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제1 장 통계학의 이해
1.1 통계학의 의미 ······························································································· 3 1.2 통계학의 분류 ······························································································· 4 1.3 모집단과 표본 ······························································································· 7 1.4 데이터 마이닝 ····························································································· 13 4차 산업혁명 _ 13 빅데이터 _ 15 비즈니스 분석론 _ 16 인공지능 _ 19 데이터 마이닝 _ 20 ▶ 연습문제 ········································································································· 22 제2 장 기술통계학Ⅰ:데이터의 정리 및 표현 2.1 데이터의 종류 ····························································································· 27 범주 데이터와 수치 데이터 _ 28 이산 데이터와 연속 데이터 _ 29 단변수 데이터와 다변수 데이터 _ 30 2.2 측정척도의 형태 ························································································· 32 명목척도 _ 32 서열척도 _ 33 구간척도 _ 34 비율척도 _ 34 2.3 도수분포표 ·································································································· 36 기본 개념 _ 36 도수분포표의 그래프 _ 37 2.4 범주 데이터의 정리 ···················································································· 37 도수분포표 _ 37 도수분포표의 그래프 _ 40 2.5 수치 데이터의 정리:이산 데이터 ····························································· 45 도수분포표 _ 45 도수분포표의 그래프 _ 46 2.6 수치 데이터의 정리:연속 데이터 ····························································· 47 도수분포표의 그래프 _ 50 2.7 EXCEL 활용 ································································································ 53 ▶ 연습문제 ········································································································· 64 제3장 기술통계학Ⅱ:요약통계량 3.1 중심경향의 측정치 ······················································································ 73 산술평균 _ 74 중앙치 _ 75 최빈치 _ 76 평균, 중앙치, 최빈치의 비교 _ 77 3.2 산포의 측정치 ····························································································· 78 범위 _ 80 중간범위 _ 81 평균절대편차 _ 82 분산과 표준편차 _ 83 Chebyshev의 정리 _ 88 변동계수 _ 90 3.3 상대위치의 측정치 ······················································································ 91 백분위수 _ 92 사분위수 _ 93 Z 값 _ 94 3.4 형태의 측정치 ····························································································· 97 비대칭도 _ 97 첨도 _ 99 3.5 EXCEL 활용 ·······························································································100 ▶ 연습문제 ········································································································108 제4장 확률이론 4.1 사상과 표본공간 ························································································113 4.2 집합이론 ····································································································118 집합의 개념 _ 118 집합의 종류 _ 119 4.3 확률의 정의 ·······························································································124 고전적 방법 _ 125 상대도수 방법 _ 125 주관적 방법 _ 127 4.4 확률의 공리 ·······························································································127 4.5 확률의 연산법칙 ························································································129 덧셈법칙 _ 129 조건확률 _ 132 곱셈법칙 _ 140 4.6 Bayes 정리 ································································································142 개념 _ 142 표의 이용 _ 144 4.7 EXCEL 활용 ·······························································································146 ▶ 연습문제 ········································································································147 제5장 확률변수와 확률분포 5.1 확률변수 ····································································································155 5.2 확률분포 ····································································································157 이산확률분포 _ 158 연속확률분포 _ 160 5.3 확률함수 ····································································································161 확률질량함수 _ 162 확률밀도함수 _ 164 5.4 확률변수의 기대값과 분산 ·········································································167 기대값의 의미 _ 167 기대값의 특성 _ 168 분산 _ 169 5.5 결합확률분포 ·····························································································173 결합확률분포의 개념 _ 173 조건확률 _ 175 두 변수의 독립성 _ 176 5.6 공분산과 상관계수 ·····················································································177 공분산 _ 177 상관계수 _ 179 5.7 EXCEL 활용 ·······························································································180 ▶ 연습문제 ········································································································184 제6장 확률분포Ⅰ:이산확률분포 6.1 베르누이 시행 ····························································································191 6.2 이항분포 ····································································································192 이항 확률질량함수의 이용 _ 193 이항확률표의 이용 _ 195 6.3 이항분포의 형태 ························································································197 6.4 이항분포의 기대값과 분산 ·········································································199 6.5 포아송분포 ·································································································202 개념 _ 202 포아송 확률질량함수의 이용 _ 203 포아송 분포표의 이용 _ 204 6.6 초기하분포 ·································································································206 개념 _ 206 초기하분포의 확률질량함수 _ 207 6.7 EXCEL 활용 ·······························································································209 ▶ 연습문제 ········································································································211 제7장 확률분포Ⅱ:연속확률분포 7.1 확률밀도함수 ·····························································································217 7.2 정규분포 ····································································································219 정규분포의 사용 _ 219 정규곡선의 형태 _ 219 정규곡선의 특성 _ 220 7.3 표준정규분포 ·····························································································224 정의 _ 224 표준정규분포표의 이용 _ 230 정규분포의 응용 예 _ 238 7.4 이항분포의 정규근사 ·················································································241 7.5 지수분포 ····································································································243 개념 _ 243 지수분포의 확률 _ 245 7.6 EXCEL 활용 ·······························································································247 ▶ 연습문제 ········································································································252 제8장 표본분포 8.1 표본추출 ····································································································259 표본조사의 필요성 _ 259 표본오차와 비표본오차 _ 260 8.2 표본추출 과정 ····························································································262 8.3 표본추출 방법 ····························································································263 확률 추출방법 _ 264 비확률 추출방법 _ 266 8.4 표본분포 ····································································································266 8.5 평균의 표본분포:복원추출 ······································································269 개념 _ 269 평균의 표본분포의 기대값과 분산 _ 273 평균의 표준오차 _ 275 8.6 평균의 표본분포:비복원추출 ··································································277 8.7 중심극한정리 ·····························································································281 표본크기의 영향 _ 281 모집단이 정규분포를 따를 때 _ 282 모집단이 정규분포를 따르지 않을 때 _ 284 8.8 비율의 표본분포 ························································································287 개념 _ 287 비율의 표본분포의 기대값과 표준편차 _ 289 이항분포의 정규근사 _ 292 유한 모집단에서의 표본비율의 표준편차 _ 293 8.9 EXCEL 활용 ·······························································································294 ▶ 연습문제 ········································································································298 제9장 통계적 추정:한 모집단 9.1 점추정과 구간추정 ·····················································································305 9.2 추정량의 결정기준 ·····················································································306 불편성 _ 307 효율성 _ 308 일관성 _ 309 충족성 _ 310 9.3 신뢰구간 추정 ····························································································311 개념 _ 311 오차율 _ 313 9.4 모평균의 신뢰구간 ·····················································································314 모표준편차를 아는 경우 _ 314 모표준편차를 모르는 경우:소표본 _ 320 9.5 t 분포 ·········································································································320 모표준편차를 모르는 경우:대표본 _ 327 9.6 모비율의 신뢰구간 ·····················································································329 9.7 표본크기 결정 ····························································································331 모평균 추정 _ 331 모비율 추정 _ 334 9.8 모분산의 신뢰구간 ·····················································································336 χ2 분포의 특성 _ 337 모분산의 신뢰구간 _ 341 9.9 EXCEL 활용 ·······························································································344 ▶ 연습문제 ········································································································348 제10장 가설검정:한 모집단 10.1 가설검정 ····································································································355 가설의 의미와 종류 _ 355 가설의 설정 _ 356 가설의 형태 _ 358 가설검정의 오류 _ 360 결정규칙 _ 362 가설검정의 순서 _ 366 10.2 모평균의 가설검정 ·····················································································367 모표준편차를 아는 경우 _ 368 모표준편차를 모르는 경우 _ 378 10.3 모비율의 가설검정 ·····················································································383 10.4 모분산의 가설검정 ·····················································································387 10.5 EXCEL 활용 ·······························································································390 ▶ 연습문제 ········································································································395 제11장 통계적 추정과 가설검정:두 모집단 11.1 표본의 독립성과 종속성 ············································································403 11.2 두 표본평균 차이의 표본분포 ····································································404 11.3 두 모평균 차이에 대한 추정과 검정 ··························································406 독립표본 _ 406 대응표본 _ 414 11.4 두 모비율 차이에 대한 추정과 검정 ··························································418 11.5 두 모분산 비율에 대한 추정과 검정 ··························································423 F 분포 _ 423 두 모분산 비율의 추정 _ 427 두 모분산 비율의 검정 _ 428 11.6 EXCEL 활용 ·······························································································431 ▶ 연습문제 ········································································································438 제12장 분산분석 12.1 분산분석의 의미 ························································································447 12.2 실험설계의 기본 개념 ················································································448 12.3 분산분석의 기본 원리 ················································································450 12.4 일원배치법:반복 수가 같은 경우 ····························································452 12.5 이원배치법:반복없는 경우 ······································································462 12.6 이원배치법:반복 있는 경우 ·····································································468 12.7 EXCEL 활용 ·······························································································475 ▶ 연습문제 ········································································································480 제13장 회귀분석과 상관분석 13.1 회귀분석과 상관분석 ·················································································487 13.2 산포도 ········································································································488 13.3 단순선형회귀모델 ······················································································491 확정적 모델과 확률적 모델 _ 491 모집단 단순회귀모델 _ 492 표본 회귀모델 _ 494 오차항에 대한 가정 _ 496 13.4 최소자승법 ·································································································498 13.5 표본회귀선의 적합도 검정 ·········································································502 13.6 상관분석 ····································································································510 공분산 _ 510 상관계수 _ 512 13.7 표본회귀선의 유의성 검정 ·········································································515 13.8 종속변수 Y 의 추정과 예측 ········································································520 13.9 EXCEL 활용 ·······························································································526 ▶ 연습문제 ········································································································534 제14장 다중회귀분석 14.1 다중회귀모델 ·····························································································541 다중선형회귀모델 _ 541 다중회귀모델의 가정 _ 543 14.2 최소자승법 ·································································································544 14.3 다중표본회귀식의 적합도 검정 ·································································546 추정치의 표준오차 _ 546 결정계수 _ 548 14.4 다중회귀모델에 대한 유의성 검정 ·····························································550 F 검정 _ 550 t 검정 _ 552 14.5 종속변수 Y 의 예측 ····················································································555 14.6 범주적 독립변수 ························································································557 ▶ 연습문제 ········································································································561 제15장 χ2 검정과 비모수통계학 15.1 모수통계학과 비모수통계학 ······································································569 15.2 모집단 분포의 적합도 검정 ·······································································570 모비율의 검정 _ 571 모집단 분포의 검정 _ 575 15.3 두 변수 간의 독립성 검정 ··········································································580 15.4 EXCEL 활용 ·······························································································584 ▶ 연습문제 ········································································································586 부표 A. 이항분포표 ··································································································· 592 B. e-μ의 값 ······································································································· 595 C. 포아송분포표 ······························································································· 596 D. 표준정규분포표 ···························································································· 598 E. 난수표 ··········································································································· 599 F. t 분포표 ········································································································· 600 G. χ2분포표 ······································································································ 601 H. F 분포표 ······································································································· 603 ◈ 영문색인 ················································································································ 607 ◈ 국문색인 ················································································································ 612 |
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