# Register now to access 7 million high quality study materials (What's Course Hero?) Course Hero is the premier provider of high quality online educational resources. With millions of study documents, online tutors, digital flashcards and free courseware, Course Hero is helping students learn more efficiently and effectively. Whether you're interested in exploring new subjects or mastering key topics for your next exam, Course Hero has the tools you need to achieve your goals.

2 Pages

### HW2

Course: STA 244, Spring 2008
School: Duke
Rating:

Word Count: 539

#### Document Preview

2 Due STA244 1/22/2001 Homework 1/29/2001 1. (From CB 11.40) Consider the standard simple linear model with normal errors that has been re-parameterized as Yt = Y + t + where t = (X X) so that Y = Y and are independent. Extend Sches procedure e to construct simultaneous prediction intervals for predicting future Y at t for all t. That is nd a constant M such that P or Y (Y + t) s 1+ 1 n + t2...

Register Now

#### Unformatted Document Excerpt

Coursehero >> North Carolina >> Duke >> STA 244

Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
2 Due STA244 1/22/2001 Homework 1/29/2001 1. (From CB 11.40) Consider the standard simple linear model with normal errors that has been re-parameterized as Yt = Y + t + where t = (X X) so that Y = Y and are independent. Extend Sches procedure e to construct simultaneous prediction intervals for predicting future Y at t for all t. That is nd a constant M such that P or Y (Y + t) s 1+ 1 n + t2 SXX M t = 1 2 P t max Y (Y + t) s2 (1 + 1 n + ) SXX t2 2 M = 1 (a) Show that if a,b,c, and d are constants with c > 0 and d > 0 that max t a 2 b2 (a + bt)2 = + c + dt2 c d (b) Use the result in (a) to nd the distribution of max t Y (Y + t) s2 (1 + 1 n 2 + t2 ) SXX Hint: rewrite Y = Y + t + , where N (0, 2 ). (c) Use this to nd a value of M . If the distribution does not exist in closed form, use moment matching to show how to nd a value of M as an approximation. (See example 7.2.3 in Casella and Berger for moment matching) There may be an error in the statement/setup of the problem in Casella and Berger 11.40 (c) - be careful in your proof ! 2. The data in the le oldfaith (download from the course calendar) gives information about eruptions of the Old Faithful Geyser in Yellowstone National Park during October 1980. Variables are duration in seconds of the current eruption and interval, the time in minutes to the next eruption. The data were collected by volunteers, and except for the period from midnight and 6 AM, this is a complete record of eruptions for that month. As Old Faithful is an important tourist attraction, the service park would like to use these data to obtain a prediction equation for the time to the next eruption using the length of the current eruption. (a) Use simple linear regression to obtain a prediction equation for interval using duration. You may use any software package that you would like. Briey summarize your results in a way that might be useful for the nontechnical personnel who sta the visitors center. Include (with explanation) the following in your typed summary (max of 1 page double spaced with 12 point font): (b) Construct a 95% condence interval for E(interval | duration = 250 secs). Construct a 95% prediction interval for interval given duration = 250 secs. Explain to the sta when it would be appropriate to use each of these. (c) Estimate the 0.90 quantile of the conditional distribution of future intervals between eruptions for durations of 250 secs, assuming a normal population. (d) Suppose the park service would like to calculate prediction intervals for all possible time points in the range of the observed duration and have a computer display that automatically displays a prediction interval for the time until the next eruption. Find the value of M using the results for the Sche intervals e from problem (1). Suppose a person just arrives at the end of an eruption that lasted 250 seconds. Give the two prediction intervals (point-wise, and Sche). e Which of the two prediction intervals is best from the visitors point of view? the park services point of view? 3. Problem 7.5 in CW (do not turn in) 4. Problem 7.6 in CW 5. Problem 7.9 in CW 6. Problem 7.10 in CW
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.

Below is a small sample set of documents:

Duke - STA - 242
Week 5, Lec. 1, 2/5/02Week 5, Lec. 1, 2/5/02Regression Parameter EstimatesResiduals: Min 1Q Median 3Q Max -0.339 -0.1071 -0.01023 0.1361 0.3588 Coefficients: (Intercept) log(time) Value Std. Error 6.8115 0.1113 -0.5350 0.0609 t value Pr(&gt;|t|) 6
Duke - STA - 242
W X b i C2f6&quot;egvCvrdvh6iCvY2yvtrr2vCvyr0egvYCgEl2lv ie b u b u b u x w q i x x e b u b n q i ie e e e X X be u b s i u s u b b u v V Cgvvd&amp;v2!add6Y{ V|Xf CYElevCbhCvuYxfwvrCgr)vCy2v02)V|V 2egv26\$vEvd b b b
Duke - STA - 103
( {~ m { zyG}~ 0 G ~ t 0y k m| { 0~ p~m { 0y k { Y ym d dy ~ k { ym d k 2X B T4 RXaa22 D h 0c`C0bbSSIpap4h D2 B q { T4 2 B4 h 2 8 T4 2 22 D 2R Ta H F h h H 2 B4 2 42 1 rW) }0y YbICwD#Q`CSSYSPpHpD`AICQ8 k 5@8 ( Y}pm Y0Y
Duke - STA - 244
APMAM APSAB APSLAKE OPBPC OPRC OPSLAKE Y Year 9.13 3.58 3.91 4.1 7.43 6.47 54235 1948 5.28 4.82 5.2 7.55 11.11 10.26 67567 1949 4.2 3.77 3.67 9.52 12.2 11.35 66161 1950 4.6 4.46 3.93 11.14 15.15 11.13 68094 1951 7.15 4.99 4.88 16.34 20.05 22.81
Duke - STA - 244
BigMac Bread BusFare EngSal EngTax Service TeachSal TeachTax VacDays WorkHrs 31 9 1.27 44.3 44.1 280 21.8 28.2 31.9 1714 33 9 0.27 19.4 23.7 170 9.4 14.8 23.5 1792 98 23 0.09 15.4 20.3 100 2.2 4.3 17.4 2152 131 27 0.09 4.7 37.6 70 1.1 11.7 30.6 2
Duke - STA - 244
Exotic Sire Total Trt 9 1 9 1 5 1 8 2 5 1 8 3 6 1 8 4 3 2 9 1 0 2 9 2 5 2 9 3 5 2 8 4 5 3 8 1 5 3 8 2 6 3 9 3 5 3 6 4 7 4 7 1 7 4 8 2 3 4 6 3 4 4 8 4 8 5 9 1 4 5 8 2 4 5 7 3 6 5 9 4 5 6 9 1 5 6 9 2 4 6 9 3 2 6 7 4 8 7 9 1 4
Duke - STA - 244
Height Length Type 75 502 0 80 522 0 68 425 0 64 344 0 83 407 0 80 451 0 70 551 0 76 530 0 74 547 0 100 519 1 75 225 1 52 300 1 62 418 1 68 409 1 86 425 1 57 370 1 82 506 1 82 506 1 88 295 1 55 273 1 67 415 1 45 182 1 103 530 1
Duke - STA - 244
D F S W 7.2 0 0 10.404 8.2 0 0 18.161 10.3 0 0 25.778 10.1 0 0 20.511 10.7 0 0 21.87 13.3 0 0 47.186 5.1 1 0 4.447 7.2 1 0 8.682 10.2 1 0 19.511 11.3 1 0 37.682 12.6 1 0 25.775 17.1 1 0 67.363 5.1 0 1 4.02 6.5 0 1 7.504 8.4 0 1 13.391
Duke - STA - 244
BodyWt Dose LiverWt y 176 0.88 6.5 0.42 176 0.88 9.5 0.25 190 1 9 0.56 176 0.88 8.9 0.23 200 1 7.2 0.23 167 0.83 8.9 0.32 188 0.94 8 0.37 195 0.98 10 0.41 176 0.88 8 0.33 165 0.84 7.9 0.38 158 0.8 6.9 0.27 148 0.74 7.3 0.36 149 0.75 5.2
Duke - STA - 244
Age Score 15 95 26 71 10 83 9 91 15 102 20 87 18 93 11 100 8 104 20 94 7 113 9 96 10 83 11 84 11 102 10 100 12 105 42 57 17 121 11 86 10 100
Duke - STA - 102
smoke disease sex 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Duke - STA - 216
CASE STUDY: Bayesian Incidence Analyses from Cross-Sectional Data with Multiple Markers of Disease Severity Outline: 1. NIEHS Uterine Fibroid Study Design of Study Scientific Questions Difficulties 2. General Problem and Earlier Approaches 3. Baye
Duke - STA - 216
Discrete Time Survival Modelsj = P (Ti = j | Ti j, xi) = h(j + xi), where j is the discrete hazard, = (1, . . . , k ) are parameters characterizing the baseline hazard xi are time-independent covariates are regression coecients1Proportional
Duke - STA - 240
Fall 2003'\$1Fall 2003'Exploratory Data AnalysisNematodes 0\$2One-way ANOVA: Example X10.650 10.425 5.600 5.450s2.053 1.486 1.244 1.771How do nematodes (microscopic worms) affect plant growth? A botanist prepares 16 identical p
Duke - STA - 240
www.stat.duke.edu/courses/Fall02/sta240/quiz4/quiz4data.htmlQuiz 4: Lab Exercise, 11/11/02 I will follow the NSEES Honor Code.Name:_ Signature:_1.[3 points] Circle the terms that describe the meadowfoam study: (a) (b) (c) (d) (e) completely r
Duke - STA - 278
STA 278/BGT 208 GENE EXPRESSION ANALYSISStatistical Models, Methods &amp; Computation Mike West Institute of Statistics &amp; Decision Sciences www.isds.duke.edu Computational &amp; Applied Genomics Program www.cagp.duke.eduSTA 278/BGT 208January 12, 2004
Duke - STA - 113
STA 113 Spring 2004 I. H. DinwoodieAssignment 1Due January 29 1. Consider the data in arsenic.txt explained in Arsenic.txt. a. Do a scatter plot of the amount of arsenic in the drinking water in ppm versus theamount in a toenail.b. Find
Duke - STA - 113
0 49 376 726 736 990 2008 2574 2718 2857 2920 3423 3678 3739 4465 4879 5056 5217 6027
Duke - STA - 205
Midterm Examination #1STA 205: Probability and Measure Theory Thursday, 2004 Feb 16, 2:20-3:35 pmThis is a closed-book examination. You may use a single one-sided sheet of prepared notes, if you wish, but you may not share materials. You may use a
Duke - STA - 205
Final ExaminationSTA 205: Probability and Measure Theory Due Monday, 2002 Apr 29, 5:00 pmThis is an open-book take-home examination. You must do your own work- collaboration is not permitted. If a questions seems ambiguous or confusing please ask
Duke - STA - 113
This is from the same paper as the etchratedata.txt file.The 490 measurements in etchratedata.txt were used tocompute a measure of nonuniformity for each of the ten wafers. The nonuniformity is actually the standard deviation of the 49etch ra
Duke - CH - 113
&quot;x1&quot;&quot;x2&quot;&quot;x3&quot;&quot;x4&quot;&quot;y&quot;8410011.42418072.27418014.610712054.97418054.67718014.771314014.65416074.54714034.85110071.481014034.72410031.641018034.56712074.7101318034.84101605
Duke - CH - 113
&quot;C1&quot;&quot;C2&quot;&quot;C3&quot;1.2&quot;pH 3&quot;&quot;Diseased&quot;1.4&quot;pH 3&quot;&quot;Diseased&quot;1&quot;pH 3&quot;&quot;Diseased&quot;1.2&quot;pH 3&quot;&quot;Diseased&quot;1.4&quot;pH 3&quot;&quot;Diseased&quot;.8&quot;pH 5.5&quot;&quot;Diseased&quot;.6&quot;pH 5.5&quot;&quot;Diseased&quot;.8&quot;pH 5.5&quot;&quot;Diseased&quot;1&quot;pH 5.5&quot;&quot;Diseased&quot;.8&quot;pH 5.5&quot;&quot;Diseased&quot;1&quot;pH 7&quot;&quot;Dis
Duke - CH - 113
&quot;response&quot;&quot;type&quot;&quot;subject&quot;12111022733744815926837748919152114321443111411251136124711181329123113421313102483511461217828103910411212923934745101611
Duke - CH - 113
&quot;Obs:&quot;&quot;x:&quot;&quot;y:&quot;1.41.022.421.213.48.884.51.985.571.526.61.837.71.58.751.89.751.7410.781.6311.84212.952.813.992.48141.032.47151.123.05161.153.18171.23.76181.253.68191.253.82201.283.21211.3
Duke - CH - 113
&quot;Linoleic&quot;&quot;Kerosene&quot;&quot;Antiox&quot;&quot;Betacaro&quot;303010.7303010.63303018.41.01340405.049303010.713.183010.120405.04204015.006540205.202303010.6330301.59.04402015.132404015.15303010.73046.8210.34630
Duke - CH - 113
Duke - CH - 113
&quot;stiffness&quot;&quot;plate lengths&quot;309.24409.543114326.54316.84349.84309.74402.16347.263616404.563316348.96381.76392.48366.283518357.18409.98367.383828346.710452.910461.410433.110410.610384.210362.6104
Duke - CH - 113
&quot;temp&quot;&quot;removal%&quot;7.6898.096.5198.256.4397.825.4897.826.5797.8210.2297.9315.6998.3816.7798.8917.1398.9617.6398.916.7298.6815.4598.6912.0698.5111.4498.0910.1798.259.6498.368.5598.277.57986.9498.098.3298.2510.59
Duke - CH - 113
&quot;C1&quot;212401320533132470230421311341232284513150232106421603336123
Duke - CH - 113
&quot;c1&quot;20.919.620.420.320.820.620.520.419.919.819.520.216.518.318.719.6202019.519.619.118.818.317.617.217.818.7191918.618.81918.518.317.516.91717.818.118.818.918.919.118.818.417.81716.817.918.41919.41
Duke - STA - 113
w 88y #zu XQy u w w f8|y zu i a gb i a i j ap r i g r c i r e a n r s tQeA5rqptefet\$eAbIA`Xqp\$ilm8 y e A8q|w q v u y w y 2 w G8G u v|w o8w u s p w e q|X2w2f|w y y y y w y G8G u VG8G u GQtG u G\$G u Ev|w
Duke - STA - 113
p &quot; 8 &quot; &quot; 8 &quot; 1 &quot; U54BA05ih 547#25&amp; &quot; T &amp;U T(0S R)0@&amp;PIHGF )(E&amp;&quot; \$#! D D Q 8 ' % &quot; g F d c F F W a72 2a f@8 &amp;6eR!b2 2a !0`Y&amp;00`Y XV U) 547#25&amp; &quot; 1 &quot; &quot; T &amp;U T(0S R)0@&amp;PIHGF )(E&amp;&quot; \$#! D D Q
Duke - STA - 113
jhi Eu0ihf Q VIr60 ERqCvv U S p I hh p p t U p he i hU Q p i h w Qe h Q i h q h p w s U U p h q p i VIT@uQ (Ro R(h w@9uT(x)40vu44t V(h VI | Q W Q h Q p q p i Q h t W p j pU Q U p I tI @p xt mt' mVxh I4mu Vi k 'x6Sw4e VIrm H V hq Q h q
Duke - STA - 244
STA2441/08/2003Homework 1Due 1/15/2003.Please provide concise, neatly written or typed solutions. All work should be your own and not copied from other texts or sources. Do feel free to discuss questions with me, the TA, others in class, or po
Duke - STA - 113
Students0510152025Range: 69.38% - 96.08%, 84 Students Median = 82.07, Quantiles = [76.36, 86.09] Mean = 81.4, Std Dev = 6.255060708090100Course Averages for STA113
Duke - STA - 205
z V g # &quot; 4 w a F &quot; \$ &amp; B \$ g 0 \$ Q # rSw P6B SiGo1%S1s6E&quot; D E%GEU%651%S1\$ i # Q D \$ # &quot;4 &amp; 2 # 0F &amp; B B # &quot; &amp; B # W B c i # Q w i B W Q # &quot; i B # W B i \$4 B \$ &quot; 0 ( &quot; Q B i4 # &quot;4 \$ # B &amp; @ B B y &amp; \$ B &quot; i CS'S%bU3i G%kfC86EqS
Duke - STA - 103
The data come from http:/www.econstats.com/eq_d1.htm. After the date and day of week they are open high low close return(%)
Duke - STA - 103
The wins (1) and losses (0) of the Philadelphia Phillies in the 2001 season.
Duke - STA - 103
Review of key points about estimators Populations can be at least partially described by population parameters Population parameters include: mean, proportion, variance, etc. Because populations are often very large (maybe innite, like the output
Duke - STA - 216
Frequentist Logistic Regression &amp; ExtensionsReturning to the DDE &amp; Pre-Term Birth Example, recall: yi = 1 for pre-term birth &amp; yi = 0 otherwise di = dose of DDE for woman i zi = vector of covariatesLogistic Regression: logitPr(yi = 1 | xi) =
Duke - STA - 101
21.0 Paired Dierences Answer Questions Paired Dierences Signicance Tests121.1 Paired DierencesExample 1: You want to show that men spend less on Valentines Day than women. You could draw some random men and some random women, ask them what th
Duke - STA - 290
Introduction to Statistical Data AnalysisGiven a new set of data to analyze, how should we proceed? Faced with uncertainty, statistics provides answers to questions and addresses uncertainties p. 1/15Model BuildingWhere should we start? 1. What
Duke - STA - 104
Midterm Examination # 2Mth 135 = Sta 104 Thursday, 2000 November 16, 2:15 3:30 pmIf you dont understand something in one of the questions, please 1 ask me. You may use your own one-sided, 8 2 11 sheet of notes and calculator, but do not share m
Duke - STA - 113
3.14 (d) check whether3.37 P (X = k) = p(k) = 1=6, where k = 1; 2; :; 6. Calculate E(1=X). If it bigger than (1=3:5), gamble; otherwise, accept the guaranteed amount. s 3.48 Let X = number of drivers who will come to a complete stop among 20 random
Duke - STA - 216
Extending GLMs for Correlated DataGLMs assume that the observations y1, . . . , yn are independent draws from an exponential family distribution However, in many applications, there may be dependency in the outcome data For example, in longitudinal
Duke - STA - 216
Standard Errors &amp; Confidence Intervals - N (0, I()-1), where 2l(, ; y) I() = ij=asyWe can obtain asymptotic 100(1 - )% confidence intervals for j using: j Z1-/2se(j ) j 1.96se(j ) for = 0.05, where Zp denotes the pth percentile of the N
Duke - STA - 104
Chisquare(2) densitydensity0.00.20.401020 x3040Chisquare(18) density (sum of 9 chisquare(2) random variables)0.00 0.02 0.04 0.06density01020 x3040Normal(18,36) density0.06 density 0.00 0.02 0.0401020 Central
Duke - STA - 104
105.860106.200105.010105.750104.590104.100101.890103.960103.000106.990106.860104.950104.130100.36099.950101.490100.35098.00096.59096.47093.34096.40096.00093.40090.50094.80094.45091.30090.00091.72092.71093.77096.95097.
Duke - STA - 122
Simple Linear RegressionMarch 16, 2009Reading Lee Ch 6Simple Linear Regression p.1/12BodyFat DataPercent Bodyfat01020304080100120140Circumference of Abdomin (cm)Simple Linear Regression p.2/12Body Fat ExampleEstimat
Duke - STA - 122
STA122 Lab Session # 5Course Instructor: Prof. Merlise Clyde Teaching Assistant: Debdeep Pati (dp55@stat.duke.edu) February 16, 20091Automatic HPD interval calculation using the beta-binomial exampleLet Y bin(n, p). We assume Beta(a, b) prior
Duke - STA - 122
STA 122 ASSIGNMENT 2Due February 23, 2009 1. Chapter 3 of Lee, exercises 3, 4, 5, 7, 8, 9, 12. For problem 7, use the reference prior. For problems that require nding an HPD region use the R code for the beta distribution in HPD.R and using coda pac
Duke - STA - 122
Duke - STA - 122
OR White Mucinous Invasives - all sites utilizedSNP 8073498 has P(OR &gt; 1 | data) = .96 but is based on 2 sites -suggestive of an effect. 95% intervals do include 1. &gt; OR.wmi[1][1]\$snp[1] &quot;rs9894946n&quot;[1]\$OR 50% 2.5% 97.
Duke - STA - 205
Sta 205 : Homework 1Due : January 21, 2009I. Fields and - fields. (A) For a three-point outcome set = {a, b, c} and C := {a} , enumerate the class of all -fields F on that contain C, i.e., satisfy C F . Also find (C). (B) For each integer n
Duke - STA - 104
MTH135/STA104: ProbabilityHomework # 7 Due: Tuesday, Nov 1, 2005 Prof. Robert Wolpert1. For some number c &gt; 0 the random variable X has a continuous probability distribution with density function f (x) = c x, 0&lt;x&lt;4(so f (x) = 0 for x (0, 4); th
Duke - STA - 104
MTH135/STA104: ProbabilityHomework # 5 Due: Tuesday, Oct 4, 2005 Prof. Robert Wolpert1. setLet X1 and X2 be the numbers on two independent rolls of a fair die; Y1 min(X1 , X2 ) Y2 max(X1 , X2 )a) Give the joint distribution of X1 and X2 1 Th
Duke - STA - 290
Bayesian Inference in a Normal PopulationSeptember 22, 2005Casella &amp; Berger Chapter 7, Gelman, Carlin, Stern, Rubin Sec 2.6, 2.8, Chapter 3.Bayesian Inference in a Normal Population p. 1/15Normal ModelIID observations Y = (Y1 , Y2 , . . . Yn
Duke - STA - 113
The simple linear regression model says that the n data points satisfy the following equation yi = 0 + 1 xi + i , i = 1, 2, . . . , n (1)where 0 is the intercept of the regression line, 1 is the slope and i is the error for the i-th data point. Usi
Duke - STA - 104
Emacs Speaks Statistics (ESS): A multi-platform, multi-package intelligent environment for statistical analysisA.J. Rossini Richard M. Heiberger Martin M chler a Rodney A. Sparapani Kurt Hornik Date: 2002/03/01Revision: 1.255Abstract Computer pr
Duke - STA - 205
Sta 205 : Home Work #5Due : February 22, 2006 I. Expectation. (A) Consider the triangle with vertices (-1, 0), (1, 0), (0, 1) and suppose (X1 , X2 ) is a random vector uniformly distributed with in this triangle. Compute E(X1 + X2 ). (B) Let (0, 1],