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

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

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

Transcription

1 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 calculator and a two-sded 8.5'' '' ad sheet. If you do not understand a queston, or are havng some other dffculty, do not hestate to ask your nstructor or T.A for clarfcaton. There are 3 pages ncludng ths page. The last pages are statstcal tables. Please check that you are not mssng any page. Show all your work and answer n the space provded, n nk. Pencl may be used, but then remarks wll not be allowed. Use back of pages for rough work. Total pont: Good luck!!! Queston 3 Total Max 6 3 Score

2 Queston A study was conducted to test the mpact of 3 fertlzers on crop yeld. The 3 fertlzers were appled to 7 plots of land n a random fashon such that each fertlzer was appled to 9 plots. a) ( mark) Name the expermental desgn that was used n plannng ths study. Ths s a completely randomzed desgn. b) ( marks) Were randomzaton and replcaton used n ths experment? If yes, explan how? Randomzaton was used snce the fertlzers (treatments) were randomly assgned to each plot of land (expermental unt). Replcaton was used snce each fertlzer (treatment) was appled to 9 plots of land (expermental unts). c) ( marks) What statstcal model would you use for ths study desgn? The model s one-factor fxed effect model descrbed by the followng equaton: Y = + τ + ε, =,,3, j =,...,9 Where s the overall mean yeld τ s the effect of the th fertlzer ε s the random or expermental error d) (3 marks) What assumptons dd you make n part (c)? We assume that ε are..d. wth dstrbuton that s N(, σ ). e) (5 marks) Set up one set of orthogonal contrasts that mght be used n ths study. Snce there are three treatments a set of orthogonal contrast wll contan two orthogonal contrasts. An example of such a set s:

3 + 3 Ψ = and Ψ = 3 Checkng for orthogonalty 3 Sum c d - c d f) (3 marks) For each contrast n (d), state the null and alternatve hypotheses to whch the contrast corresponds. The frst contrast test whether the mean crop yeld wth the frst fertlzer s the same as the average mean crop yeld wth the other two fertlzers. The hypotheses are: H H a + 3 : + 3 : = The second contrast test whether the mean crop yeld wth the second fertlzer s the same as the mean crop yeld wth the thrd fertlzers. The hypotheses are: H H a : 3 = : 3 g) ( marks) Suppose that the 7 plots were selected at random from a bg feld contanng many more plots of land. How would your answers to parts (a), (c) and (d) change? Explan! If the plots of land were selected at random the desgn wll stll be a completely randomzed desgn and the model wll stll be one-factor fxed effect model. So the answers to parts (a), (c) and (d) wll not change. However, f the fertlzers were selected at random from say all avalable fertlzers n the market. Then the model wll be one-factor random effect model. The equaton of the model wll be the same; but, there wll be two addtonal assumptons: () τ are statstcally ndependent of the ε N, σ τ () the τ are..d ( ) 3

4 Queston Four dfferent desgns for a dgtal computer crcut are beng studed to compare the amount of nose present. The results are shown n the table bellow: Crcut Desgn Nose Observed Mean Std Dev SS Total = 99, SS Treat = a) (5 marks) Explan what knd of expermental desgn was used n ths experment. Are the effects of the factor random or fxed? What s the statstcal model you would use to analyze ths data? Ths s a completely randomzed desgn. The effects of the factor (crcut desgn) are fxed snce they were specfed by the expermenter rather than beng selected at random. The statstcal model we would use to analyze ths data s a one-factor fxed effect model descrbed by the equaton: Y = + τ + ε, =,,3,, j =,...,5 Where s the overall mean yeld τ s the effect of the th crcut desgn ε s the random or expermental error b) (9 marks) Construct the ANOVA table for ths experment. Fnd the P-values. The ANOVA table produced by SAS s gven below: Source DF SS MS F-rato P-value Treatment 3.78 <. Error Total 9 99

5 c) (3 marks) Do the three crcut desgns have the same mean nose observed? Use α = %. The hypotheses of nterests here are: H H a : τ = τ = τ 3 = τ = : at least oneτ The test statstc obtaned from the ANOVA table produced n part (b)s: F obs =. 78 whch has an F(3,6) dstrbuton. Snce the P-value <. < α =. we reject the null hypothess and conclude that we have sgnfcant evdence that the three crcut desgns do not have the same mean nose observed. d) (5 marks) It was suspected before the experment that crcut desgns and are smlar n the nose present. Test ths hypothess usng a t-test and α = 5%. The hypotheses to test here are: H H a : τ = τ : τ τ or H H a : τ τ = : τ τ Further, we know that an unbased estmate of the dfference between two treatment effects s Y Y j and that Y + Y j ~ N τ τ j, σ. r rj Therefore, the test statstcs s: t = Y MS Y j E + r rj whch has a t(n-a) dstrbuton Substtutng all the values we get t obs = =. wth df = The P-value can be estmated as follows: ( t( 6) > t ) = P( t( 6) >.). P value = > P obs Snce P-value s very large we cannot reject H and we able to conclude that that crcut desgns and are not dfferent n the nose present. 5

6 e) (5 marks) How many dfferent orthogonal contrasts you can create smultaneously n ths experment? Create two contrasts, one to test the queston n part (d), the other to test whether the mean response for crcut desgn 3 s the same as for the average for crcut desgn and. Are these contrasts orthogonal? Snce the factor (crcut desgn) has a = levels, a - = 3 dfferent orthogonal contrasts can be created smultaneously. The contrast to test the queston n part (d) s: Ψ =. The contrast to test whether the mean response for crcut desgn 3 s the same as for + the average for crcut desgn and s: Ψ = 3. Checkng for orthogonalty 3 Sum c - d c d So yes, these contrasts are orthogonal. f) (8 marks) Calculate SS for both contrasts n part (e). Test the hypothess regardng these two contrasts usng F-test. How do they compare wth part (c)? Contrast : the hypotheses are H = vs H :. The sum of square of the contrast s: : a SS contrast a ( cy ) ( ) = = a c / = r = ( / 5) + ( / 5) SSContrast /. The test statstcs s: F obs = = =. 37 wth df = (, 6) MS 8.35 The P-value can then be estmated as follow: E ( F(,6) > F ) = P( F(,6) >.37). P value = P obs >. So cannot reject H. =. Note, the F statstcs n ths case s smply the square of the t statstcs from part (d). Contrast : the hypotheses are: ( + )/ = vs H : ( + )/ The sum of square of the contrast s: SS = H. : 3 a 3 contrast The test statstcs s: F obs = = wth df = (, 6) 8.35 P value = P F,6 > 6.53 <.. The P-value can then be estmated as follow: ( ( ) ) So we reject H. Combnaton of these two results s n agreement wth (c), meanng that not all means are equal (two may be). 6

7 g) (3 marks) How can you calculate the SS for the contrast comparng crcut desgn wth the average of the other three wthout usng the formula for SS contrast? Do t! The contrast comparng crcut desgn wth the average of the other three s orthogonal to the two contrasts n part (e), therefore formng a set of orthogonal contrasts. For any set of orthogonal contrasts we have that SS. Treat = SScontrast + SScontrast + + SScontrast a- Therefore, the SS of ths contrast s SS 3 SS SS = = 69.7 contrast = Treat contrast SScontrast Below are plot of the resduals versus the ftted values and a normal quantle plot of the resduals for the model used to analyze the data above. z ftted z Normal Percent l es 7

8 h) (5 marks) What are the assumptons of the model used to construct the ANOVA table n part (c)? Comment on the valdty of these assumptons. The assumptons are: The model form s as specfed n part (a), that s E(Y ) = + τ. The resduals, ε, are..d. N(, σ ). Based on the resdual plots above, t looks lke all of these assumptons are vald for ths data. ) (3 marks) Based on the plots above are there any outlers n ths data? Explan. Yes, t looks lke there s one outler n ths data. It appears n the plot of the resduals versus ftted value as the rght-most and lowest pont (.e., large negatve resdual). In addton, t appears on the normal quantle plot as the lowst pont on the left. Lookng at the data we see that the value of 5 th observaton taken on crcut desgn s 8 whch s much smaller than the rest of the observatons, suggestng agan that ths may be an outler. Queston 3 An experment was conducted to study the lfe (n hours) of two dfferent brands of batteres (brand A and B) n three dfferent devces (rado, camera and portable DVD player). A completely randomzed two-factor factoral experment was conducted. Some SAS outputs used to analyze the data from ths experment are gven below: 8

9 a) (5 marks) What statstcal model was used to analyze ths data? Wrte the model and descrbe each term n the model n the context of ths study. Lst all assumptons requred for the model. Ths s a two-factor fxed-effect model. Its equaton s: Y k = + α + β j + γ + ε k where: Overall mean α Battery effect (factor A) of level =, β j Devce effect (factor B) of level j =,, 3 γ Interacton effect of batter (factor A) level and devce (factor B) level j Expermental error ε The assumptons of the model are: ε k are..d. N(, σ ) In order to obtan unbased estmators, we requre that: a = b j= a = α = β = j b γ = γ j= = 9

10 b) ( marks) Create the ANOVA table that was used n the analyss of ths data usng the results from the SAS output above, ncludng P-values. The ANOVA table s: Source DF SS MS F-rato P-value Factor A Factor B Interacton A B <..63 Error Total 3.85 c) (5 marks) Plot an nteracton plot usng the cell means as gven n the output above. Use dfferent symbols/colors for the dfferent battery brand. What do you learn from ths plot? Here s an nteracton plot produced by MINITAB Interacton Plot (data means) Battery A B 8. Mean Camera DVD Devce Rado From the plots, t appears that there s no nteracton between battery type and devce. Further, for every devce the mean lfetme for battery B appears to be larger than that of batter A suggestng that there mght be a battery effect. Fnally, t looks lke batteres used n DVDs have the smallest lfetme whle batteres used n Rados last the longest. Ths, n turn, suggests that there mght be a devce effect.

11 d) (9 marks) Do battery brand and devce type nteract? Is there any dfference n lfe tme of the two battery brands? Does devce type have any effect on battery lfe tme? Answer these three questons, f approprate, usng sgnfcant level 5%. State each queston n terms of the model and state your conclusons n plan language n the context of ths experment. Frst we need to test for nteracton. The hypotheses of nterest are: H : γ =, for all, j vs H a : at least one γ. From the ANOVA table we get the test statstcs F obs =.8, wth P-value =.63, therefore we cannot reject the null hypothess and we conclude that there s no sgnfcant nteracton between battery type and devce type. Snce there s no nteracton we can proceed to test for man effects of battery and devce. Man effect of battery: The hypotheses f nterest are: H : α =, for =, vs H a : at least one α. From the ANOVA table we get the test statstcs F obs = 9.33, wth P-value =.. Hence, we can reject the null hypothess at α = 5% and we conclude that there s a sgnfcant effect of battery type on lfetme. Note, that ths s moderate evdence of sgnfcance as we would not be able to reject the null hypothess at α = %. Man effect of devce: The hypotheses f nterest are: H : β =, for =,, 3 vs H a : at least one β. From the ANOVA table we get the test statstcs F obs = 3.75, wth P-value<.. Hence, we have strong evdence to reject the null hypothess and we conclude that there s a sgnfcant effect of devce type on lfetme. e) ( marks) If the researchers assumed (from experence) before the experment that battery brand and devce type don t nteract, how would ths affect the model used to analyze ths data? Wrte the model and descrbe each term n the context of ths study. In ths case the model wll not nclude an nteracton effect term, that s, the model equaton wll be: Y k = + α + β j + ε k (addtve model) where: s the overall mean, α are effects of battery, β j are effects of devce and ε are expermental errors.

12 f) (5 marks) Create the ANOVA table that would be used n part (e), ncludng P-value, and test the man effects. Are the results consstent wth the orgnal model used n the study? Snce we omt the nteracton term from the model, both the degrees of freedom and sums of squares of the nteracton term n the ANOVA table go to the error. The ANOVA table s then: Source DF SS MS F-rato P-value Factor A Factor B < P <.5 <. Error Total 3.85 END!

# c i. INFERENCE FOR CONTRASTS (Chapter 4) It's unbiased: Recall: A contrast is a linear combination of effects with coefficients summing to zero:

# c i. INFERENCE FOR CONTRASTS (Chapter 4) It's unbiased: Recall: A contrast is a linear combination of effects with coefficients summing to zero: 1 INFERENCE FOR CONTRASTS (Chapter 4 Recall: A contrast s a lnear combnaton of effects wth coeffcents summng to zero: " where " = 0. Specfc types of contrasts of nterest nclude: Dfferences n effects Dfferences

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

ANOVA. The Observations y ij

ANOVA. The Observations y ij ANOVA Stands for ANalyss Of VArance But t s a test of dfferences n means The dea: The Observatons y j Treatment group = 1 = 2 = k y 11 y 21 y k,1 y 12 y 22 y k,2 y 1, n1 y 2, n2 y k, nk means: m 1 m 2

More information

Chapter 11: I = 2 samples independent samples paired samples Chapter 12: I 3 samples of equal size J one-way layout two-way layout

Chapter 11: I = 2 samples independent samples paired samples Chapter 12: I 3 samples of equal size J one-way layout two-way layout Serk Sagtov, Chalmers and GU, February 0, 018 Chapter 1. Analyss of varance Chapter 11: I = samples ndependent samples pared samples Chapter 1: I 3 samples of equal sze one-way layout two-way layout 1

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

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

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

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

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

Dr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur

Dr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur Analyss of Varance and Desgn of Experment-I MODULE VIII LECTURE - 34 ANALYSIS OF VARIANCE IN RANDOM-EFFECTS MODEL AND MIXED-EFFECTS EFFECTS MODEL Dr Shalabh Department of Mathematcs and Statstcs Indan

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

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

[The following data appear in Wooldridge Q2.3.] The table below contains the ACT score and college GPA for eight college students.

[The following data appear in Wooldridge Q2.3.] The table below contains the ACT score and college GPA for eight college students. PPOL 59-3 Problem Set Exercses n Smple Regresson Due n class /8/7 In ths problem set, you are asked to compute varous statstcs by hand to gve you a better sense of the mechancs of the Pearson correlaton

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

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

Chapter 11: Simple Linear Regression and Correlation

Chapter 11: Simple Linear Regression and Correlation Chapter 11: Smple Lnear Regresson and Correlaton 11-1 Emprcal Models 11-2 Smple Lnear Regresson 11-3 Propertes of the Least Squares Estmators 11-4 Hypothess Test n Smple Lnear Regresson 11-4.1 Use of t-tests

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

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

/ 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 6 More on Complete Randomized Block Design (RBD)

Lecture 6 More on Complete Randomized Block Design (RBD) Lecture 6 More on Complete Randomzed Block Desgn (RBD) Multple test Multple test The multple comparsons or multple testng problem occurs when one consders a set of statstcal nferences smultaneously. For

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

17 Nested and Higher Order Designs

17 Nested and Higher Order Designs 54 17 Nested and Hgher Order Desgns 17.1 Two-Way Analyss of Varance Consder an experment n whch the treatments are combnatons of two or more nfluences on the response. The ndvdual nfluences wll be called

More information

F statistic = s2 1 s 2 ( F for Fisher )

F statistic = s2 1 s 2 ( F for Fisher ) Stat 4 ANOVA Analyss of Varance /6/04 Comparng Two varances: F dstrbuton Typcal Data Sets One way analyss of varance : example Notaton for one way ANOVA Comparng Two varances: F dstrbuton We saw that the

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

Lecture 4 Hypothesis Testing

Lecture 4 Hypothesis Testing Lecture 4 Hypothess Testng We may wsh to test pror hypotheses about the coeffcents we estmate. We can use the estmates to test whether the data rejects our hypothess. An example mght be that we wsh to

More information

Durban Watson for Testing the Lack-of-Fit of Polynomial Regression Models without Replications

Durban Watson for Testing the Lack-of-Fit of Polynomial Regression Models without Replications Durban Watson for Testng the Lack-of-Ft of Polynomal Regresson Models wthout Replcatons Ruba A. Alyaf, Maha A. Omar, Abdullah A. Al-Shha ralyaf@ksu.edu.sa, maomar@ksu.edu.sa, aalshha@ksu.edu.sa Department

More information

Chapter 14 Simple Linear Regression

Chapter 14 Simple Linear Regression Chapter 4 Smple Lnear Regresson Chapter 4 - Smple Lnear Regresson Manageral decsons often are based on the relatonshp between two or more varables. Regresson analss can be used to develop an equaton showng

More information

ANSWERS CHAPTER 9. TIO 9.2: If the values are the same, the difference is 0, therefore the null hypothesis cannot be rejected.

ANSWERS CHAPTER 9. TIO 9.2: If the values are the same, the difference is 0, therefore the null hypothesis cannot be rejected. ANSWERS CHAPTER 9 THINK IT OVER thnk t over TIO 9.: χ 2 k = ( f e ) = 0 e Breakng the equaton down: the test statstc for the ch-squared dstrbuton s equal to the sum over all categores of the expected frequency

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

28. SIMPLE LINEAR REGRESSION III

28. SIMPLE LINEAR REGRESSION III 8. SIMPLE LINEAR REGRESSION III Ftted Values and Resduals US Domestc Beers: Calores vs. % Alcohol To each observed x, there corresponds a y-value on the ftted lne, y ˆ = βˆ + βˆ x. The are called ftted

More information

Midterm Examination. Regression and Forecasting Models

Midterm Examination. Regression and Forecasting Models IOMS Department Regresson and Forecastng Models Professor Wllam Greene Phone: 22.998.0876 Offce: KMC 7-90 Home page: people.stern.nyu.edu/wgreene Emal: wgreene@stern.nyu.edu Course web page: people.stern.nyu.edu/wgreene/regresson/outlne.htm

More information

18. SIMPLE LINEAR REGRESSION III

18. SIMPLE LINEAR REGRESSION III 8. SIMPLE LINEAR REGRESSION III US Domestc Beers: Calores vs. % Alcohol Ftted Values and Resduals To each observed x, there corresponds a y-value on the ftted lne, y ˆ ˆ = α + x. The are called ftted values.

More information

Two-factor model. Statistical Models. Least Squares estimation in LM two-factor model. Rats

Two-factor model. Statistical Models. Least Squares estimation in LM two-factor model. Rats tatstcal Models Lecture nalyss of Varance wo-factor model Overall mean Man effect of factor at level Man effect of factor at level Y µ + α + β + γ + ε Eε f (, ( l, Cov( ε, ε ) lmr f (, nteracton effect

More information

STAT 3008 Applied Regression Analysis

STAT 3008 Applied Regression Analysis STAT 3008 Appled Regresson Analyss Tutoral : Smple Lnear Regresson LAI Chun He Department of Statstcs, The Chnese Unversty of Hong Kong 1 Model Assumpton To quantfy the relatonshp between two factors,

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

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

LINEAR REGRESSION ANALYSIS. MODULE VIII Lecture Indicator Variables

LINEAR REGRESSION ANALYSIS. MODULE VIII Lecture Indicator Variables LINEAR REGRESSION ANALYSIS MODULE VIII Lecture - 7 Indcator Varables Dr. Shalabh Department of Maematcs and Statstcs Indan Insttute of Technology Kanpur Indcator varables versus quanttatve explanatory

More information

NANYANG TECHNOLOGICAL UNIVERSITY SEMESTER I EXAMINATION MTH352/MH3510 Regression Analysis

NANYANG TECHNOLOGICAL UNIVERSITY SEMESTER I EXAMINATION MTH352/MH3510 Regression Analysis NANYANG TECHNOLOGICAL UNIVERSITY SEMESTER I EXAMINATION 014-015 MTH35/MH3510 Regresson Analyss December 014 TIME ALLOWED: HOURS INSTRUCTIONS TO CANDIDATES 1. Ths examnaton paper contans FOUR (4) questons

More information

MAE140 - Linear Circuits - Winter 16 Midterm, February 5

MAE140 - Linear Circuits - Winter 16 Midterm, February 5 Instructons ME140 - Lnear Crcuts - Wnter 16 Mdterm, February 5 () Ths exam s open book. You may use whatever wrtten materals you choose, ncludng your class notes and textbook. You may use a hand calculator

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

DO NOT OPEN THE QUESTION PAPER UNTIL INSTRUCTED TO DO SO BY THE CHIEF INVIGILATOR. Introductory Econometrics 1 hour 30 minutes

DO NOT OPEN THE QUESTION PAPER UNTIL INSTRUCTED TO DO SO BY THE CHIEF INVIGILATOR. Introductory Econometrics 1 hour 30 minutes 25/6 Canddates Only January Examnatons 26 Student Number: Desk Number:...... DO NOT OPEN THE QUESTION PAPER UNTIL INSTRUCTED TO DO SO BY THE CHIEF INVIGILATOR Department Module Code Module Ttle Exam Duraton

More information

Chapter 13 Analysis of Variance and Experimental Design

Chapter 13 Analysis of Variance and Experimental Design Chapter 3 Analyss of Varance and Expermental Desgn Learnng Obectves. Understand how the analyss of varance procedure can be used to determne f the means of more than two populatons are equal.. Know the

More information

x i1 =1 for all i (the constant ).

x i1 =1 for all i (the constant ). Chapter 5 The Multple Regresson Model Consder an economc model where the dependent varable s a functon of K explanatory varables. The economc model has the form: y = f ( x,x,..., ) xk Approxmate ths by

More information

Chapter 15 - Multiple Regression

Chapter 15 - Multiple Regression Chapter - Multple Regresson Chapter - Multple Regresson Multple Regresson Model The equaton that descrbes how the dependent varable y s related to the ndependent varables x, x,... x p and an error term

More information

January Examinations 2015

January Examinations 2015 24/5 Canddates Only January Examnatons 25 DO NOT OPEN THE QUESTION PAPER UNTIL INSTRUCTED TO DO SO BY THE CHIEF INVIGILATOR STUDENT CANDIDATE NO.. Department Module Code Module Ttle Exam Duraton (n words)

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

ECON 351* -- Note 23: Tests for Coefficient Differences: Examples Introduction. Sample data: A random sample of 534 paid employees.

ECON 351* -- Note 23: Tests for Coefficient Differences: Examples Introduction. Sample data: A random sample of 534 paid employees. Model and Data ECON 35* -- NOTE 3 Tests for Coeffcent Dfferences: Examples. Introducton Sample data: A random sample of 534 pad employees. Varable defntons: W hourly wage rate of employee ; lnw the natural

More information

ISQS 6348 Final Open notes, no books. Points out of 100 in parentheses. Y 1 ε 2

ISQS 6348 Final Open notes, no books. Points out of 100 in parentheses. Y 1 ε 2 ISQS 6348 Fnal Open notes, no books. Ponts out of 100 n parentheses. 1. The followng path dagram s gven: ε 1 Y 1 ε F Y 1.A. (10) Wrte down the usual model and assumptons that are mpled by ths dagram. Soluton:

More information

Chapter 5 Multilevel Models

Chapter 5 Multilevel Models Chapter 5 Multlevel Models 5.1 Cross-sectonal multlevel models 5.1.1 Two-level models 5.1.2 Multple level models 5.1.3 Multple level modelng n other felds 5.2 Longtudnal multlevel models 5.2.1 Two-level

More information

Chapter 15 Student Lecture Notes 15-1

Chapter 15 Student Lecture Notes 15-1 Chapter 15 Student Lecture Notes 15-1 Basc Busness Statstcs (9 th Edton) Chapter 15 Multple Regresson Model Buldng 004 Prentce-Hall, Inc. Chap 15-1 Chapter Topcs The Quadratc Regresson Model Usng Transformatons

More information

Testing for seasonal unit roots in heterogeneous panels

Testing for seasonal unit roots in heterogeneous panels Testng for seasonal unt roots n heterogeneous panels Jesus Otero * Facultad de Economía Unversdad del Rosaro, Colomba Jeremy Smth Department of Economcs Unversty of arwck Monca Gulett Aston Busness School

More information

ECONOMICS 351*-A Mid-Term Exam -- Fall Term 2000 Page 1 of 13 pages. QUEEN'S UNIVERSITY AT KINGSTON Department of Economics

ECONOMICS 351*-A Mid-Term Exam -- Fall Term 2000 Page 1 of 13 pages. QUEEN'S UNIVERSITY AT KINGSTON Department of Economics ECOOMICS 35*-A Md-Term Exam -- Fall Term 000 Page of 3 pages QUEE'S UIVERSITY AT KIGSTO Department of Economcs ECOOMICS 35* - Secton A Introductory Econometrcs Fall Term 000 MID-TERM EAM ASWERS MG Abbott

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

7.1. Single classification analysis of variance (ANOVA) Why not use multiple 2-sample 2. When to use ANOVA

7.1. Single classification analysis of variance (ANOVA) Why not use multiple 2-sample 2. When to use ANOVA Sngle classfcaton analyss of varance (ANOVA) When to use ANOVA ANOVA models and parttonng sums of squares ANOVA: hypothess testng ANOVA: assumptons A non-parametrc alternatve: Kruskal-Walls ANOVA Power

More information

Dr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur

Dr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur Analyss of Varance and Desgn of Experment-I MODULE VII LECTURE - 3 ANALYSIS OF COVARIANCE Dr Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur Any scentfc experment s performed

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

UCLA STAT 13 Introduction to Statistical Methods for the Life and Health Sciences. Chapter 11 Analysis of Variance - ANOVA. Instructor: Ivo Dinov,

UCLA STAT 13 Introduction to Statistical Methods for the Life and Health Sciences. Chapter 11 Analysis of Variance - ANOVA. Instructor: Ivo Dinov, UCLA STAT 3 ntroducton to Statstcal Methods for the Lfe and Health Scences nstructor: vo Dnov, Asst. Prof. of Statstcs and Neurology Chapter Analyss of Varance - ANOVA Teachng Assstants: Fred Phoa, Anwer

More information

Introduction to Vapor/Liquid Equilibrium, part 2. Raoult s Law:

Introduction to Vapor/Liquid Equilibrium, part 2. Raoult s Law: CE304, Sprng 2004 Lecture 4 Introducton to Vapor/Lqud Equlbrum, part 2 Raoult s Law: The smplest model that allows us do VLE calculatons s obtaned when we assume that the vapor phase s an deal gas, and

More information

Chapter 8 Indicator Variables

Chapter 8 Indicator Variables Chapter 8 Indcator Varables In general, e explanatory varables n any regresson analyss are assumed to be quanttatve n nature. For example, e varables lke temperature, dstance, age etc. are quanttatve n

More information

Lecture 6: Introduction to Linear Regression

Lecture 6: Introduction to Linear Regression Lecture 6: Introducton to Lnear Regresson An Manchakul amancha@jhsph.edu 24 Aprl 27 Lnear regresson: man dea Lnear regresson can be used to study an outcome as a lnear functon of a predctor Example: 6

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

a. (All your answers should be in the letter!

a. (All your answers should be in the letter! Econ 301 Blkent Unversty Taskn Econometrcs Department of Economcs Md Term Exam I November 8, 015 Name For each hypothess testng n the exam complete the followng steps: Indcate the test statstc, ts crtcal

More information

Reminder: Nested models. Lecture 9: Interactions, Quadratic terms and Splines. Effect Modification. Model 1

Reminder: Nested models. Lecture 9: Interactions, Quadratic terms and Splines. Effect Modification. Model 1 Lecture 9: Interactons, Quadratc terms and Splnes An Manchakul amancha@jhsph.edu 3 Aprl 7 Remnder: Nested models Parent model contans one set of varables Extended model adds one or more new varables to

More information

1. Inference on Regression Parameters a. Finding Mean, s.d and covariance amongst estimates. 2. Confidence Intervals and Working Hotelling Bands

1. Inference on Regression Parameters a. Finding Mean, s.d and covariance amongst estimates. 2. Confidence Intervals and Working Hotelling Bands Content. Inference on Regresson Parameters a. Fndng Mean, s.d and covarance amongst estmates.. Confdence Intervals and Workng Hotellng Bands 3. Cochran s Theorem 4. General Lnear Testng 5. Measures of

More information

Interval Estimation in the Classical Normal Linear Regression Model. 1. Introduction

Interval Estimation in the Classical Normal Linear Regression Model. 1. Introduction ECONOMICS 35* -- NOTE 7 ECON 35* -- NOTE 7 Interval Estmaton n the Classcal Normal Lnear Regresson Model Ths note outlnes the basc elements of nterval estmaton n the Classcal Normal Lnear Regresson Model

More information

Diagnostics in Poisson Regression. Models - Residual Analysis

Diagnostics in Poisson Regression. Models - Residual Analysis Dagnostcs n Posson Regresson Models - Resdual Analyss 1 Outlne Dagnostcs n Posson Regresson Models - Resdual Analyss Example 3: Recall of Stressful Events contnued 2 Resdual Analyss Resduals represent

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

Econometrics of Panel Data

Econometrics of Panel Data Econometrcs of Panel Data Jakub Mućk Meetng # 8 Jakub Mućk Econometrcs of Panel Data Meetng # 8 1 / 17 Outlne 1 Heterogenety n the slope coeffcents 2 Seemngly Unrelated Regresson (SUR) 3 Swamy s random

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

Topic 10: ANOVA models for random and mixed effects Fixed and Random Models in One-way Classification Experiments

Topic 10: ANOVA models for random and mixed effects Fixed and Random Models in One-way Classification Experiments Topc 10: ANOVA models for random and mxed effects eferences: ST&D Topc 7.5 (15-153), Topc 9.9 (5-7), Topc 15.5 (379-384); rules for expected on ST&D page 381 replaced by Chapter 8 from Montgomery, 1991.

More information

Statistics for Business and Economics

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

More information

Chapter 6. Supplemental Text Material

Chapter 6. Supplemental Text Material Chapter 6. Supplemental Text Materal S6-. actor Effect Estmates are Least Squares Estmates We have gven heurstc or ntutve explanatons of how the estmates of the factor effects are obtaned n the textboo.

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

Exam. Econometrics - Exam 1

Exam. Econometrics - Exam 1 Econometrcs - Exam 1 Exam Problem 1: (15 ponts) Suppose that the classcal regresson model apples but that the true value of the constant s zero. In order to answer the followng questons assume just one

More information

Statistical tables are provided Two Hours UNIVERSITY OF MANCHESTER. Date: Wednesday 4 th June 2008 Time: 1400 to 1600

Statistical tables are provided Two Hours UNIVERSITY OF MANCHESTER. Date: Wednesday 4 th June 2008 Time: 1400 to 1600 Statstcal tables are provded Two Hours UNIVERSITY OF MNCHESTER Medcal Statstcs Date: Wednesday 4 th June 008 Tme: 1400 to 1600 MT3807 Electronc calculators may be used provded that they conform to Unversty

More information

2016 Wiley. Study Session 2: Ethical and Professional Standards Application

2016 Wiley. Study Session 2: Ethical and Professional Standards Application 6 Wley Study Sesson : Ethcal and Professonal Standards Applcaton LESSON : CORRECTION ANALYSIS Readng 9: Correlaton and Regresson LOS 9a: Calculate and nterpret a sample covarance and a sample correlaton

More information

Using Multivariate Rank Sum Tests to Evaluate Effectiveness of Computer Applications in Teaching Business Statistics

Using Multivariate Rank Sum Tests to Evaluate Effectiveness of Computer Applications in Teaching Business Statistics Usng Multvarate Rank Sum Tests to Evaluate Effectveness of Computer Applcatons n Teachng Busness Statstcs by Yeong-Tzay Su, Professor Department of Mathematcs Kaohsung Normal Unversty Kaohsung, TAIWAN

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

Dr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur

Dr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur Analyss of Varance and Desgn of Experments- MODULE LECTURE - 6 EXPERMENTAL DESGN MODELS Dr. Shalabh Department of Mathematcs and Statstcs ndan nsttute of Technology Kanpur Two-way classfcaton wth nteractons

More information

Scatter Plot x

Scatter Plot x Construct a scatter plot usng excel for the gven data. Determne whether there s a postve lnear correlaton, negatve lnear correlaton, or no lnear correlaton. Complete the table and fnd the correlaton coeffcent

More information

Joint Statistical Meetings - Biopharmaceutical Section

Joint Statistical Meetings - Biopharmaceutical Section Iteratve Ch-Square Test for Equvalence of Multple Treatment Groups Te-Hua Ng*, U.S. Food and Drug Admnstraton 1401 Rockvlle Pke, #200S, HFM-217, Rockvlle, MD 20852-1448 Key Words: Equvalence Testng; Actve

More information

1-FACTOR ANOVA (MOTIVATION) [DEVORE 10.1]

1-FACTOR ANOVA (MOTIVATION) [DEVORE 10.1] 1-FACTOR ANOVA (MOTIVATION) [DEVORE 10.1] Hgh varance between groups Low varance wthn groups s 2 between/s 2 wthn 1 Factor A clearly has a sgnfcant effect!! Low varance between groups Hgh varance wthn

More information

EPR Paradox and the Physical Meaning of an Experiment in Quantum Mechanics. Vesselin C. Noninski

EPR Paradox and the Physical Meaning of an Experiment in Quantum Mechanics. Vesselin C. Noninski EPR Paradox and the Physcal Meanng of an Experment n Quantum Mechancs Vesseln C Nonnsk vesselnnonnsk@verzonnet Abstract It s shown that there s one purely determnstc outcome when measurement s made on

More information

MD. LUTFOR RAHMAN 1 AND KALIPADA SEN 2 Abstract

MD. LUTFOR RAHMAN 1 AND KALIPADA SEN 2 Abstract ISSN 058-71 Bangladesh J. Agrl. Res. 34(3) : 395-401, September 009 PROBLEMS OF USUAL EIGHTED ANALYSIS OF VARIANCE (ANOVA) IN RANDOMIZED BLOCK DESIGN (RBD) ITH MORE THAN ONE OBSERVATIONS PER CELL HEN ERROR

More information

Chapter 5: Hypothesis Tests, Confidence Intervals & Gauss-Markov Result

Chapter 5: Hypothesis Tests, Confidence Intervals & Gauss-Markov Result Chapter 5: Hypothess Tests, Confdence Intervals & Gauss-Markov Result 1-1 Outlne 1. The standard error of 2. Hypothess tests concernng β 1 3. Confdence ntervals for β 1 4. Regresson when X s bnary 5. Heteroskedastcty

More information

Professor Chris Murray. Midterm Exam

Professor Chris Murray. Midterm Exam Econ 7 Econometrcs Sprng 4 Professor Chrs Murray McElhnney D cjmurray@uh.edu Mdterm Exam Wrte your answers on one sde of the blank whte paper that I have gven you.. Do not wrte your answers on ths exam.

More information

Lecture 10 Support Vector Machines II

Lecture 10 Support Vector Machines II Lecture 10 Support Vector Machnes II 22 February 2016 Taylor B. Arnold Yale Statstcs STAT 365/665 1/28 Notes: Problem 3 s posted and due ths upcomng Frday There was an early bug n the fake-test data; fxed

More information

Lecture 9: Linear regression: centering, hypothesis testing, multiple covariates, and confounding

Lecture 9: Linear regression: centering, hypothesis testing, multiple covariates, and confounding Recall: man dea of lnear regresson Lecture 9: Lnear regresson: centerng, hypothess testng, multple covarates, and confoundng Sandy Eckel seckel@jhsph.edu 6 May 8 Lnear regresson can be used to study an

More information

Modeling and Simulation NETW 707

Modeling and Simulation NETW 707 Modelng and Smulaton NETW 707 Lecture 5 Tests for Random Numbers Course Instructor: Dr.-Ing. Magge Mashaly magge.ezzat@guc.edu.eg C3.220 1 Propertes of Random Numbers Random Number Generators (RNGs) must

More information

Outline. EEC 686/785 Modeling & Performance Evaluation of Computer Systems. Lecture k r Factorial Designs with Replication

Outline. EEC 686/785 Modeling & Performance Evaluation of Computer Systems. Lecture k r Factorial Designs with Replication EEC 66/75 Modelng & Performance Evaluaton of Computer Systems Lecture 3 Department of Electrcal and Computer Engneerng Cleveland State Unversty wenbng@eee.org (based on Dr. Ra Jan s lecture notes) Outlne

More information

See Book Chapter 11 2 nd Edition (Chapter 10 1 st Edition)

See Book Chapter 11 2 nd Edition (Chapter 10 1 st Edition) Count Data Models See Book Chapter 11 2 nd Edton (Chapter 10 1 st Edton) Count data consst of non-negatve nteger values Examples: number of drver route changes per week, the number of trp departure changes

More information

Lecture 9: Linear regression: centering, hypothesis testing, multiple covariates, and confounding

Lecture 9: Linear regression: centering, hypothesis testing, multiple covariates, and confounding Lecture 9: Lnear regresson: centerng, hypothess testng, multple covarates, and confoundng Sandy Eckel seckel@jhsph.edu 6 May 008 Recall: man dea of lnear regresson Lnear regresson can be used to study

More information

Factor models with many assets: strong factors, weak factors, and the two-pass procedure

Factor models with many assets: strong factors, weak factors, and the two-pass procedure Factor models wth many assets: strong factors, weak factors, and the two-pass procedure Stanslav Anatolyev 1 Anna Mkusheva 2 1 CERGE-EI and NES 2 MIT December 2017 Stanslav Anatolyev and Anna Mkusheva

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

STAT 3340 Assignment 1 solutions. 1. Find the equation of the line which passes through the points (1,1) and (4,5).

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

More information

Biostatistics 360 F&t Tests and Intervals in Regression 1

Biostatistics 360 F&t Tests and Intervals in Regression 1 Bostatstcs 360 F&t Tests and Intervals n Regresson ORIGIN Model: Y = X + Corrected Sums of Squares: X X bar where: s the y ntercept of the regresson lne (translaton) s the slope of the regresson lne (scalng

More information

CHAPTER 6 GOODNESS OF FIT AND CONTINGENCY TABLE PREPARED BY: DR SITI ZANARIAH SATARI & FARAHANIM MISNI

CHAPTER 6 GOODNESS OF FIT AND CONTINGENCY TABLE PREPARED BY: DR SITI ZANARIAH SATARI & FARAHANIM MISNI CHAPTER 6 GOODNESS OF FIT AND CONTINGENCY TABLE Expected Outcomes Able to test the goodness of ft for categorcal data. Able to test whether the categorcal data ft to the certan dstrbuton such as Bnomal,

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