratel and C. Michotte BIPM BIPM comparson BIPM.RI(II)-K1.Eu-155 of the actvty measurements of the radonuclde 155 Eu G. Ratel and C. Mchotte BIPM Abstract In 1993, a natonal metrology nsttute, the NPL (UK), submtted a sample of known

More information

First Year Examination Department of Statistics, University of Florida

First Year Examination Department of Statistics, University of Florida Frst Year Examnaton Department of Statstcs, Unversty of Florda May 7, 010, 8:00 am - 1:00 noon Instructons: 1. You have four hours to answer questons n ths examnaton.. You must show your work to receve

More information

4 Analysis of Variance (ANOVA) 5 ANOVA. 5.1 Introduction. 5.2 Fixed Effects ANOVA

4 Analysis of Variance (ANOVA) 5 ANOVA. 5.1 Introduction. 5.2 Fixed Effects ANOVA 4 Analyss of Varance (ANOVA) 5 ANOVA 51 Introducton ANOVA ANOVA s a way to estmate and test the means of multple populatons We wll start wth one-way ANOVA If the populatons ncluded n the study are selected

More information

Computation of Higher Order Moments from Two Multinomial Overdispersion Likelihood Models

Computation of Higher Order Moments from Two Multinomial Overdispersion Likelihood Models Computaton of Hgher Order Moments from Two Multnomal Overdsperson Lkelhood Models BY J. T. NEWCOMER, N. K. NEERCHAL Department of Mathematcs and Statstcs, Unversty of Maryland, Baltmore County, Baltmore,

More information

is the calculated value of the dependent variable at point i. The best parameters have values that minimize the squares of the errors

is the calculated value of the dependent variable at point i. The best parameters have values that minimize the squares of the errors Multple Lnear and Polynomal Regresson wth Statstcal Analyss Gven a set of data of measured (or observed) values of a dependent varable: y versus n ndependent varables x 1, x, x n, multple lnear regresson

More information

Online Appendix to: Axiomatization and measurement of Quasi-hyperbolic Discounting

Online Appendix to: Axiomatization and measurement of Quasi-hyperbolic Discounting Onlne Appendx to: Axomatzaton and measurement of Quas-hyperbolc Dscountng José Lus Montel Olea Tomasz Strzaleck 1 Sample Selecton As dscussed before our ntal sample conssts of two groups of subjects. Group

More information

e i is a random error

e i is a random error Chapter - The Smple Lnear Regresson Model The lnear regresson equaton s: where + β + β e for,..., and are observable varables e s a random error How can an estmaton rule be constructed for the unknown

More information

Indeterminate pin-jointed frames (trusses)

Indeterminate pin-jointed frames (trusses) Indetermnate pn-jonted frames (trusses) Calculaton of member forces usng force method I. Statcal determnacy. The degree of freedom of any truss can be derved as: w= k d a =, where k s the number of all

More information

since [1-( 0+ 1x1i+ 2x2 i)] [ 0+ 1x1i+ assumed to be a reasonable approximation

since [1-( 0+ 1x1i+ 2x2 i)] [ 0+ 1x1i+ assumed to be a reasonable approximation Econ 388 R. Butler 204 revsons Lecture 4 Dummy Dependent Varables I. Lnear Probablty Model: the Regresson model wth a dummy varables as the dependent varable assumpton, mplcaton regular multple regresson

More information

Lecture 15 Statistical Analysis in Biomaterials Research

Lecture 15 Statistical Analysis in Biomaterials Research 3.05/BE.340 Lecture 5 tatstcal Analyss n Bomaterals Research. Ratonale: Why s statstcal analyss needed n bomaterals research? Many error sources n measurements on lvng systems! Eamples of Measured Values

More information

Structure and Drive Paul A. Jensen Copyright July 20, 2003

Structure and Drive Paul A. Jensen Copyright July 20, 2003 Structure and Drve Paul A. Jensen Copyrght July 20, 2003 A system s made up of several operatons wth flow passng between them. The structure of the system descrbes the flow paths from nputs to outputs.

More information

Discussion 11 Summary 11/20/2018

Discussion 11 Summary 11/20/2018 Dscusson 11 Summary 11/20/2018 1 Quz 8 1. Prove for any sets A, B that A = A B ff B A. Soluton: There are two drectons we need to prove: (a) A = A B B A, (b) B A A = A B. (a) Frst, we prove A = A B B A.

More information

Analysis of Dynamic Cross Response between Spindles in a Dual Spindle Type Multi-Functional Turning Machine

Analysis of Dynamic Cross Response between Spindles in a Dual Spindle Type Multi-Functional Turning Machine Journal of Power and Energy Engneerng, 2013, 1, 20-24 http://dx.do.org/10.4236/jpee.2013.17004 Publshed Onlne December 2013 (http://www.scrp.org/journal/jpee) Analyss of Dynamc Cross Response between Spndles

More information

Lecture 3 Stat102, Spring 2007

Lecture 3 Stat102, Spring 2007 Lecture 3 Stat0, Sprng 007 Chapter 3. 3.: Introducton to regresson analyss Lnear regresson as a descrptve technque The least-squares equatons Chapter 3.3 Samplng dstrbuton of b 0, b. Contnued n net lecture

More information

Statistics for Managers Using Microsoft Excel/SPSS Chapter 13 The Simple Linear Regression Model and Correlation

Statistics for Managers Using Microsoft Excel/SPSS Chapter 13 The Simple Linear Regression Model and Correlation Statstcs for Managers Usng Mcrosoft Excel/SPSS Chapter 13 The Smple Lnear Regresson Model and Correlaton 1999 Prentce-Hall, Inc. Chap. 13-1 Chapter Topcs Types of Regresson Models Determnng the Smple Lnear

More information