目次

はじめに...................................................................................................... iii
第1章

ビジネス統計分析への招待
1-1 近年のデータ分析を取り巻く状況....................................................................... 1
1-2 ビジネス統計分析の利用場面. ............................................................................. 2
1-3 データ分析に必要なプロセス. ............................................................................. 4
1-3-1 データ分析の業務としての流れ............................................................ 4
1-3-2 ビジネス統計における分析プロセス. ................................................... 5
1-3-3 データ分析プロセスにおける必要な統計分析の知識........................... 7
1-4 データ分析者としての基本スキル....................................................................... 8第2章

母集団と統計データ
2-1 統計分析の考え方.............................................................................................. 112-2 母集団とサンプリング. ..................................................................................... 122-2-1 母集団と標本. ..................................................................................... 122-2-2 サンプリング. ..................................................................................... 122-2-3 記述統計と推測統計. .......................................................................... 142-3 統計データの種類.............................................................................................. 152-3-1 質的データと量的データ.................................................................... 152-3-2 尺度水準.............................................................................................. 15コラム. .......................................................................................................................... 16章末問題........................................................................................................................ 17

第3章

iv

1変量データのまとめ方3-1 円グラフと棒グラフ.......................................................................................... 213-2 度数分布表とヒストグラム............................................................................... 223-2-1 度数分布表とヒストグラムの読み方. ................................................ 223-3 データの中心を表す統計量............................................................................... 253-3-1 平均値. ................................................................................................ 253-3-2 中央値. ................................................................................................ 263-3-3 最頻値. ................................................................................................ 26
3-3-4 平均値・中央値・最頻値の関係......................................................... 263-4 データのばらつきを表す統計量........................................................................ 273-4-1 範囲..................................................................................................... 273-4-2 四分位範囲.......................................................................................... 28
3-4-3 平均偏差.............................................................................................. 283-4-4 分散と標準偏差................................................................................... 293-4-5 変動係数.............................................................................................. 29
3-5 データの歪みや尖りを表す統計量.................................................................... 303-5-1 歪度..................................................................................................... 30
3-5-2 尖度..................................................................................................... 30
3-6 データの標準化と偏差値................................................................................... 31

3-7

時系列データの分析.......................................................................................... 32
3-7-1 時系列データと移動平均.................................................................... 32
3-7-2 比率の推移と幾何平均........................................................................ 34

コラム. .......................................................................................................................... 35章末問題........................................................................................................................ 36
第4章

2変量データのまとめ方
4-1 2変量質的データのまとめ方............................................................................. 39
4-1-1 分割表データ. ..................................................................................... 39
4-1-2 独立な状況の計算............................................................................... 40
4-1-3 関連性の尺度. ..................................................................................... 424-2 2変量量的データのまとめ方............................................................................. 434-2-1 散布図. ................................................................................................ 434-2-2 共分散と相関係数............................................................................... 444-3 層別の重要性..................................................................................................... 464-3-1 質的変数の場合................................................................................... 464-3-2 見せかけの相関................................................................................... 47
コラム. .......................................................................................................................... 49
章末問題........................................................................................................................ 50

第5章

確率と確率分布5-1 標本空間と確率. ................................................................................................ 535-1-1 事象と標本空間................................................................................... 535-1-2 確率の定義.......................................................................................... 555-1-3 確率の解釈.......................................................................................... 56
5-2 確率分布と期待値.............................................................................................. 575-2-1 確率変数と確率分布. .......................................................................... 575-2-2 期待値. ................................................................................................ 605-2-3 期待値の性質. ..................................................................................... 625-2-4 大数の法則.......................................................................................... 62コラム. .......................................................................................................................... 64章末問題........................................................................................................................ 65第6章

さまざまな確率分布
6-1 離散変数の確率分布.......................................................................................... 676-1-1 二項分布.............................................................................................. 676-1-2 多項分布.............................................................................................. 706-1-3 ポアソン分布. ..................................................................................... 706-2 連続変数の確率分布.......................................................................................... 726-2-1 正規分布.............................................................................................. 726-2-2 正規分布に関するいくつかの性質..................................................... 73
6-2-3 正規分布の確率，パーセント点の求め方.......................................... 76
コラム. .......................................................................................................................... 80v

章末問題........................................................................................................................ 81
第7章

標本分布
7-1 標本分布と統計的推測. ..................................................................................... 83
7-1-1 統計的推測.......................................................................................... 83
7-1-2 標本分布.............................................................................................. 84
7-1-3 算術平均の標本分布. .......................................................................... 84
7-2 正規母集団からの標本分布............................................................................... 85
7-2-1 正規母集団からの統計量.................................................................... 86
7-2-2 χ2 分布（カイ二乗分布）. .................................................................. 87
7-2-3 t 分布................................................................................................... 89
7-2-4 F 分布.................................................................................................. 91
コラム. .......................................................................................................................... 93章末問題........................................................................................................................ 94

第8章

検定と推定
8-1 仮説検定............................................................................................................. 97
8-1-1 仮説検定の考え方............................................................................... 97
8-1-2 両側検定と片側検定. ........................................................................ 101
8-1-3 仮説検定の誤り................................................................................. 102
8-1-4 母平均の仮説検定............................................................................. 103
8-2 統計的推定....................................................................................................... 104
8-2-1 推定の考え方. ................................................................................... 104
8-2-2 点推定. .............................................................................................. 105
8-2-3 区間推定............................................................................................ 107
コラム. ........................................................................................................................ 110
章末問題...................................................................................................................... 111

第9章

母平均の検定と推定
9-1 母平均の検定................................................................................................... 115
9-1-1 母分散がわかっている場合の母平均の検定. ................................... 116
9-1-2 母分散がわかっていない場合の母平均の検定................................. 119
9-2 母平均の差の検定............................................................................................ 122
9-2-1 対応のない 2 組の標本に対する母平均の差の検定......................... 124
9-2-2 対応のある 2 組のデータの母平均の差の検定................................ 132
コラム. ........................................................................................................................ 136
章末問題...................................................................................................................... 137

第 10 章vi

さまざまな仮説検定
10-1 比率に関する検定............................................................................................ 141
10-2 適合度検定....................................................................................................... 143
10-3 分割表における独立性の検定. ........................................................................ 146
10-4 分散分析........................................................................................................... 148

コラム. ........................................................................................................................ 154
章末問題...................................................................................................................... 155
第 11 章

相関と回帰
11-1 相関分析........................................................................................................... 157
11-1-1 散布図と相関係数............................................................................. 157
11-1-2 相関の検定........................................................................................ 159
11-1-3 見せかけの相関................................................................................. 162
11-2 単回帰分析....................................................................................................... 162
11-2-1 単回帰モデル. ................................................................................... 163
11-2-2 回帰係数の推定方法. ........................................................................ 164
11-2-3 あてはまりのよさの検討.................................................................. 167
11-2-4 残差の検討........................................................................................ 169
11-2-5 最小二乗推定量の確率分布.............................................................. 170
コラム. ........................................................................................................................ 172
章末問題...................................................................................................................... 173

第 12 章重回帰分析
12-1 重回帰モデルと回帰分析................................................................................. 175
12-2 回帰係数の推定方法........................................................................................ 178
12-3 モデルの妥当性の検討. ................................................................................... 180
12-4 説明変数の選択. .............................................................................................. 183
12-4-1 偏回帰係数の t 値.............................................................................. 183
12-4-2 偏相関係数........................................................................................ 185
12-4-3 変数選択の手続き............................................................................. 185
12-5 多重共線性....................................................................................................... 186
12-6 回帰分析の拡張. .............................................................................................. 187
コラム. ........................................................................................................................ 188
章末問題...................................................................................................................... 190

第 13 章ロジスティック回帰分析
13-1 目的変数が質的変数の場合の問題.................................................................. 193
13-2 ロジスティック回帰モデル............................................................................. 196
13-3 多重ロジスティック回帰モデル...................................................................... 198
13-4 モデルの評価と変数選択................................................................................. 199
13-5 データ収集の問題............................................................................................ 200
コラム. ........................................................................................................................ 201
章末問題...................................................................................................................... 203

章末問題

解答と解説.............................................................................................................. 205

索引. ................................................................................................................................... 225

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