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464 CHAPTER 9 SIMPLE LINEAR REGRESSION AND CORRELATION REVIEW QUESTIONS AND EXERCISES 1. What are the assumptions underlying simple linear regression analysis when one of the objectives is to make inferences about the population from which the sample data were drawn? 2. Why is the regression equation called the least-squares equation? 3. Explain the meaning of ^b 0 in the sample regression equation. 4. Explain the meaning of ^b 1 in the sample regression equation. 5. Explain the following terms: (a) Total sum of squares (b) Explained sum of squares (c) Unexplained sum of squares 6. Explain the meaning of and the method of computing the coefficient of determination. 7. What is the function of the analysis of variance in regression analysis? 8. Describe three ways in which one may test the null hypothesis that ^b 1 ¼ 0. 9. For what two purposes can a regression equation be used? 10. What are the assumptions underlying simple correlation analysis when inference is an objective? 11. What is meant by the unit of association in regression and correlation analysis? 12. What are the possible explanations for a significant sample correlation coefficient? 13. Explain why it is risky to use a sample regression equation to predict or to estimate outside the range of values of the independent variable represented in the sample. 14. Describe a situation in your particular area of interest where simple regression analysis would be useful. Use real or realistic data and do a complete regression analysis. 15. Describe a situation in your particular area of interest where simple correlation analysis would be useful. Use real or realistic data and do a complete correlation analysis. In each of the following exercises, carry out the required analysis and test hypotheses at the indicated significance levels. Compute the p value for each test. 16. A study by Scrogin et al. (A-11) was designed to assess the effects of concurrent manipulations of dietary NaCl and calcium on blood pressure as well as blood pressure and catecholamine responses to stress. Subjects were salt-sensitive, spontaneously hypertensive male rats. Among the analyses performed by the investigators was a correlation between baseline blood pressure and plasma epinephrine concentration (E). The following data on these two variables were collected. Let a ¼ :01. BP PlasmaE BP PlasmaE 163.90 248.00 143.20 179.00 195.15 339.20 166.00 160.40 170.20 193.20 160.40 263.50 171.10 307.20 170.90 184.70 (Continued )
REVIEW QUESTIONS AND EXERCISES 465 BP PlasmaE BP PlasmaE 148.60 80.80 150.90 227.50 195.70 550.00 159.60 92.35 151.00 70.00 141.60 139.35 166.20 66.00 160.10 173.80 177.80 120.00 166.40 224.80 165.10 281.60 162.00 183.60 174.70 296.70 214.20 441.60 164.30 217.30 179.70 612.80 152.50 88.00 178.10 401.60 202.30 268.00 198.30 132.00 171.70 265.50 Source: Data provided courtesy of Karie E. Scrogin. 17. Dean Parmalee (A-12) wished to know if the year-end grades assigned to Wright State University Medical School students are predictive of their second-year board scores. The following table shows, for 89 students, the year-end score (AVG, in percent of 100) and the score on the second-year medical board examination (BOARD). AVG BOARD AVG BOARD AVG BOARD 95.73 257 85.91 208 82.01 196 94.03 256 85.81 210 81.86 179 91.51 242 85.35 212 81.70 207 91.49 223 85.30 225 81.65 202 91.13 241 85.27 203 81.51 230 90.88 234 85.05 214 81.07 200 90.83 226 84.58 176 80.95 200 90.60 236 84.51 196 80.92 160 90.30 250 84.51 207 80.84 205 90.29 226 84.42 207 80.77 194 89.93 233 84.34 211 80.72 196 89.83 241 84.34 202 80.69 171 89.65 234 84.13 229 80.58 201 89.47 231 84.13 202 80.57 177 88.87 228 84.09 184 80.10 192 88.80 229 83.98 206 79.38 187 88.66 235 83.93 202 78.75 161 88.55 216 83.92 176 78.32 172 88.43 207 83.73 204 78.17 163 88.34 224 83.47 208 77.39 166 87.95 237 83.27 211 76.30 170 87.79 213 83.13 196 75.85 159 87.01 215 83.05 203 75.60 154 86.86 187 83.02 188 75.16 169 86.85 204 82.82 169 74.85 159 86.84 219 82.78 205 74.66 167 (Continued )
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TENTH EDITION BIOSTATISTICS A Found
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VP & EXECUTIVE PUBLISHER: ACQUISITI
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PREFACE This 10th edition of Biosta
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PREFACE ix SUPPLEMENTS Instructor
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BRIEF CONTENTS 1 INTRODUCTION TO BI
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xiv CONTENTS 6.3 The t Distribution
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CHAPTER1 INTRODUCTION TO BIOSTATIST
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1.2 SOME BASIC CONCEPTS 3 Sources o
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1.3 MEASUREMENT AND MEASUREMENT SCA
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1.4 SAMPLING AND STATISTICAL INFERE
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1.5 THE SCIENTIFIC METHOD AND THE D
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1.6 COMPUTERS AND BIOSTATISTICAL AN
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REVIEW QUESTIONS AND EXERCISES 17 a
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CHAPTER2 DESCRIPTIVE STATISTICS CHA
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2.2 THE ORDERED ARRAY 21 TABLE 2.2.
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2.3 GROUPED DATA: THE FREQUENCY DIS
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EXERCISES 31 3 ¼ an abundance of s
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EXERCISES 33 25.21 30.49 27.38 36.4
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EXERCISES 35 2.3.7 In a study of ph
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EXERCISES 37 0.6870 0.6900 0.6910 0
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2.4 DESCRIPTIVE STATISTICS: MEASURE
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EXERCISES 53 2.5.1 Porcellini et al
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SUMMARY OF FORMULAS FOR CHAPTER 2 5
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REVIEW QUESTIONS AND EXERCISES 57 R
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REVIEW QUESTIONS AND EXERCISES 59 1
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REFERENCES 63 DRINK TOUNCES TGRAMS
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CHAPTER3 SOME BASIC PROBABILITY CON
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3.2 TWO VIEWS OF PROBABILITY: OBJEC
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3.4 CALCULATING THE PROBABILITY OF
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EXERCISES 77 (d) If we pick a subje
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3.5 BAYES’ THEOREM, SCREENING TES
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3.5 BAYES’ THEOREM, SCREENING TES
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EXERCISES 83 EXERCISES 3.5.1 A medi
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REVIEW QUESTIONS AND EXERCISES 87 (
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REVIEW QUESTIONS AND EXERCISES 89 i
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REFERENCES 91 Applications Referenc
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4.2 PROBABILITY DISTRIBUTIONS OF DI
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4.3 THE BINOMIAL DISTRIBUTION 99 TA
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4.3 THE BINOMIAL DISTRIBUTION 101 E
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4.3 THE BINOMIAL DISTRIBUTION 103 f
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EXAMPLE 4.3.4 According to a June 2
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EXERCISES 107 Data: C1: 0 1 2 3 4 5
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4.4 THE POISSON DISTRIBUTION 109 pr
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4.4 THE POISSON DISTRIBUTION 111 or
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4.5 CONTINUOUS PROBABILITY DISTRIBU
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4.5 CONTINUOUS PROBABILITY DISTRIBU
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4.6 THE NORMAL DISTRIBUTION 117 .68
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4.6 THE NORMAL DISTRIBUTION 119 σ
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4.6 THE NORMAL DISTRIBUTION 121 _ 2
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4.7 NORMAL DISTRIBUTION APPLICATION
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TableD,wefindthattheareatotheleftof
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EXERCISES 127 Data: C1:-3-2-10123 D
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SUMMARY OF FORMULAS FOR CHAPTER 4 S
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REVIEW QUESTIONS AND EXERCISES 131
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REFERENCES 133 REFERENCES Methodolo
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5.2 SAMPLING DISTRIBUTIONS 135 voca
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5.3 DISTRIBUTION OF THE SAMPLE MEAN
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5.4 DISTRIBUTION OF THE DIFFERENCE
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EXERCISES 149 FIGURE 5.4.2 Sampling
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5.5 DISTRIBUTION OF THE SAMPLE PROP
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EXERCISES 153 51 percent had adequa
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CHAPTER6 ESTIMATION CHAPTER OVERVIE
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6.1 INTRODUCTION 163 We will find t
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6.2 CONFIDENCE INTERVAL FOR A POPUL
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6.3 THE t DISTRIBUTION 171 someone
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6.3 THE t DISTRIBUTION 173 Normal d
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EXERCISES 175 Yes Population normal
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6.4 CONFIDENCE INTERVAL FOR THE DIF
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EXERCISES 183 EXERCISES R Code: > t
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6.7 DETERMINATION OF SAMPLE SIZE FO
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6.8 DETERMINATION OF SAMPLE SIZE FO
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6.9 CONFIDENCE INTERVAL FOR THE VAR
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6.9 CONFIDENCE INTERVAL FOR THE VAR
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EXERCISES 197 x 2 1 ða=2Þ ¼ 14:4
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6.10 CONFIDENCE INTERVAL FOR THE RA
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6.10 CONFIDENCE INTERVAL FOR THE RA
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REFERENCES 211 3. W. V. BEHRENS,
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REFERENCES 213 A-30. ELENI KOUSTA,
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7.1 INTRODUCTION 215 7.1 INTRODUCTI
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7.1 INTRODUCTION 217 question: Can
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7.1 INTRODUCTION 219 DEFINITION The
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7.1 INTRODUCTION 221 Evaluate data
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7.2 HYPOTHESIS TESTING: A SINGLE PO
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EXERCISES 233 Dialog box: Session c
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EXERCISES 235 7.2.10 Following a we
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7.3 HYPOTHESIS TESTING: THE DIFFERE
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EXAMPLE 7.3.2 The purpose of a stud
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EXERCISES 245 The SAS System The TT
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EXERCISES 247 Primary Hypertensive
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7.4 PAIRED COMPARISONS 249 7.3.10 R
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7.4 PAIRED COMPARISONS 251 where d
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7.4 PAIRED COMPARISONS 253 a = .05
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EXERCISES 255 7.4.1 Ellen Davis Jon
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EXERCISES 263 MINITAB Output Test a
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7.8 HYPOTHESIS TESTING: THE RATIO O
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7.8 HYPOTHESIS TESTING: THE RATIO O
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EXERCISES 271 EXERCISES In the foll
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7.9 THE TYPE II ERROR AND THE POWER
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7.9 THE TYPE II ERROR AND THE POWER
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7.10 DETERMINING SAMPLE SIZE TO CON
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EXERCISES 279 We set the right-hand
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REFERENCES 301 A-17. JOHN S. MORLEY
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REFERENCES 303 A-56. LUIGI BENINI,
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8.1 INTRODUCTION 305 8.1 INTRODUCTI
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8.1 INTRODUCTION 307 who received d
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8.2 THE COMPLETELY RANDOMIZED DESIG
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Dependent Variable: Selenium Tukey
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EXERCISES 329 Elbow Angle (Degrees)
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EXERCISES 331 Age Groups (Years) Ag
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EXERCISES 333 Group 1 Group 2 Group
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Objective The objective in using th
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8.3 THE RANDOMIZED COMPLETE BLOCK D
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EXERCISES 343 The SAS System Analys
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EXERCISES 345 group were randomly a
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8.4 THE REPEATED MEASURES DESIGN 34
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EXERCISES 357 Is there sufficient e
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8.5 THE FACTORIAL EXPERIMENT 359 In
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8.5 THE FACTORIAL EXPERIMENT 361 In
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8.5 THE FACTORIAL EXPERIMENT 363 Be
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8.5 THE FACTORIAL EXPERIMENT 365 TA
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8.5 THE FACTORIAL EXPERIMENT 367 Ro
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EXERCISES 369 The SAS System Analys
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EXERCISES 371 Physical Psychiatric
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8.6 SUMMARY 373 Percent Change in C
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REFERENCES 409 Applications Referen
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REFERENCES 411 Postmenopausal Women
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Page 433 and 434: 9.2 THE REGRESSION MODEL 415 some e
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Page 441 and 442: EXERCISES EXERCISES 423 The Least-S
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Page 473 and 474: EXERCISES 455 is employed. We first
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Page 477 and 478: 9.8 SOME PRECAUTIONS 459 X Y X Y 5.
Page 479 and 480: 9.9 SUMMARY 461 variance, which tes
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Page 485 and 486: REVIEW QUESTIONS AND EXERCISES 467
Page 505 and 506: REFERENCES 487 A-4. ROBERT B. PARKE
Page 507 and 508: CHAPTER10 MULTIPLE REGRESSION AND C
Page 509 and 510: Assumptions follows. 10.2 THE MULTI
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Page 515 and 516: EXERCISES 497 EXERCISES Obtain the
Page 517 and 518: EXERCISES 499 10.3.3 In a study of
Page 519 and 520: 10.4 EVALUATING THE MULTIPLE REGRES
Page 525 and 526: 10.5 USING THE MULTIPLE REGRESSION
Page 527 and 528: EXERCISES 509 and has an education
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10.6 THE MULTIPLE CORRELATION MODEL
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EXERCISES 521 HIV DNA Blood (Y) HIV
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SUMMARY OF FORMULAS FOR CHAPTER 10
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10.6.7 t statistic for testing hypo
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REFERENCES 537 4. Refer to the data
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CHAPTER11 REGRESSION ANALYSIS: SOME
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11.1 INTRODUCTION 541 TABLE 11.1.1
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11.2 QUALITATIVE INDEPENDENT VARIAB
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EXERCISES 557 11.2.1 For subjects u
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EXERCISES 559 11.2.4 Refer to Exerc
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11.3 VARIABLE SELECTION PROCEDURES
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11.3 VARIABLE SELECTION PROCEDURES
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EXERCISES 565 CGAGE CGINCOME CGDUR
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EXERCISES 567 11.3.2 Machiel Naeije
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11.4 LOGISTIC REGRESSION 569 REACTI
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11.4 LOGISTIC REGRESSION 571 betwee
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11.4 LOGISTIC REGRESSION 573 The LO
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11.4 LOGISTIC REGRESSION 575 Standa
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11.4 LOGISTIC REGRESSION 577 Parame
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11.4 LOGISTIC REGRESSION 579 Model
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EXERCISES EXERCISES 581 Further Rea
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REFERENCES 597 KNOW ¼ Knowledge. S
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REFERENCES 599 A-26. EITHNE MULLOYa
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12.1 INTRODUCTION 12.2 THE MATHEMAT
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12.2 THE MATHEMATICAL PROPERTIES OF
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12.3 TESTS OF GOODNESS-OF-FIT 605 W
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12.3 TESTS OF GOODNESS-OF-FIT 607 x
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12.3 TESTS OF GOODNESS-OF-FIT 609 9
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that the first expected frequency i
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12.3 TESTS OF GOODNESS-OF-FIT 613 T
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12.3 TESTS OF GOODNESS-OF-FIT 615 V
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EXERCISES 617 EXERCISES 12.3.1 The
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12.4 TESTS OF INDEPENDENCE 619 12.3
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Observed Versus Expected Frequencie
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12.4 TESTS OF INDEPENDENCE 623 Comp
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12.4 TESTS OF INDEPENDENCE 625 Note
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12.4 TESTS OF INDEPENDENCE 627 9. C
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EXERCISES 629 Performed Baseline Te
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12.5 TESTS OF HOMOGENEITY 631 TABLE
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12.5 TESTS OF HOMOGENEITY 633 8. St
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EXERCISES 635 12.5.2 Coughlin et al
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Hypotheses alternatives. 12.6 THE F
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12.6 THE FISHER EXACT TEST 639 TABL
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12.7 RELATIVE RISK, ODDS RATIO, AND
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EXERCISES 653 Smoking_status * Obse
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12.8 SUMMARY 655 collected data on
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REFERENCES 667 12. R. LATSCHA, “T
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REFERENCES 669 A-35. CRAIG R. COHEN
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13.1 INTRODUCTION 671 2. be able to
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13.3 THE SIGN TEST 673 13.3 THE SIG
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13.3 THE SIGN TEST 675 TABLE 13.3.2
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13.3 THE SIGN TEST 677 EXAMPLE 13.3
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13.3 THE SIGN TEST 679 one sample i
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13.4 THE WILCOXON SIGNED-RANK TEST
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13.4 THE WILCOXON SIGNED-RANK TEST
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13.5 THE MEDIAN TEST 687 TABLE 13.5
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EXAMPLE 13.6.1 A researcher designe
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13.6 THE MANN-WHITNEY TEST 693 to t
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13.6 THE MANN-WHITNEY TEST 695 Dial
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EXERCISES 697 deficit in Sprague-Da
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Assumptions the following: 1. The s
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13.7 THE KOLMOGOROV-SMIRNOV GOODNES
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EXERCISES 703 1.0 .9 Cumulative rel
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13.8 THE KRUSKAL-WALLIS ONE-WAY ANA
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13.8 THE KRUSKAL-WALLIS ONE-WAY ANA
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EXERCISES 709 Data: C1: 12.22 28.44
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EXERCISES 711 Improvement (Control)
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13.9 THE FRIEDMAN TWO-WAY ANALYSIS
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13.9 THE FRIEDMAN TWO-WAY ANALYSIS
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EXERCISES 717 Subject Area Student
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13.10 THE SPEARMAN RANK CORRELATION
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EXERCISES 725 Rank by Rank by Area
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13.11 NONPARAMETRIC REGRESSION ANAL
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13.11 NONPARAMETRIC REGRESSION ANAL
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REFERENCES 747 cardiac operations.
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REFERENCES 749 A-14. WENDY GANTT an
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14.2 TIME-TO-EVENT DATA AND CENSORI
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14.3 THE KAPLAN-MEIER PROCEDURE 757
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14.3 THE KAPLAN-MEIER PROCEDURE 759
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EXERCISES 761 1.0 .8 73% Low-grade
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14.4 COMPARING SURVIVAL CURVES 763
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14.4 COMPARING SURVIVAL CURVES 765
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EXERCISES 767 EXERCISES 14.4.1 If a
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14.5 COX REGRESSION: THE PROPORTION
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14.5 COX REGRESSION: THE PROPORTION
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REFERENCES 777 REFERENCES Methodolo
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A-2 APPENDIX STATISTICAL TABLES
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ANSWERS TO ODD-NUMBERED EXERCISES C
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ANSWERS TO ODD-NUMBERED EXERCISES A
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I-2 INDEX Confidence coefficient, 1
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I-4 INDEX Median test, 686-689 MINI
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I-6 INDEX SAS: and chi-square analy
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