ENGI 4421 Probability and Statistics Faculty of Engineering and Applied Science Problem Set 10 Solutions Chi-Square Tests; Simple Linear Regression
|
|
|
- Ami Fields
- 5 years ago
- Views:
Transcription
1 ENGI 441 Prbbly nd Sscs Fculy f Engneerng nd Appled Scence Prblem Se 10 Sluns Ch-Squre Tess; Smple Lner Regressn 1. Is he fllwng se f bservns f bjecs n egh dfferen drecns cnssen wh unfrm dsrbun? Drecn Number f bjecs bserved N 4 NE 6 E 13 SE 11 S 1 SW 18 W 11 NW 5 There re egh cegres, cnnng l f O = E = = 10 > 5 8 Tes : d re frm unfrm dsrbun vs. : n. Exendng he ble, Drecn O E O E ( O ( O E E E N NE E SE S SW W NW Tl:
2 ENGI 441 Prblem Se 10 Sluns Pge f 14 1 (cnnued The ch-squre es ssc s χ bs = The number f degrees f freedm s ν = n 1= 7 The crcl vlue s χ α,7. A α =.05, c = χ = , bu α =.01, c = χ = , 7.01, 7 χ bs = 15.6 The decsn depends n he level f sgnfcnce α chsen. A α =.05, χ > c rejec, bu bs bs A α =.01, χ < c d n rejec. Ths resul s mrgnlly sgnfcn. Frm he ssced Excel fle, he p-vlue s.09, s h.01 < p <.05. The nswer s NO YES f α =.05 f α =.01. A mdel f chemcl prcess predcs he numbers f runs f prcess h shuld fll n ech f fve me nervls. Are he vlues shwn n he ble belw cnssen wh he vlues expeced frm he mdel 5% level f sgnfcnce? Tme nervl bserved expeced > O = E = 100 nd every expeced vlue s > 5. Tes : d re frm he mdel dsrbun vs. Exendng he ble, : n, α =.05.
3 ENGI 441 Prblem Se 10 Sluns Pge 3 f 14 (cnnued Tme nervl O E O E O ( E ( O E E > Tl: The ch-squre es ssc s χ bs = The number f degrees f freedm s ν = n 1= 4 The crcl vlue s c = χα,4 = χ.05,4 = A α =.05, χ < c d n rejec. bs Frm he ssced Excel fle, he p-vlue s.104, s h p >.05. The nswer s YES 3. Rndm smples f cbles re ken frm shpmens frm fur mnufcurers. Ech cble n ech smple s grded ccrdng he ld ppled when h cble breks. The resuls re summrzed n hs cnngency ble. Mnufcurer Quly f cble A B C D X Y Z Are hese d cnssen wh ndependence beween mnufcurer nd quly f cble? Tes : he fcrs mnufcurer nd quly re ndependen vs. ν = I 1 J 1 = 3 = 6 ( ( : n.
4 ENGI 441 Prblem Se 10 Sluns Pge 4 f 14 3 (cnnued Exendng he ble, Mnufcurer Quly f cble A B C D Tl X Y Z Tl The ble f vlues expeced when s rue s clculed by ej = Fr exmple, e3 = = = Expeced vlues: Quly f cble A B C D Tl X Mnufcurer Y Z Tl ( j ej All expeced vlues re > 5. The vlues f ej re: Quly f cble A B C D X Mnufcurer Y Z j. 3 4 = 1 j= 1 ( j ej χbs = = e j 9.94 c= χ = χ = 1.59 r χ = χ < c,6.05,6.01,6 bs α Frm he ssced Excel fle, he p-vlue s.17, s h p >.05. D n rejec. Therefre YES These d re cnssen wh ndependence beween mnufcurer nd quly f cble.
5 ENGI 441 Prblem Se 10 Sluns Pge 5 f A prculr ype f mr s knwn hve n upu rque whse rnge n nrml pern fllws nrml dsrbun. Seven mrs re chsen rndm nd re esed wh he ld nd new mehds f cnrllng he rnge f rque vlues. The resuls f he ess re s fllws: Mr: New mehd: Old mehd: ( Jusfy yur chce f mehd n (b belw. The d re prs f mesuremens n sngle se f ndvduls (he seven mrs. Therefre he pprpre mehd s pred w-smple -es (b Cnduc n pprpre hyphess es deermne wheher here s suffcen evdence cnclude h he rnge f rques wh he new mehd s les uns less hn wh he ld mehd. Le X = rque (new mehd Y = rque (ld mehd nd D = X Y Tes : µ D = vs. : µ D < Free chce f α. I chse α =.01. Mr: Sum SSq x = New Mehd: y = Old Mehd: d = Dfference: D: n= 7, d = 0.1, d = d = , sd = = , sd =
6 ENGI 441 Prblem Se 10 Sluns Pge 6 f 14 4 (b (cnnued Mehd 1 s c = µ D.01, 6 n = = = =.396 OR OR d =.87 < c Rejec n fvur f. Mehd d µ D.87 ( bs = = = 6.9 s 0.16 n = = c bs <.01, c Rejec n fvur f. Mehd 3 bs = = 6.9 Clerly P[T < 6.9] <<.01 [Frm sfwre, P[T < 6.9] < ] Rejec n fvur f ny resnble vlue f α. An Excel spredshee fle s ls vlble llusre hs slun. (c Use he smple lner regressn mdel n hese d fnd he equn f he lne f bes f hese d. Ne h he lne f bes f depends n whch vrble s he predcr nd whch s he respnse. The rles f X nd Y re nerchnged f he new mehd s he respnse, (whch s he mre nurl ssgnmen.
7 ENGI 441 Prblem Se 10 Sluns Pge 7 f 14 4 (c (cnnued Summry sscs (respnse = Y = ld mehd: n= 7 x= 3.93 x = nsxx = n x ( x = n S xy = n xy ( x( y = nsyy = n y ( y = xy= y= y = S ˆ xy β1 = = = S xx nd β 1 0 ( y β1 x ˆ = ˆ = n Therefre, (crrec 3 s.f. n ech ceffcen, OR y = x Summry sscs (respnse = Y = new mehd: n= 7 x= x = xy= y= y = xx ( ( ( ( ns = n x x = n S = n xy x y = xy ns = n y y = yy S ˆ xy β1 = = = S xx nd β 1 0 ( y β1 x ˆ = ˆ = n Therefre, (crrec 3 s.f. n ech ceffcen, y = 1.0 x 4.4 An Excel spredshee fle s vlble llusre he secnd versn f hs slun.
8 ENGI 441 Prblem Se 10 Sluns Pge 8 f 14 4 (d Fnd he ceffcen f deermnn R nd use cmmen n yur nswer pr ( bve. Irrespecve f whch f ld r new mehds s he regressr, ( nsxy ( nsxx ( nsyy ( r = = = r = 97.9% (crrec 3 s.f. Very hgh crreln cnn use unpred -es Chce n ( s crrec. A Mnb prjec fle nd Mnb Repr Pd RTF fle re ls vlble llusre hs slun. 5. A sudy ws cnduced nlyze he relnshp beween dversng expendure nd sles. The fllwng d were recrded: X Y Adversng ($ Sles ($ Assume smple lner regressn beween sles Y nd dversng X. Clcule he ceffcens β 0 nd β 1 f he lne f bes f hese d nd esme he sles when $8 re spen n dversng. Is here sgnfcn lner sscn beween Y nd X? Exendng he ble: x y x x y y Sum:
9 ENGI 441 Prblem Se 10 Sluns Pge 9 f 14 5 (cnnued n S xx = n Σ x (Σ x = (141 = = 744 n S xy = n Σ xy (Σ x Σ y = = = 8390 n S yy = n Σ y (Σ y = (1960 = = S ˆ xy 8390 β1 = = = S 744 xx 1 nd β0 ( y β1 x ( ˆ ˆ = = = n 5 The regressn lne ( 4 s.f. s y = 11.8 x x = 8 y = = When $8 s spen n dversng, we predc $390 f sles (crrec he neres dllr. There re mny chces f mehd fr n hyphess es fr lner sscn. Tes : ρ = 0 vs. : ρ 0 r, equvlenly, es : β 1 = 0 vs. : β1 0 ( nsxy ( nsxx ( nsyy 8390 r = = = jus ver 95% f ll vrn n y s explned by he lner regressn. The crreln ( s very srng, (whch suggess h here s lner sscn, bu he smple sze s very smll, s we shuld prceed wh frml hyphess es. r n.95 3 = = 1 r r
10 ENGI 441 Prblem Se 10 Sluns Pge 10 f 14 5 (cnnued ( nsxy ( n ( nsxx ( nsyy ( nsxy = = r clcule he enres n he ANOVA ble s fllws: ( nsxy n( nsxx 8390 SSR = ( yˆ y = = = nsyy SST = y y = S yy = = = n 5 ( SSE = SST SSR = MSR = SSR / ν R = SSR = MSE = SSE / ν E = SSE / 3 = f = MSR / MSE = d.f. SS MS f R E T = + f = r MSE n MSE sb = = = = S 744 xx ( nsxx ˆ β s.14 1 = = = b Cmpre he bserved = , 3 = > α/, 3 fr ny resnble chce f α. [The p-vlue s less hn.0046.] Rejec n fvur f YES, here s sgnfcn lner sscn beween Y nd X. [See ls he ssced Excel, Mnb prjec nd Mnb RTF fles.]
11 ENGI 441 Prblem Se 10 Sluns Pge 11 f [Ths s n exensn f Exmple 1.06 frm he lecure nes.] A smple f 10 desel rucks were run bh h nd cld esme he dfference n fuel ecnmy. The resuls, n mles per glln, re presened n he fllwng ble. (frm In-use Emssns frm evy-duy Desel Vehcles, J. Ynwz, Ph.D. hess, Clrd Schl f Mnes, 001. Truck Cld ( Use he smple lner regressn mdel n hese d fnd he equn f he lne f bes f (fr s he respnse nd Cld s he regressr hese d mnully. Summry sscs: n= 10, x= 45.86, y = ns ( xx = n x x = nsxy = n xy ( x( y = ns ( yy = n y y = x = , xy= , y = S ˆ xy β1 = = = Sxx ˆ β0 = ( y ˆ β1 x = n Therefre, crrec hree sgnfcn fgures n ech ceffcen, he regressn lne s y = 1.1 x 0.16
12 ENGI 441 Prblem Se 10 Sluns Pge 1 f 14 6 (b Clcule he 95% predcn nervl fr sngle fuure bservn f fuel effcency when run h, fr ruck whse fuel effcency when run cld s 4.00 mles per glln. The frmul fr he predcn nervl s ( ˆ ˆ 1 n x β0 + β1x ± α /, ( n s n ( nsxx ( nsyy ( nsxy ( ( ns ( x ( ns xx ( s = MSE = = n n = s = α =.05 = = α /, n x x = = = n 10 xx.05, 8 ( ( x = 4.00 x x = ˆ = ˆ + ˆ = = Therefre he 95% PI x = 4 s nd y β0 β1x ± = ± = ( 4.018, 4.634] ( 3 d.p.
13 ENGI 441 Prblem Se 10 Sluns Pge 13 f 14 6 (c Use Mnb (r nher sfwre pckge check h he dsrbun f he resduls s cnssen wh nrml dsrbun. Ths nrml prbbly pl clerly demnsres cnssency wh nrml dsrbun. (d Use Mnb (r nher sfwre pckge shw he ANOVA ble, he equn f he lne f bes f nd dsply he lne f bes f, he 95% cnfdence nervls nd he 95% predcn nervls n sngle dgrm. Regressn Anlyss: versus Cld The regressn equn s = Cld S = R-Sq = 98.5% R-Sq(dj = 98.3% Anlyss f Vrnce Surce DF SS MS F P Regressn Errr Tl
14 ENGI 441 Prblem Se 10 Sluns Pge 14 f 14 6 (d (cnnued ENGI 441 Prblem Se 10 Quesn 6 = Cld Regressn 95% CI 95% PI S R-Sq 98.5% R-Sq(dj 98.3% Cld (e Fnd he smple crreln ceffcen r beween h nd cld fuel effcences, crrec hree sgnfcn fgures. SSR r = = =.984 =.99 SST Crrec hree sgnfcn fgures, r =.99 (whch verfes he clm f srng crreln mde n Exmple An Excel fle, Mnb prjec fle nd Mnb RTF fle re vlble fr hs quesn. Bck he ndex f sluns
Use 10 m/s 2 for the acceleration due to gravity.
ANSWERS Prjecle mn s he ecrl sum w ndependen elces, hrznl cmpnen nd ercl cmpnen. The hrznl cmpnen elcy s cnsn hrughu he mn whle he ercl cmpnen elcy s dencl ree ll. The cul r nsnneus elcy ny pn lng he prblc
Chapter 2 Linear Mo on
Chper Lner M n .1 Aerge Velcy The erge elcy prcle s dened s The erge elcy depends nly n he nl nd he nl psns he prcle. Ths mens h prcle srs rm pn nd reurn bck he sme pn, s dsplcemen, nd s s erge elcy s
PRINCE SULTAN UNIVERSITY Department of Mathematical Sciences Final Examination Second Semester (072) STAT 271.
PRINCE SULTAN UNIVERSITY Deparmen f Mahemaical Sciences Final Examinain Secnd Semeser 007 008 (07) STAT 7 Suden Name Suden Number Secin Number Teacher Name Aendance Number Time allwed is ½ hurs. Wrie dwn
PRINCE SULTAN UNIVERSITY Department of Mathematical Sciences Final Examination First Semester ( ) STAT 271.
PRINCE SULTAN UNIVERSITY Deprtment f Mthemticl Sciences Finl Exmintin First Semester (007 008) STAT 71 Student Nme: Mrk Student Number: Sectin Number: Techer Nme: Time llwed is ½ hurs. Attendnce Number:
Dishonest casino as an HMM
Dshnes casn as an HMM N = 2, ={F,L} M=2, O = {h,} A = F B= [. F L F L 0.95 0.0 0] h 0.5 0. L 0.05 0.90 0.5 0.9 c Deva ubramanan, 2009 63 A generave mdel fr CpG slands There are w hdden saes: CpG and nn-cpg.
ENGI 4421 Probability & Statistics
Lecture Ntes fr ENGI 441 Prbablty & Statstcs by Dr. G.H. Gerge Asscate Prfessr, Faculty f Engneerng and Appled Scence Seventh Edtn, reprnted 018 Sprng http://www.engr.mun.ca/~ggerge/441/ Table f Cntents
In the complete model, these slopes are ANALYSIS OF VARIANCE FOR THE COMPLETE TWO-WAY MODEL. (! i+1 -! i ) + [(!") i+1,q - [(!
ANALYSIS OF VARIANCE FOR THE COMPLETE TWO-WAY MODEL The frs hng o es n wo-way ANOVA: Is here neracon? "No neracon" means: The man effecs model would f. Ths n urn means: In he neracon plo (wh A on he horzonal
Comparing Several Means: ANOVA. Group Means and Grand Mean
STAT 511 ANOVA and Regressin 1 Cmparing Several Means: ANOVA Slide 1 Blue Lake snap beans were grwn in 12 pen-tp chambers which are subject t 4 treatments 3 each with O 3 and SO 2 present/absent. The ttal
Comparing Possibly Misspeci ed Forecasts
Supplemenl Appendx : Cmprng Pssbly Msspec ed Frecss Andrew J. Pn Duke Unversy 4 Augus Ts supplemenl ppendx cnns w prs. Appendx SA. cnns dervns used n e nlycl resuls presened n e pper. Appendx SA. cnns
Applied Statistics Qualifier Examination
Appled Sttstcs Qulfer Exmnton Qul_june_8 Fll 8 Instructons: () The exmnton contns 4 Questons. You re to nswer 3 out of 4 of them. () You my use ny books nd clss notes tht you mght fnd helpful n solvng
R th is the Thevenin equivalent at the capacitor terminals.
Chaper 7, Slun. Applyng KV Fg. 7.. d 0 C - Takng he derae f each erm, d 0 C d d d r C Inegrang, () ln I 0 - () I 0 e - C C () () r - I 0 e - () V 0 e C C Chaper 7, Slun. h C where h s he Theenn equalen
Ch 2: Simple Linear Regression
Ch 2: Simple Linear Regression 1. Simple Linear Regression Model A simple regression model with a single regressor x is y = β 0 + β 1 x + ɛ, where we assume that the error ɛ is independent random component
Estimating σ 2. We can do simple prediction of Y and estimation of the mean of Y at any value of X.
Estimating σ 2 We can do simple prediction of Y and estimation of the mean of Y at any value of X. To perform inferences about our regression line, we must estimate σ 2, the variance of the error term.
The Components of Vector B. The Components of Vector B. Vector Components. Component Method of Vector Addition. Vector Components
Upcming eens in PY05 Due ASAP: PY05 prees n WebCT. Submiing i ges yu pin ward yur 5-pin Lecure grade. Please ake i seriusly, bu wha cuns is wheher r n yu submi i, n wheher yu ge hings righ r wrng. Due
Exercises H /OOA> f Wo AJoTHS l^»-l S. m^ttrt /A/ ?C,0&L6M5 INFERENCE FOR DISTRIBUTIONS OF CATEGORICAL DATA. tts^e&n tai-ns 5 2%-cas-hews^, 27%
/A/ mttrt?c,&l6m5 INFERENCE FOR DISTRIBUTIONS OF CATEGORICAL DATA Exercses, nuts! A cmpany clams that each batch f ttse&n ta-ns 5 2%-cas-hews, 27% almnds, 13% macadama nuts, and 8% brazl nuts. T test ths
TSS = SST + SSE An orthogonal partition of the total SS
ANOVA: Topc 4. Orhogonal conrass [ST&D p. 183] H 0 : µ 1 = µ =... = µ H 1 : The mean of a leas one reamen group s dfferen To es hs hypohess, a basc ANOVA allocaes he varaon among reamen means (SST) equally
Statistics 423 Midterm Examination Winter 2009
Sttstcs 43 Mdterm Exmnton Wnter 009 Nme: e-ml: 1. Plese prnt your nme nd e-ml ddress n the bove spces.. Do not turn ths pge untl nstructed to do so. 3. Ths s closed book exmnton. You my hve your hnd clcultor
Lecture 1 Linear Regression with One Predictor Variable.p2
Lecture Linear Regression with One Predictor Variablep - Basics - Meaning of regression parameters p - β - the slope of the regression line -it indicates the change in mean of the probability distn of
4.8 Improper Integrals
4.8 Improper Inegrls Well you ve mde i hrough ll he inegrion echniques. Congrs! Unforunely for us, we sill need o cover one more inegrl. They re clled Improper Inegrls. A his poin, we ve only del wih inegrls
Decompression diagram sampler_src (source files and makefiles) bin (binary files) --- sh (sample shells) --- input (sample input files)
. Iroduco Probblsc oe-moh forecs gudce s mde b 50 esemble members mproved b Model Oupu scs (MO). scl equo s mde b usg hdcs d d observo d. We selec some prmeers for modfg forecs o use mulple regresso formul.
Asynchrnus Sequen Lecture Notes for STATISTICAL METHODS FOR BUSINESS II BMGT 212. Chapters 14, 15 & 16. Professor Ahmadi, Ph.D. Department of Management
Lecture Notes for STATISTICAL METHODS FOR BUSINESS II BMGT 1 Chapters 14, 15 & 16 Professor Ahmad, Ph.D. Department of Management Revsed August 005 Chapter 14 Formulas Smple Lnear Regresson Model: y =
Lecture 4 ( ) Some points of vertical motion: Here we assumed t 0 =0 and the y axis to be vertical.
Sme pins f erical min: Here we assumed and he y axis be erical. ( ) y g g y y y y g dwnwards 9.8 m/s g Lecure 4 Accelerain The aerage accelerain is defined by he change f elciy wih ime: a ; In analgy,
Natural Language Processing NLP Hidden Markov Models. Razvan C. Bunescu School of Electrical Engineering and Computer Science
Naural Language rcessng NL 6840 Hdden Markv Mdels Razvan C. Bunescu Schl f Elecrcal Engneerng and Cmpuer Scence bunescu@h.edu Srucured Daa Fr many applcans he..d. assumpn des n hld: pels n mages f real
The Buck Resonant Converter
EE646 Pwer Elecrnics Chaper 6 ecure Dr. Sam Abdel-Rahman The Buck Resnan Cnverer Replacg he swich by he resnan-ype swich, ba a quasi-resnan PWM buck cnverer can be shwn ha here are fur mdes f pera under
Correlation Analysis
Simple Regression Correlation Analysis Correlation analysis is used to measure strength of the association (linear relationship) between two variables Correlation is only concerned with strength of the
Experimental Design and the Analysis of Variance
Expermenl Desgn nd he nlyss of Vrnce Comprng > Groups - Numerc Responses Exenson of Mehods used o Compre Groups Independen Smples nd Pred D Desgns Norml nd non-norml d dsruons D Desgn Independen Smples
The Perceptron. Nuno Vasconcelos ECE Department, UCSD
he Perceprn Nun Vscncels ECE Deprmen, UCSD Clssfcn clssfcn prblem hs pes f vrbles e.g. X - vecr f bservns feures n he rld Y - se clss f he rld X R = fever, bld pressure Y = {dsese, n dsese} X, Y reled
Topic 7: Analysis of Variance
Topc 7: Analyss of Varance Outlne Parttonng sums of squares Breakdown the degrees of freedom Expected mean squares (EMS) F test ANOVA table General lnear test Pearson Correlaton / R 2 Analyss of Varance
Interval Estimation. Consider a random variable X with a mean of X. Let X be distributed as X X
ECON 37: Ecoomercs Hypohess Tesg Iervl Esmo Wh we hve doe so fr s o udersd how we c ob esmors of ecoomcs reloshp we wsh o sudy. The queso s how comforble re we wh our esmors? We frs exme how o produce
e t dt e t dt = lim e t dt T (1 e T ) = 1
Improper Inegrls There re wo ypes of improper inegrls - hose wih infinie limis of inegrion, nd hose wih inegrnds h pproch some poin wihin he limis of inegrion. Firs we will consider inegrls wih infinie
CHAPTER 24: INFERENCE IN REGRESSION. Chapter 24: Make inferences about the population from which the sample data came.
MATH 1342 Ch. 24 April 25 and 27, 2013 Page 1 f 5 CHAPTER 24: INFERENCE IN REGRESSION Chapters 4 and 5: Relatinships between tw quantitative variables. Be able t Make a graph (scatterplt) Summarize the
AP Statistics Practice Test Unit Three Exploring Relationships Between Variables. Name Period Date
AP Statistics Practice Test Unit Three Explring Relatinships Between Variables Name Perid Date True r False: 1. Crrelatin and regressin require explanatry and respnse variables. 1. 2. Every least squares
2015 Sectional Physics Exam Solution Set
. Crrec answer: D Ne: [quan] denes: uns quan WYSE cadec Challenge 05 Secnal Phscs Ea SOLUTION SET / / / / rce lengh lengh rce enu ass lengh e a) / ass ass b) energ c) wrk lengh e pwer energ e d) (crrec
Confidence Interval for the mean response
Week 3: Prediction and Confidence Intervals at specified x. Testing lack of fit with replicates at some x's. Inference for the correlation. Introduction to regression with several explanatory variables.
Inference for Regression
Inference for Regression Section 9.4 Cathy Poliak, Ph.D. cathy@math.uh.edu Office in Fleming 11c Department of Mathematics University of Houston Lecture 13b - 3339 Cathy Poliak, Ph.D. cathy@math.uh.edu
Distribution of Mass and Energy in Five General Cosmic Models
Inerninl Jurnl f Asrnmy nd Asrpysics 05 5 0-7 Publised Online Mrc 05 in SciRes p://wwwscirprg/jurnl/ij p://dxdirg/0436/ij055004 Disribuin f Mss nd Energy in Five Generl Csmic Mdels Fdel A Bukri Deprmen
17 - LINEAR REGRESSION II
Topc 7 Lnear Regresson II 7- Topc 7 - LINEAR REGRESSION II Testng and Estmaton Inferences about β Recall that we estmate Yˆ ˆ β + ˆ βx. 0 μ Y X x β0 + βx usng To estmate σ σ squared error Y X x ε s ε we
PH2200 Practice Exam I Summer 2003
PH00 Prctice Exm I Summer 003 INSTRUCTIONS. Write yur nme nd student identifictin number n the nswer sheet.. Plese cver yur nswer sheet t ll times. 3. This is clsed bk exm. Yu my use the PH00 frmul sheet
UniSuper s Approach to Risk Budgeting
UnSuper s Apprch Rs Budgeng Prepred by Dvd H. Schneder Denns Sms Presened he Insue f Acures f Ausrl 009 Bennl Cnvenn 9- Aprl 009 Perh Wesern Ausrl Ths pper hs been prepred fr he Insue f Acures f Ausrl
Faculty of Engineering
Faculty f Engneerng DEPARTMENT f ELECTRICAL AND ELECTRONIC ENGINEERING EEE 223 Crcut Thery I Instructrs: M. K. Uygurğlu E. Erdl Fnal EXAMINATION June 20, 2003 Duratn : 120 mnutes Number f Prblems: 6 Gd
10.7 Power and the Poynting Vector Electromagnetic Wave Propagation Power and the Poynting Vector
L 333 lecmgnec II Chpe 0 lecmgnec W Ppgn Pf. l J. l Khnd Islmc Unves f G leccl ngneeng Depmen 06 0.7 Pwe nd he Pnng Vec neg cn be sped fm ne pn (whee nsme s lced) nhe pn (wh eceve) b mens f M ws. The e
Lecture 3: Inference in SLR
Lecture 3: Inference in SLR STAT 51 Spring 011 Background Reading KNNL:.1.6 3-1 Topic Overview This topic will cover: Review of hypothesis testing Inference about 1 Inference about 0 Confidence Intervals
Statistics for Managers Using Microsoft Excel/SPSS Chapter 14 Multiple Regression Models
Statstcs for Managers Usng Mcrosoft Excel/SPSS Chapter 14 Multple Regresson Models 1999 Prentce-Hall, Inc. Chap. 14-1 Chapter Topcs The Multple Regresson Model Contrbuton of Indvdual Independent Varables
DCDM BUSINESS SCHOOL NUMERICAL METHODS (COS 233-8) Solutions to Assignment 3. x f(x)
DCDM BUSINESS SCHOOL NUMEICAL METHODS (COS -8) Solutons to Assgnment Queston Consder the followng dt: 5 f() 8 7 5 () Set up dfference tble through fourth dfferences. (b) Wht s the mnmum degree tht n nterpoltng
CHAPTER EIGHT Linear Regression
7 CHAPTER EIGHT Linear Regression 8. Scatter Diagram Example 8. A chemical engineer is investigating the effect of process operating temperature ( x ) on product yield ( y ). The study results in the following
Inference for Regression Simple Linear Regression
Inference for Regression Simple Linear Regression IPS Chapter 10.1 2009 W.H. Freeman and Company Objectives (IPS Chapter 10.1) Simple linear regression p Statistical model for linear regression p Estimating
Principle Component Analysis
Prncple Component Anlyss Jng Go SUNY Bufflo Why Dmensonlty Reducton? We hve too mny dmensons o reson bout or obtn nsghts from o vsulze oo much nose n the dt Need to reduce them to smller set of fctors
Biostatistics 380 Multiple Regression 1. Multiple Regression
Biostatistics 0 Multiple Regression ORIGIN 0 Multiple Regression Multiple Regression is an extension of the technique of linear regression to describe the relationship between a single dependent (response)
***SECTION 12.1*** Tests about a Population Mean
***SECTION 12.1*** Tests but Ppultin Men CHAPTER 12 ~ Significnce Tests in Prctice We begin by drpping the ssumptin tht we knw the ppultin stndrd devitin when testing clims but ppultin men. As with cnfidence
Group Theory Problems
Grup Thery Prblems The fllwing table shws the vibratinal frequencies f CH. Assuming CH belngs t the T d pint grup, fill in the gaps in the table. Use fr and fr t designate type f vibratin. tretchorend
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.
Minimum Squared Error
Minimum Squred Error LDF: Minimum Squred-Error Procedures Ide: conver o esier nd eer undersood prolem Percepron y i > for ll smples y i solve sysem of liner inequliies MSE procedure y i = i for ll smples
Design of Diaphragm Micro-Devices. (Due date: Nov 2, 2017)
Design f Diphrgm Micr-Devices (Due de: Nv, 017) 1. Bckgrund A number f micr-devices depend upn diphrgm fr heir perin. Such devices re vlve, pump, nd pressure sensr. The generlized mdel f hese devices is
Minimum Squared Error
Minimum Squred Error LDF: Minimum Squred-Error Procedures Ide: conver o esier nd eer undersood prolem Percepron y i > 0 for ll smples y i solve sysem of liner inequliies MSE procedure y i i for ll smples
OVERVIEW Using Similarity and Proving Triangle Theorems G.SRT.4
OVRVIW Using Similrity nd Prving Tringle Therems G.SRT.4 G.SRT.4 Prve therems ut tringles. Therems include: line prllel t ne side f tringle divides the ther tw prprtinlly, nd cnversely; the Pythgren Therem
Modeling and Predicting Sequences: HMM and (may be) CRF. Amr Ahmed Feb 25
Modelg d redcg Sequeces: HMM d m be CRF Amr Ahmed 070 Feb 25 Bg cure redcg Sgle Lbel Ipu : A se of feures: - Bg of words docume - Oupu : Clss lbel - Topc of he docume - redcg Sequece of Lbels Noo Noe:
Motion. Part 2: Constant Acceleration. Acceleration. October Lab Physics. Ms. Levine 1. Acceleration. Acceleration. Units for Acceleration.
Moion Accelerion Pr : Consn Accelerion Accelerion Accelerion Accelerion is he re of chnge of velociy. = v - vo = Δv Δ ccelerion = = v - vo chnge of velociy elpsed ime Accelerion is vecor, lhough in one-dimensionl
Lecture 10 Multiple Linear Regression
Lecture 10 Multiple Linear Regression STAT 512 Spring 2011 Background Reading KNNL: 6.1-6.5 10-1 Topic Overview Multiple Linear Regression Model 10-2 Data for Multiple Regression Y i is the response variable
REVIEW OF ENGINEERING THERMODYNAMICS
Deprtment f Mnng nd Mterls Engneerng REVIEW OF ENINEERIN HERMODYNMICS Ferrus pplctns Engneerng hermdynmcs 1 bbs energy = H S; : bbs Energy, H: Enthlpy, S: Entrpy 1. Fr pure elements r pure cmpunds (l,
Statistics for Managers using Microsoft Excel 6 th Edition
Statistics for Managers using Microsoft Excel 6 th Edition Chapter 13 Simple Linear Regression 13-1 Learning Objectives In this chapter, you learn: How to use regression analysis to predict the value of
K The slowest step in a mechanism has this
CM 6 Generl Chemisry II Nme SLUTINS Exm, Spring 009 Dr. Seel. (0 pins) Selec he nswer frm he clumn n he righ h bes mches ech descripin frm he clumn n he lef. Ech nswer cn be used, ms, nly nce. E G This
11.2. Infinite Series
.2 Infinite Series 76.2 Infinite Series An infinite series is the sum f n infinite seuence f numbers + 2 + 3 + Á + n + Á The gl f this sectin is t understnd the mening f such n infinite sum nd t develp
T h e C S E T I P r o j e c t
T h e P r o j e c t T H E P R O J E C T T A B L E O F C O N T E N T S A r t i c l e P a g e C o m p r e h e n s i v e A s s es s m e n t o f t h e U F O / E T I P h e n o m e n o n M a y 1 9 9 1 1 E T
Physics 201 Lecture 2
Physcs 1 Lecure Lecure Chper.1-. Dene Poson, Dsplcemen & Dsnce Dsngush Tme nd Tme Inerl Dene Velocy (Aerge nd Insnneous), Speed Dene Acceleron Undersnd lgebrclly, hrough ecors, nd grphclly he relonshps
Simplified Variance Estimation for Three-Stage Random Sampling
Deprmen of ppled Sscs Johnnes Kepler Unversy Lnz IFS Reserch Pper Seres 04-67 Smplfed rnce Esmon for Three-Sge Rndom Smplng ndres Quember Ocober 04 Smplfed rnce Esmon for Three-Sge Rndom Smplng ndres Quember
Determining the Accuracy of Modal Parameter Estimation Methods
Determining the Accuracy f Mdal Parameter Estimatin Methds by Michael Lee Ph.D., P.E. & Mar Richardsn Ph.D. Structural Measurement Systems Milpitas, CA Abstract The mst cmmn type f mdal testing system
Average & instantaneous velocity and acceleration Motion with constant acceleration
Physics 7: Lecure Reminders Discussion nd Lb secions sr meeing ne week Fill ou Pink dd/drop form if you need o swich o differen secion h is FULL. Do i TODAY. Homework Ch. : 5, 7,, 3,, nd 6 Ch.: 6,, 3 Submission
Linear models and their mathematical foundations: Simple linear regression
Linear models and their mathematical foundations: Simple linear regression Steffen Unkel Department of Medical Statistics University Medical Center Göttingen, Germany Winter term 2018/19 1/21 Introduction
Solutions to Problems. Then, using the formula for the speed in a parabolic orbit (equation ), we have
Slutins t Prblems. Nttin: V speed f cmet immeditely befre cllisin. V speed f cmbined bject immeditely fter cllisin, mmentum is cnserved. V, becuse liner + k q perihelin distnce f riginl prblic rbit, s
https://goo.gl/eaqvfo SUMMER REV: Half-Life DUE DATE: JULY 2 nd
NAME: DUE DATE: JULY 2 nd AP Chemistry SUMMER REV: Half-Life Why? Every radiistpe has a characteristic rate f decay measured by its half-life. Half-lives can be as shrt as a fractin f a secnd r as lng
Overview Scatter Plot Example
Overview Topic 22 - Linear Regression and Correlation STAT 5 Professor Bruce Craig Consider one population but two variables For each sampling unit observe X and Y Assume linear relationship between variables
Statistics MINITAB - Lab 2
Statstcs 20080 MINITAB - Lab 2 1. Smple Lnear Regresson In smple lnear regresson we attempt to model a lnear relatonshp between two varables wth a straght lne and make statstcal nferences concernng that
AP Physics 1 MC Practice Kinematics 1D
AP Physics 1 MC Pracice Kinemaics 1D Quesins 1 3 relae w bjecs ha sar a x = 0 a = 0 and mve in ne dimensin independenly f ne anher. Graphs, f he velciy f each bjec versus ime are shwn belw Objec A Objec
Square law expression is non linear between I D and V GS. Need to operate in appropriate region for linear behaviour. W L
MOS Feld-Effec Trassrs (MOSFETs ecure # 4 MOSFET as a Amplfer k ( S Square law express s lear bewee ad. Need perae apprprae reg fr lear behaur. Cpyrgh 004 by Oxfrd Uersy Press, c. MOSFET as a Amplfer S
STA 302 H1F / 1001 HF Fall 2007 Test 1 October 24, 2007
STA 302 H1F / 1001 HF Fall 2007 Test 1 October 24, 2007 LAST NAME: SOLUTIONS FIRST NAME: STUDENT NUMBER: ENROLLED IN: (circle one) STA 302 STA 1001 INSTRUCTIONS: Time: 90 minutes Aids allowed: calculator.
where x and ȳ are the sample means of x 1,, x n
y y Animal Studies of Side Effects Simple Linear Regression Basic Ideas In simple linear regression there is an approximately linear relation between two variables say y = pressure in the pancreas x =
Basic Business Statistics, 10/e
Chapter 13 13-1 Basc Busness Statstcs 11 th Edton Chapter 13 Smple Lnear Regresson Basc Busness Statstcs, 11e 009 Prentce-Hall, Inc. Chap 13-1 Learnng Objectves In ths chapter, you learn: How to use regresson
Chapter 2. Continued. Proofs For ANOVA Proof of ANOVA Identity. the product term in the above equation can be simplified as n
Chapter 2. Continued Proofs For ANOVA Proof of ANOVA Identity We are going to prove that Writing SST SSR + SSE. Y i Ȳ (Y i Ŷ i ) + (Ŷ i Ȳ ) Squaring both sides summing over all i 1,...n, we get (Y i Ȳ
Objective of curve fitting is to represent a set of discrete data by a function (curve). Consider a set of discrete data as given in table.
CURVE FITTING Obectve curve ttg s t represet set dscrete dt b uct curve. Csder set dscrete dt s gve tble. 3 3 = T use the dt eectvel, curve epress s tted t the gve dt set, s = + = + + = e b ler uct plml
STA 108 Applied Linear Models: Regression Analysis Spring Solution for Homework #6
STA 8 Applied Linear Models: Regression Analysis Spring 011 Solution for Homework #6 6. a) = 11 1 31 41 51 1 3 4 5 11 1 31 41 51 β = β1 β β 3 b) = 1 1 1 1 1 11 1 31 41 51 1 3 4 5 β = β 0 β1 β 6.15 a) Stem-and-leaf
STAT 350 Final (new Material) Review Problems Key Spring 2016
1. The editor of a statistics textbook would like to plan for the next edition. A key variable is the number of pages that will be in the final version. Text files are prepared by the authors using LaTeX,
Trigonometry. Trigonometry. Solutions. Curriculum Ready ACMMG: 223, 224, 245.
Trgonometry Trgonometry Solutons Currulum Redy CMMG:, 4, 4 www.mthlets.om Trgonometry Solutons Bss Pge questons. Identfy f the followng trngles re rght ngled or not. Trngles,, d, e re rght ngled ndted
Chapter 14 Student Lecture Notes Department of Quantitative Methods & Information Systems. Business Statistics. Chapter 14 Multiple Regression
Chapter 14 Student Lecture Notes 14-1 Department of Quantitative Methods & Information Systems Business Statistics Chapter 14 Multiple Regression QMIS 0 Dr. Mohammad Zainal Chapter Goals After completing
Chapter Summary. Mathematical Induction Strong Induction Recursive Definitions Structural Induction Recursive Algorithms
Chapter 5 1 Chapter Summary Mathematical Inductin Strng Inductin Recursive Definitins Structural Inductin Recursive Algrithms Sectin 5.1 3 Sectin Summary Mathematical Inductin Examples f Prf by Mathematical
Multiple Regression. Inference for Multiple Regression and A Case Study. IPS Chapters 11.1 and W.H. Freeman and Company
Multiple Regression Inference for Multiple Regression and A Case Study IPS Chapters 11.1 and 11.2 2009 W.H. Freeman and Company Objectives (IPS Chapters 11.1 and 11.2) Multiple regression Data for multiple
(b) 10 yr. (b) 13 m. 1.6 m s, m s m s (c) 13.1 s. 32. (a) 20.0 s (b) No, the minimum distance to stop = 1.00 km. 1.
Answers o Een Numbered Problems Chper. () 7 m s, 6 m s (b) 8 5 yr 4.. m ih 6. () 5. m s (b).5 m s (c).5 m s (d) 3.33 m s (e) 8. ().3 min (b) 64 mi..3 h. ().3 s (b) 3 m 4..8 mi wes of he flgpole 6. (b)
The Multiple Regression Model
Multiple Regression The Multiple Regression Model Idea: Examine the linear relationship between 1 dependent (Y) & or more independent variables (X i ) Multiple Regression Model with k Independent Variables:
Multiple Linear Regression
Multiple Linear Regression Simple linear regression tries to fit a simple line between two variables Y and X. If X is linearly related to Y this explains some of the variability in Y. In most cases, there
INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING Volume 1, No 3, 2010
Prbabilistic Analysis f Lateral Displacements f Shear in a 20 strey building Samir Benaissa 1, Belaid Mechab 2 1 Labratire de Mathematiques, Université de Sidi Bel Abbes BP 89, Sidi Bel Abbes 22000, Algerie.
STAT 3340 Assignment 1 solutions. 1. Find the equation of the line which passes through the points (1,1) and (4,5).
(out of 15 ponts) STAT 3340 Assgnment 1 solutons (10) (10) 1. Fnd the equaton of the lne whch passes through the ponts (1,1) and (4,5). β 1 = (5 1)/(4 1) = 4/3 equaton for the lne s y y 0 = β 1 (x x 0
ELG3150 DGD 6 P9.5; P9.7; P9.13; P9.18; AP9.5; DP9.2
ELG3150 DGD 6 P9.5; P9.7; P9.13; P9.18; AP9.5; DP9.2 P9.5 A speed cntrl fr gsline engine is shwn in Figure P9.5 in the textbk. () Determine the necessry gin if the stedy-stte speed errr is required t be
Probability and. Lecture 13: and Correlation
933 Probablty ad Statstcs for Software ad Kowledge Egeers Lecture 3: Smple Lear Regresso ad Correlato Mocha Soptkamo, Ph.D. Outle The Smple Lear Regresso Model (.) Fttg the Regresso Le (.) The Aalyss of
Statistics for Business and Economics
Statstcs for Busness and Economcs Chapter 11 Smple Regresson Copyrght 010 Pearson Educaton, Inc. Publshng as Prentce Hall Ch. 11-1 11.1 Overvew of Lnear Models n An equaton can be ft to show the best lnear
Supporting information How to concatenate the local attractors of subnetworks in the HPFP
n Effcen lgorh for Idenfyng Prry Phenoype rcors of Lrge-Scle Boolen Newor Sng-Mo Choo nd Kwng-Hyun Cho Depren of Mhecs Unversy of Ulsn Ulsn 446 Republc of Kore Depren of Bo nd Brn Engneerng Kore dvnced
Inference for the Regression Coefficient
Inference for the Regression Coefficient Recall, b 0 and b 1 are the estimates of the slope β 1 and intercept β 0 of population regression line. We can shows that b 0 and b 1 are the unbiased estimates
ALGEBRA 2/TRIGONMETRY TOPIC REVIEW QUARTER 3 LOGS
ALGEBRA /TRIGONMETRY TOPIC REVIEW QUARTER LOGS Cnverting frm Epnentil frm t Lgrithmic frm: E B N Lg BN E Americn Ben t French Lg Ben-n Lg Prperties: Lg Prperties lg (y) lg + lg y lg y lg lg y lg () lg
ACE 564 Spring Lecture 7. Extensions of The Multiple Regression Model: Dummy Independent Variables. by Professor Scott H.
ACE 564 Spring 2006 Lecure 7 Exensions of The Muliple Regression Model: Dumm Independen Variables b Professor Sco H. Irwin Readings: Griffihs, Hill and Judge. "Dumm Variables and Varing Coefficien Models
Hubble s Law PHYS 1301
1 PHYS 1301 Hubble s Law Why: The lab will verify Hubble s law fr the expansin f the universe which is ne f the imprtant cnsequences f general relativity. What: Frm measurements f the angular size and
CH.3. COMPATIBILITY EQUATIONS. Continuum Mechanics Course (MMC) - ETSECCPB - UPC
CH.3. COMPATIBILITY EQUATIONS Connuum Mechancs Course (MMC) - ETSECCPB - UPC Overvew Compably Condons Compably Equaons of a Poenal Vecor Feld Compably Condons for Infnesmal Srans Inegraon of he Infnesmal