MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C80B6E.3C9EB040" このドキュメントは単一ファイル Web ページ (Web アーカイブ ファイル) です。お使いのブラウザ、またはエディタは Web アーカイブ ファイルをサポートしていません。Microsoft Internet Explorer など、Web アーカイブをサポートするブラウザをダウンロードしてください。 ------=_NextPart_01C80B6E.3C9EB040 Content-Location: file:///C:/8ECB5C11/07dist_1.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　1．1次元と2次元のデータ

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マスタ タイトルの書式設定
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file:///C:/8ECB5C11/07dist_1.files/master12.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis"
マスタ タイトルの書式設定
マスタ サブタイトルの書式設定
<日付/時刻>
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データ分布と予測
n1次元のデータ
q度数分布・ヒストグラム
q代表値と散らばり
n2次元のデータ
q散布図，相関関係・共分散
堀田　敬介
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1次元のデータ
<= span style=3D'mso-fareast-hint:yes'>n度数分布
<= span style=3D'mso-fareast-hint:yes'>nヒストグラム
<= span style=3D'mso-fareast-hint:yes'>n幹葉プロット
<= span style=3D'mso-fareast-hint:yes'>n箱ひげ図
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n個
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度数分布
nデータ [土日の来店客数の<= /span>1年間のデータ]
データが多すぎて全体の傾向がよくわからない！
= 週末はどのぐらいお客さんが来てくれたの？
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+y7iYMuHELOLD8ohPHmfDcybO5cAsoLy6dSrW7+OHQI4Pti7e/8O3jvx0O64hz+PPr167bnMq38P Pz513LDcy7+PP78B4n9g6y//D2B87ClkX4AGHhgefy4UiGCDDl5HXxsMPkhhhcINOKGFGm4Y2wMc fgjicB8UAAA7 ------=_NextPart_01C80B6E.3C9EB040 Content-Location: file:///C:/8ECB5C11/07dist_1.files/slide0003.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　1．1次元と2次元のデータ
度数分布
n度数分布表[土日の来店客数の<= /span>1年間のデータ]
階級値 <= /div>
各階級の上限・下限値の中間値
〔例〕344.5←330-359
〔例〕 345  ←330-360
なるほど，週末の来店= 客数はだいたいこのぐらいのことが多いんだ&= #13;
全体の傾= がよくわかる！
度数
(frequency)
階級
(class) <= /span>
階級= :10
階級幅:30<= /span>
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度数分布
n度数分布表[土日の来店客数の<= /span>1年間のデータ]
階級数:6
階級幅:50
階級数:28
階級幅:10
階級数（階級幅）を
どうするかが問題
階級数:10
階級幅:30
度数分布にすると全体の傾向がわかりやすくなるが，生データと= 比べて情報量が少なくなるため，このよう= なことがおこる．
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------=_NextPart_01C80B6E.3C9EB040 Content-Location: file:///C:/8ECB5C11/07dist_1.files/slide0005.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　1．1次元と2次元のデータ
度数分布
nスタージェスの公式 [階級数の目安]
（k：階級数，n<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 133%'>：データ数）
例では
より，階級数は8ぐらいで十分
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度数分布
n階級数8（階級幅38）で書くと…
なるほど，週末の来店客数の全体傾向はだいたいわかったぞ&= #13;
でも，度数の多い階級= は全体からみてどのぐらいの割合なの？&= #13;
相対度= 数
(relative frequen= cy)
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度数分布
n度数分布表[相対度数]
データ数が異なる2つの =
グループの比較ができる
=
Ｂさんのお店と比べて，うちのお客さんの来店傾向はどうなのか比較したいな…
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charset="shift_jis" データ分布と予測　1．1次元と2次元のデータ
度数分布
n累積度数分布表[累積度数，累積相= ﾎ度数]
累積度数
(cumulative frequency)
累積相対度数
(cumulative relative frequency)
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度数分布
n問題：以下の度数分布が与えられているとき，平均来店客数を求めなさい．
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ヒストグラム
nヒストグラム(histogram)・柱状グラフ
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ヒストグラム
nヒストグラム(histogram)・柱状グラフ
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度数分布
n階級数8で書くと…
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ヒストグラム
nヒストグラムの形状
(unimodal)
双峰型 (bimodal)
左に歪んだ分布
層別（適当にグループ分けすること）を行うと単峰型分布が出
峰が中央から左に寄っていて，右側に長く裾を引く分布
峰が中央から右に寄っていて，左側に長く裾を引く分布
=
峰が２つ以上ある分布=
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その他の手= 法１
n幹葉プロット，ステムプロット（stem-and-leaf diagram[plot]）
q野球選手の打率一覧
nAチーム
幹
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幹葉プロッ= トがヒストグラ= ムより優れているのはどんなところ= ？
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その他の手= 法２
n箱ひげ図，箱型図 （box plot）
q野球選手の打率一覧
nAチーム
<= span style=3D'font-family:"Times New Roman";font-size:91%'>nBチーム
= 〔Aチーム〕
max.0.392
Q3    0.338 <= /span>
med.0.288
Q1    0.265 <= /span>
min. 0.217
〔Bチーム〕
0.418 max.
0.332    Q3
0.309 med.
0.276    Q1
0.214 min.
0.214
0.276
0.309
0.332
0.418
0.217
0.265
0.288
0.338
0.392
注<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 89%;mso-fareast-hint:yes'>：ひげの上端・下端は，必ずmax，minを使うわけではない．=
r:=3Dq3-q1 としたとき，上端は区間(q3, q3+1.5r]内の最大値，
下端は区間[q1-1.5r, q1)内の最小値を用いる，= など．
ひげ
箱
全体の <= /span>
50%
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演習
n男女20
q男女それぞれのデータ= について，101幹葉プロットを描け．
q男女それぞれのデータ= について，箱ひげ図を描け．
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1次元のデータ
nデータ測定の尺度
23
5
14
-3
9
11
x
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＝
＝
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n個
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データの<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック"'>測定尺度による分類
n測定(measurem= ent)と尺度(scale)&#= 13;
q名義（名目）尺度 nominal scale
n属性を表す基準（対象に区別がつけられる）
q例：性別（男，女，それ以外）= ，パソコン保有（保有，非保有）
q順序尺度 ordinal scale
n対象間に順序がつけられる基準
q例：成績（A＞B＞C＞D），居住性（住= ﾝやすい＞まあまあ＞すみにくい）
q間隔尺度 interval scale
n間隔のみが意味を持つ基準
q例：温度（摂氏℃，華氏゜F），時刻（午後= 3時から1時間後）
q比率尺度 ratio scale
n比が意味を持つ基準
q例：身長（父は子の1.5倍の背），体重（5kg重い），絶対温度（゜<= /span>K，絶対零度）
測定が
厳密
3D"ホームベース:
質的（カテゴリ）データ
3D"ホームベース:
質的（カテゴリ）データ
3D"ホームベース:
量的（数値）データ
3D"ホームベース:
量的（数値）データ
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データの<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック"'>測定尺度による分類
n質的データと量的データの集計例
質的データ=
量的データ=
性別
（= j，女）
成績
（<= /span>A，B，<= /span>C，D）
（= j，女）
（<= /span>A，B，<= /span>C，D）
（= j，女）
（<= /span>A，B，<= /span>C，D）
（= j，女）
（<= /span>A，B，<= /span>C，D）
（= j，女）
（<= /span>A，B，<= /span>C，D）
（= j，女）
（<= /span>A，B，<= /span>C，D）
（= j，女）
（<= /span>A，B，<= /span>C，D）
（= j，女）
（<= /span>A，B，<= /span>C，D）
（= j，女）
（<= /span>A，B，<= /span>C，D）
（= j，女）
（<= /span>A，B，<= /span>C，D）
（= j，女）
（<= /span>A，B，<= /span>C，D）
データ例
集計例
2
2
0
D
5
2
0
1
女
2
2
B
3
1
C
11
4
計
6
3
男
計
A
=
女性身長
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データの代表値を考える
n例：16個のデータ
このデータを= 代表する値って何だろう？
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1次元のデータ
nデータの代表値
q算術平均
q幾何平均，調和平均
q中央値，最頻値
q四分位点
qミッド・レンジ
23
5
14
-3
9
11
x
＝
＝
＝
＝
＝
＝
n個
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Coffee Break
n記号の定義
q= 和を表す記号：Σ（しぐま） <= /div>
q
q
q
q
q= 積を表す記号：Π（ぱい）
x<= /span>i を i = を 1から<= span style=3D'font-family:"Times New Roman";mso-ascii-font-family:"Times New Ro= man"; mso-hansi-font-family:"Times New Roman"'> n = まで動かして足す
x<= /span>i を i = を 1から<= span style=3D'font-family:"Times New Roman";mso-ascii-font-family:"Times New Ro= man"; mso-hansi-font-family:"Times New Roman"'> n = まで動かして掛ける
例）
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代表値 averages<= /span>
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Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQAPAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAU AAkAgAAAADOZZgIXhI8Wya3rYpgQ0Ivz0hzHdH3gJI4l6BQAOx== ------=_NextPart_01C80B6E.3C9EB040 Content-Location: file:///C:/8ECB5C11/07dist_1.files/slide0014.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　1．1次元と2次元のデータ
代表値 averages<= /span>
n幾何平均 geometric mean
☆どんなときに幾= 何平均が役に立つ？
　　例題：次の表か= ら平均地価上昇率を求めよ=
補足：対数を利用すると計= 算が楽になる
5%
4%
3%
2%
1%
2006
2005
2004
2003
2002
年度
×
○
幾何平均
＝
nn乗根
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Content-Location: file:///C:/8ECB5C11/07dist_1.files/slide0015.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　1．1次元と2次元のデータ
代表値 averages<= /span>
n調和平均 harmonic mean
調和平均
＝
逆数の算術平均
の
逆数
= ☆どんなときに調= 和平均が役に立つ？
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×
○
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代表値 averages<= /span>
n中央値 median =
qデータをソート したとき，ちょうど真ん中に来る値
n最頻値 mode
qデータの中で最も頻繁に出てくる値
(sort, 値の小さい（大きい）順に並べること）
補足：データ数が偶数の場合は，中央値は真ん中2つの算術平均 補足：最も頻繁に出てくる値= がない場合は最頻値はなし
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------=_NextPart_01C80B6E.3C9EB040 Content-Location: file:///C:/8ECB5C11/07dist_1.files/slide0017.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　1．1次元と2次元のデータ
代表値 averages<= /span>
n中央値や最頻値は何故必要なのか？
q例：年収（単位：万円）の代表値は？
q算術平均
n1130万円
q中央値
n(700+800) / 2 =3D 750万円
q最頻値
n700万円，800万円
ここが平均?
ここが平均
300
500
700
800
1000
5000
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代表値 averages<= /span>
n算術平均，中央値，最頻値の関係
左に歪んだ分布
平均
中央値
最頻値
中央値
最頻= l
平均
中央値
最頻= l
平均
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Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　1．1次元と2次元のデータ
<= span style=3D'text-shadow:auto;layout-flow:horizontal'>n四分位点 quartile= 3;
qデータをソートし，4<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Times New Ro= man"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"'>等分したときの3<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Times New Ro= man"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"'>つの分割点の値
nQ<= /span>1：第1四分位点，Q<= /span>3：第3四分位点
n
<= span style=3D'font-family:"Times New Roman";color:red;mso-fareast-hint:yes'>q注意：四<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Times New Ro= man"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"'>分位数の定義は複数ある
<= span style=3D'font-family:"Times New Roman"'>nk1 :=3D 0.25= ×(<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-fareast-language:JA'>n-= 1), k<= /span>3 :=3D 0.75= ×(<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-fareast-language:JA'>n-= 1) とし，
q
q
<= span style=3D'font-family:"Times New Roman"'>n  など
代表値 averages<= /span>
MS Excel の 関数QUARTILE() では，Q1 =3D5.75, Q3 =3D9.25
Mathematica の関数quantile[]では，Q1 =3D5, Q3 =3D9
Rの関数quantile() では，Q1 =3D5.75, Q3 =3D9.25
※quartile：四分位数 = ;
 quantile：分位数&#= 13;
Q<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";font-size:81%;position:relative; top:.37em;mso-text-raise:-25%;mso-fareast-language:JA'>1
Q<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";font-size:81%;position:relative; top:.37em;mso-text-raise:-25%;mso-fareast-language:JA'>2
Q<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";font-size:81%;position:relative; top:.37em;mso-text-raise:-25%;mso-fareast-language:JA'>3
補足：Q2第2四分位点は中央値 xm= ed である
xmed
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代表値 averages<= /span>
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qデータの最大値と最小値の中間点
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演習２&#= 13;
n代表値を計算しよう
q総務省統計局（= http://www.stat.go.jp）の [家計調査]ｰ[貯蓄・負債編]ｰ[調査結果]ｰ[詳細結果表：年度平均]ｰ[表8-11<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 77%;color:#666699'>：貯蓄・純貯蓄・負債現在高階級別]から，貯蓄額を世帯ごとの度数で表し= たデータを取得し，グラフ化せよ．グラフの形状はどのよ= うになるか？
q次に，このデータの「算術平均」「中= 央値」「最頻値」を計算し，分布の代表値として最も適切だと思われるの= はどれか考察せよ．ただし，100万未満= ，及び4000万以上= の階級値はそれぞれ50万，5000万とする．
q中央値以外の四分位点と，ミッドレン= ジを計算せよ．
q
n以下の10個のデータについて「算術平均」「中央値」「最頻値」「第1四分位数」「第3四分位数」「ミッドレンジ」を求めよ．
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1次元のデータ
nデータの散らばり
q範囲
q四分位偏差
q平均偏差
q分散，標準偏差
23
5
14
-3
9
11
x
＝
＝
＝
＝
＝
＝
n個
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n例：16個のデータ
データの値らばりを考える
このデータの= 散らばり具合<= /span>はどのように測るの？
散らばりの度合いを= 黷ﾂの数値で示し，利用したい
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散らばり dispersio= n
n範囲 range <= /b>
q最大値と最小値の差
（n個の観測値　　　　　　　　に対して）
<= span style=3D'font-family:"Times New Roman";text-shadow:auto;layout-flow:horizo= ntal'>n四分位偏差 quartile deviation
q第3四分位点 Q<= i>3 と第1四分位点 Q<= i>1 の差の半分
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散らばり dispersio= n
n偏差 deviation&#= 13;
q各データと平均との差
<= span style=3D'font-family:"Times New Roman";text-shadow:auto;layout-flow:horizo= ntal'>n平均偏差 mean deviation
q= 偏差の絶対値の合計を平均化した値
散らばり具合の度合= ｢
＝
平均値からの平均的な差
偏差の和は必ず0になる（意味がない・使えない） <= /div>
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Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKAATAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAo ABMAgAAAAP8AAAJFhI9pwR0KY3K0UhktPnUD52EgNIZeMzHm+qncw7KuG8sPXNt0bqo4H/L9gKIX cUNDHRVKRHP5dEZjJYkG2dFZtjtoNVQAADs= ------=_NextPart_01C80B6E.3C9EB040 Content-Location: file:///C:/8ECB5C11/07dist_1.files/slide0021_image333.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKAATAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAo ABMAgAAAAP8AAAJGhI+JEeoPmZx0wlvZy/oC6kXW1oXheEjmmpZfw8bqG9f0Z9tovmow32u4gBjh jyhqHZGL5YxpeCZ2OaoCxKpkOVyrrrsqAAA7 ------=_NextPart_01C80B6E.3C9EB040 Content-Location: file:///C:/8ECB5C11/07dist_1.files/slide0022.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　1．1次元と2次元のデータ
散らばり dispersio= n
n分散 variance= 3;
q= 偏差の2乗の合計を平均化した値
n標準偏差 standard deviation
q分散の平方根
補足：分散は，データの2乗の平均から平均の2乗を引いても計算できる
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散らばり dispersio= n
n例：16個のデータ
n範囲 50 – 3 =3D 47
n四分位偏差 (9.75 – 5.25) / 2 =3D 2.25
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演習３&#= 13;
n以下の10<= /span>個のデータについて散らばりを計算せよ．（式だ= けでもよい）
q=
q
qこのデータの「範囲」を計算せよ．
n例） data[ = 1, 5, 7, 9, 3 ] → 範囲：9 – 1=3D 8
qこのデータの「四分位偏差」を計算せ= よ．
qこのデータの「偏差」をだし，合計が= ０になることを確かめよ．
qこのデータの「平均偏差」を計算せよ= ．
qこのデータの「分散」を計算せよ．
qこのデータの「標準偏差」を計算せよ= ．
------=_NextPart_01C80B6E.3C9EB040 Content-Location: file:///C:/8ECB5C11/07dist_1.files/slide0041_image355.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhlQEbAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQCU ARoAggAAAAAAAACAAMz/zP///wECAwECAwECAwP/KEpMuu2J5h6V10bN8IYdV4Hj9Jkh6aVomani 6p5vK99xDu+23vO1IG3IEhaJs6MyycQBaT5jM4p0/q5Sa5a61Fa502cX7B2Lw9jvuYzerslRxWBO r9vv+Lx+z+/7/4CBgoOEhYaHiImKi4yHEI2QkZKTlJWWl5iZmBSanZ6foKGio6R+nKWoqaqrrK2f p66xsrO0tawhjQGLAby6eL27wL+8ir2+dsbFwsjLh8l6xIjPdcbNhNN31oXY1NHO1cd02nMSjN7O 1Mzi4dfp3evo4sjuhuHs9tL08+yD+PqJ/t7NOdfvnzeCgvgJHICwHMBxCbMZjKfvXj2JAzG2m5eR /+PGfxkVAuIXEKDGjvK2nbR4EZpHOg53mfSoUKQfkilfBsKJMmdBmicj6mTY82dFcytzabSpMk9N O4+Q5gMadOfSX03p8fzos+rIoMeY9tlKFOLXl2KFaoWky9rTOrCKSQqLVSpRr1nrynTKlqpdhnSV yuMmN6TZkYGLFo07U7Diu4Ufp/3DdPJZZpYv98x8UydnPvdKNgYMUi3Kt3QYT/0LuTTX1l3z4pU9 26jPz3vS4uY7dLdexb55w15cwXHk2MNfJw+OvDnt3y0nHnc5OjZz67WNoib3wPjq0teXQ7ed3TT2 7+vAXbccXiTZ5+9Xbx8Qc3r0ocmtjs9PObf38833+YcegM8BN6CBtCX2T33VFVjUegI61xl1e43H XGYQCifhWBFuCBqFHoK42VBRVRhgNmFdCFqKJ7rm4IgtimheUjEeVSOM94UGjx2qUVSPeii2ByRm 0gwJGDg/ItkNQgkZWV5uTh65XpRSFqlkeuFVOYxIPdri5ZdghilmH12OaeaZaKZJCi5qtunmm3BC IkEaZtDZhhp2sqEnHG/0mSeff/rpRqCEDmoonofWmeidigK66J6CIiqpopMyaimkhVaK6aOOatop paBe6mgCADs= ------=_NextPart_01C80B6E.3C9EB040 Content-Location: file:///C:/8ECB5C11/07dist_1.files/slide0055.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　1．1次元と2次元のデータ
1次元のデータ
nデータの変換
q標準化（正規化）
Cf. 偏差値
q<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";mso-special-format: lastCR;display:none'>
23
5
14
-3
9
11
x
＝
＝
＝
＝
＝
＝
n個
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データの一次変換
n標準化 standardi= zation
q各データについて，平均を引き標準偏差で割る
標準得点 standard score，Z得点
変換後のデータは
　　平均0，
　　標準偏差1
となる．
60
80
70
90
100
-20
0
-10
10
20
= 「平均を引く」ということは， = ;
全体の位置を移動し， = ;
真ん中（平均）を0にすること．
-2
0
-1
1
2
= 「標準偏差で割る」ということは，
全体を左右から圧縮して， = ;
標準偏差を1にすること．&#= 13;
どんな1次元データも
標準化しちゃえば= 3;
同じ土俵で比較できるね！
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データの一次変換
偏差値得点，T<= /span>得点
n偏差値
q標準得点に以下の一次変換を施す
60
80
70
90
100
-20
0
-10
10
20
-2
0
-1
1
2
-20
0
-10
10
20<= /div>
-30
50
-40
60
70
変換後のデータは
　平均50，
　標準偏差10
となる．
標準化&#= 13;
元の点数
偏差値
ｚ値
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データの一次変換
n<= /span>例：10人の中間・期末試験の得点，z得点と偏差値
平均88, 標準偏差9.8
平均33, 標準偏差16
中間試験
期末試験
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Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhVQA9AHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAABV ADwAgQAAAAAAAJaWlv///wL/hI+pu8IPo5w0iVuz3lWM4XDiyHlfSKYqY57rC7cuTIvXh4P1nsk5 yguyckSg8GjwFZHMG3HJFCqfuihvSjVaV9jsltb1flVOqlk71oTN1TTlAl+z4/S6/Y7HvMvsvv8P OKfHIhdoeHg4eMCH2OjoOFj4OEkJJXkYEJCTqfnB+ffpmZl4idg5cKqZ2re6GshYuYnTOsta6woI G+tZy4trFoo6aqi7i6vayxmM7Eu6S3WM2gt8O/1XHBv9+0TL+6o0vBnutxwezFZ+mjulLu39DN+n 2y4bb5/Fjj6rTH//OE/Nn8AT+bgR4ZcKocKFDBUSK1iv38BdsEKpUjax0Th8vBk7SsSBbeI5UR8N +gkp8Nc2Sij9qbRWqeW9bSNjloKHUVbJRjJTHoTJ8ibOdisn9Yy3sVPNoB2byhPqFN7RqPawDVt6 sB9WUeJ2kvxKEFo0cibdBTRL9Oe0TgChgbKFdi1MomMrCiuLEGg9aerG6lXaqyJgvWULm33nyqHO wAB8+CW57Gwzue8qL+aFQkZiy25NDo6LWK3BVUA0X82JzpywrekKo+akKMlUqqQixKEdFI6aPLx7 +/4dW0EBADs= ------=_NextPart_01C80B6E.3C9EB040 Content-Location: file:///C:/8ECB5C11/07dist_1.files/slide0042.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　1．1次元と2次元のデータ
演習４&#= 13;
n偏差値を計算しよう
q以下のデータはある試験の16人の学生の結果である．
q英語の結果について，各学生の得点を= 標準化し，z得点を出せ．
q国語の結果について，各学生の偏差値を計算せよ．<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 77%;color:#666699;display:none'>
q３教科合計点について，各学生の偏差= 値を計算せよ．
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データ分布と予測
n1次元のデータ
q度数分布・ヒストグラム
q代表値と散らばり
n2次元のデータ
q散布図，相関関係・共分散
堀田　敬介
23
5
14
-3
9
11
x
-4
7
-2
5
0
3
y
23
5
14
-3
9
11
x
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2次元のデータ
<= span style=3D'mso-fareast-hint:yes'>n相関と回帰
<= span style=3D'mso-fareast-hint:yes'>n共分散
<= span style=3D'mso-fareast-hint:yes'>n相関係数
------=_NextPart_01C80B6E.3C9EB040 Content-Location: file:///C:/8ECB5C11/07dist_1.files/slide0025.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" データ分布と予測　1．1次元と2次元のデータ
2次元のデータ
n2次元データ x , y の比較 <= /div>
<= span style=3D'font-family:"Times New Roman"'>q相関 correlation
<= span style=3D'font-family:"Times New Roman"'>nx <= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Times New Ro= man"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"'>と y<= /span> <= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Times New Ro= man"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"'>との間に区別をつけず対等に見る見方・方法
<= span style=3D'font-family:"Times New Roman"'>q例：身長と体重，数学の成績と英語= ﾌ成績
n
<= span style=3D'font-family:"Times New Roman"'>q回帰 regression
<= span style=3D'font-family:"Times New Roman";layout-flow:horizontal'>nx から y を見る見方・方法
<= span style=3D'font-family:"Times New Roman";layout-flow:horizontal'>nある一方が他方を左右する場合
q例：年齢と血圧，所得と消費，人口と商業，気候と住環= 境
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散布図 scattergr= am
n2つを同時に見=
q例：身長と体重
背が高い人ほ= ﾇ体重が重い？
相関の度合いを
= 白l化することで，
比較・分析できないか？
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相関関係
n共分散 = covariance
i 番目のデータについて，　　と平均　　　との差と，　　と平均　　との差が共に大きいとき，共分散の値は大きくなり，そうではないとき共分散の値は小さく= なる．すなわち，2種類のデータの関係の強さ
q例：文教太郎君と湘南花子さんの昼食に掛けた費用 =
\200
\400
\300
\200
\100
花子
\200
\200
\100
\300
\400
太郎
金
木
水
火
月
=
太郎君がリッチな食事をとるとき，花子= さんは貧乏な食事で我慢してるの？
（2次元データ{x1,…,xn},{y1,…,yn}について）
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相関関係
n共分散と相関
= <= ![endif]> <= ![endif]>
正の相関&#= 13;
無相関&= #13;
負の相関&= #13;
<= ![endif]>
じゃぁ，
「相関の強さ」
を
「共分散の大きさ」=
で表せる？
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相関関係
n共分散と関係の強さ
q例：文教太郎君と湘南花子さんの昼食費
測定単位が変わる相関の度合い（強さ）が変わってしまう！
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太郎君がリッチな食事をとるとき，花子さんは貧乏な食事で我慢してるの？
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<= span style=3D'font-size:85%'>q例：文教次郎君と湘南花子さんの昼食費 <= /div>
超リッチな食事をとる次郎君と比べたら，<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 89%;mso-fareast-hint:yes'>花子さんの食事ってどうなの？
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Content-Type: text/html; charset="shift_jis" データ分布と予測　1．1次元と2次元のデータ
相関関係
n相関係数= correlation coefficient
（2次元データ{x1,…,xn},{y1,…,yn}について）
xi, yi 標準偏差で割る単位を気にせずに，2種類のデータの関係の強= さを表せる．
（ピアソンの）積率相関係数
(Peason’s) productmoment correlation coefficient=
n注意&= #13;
q相関係数は，2つの変数の直線的関係を見るためのもの．曲線関係が認められる場合等には向か= ﾈい
q相関係数は，因果関係を保= ﾘするものではない．
正の相関
無相関&= #13;
負の相関
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★順位相関係数を使うときとは？
　データが選好順位（順序尺度）で与= えられている場合
相関関係
n参考：その他の相関係数
q（スピアマンの）<= /span>順位相関係数 rank correlation coefficient <= /div>
q
n
n
n
q（ケンドールの）<= /span>順位相関係数 rank correlation coefficient <= /div>
n
n
n
q
q偏相関係数 partial correlation coefficient
q（時系列データに対する自己相関係数
q auto-correlation coefficient
= Q<= i>1, Q<= i>2, = …, Q<= i>n
B
= R<= i>1, R<= i>2, = …, R<= i>n
A
（R<= i>i ： A が i を好きな順番）
順位が完全に一致しているとき rK =3D +1
順位が完全に逆のとき rK =3D 1
順位が完全に一致しているとき rS =3D +1
順位が完全に逆のとき rS =3D 1
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相関関係
n参考：その他の相関係数
q例題：男女それぞれが好= きな花の順番
8
6
7
4
5
2
1
3
女
8
7
6
5
4
3
2
1
男
椿
カーネーション <= /span>
鬱金香
百合
梅
薔薇
菊
桜
=
出展：=
（『統= 計学入門』p.55）
☆（スピアマンの）順位相関係数
☆（ケンドールの）順位相関係数
○
カ
○
×
鬱
○
○
○
百
○
○
○
×
梅
○
○
○
○
○
薔
○
○
○
○
○
○
菊
○
○
○
○
○
×
×
桜
椿
カ
鬱
百
梅
薔
菊
桜 v.s. 椿= 囃j：1<8
★女：3<8
正順
鬱 v.s. カ= 囃j：6<7
★女：7>6
逆順
G：正順の数=3D24
H：逆順の数=3D4<= span lang=3DEN-US style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:= "Times New Roman"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; font-size:89%;layout-flow:horizontal;color:#663300;mso-fareast-language:JA; mso-special-format:lastCR;display:none'>
ピアソンの積率相関係数を順序尺度に素直にあてはめたもの
全対（n(n-1)/2個）について，正順と逆順の個数の差を比較したもの
★順位相関係数を使うときとは？
　データが選好順位（順序尺度）で与= えられている場合
= Q<= i>1, Q<= i>2, = …, Q<= i>n
B
= R<= i>1, R<= i>2, = …, R<= i>n
A
（R<= i>i ： A が i を好きな順番）
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演習５&#= 13;
n相関係数を計算しよう
q右のデータ x, y について，
nそれぞれの分散 S<= i>x<= i>2, S<= i>y<= i>2 を計算せよ．
n共分散 covxy を計算せよ．
n（ピアソンの積率)相関係数 = r<= i>xy を計算せ= よ．
q
q
q右のA君, Bさんの色の好みに関する選好順位データについて，
n（スピアマンの）順位相関係数 = r<= i>S を計算せよ．
n（ケンドールの）順位相関係数 = r<= i>K を計算せよ．
3<= /div>
0<= /div>
2<= /div>
6<= /div>
4<= /div>
y<= /span>
9<= /div>
7<= /div>
5<= /div>
3<= /div>
1<= /div>
x<= /span>
紫
緑
橙
青
赤
3<= /div>
1<= /div>
2<= /div>
5<= /div>
4<= /div>
B
5<= /div>
4<= /div>
3<= /div>
2<= /div>
1<= /div>
A
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参考：散らばりの比較
n変動係数 = coefficie= nt of variation
q分布の中心が著しく異なる場合，分散で単純に散らばりを比較できない　⇒　相対比を指標として用いる
（n個の観測値　　　　　　　　に対して）
1965年：7.5/26.6 =3D 0.28 (28%)
1975年：23.8/117.5 =3D 0.20 (20%)
q例：県民所得（単位：万円）の比較
単純には所得格差は3倍に
広がっているように見える
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最後に…
n統計解析・予測手法
記述統計学
descriptive statistics
推測統計学&#= 13;
inferential statistics
多変量解析= 3;
multivariate analysis
3D"フローチャート
統計学
3D"フローチャート
統計解析
度数分布，代表値，
散らばり，相関関係，
etc.
確率分布，
母集団・標本，
推定，検定，etc.
重回帰分析，主成分分析，
判別分析，数量化理論，
etc.
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<= span style=3D'font-size:85%'>q宮川公男他　「入門経営科学」　実教出版(1999)
<= span style=3D'font-family:"Times New Roman";font-size:85%;layout-flow:horizonta= l'>q荒木勉他 「Excelで学ぶ統計解析」 実教出版(2000)
<= span style=3D'font-family:"Times New Roman";font-size:85%;layout-flow:horizonta= l'>q荒木勉 「<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";layout-flow:horizontal;mso-fareast= -language: JA'>Excelで学ぶ需要予測」 実教出版(2000)
<= span style=3D'font-family:"Times New Roman";font-size:85%;layout-flow:horizonta= l'>q多田実他 「Excelで学ぶ経営科学」 オーム社(2003)
<= span style=3D'font-family:"Times New Roman";font-size:85%;layout-flow:horizonta= l'>q桑田秀夫 「経営・経済系のための統計学」 日科技連(1992)
<= span style=3D'font-family:"Times New Roman";font-size:69%;layout-flow:horizonta= l'>qJ.アルバート&= J.ベネット「メジャーリーグの数理科学 上・下」シュプリンガー(2004<= /span>)
<= span style=3D'font-family:"Times New Roman";font-size:85%;mso-fareast-hint:yes; layout-flow:horizontal'>q間瀬茂他「工学のためのデータサイエンス入門」数理工学社(2004)
<= span style=3D'font-family:"Times New Roman";font-size:85%;layout-flow:horizonta= l'>qetc.
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<ヘッダー>= ;
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<日付/時刻>
マスタ テキストの書式設定
第 2 レベル
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<#>
初期値がAの時，
　A×xG^5 =3D ((((1.218A)= ×1.305)×1.536)×1.500)×1.129
なので，xG =3D (1.218*1.305*1.536*1.5*1.129)^(1/5) = となる．
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g_origSz=3DparseInt(SlideObj.style.fontSize) g_origH=3Dsld.style.posHeight g_origW=3Dsld.style.posWidth g_scaleHyperlinks=3D(document.all.tags("AREA").length>0) if( g_scaleHyperlinks ) InitHLinkArray() if( g_scaleInFrame||(IsWin("PPTSld") && parent.IsFullScrMode() ) ) document.body.scroll=3D"no" _RSW() if( IsWin("PPTSld") && parent.IsFullScrMode() ) FullScrInit(); =09 MakeSldVis(); ChkAutoAdv() if( runAnimations ) { if( document.all("NSPlay") ) document.all("NSPlay").autoStart =3D false; if( sld.filters && sld.filters.revealtrans ) setTimeout( "document.body.start()", sld.filters.revealtrans.duration * = 1000 ); else document.body.start(); } } function MakeSldVis()=20 { var fTrans=3Dg_showAnimation && SldHasTrans() if( fTrans )=09 { if( g_bgSound ) { idx=3Dg_bgSound.indexOf(","); pptSound.src=3Dg_bgSound.substr( 0, idx ); pptSound.loop=3D -(parseInt(g_bgSound.substr(idx+1))); } SlideObj.filters.revealtrans.Apply()=09 } SlideObj.style.visibility=3D"visible" if( fTrans ) SlideObj.filters.revealtrans.Play() } function MakeNotesVis()=20 { if( !IsNts() ) return false=20 SlideObj.style.display=3D"none" nObj =3D document.all.item("NotesObj") parent.SetHasNts(0) if( nObj ) {=20 nObj.style.display=3D"" parent.SetHasNts(1) } return 1 } function ChkAutoAdv() { if(SldHasTrans()) SlideObj.onfilterchange=3DAutoAdv else AutoAdv() } function AutoAdv() { if(!IsWin("PPTSld") || !gUseSldTimings )return var sld=3DGetCurSld() if( (sld.mAdvDelay>0) && !parent.IsFramesMode() ) setTimeout("parent.GoToNextSld()",sld.mAdvDelay) } function GetObj(id) { if(g_supportsPPTHTML) return document.all(id); else return document.getElementById(id); } function SldHasTrans() { return SlideObj.style.filter !=3D ""; } function GetSldId()=20 { var regExp =3D /file:\/\/\//i var pos =3D location.href.search(regExp) if (MHTMLPrefix !=3D "" && pos !=3D -1) sId =3D location.href.substring(pos) else { sId =3D RemoveFilePrefixFromHref(location.href); var regExp =3D /\// var fixedHref =3D sId var pos =3D -1 =09 pos =3D fixedHref.search(regExp) while (pos !=3D -1) { fixedHref =3D fixedHref.replace(regExp, "\\") pos =3D fixedHref.search(regExp) } =09 if (g_fBaseHyperlink =3D=3D true) sId =3D "file:///" + fixedHref; else sId =3D fixedHref.substring(fixedHref.lastIndexOf('\\') + 1) } =09 return sId } function HideMenu() { if( frames["PPTSld"] && PPTSld.document.all.item("ctx= tmenu") && PPTSld.ctxtmenu.style.display!=3D"none" ) { PPTSld.ctxtmenu.styl= e.display=3D'none'; return true } return false } function IsWin( name ) { return window.name =3D=3D name } function IsNts() { return IsWin("PPTNts") } function IsSldOrNts() { return( IsWin("PPTSld")||IsWin("PPTNts") ) } function SupportsPPTAnimation() { return( navigator.platform =3D=3D "Win32"= && navigator.appVersion.indexOf("Windows")>0 ) } function SupportsPPTHTML() { var appVer=3Dnavigator.appVersion, msie=3DappVer.indexOf("MSIE "), ver=3D0 if( msie >=3D 0 ) ver=3DparseFloat( appVer.substring( msie+5, appVer.indexOf(";",msie) ) ) else ver=3DparseInt(appVer) return( ver >=3D 4 && msie >=3D 0 ) } function _RSW() { if( !g_supportsPPTHTML || IsNts() || ( !g_scaleInFrame && (!IsWin("PPTSld") || !parent.IsFullScrMode()) ) ) return var padding=3D0; if( IsWin("PPTSld") && parent.IsFramesMode() ) padding=3D6 cltWidth=3Ddocument.body.clientWidth-padding cltHeight=3Ddocument.body.clientHeight-padding factor=3D(1.0*cltWidth)/g_origW if( cltHeight < g_origH*factor ) factor=3D(1.0*cltHeight)/g_origH newSize =3D g_origSz * factor if( newSize < 1 ) newSize=3D1 s=3DSlideObj.style s.fontSize=3DnewSize+"px" s.posWidth=3Dg_origW*factor s.posHeight=3Dg_origH*factor s.posLeft=3D(cltWidth-s.posWidth+padding)/2 s.posTop=3D(cltHeight-s.posHeight+padding)/2 if( g_scaleHyperlinks ) ScaleHyperlinks( factor ) } function _InitAnimations() { animRuntimeInstalled =3D ''+document.body.localTime !=3D 'undefined'; isFullScreen =3D (window.name =3D=3D "PPTSld") && !parent.IsFramesMode(); g_animUseRuntime =3D g_showAnimation && animRuntimeInstalled && !(isFullSc= reen && parent.IsSldVisited()); if( g_animUseRuntime ) { collSeq =3D document.all.tags("seq"); if( collSeq !=3D null ) { for(ii=3D0;ii numSlds ) gSldJumpIdx =3D numSlds; if ( gSldJumpIdx >=3D 0 ) { if ( gSldJumpIdx =3D=3D 0 ) gSldJumpIdx =3D 1; var jumpTo =3D parseInt(gSldJumpIdx); gSldJump =3D 0; gSldJumpIdx =3D ""; win.GoToSld( parent.GetSldList().mList[jumpTo-1].mSldHref ) } } } function _KDH() { if( event.keyCode =3D=3D 8 ) { event.returnValue =3D 0; parent.GoToPrevSld(); } } var g_HLinkArray =3D new Array(); =20 function IMapAreaObj( areaObj, coords ) { this.areaObj =3D areaObj; this.coords =3D coords; } function InitHLinkArray() { var appVer =3D navigator.appVersion; var msie =3D appVer.indexOf ( "MSIE " ) var ver =3D 0; if ( msie >=3D 0 ) ver =3D parseInt ( appVer.substring( msie+5 ) ); linkNum =3D 0; for (i=3D0; i 4 ) ) g_HLinkArray[linkNum++] =3D new IMapAreaObj( areaObj, ParseCoords( ar= eaObj.coords ) ); } } function ScaleHyperlinks( factor ) { =20 for ( ii=3D0; ii< g_HLinkArray.length; ii++) { coordsStr=3D""; imaObj =3D g_HLinkArray[ii]; for ( jj=3D0; jj < imaObj.coords.length-1; jj++ ) coordsStr +=3D (imaObj.coords[jj]*factor) + ","; coordsStr +=3D (imaObj.coords[jj]*factor); imaObj.areaObj.coords =3D coordsStr; } } function ParseCoords( coordsStr ) { var numArray =3D new Array(); var i =3D curPos =3D commaPos =3D 0; while ( ( commaPos =3D coordsStr.indexOf(",", curPos) ) !=3D -1 ) {=20 numArray[i++] =3D parseInt( coordsStr.substr( curPos, commaPos ) ); curPos =3D commaPos + 1; } numArray[i] =3D parseInt( coordsStr.substr( curPos ) ); return numArray; } function DocumentOnClick() { if( IsNts() || parent.HideMenu() ) return; if( ( g_allowAdvOnClick && (window.name=3D=3D"PPTSld") && !parent.IsFrames= Mode() ) || (event && event.keyCode=3D=3D32) ) { =09 if( g_animUseRuntime && g_animMainSequence && g_animMainSequence.cangonex= t ) return; parent.GoToNextSld(); } } var g_supportsPPTHTML =3D SupportsPPTHTML(), g_scaleInFrame =3D 1, gId=3D""= , g_bgSound=3D"", g_scaleHyperlinks =3D false, g_allowAdvOnClick =3D 1, g_showInBrowser = =3D 0, gLoopCont =3D 0, gUseSldTimings =3D 1; var g_showAnimation =3D g_supportsPPTHTML && SupportsPPTAnimation() && ( (w= indow.name=3D=3D"PPTSld" && !parent.IsFramesMode()) || g_showInBrowser );va= r g_animManager =3D null; var g_animUseRuntime =3D false; var g_animItemsToHide, g_animInteractiveItems, g_animSlideTime; var g_animMainSequence =3D null; var ENDSHOW_MESG=3D"スライド ショーの最後です。 クリックすると終了します。"= , SCREEN_MODE=3D"Frames", gIsEndShow=3D0, NUM_VIS_SLDS=3D59, SCRIPT_HREF=3D= "script.js", FULLSCR_HREF=3D"fullscreen.htm"; var gCurSld =3D gPrevSld =3D 1, g_offset =3D 0, gNtsOpen =3D gHasNts =3D gO= tlTxtExp =3D 0, gHasNarration =3D 0, gOtlOpen =3D true window.gPPTHTML=3DSupportsPPTHTML() var g_fBaseHyperlink =3D false; var gMainDoc=3Dnew Array(new hrefList("slide0001.htm",1,-1,1),new hrefList(= "slide0052.htm",1,-1,1),new hrefList("slide0002.htm",1,-1,1),new hrefList("= slide0003.htm",1,-1,1),new hrefList("slide0004.htm",1,-1,1),new hrefList("s= lide0005.htm",1,-1,1),new hrefList("slide0033.htm",1,-1,1),new hrefList("sl= ide0006.htm",1,-1,1),new hrefList("slide0007.htm",1,-1,1),new hrefList("sli= de0050.htm",1,-1,1),new hrefList("slide0008.htm",1,-1,1),new hrefList("slid= e0009.htm",1,-1,1),new hrefList("slide0034.htm",1,-1,1),new hrefList("slide= 0011.htm",1,-1,1),new hrefList("slide0045.htm",1,-1,1),new hrefList("slide0= 046.htm",1,-1,1),new hrefList("slide0051.htm",1,-1,1),new hrefList("slide00= 53.htm",1,-1,1),new hrefList("slide0010.htm",1,-1,1),new hrefList("slide006= 2.htm",1,-1,1),new hrefList("slide0035.htm",1,-1,1),new hrefList("slide0059= .htm",1,-1,1),new hrefList("slide0013.htm",1,-1,1),new hrefList("slide0061.= htm",1,-1,1),new hrefList("slide0014.htm",1,-1,1),new hrefList("slide0015.h= tm",1,-1,1),new hrefList("slide0016.htm",1,-1,1),new hrefList("slide0017.ht= m",1,-1,1),new hrefList("slide0018.htm",1,-1,1),new hrefList("slide0019.htm= ",1,-1,1),new hrefList("slide0047.htm",1,-1,1),new hrefList("slide0040.htm"= ,1,-1,1),new hrefList("slide0054.htm",1,-1,1),new hrefList("slide0036.htm",= 1,-1,1),new hrefList("slide0020.htm",1,-1,1),new hrefList("slide0021.htm",1= ,-1,1),new hrefList("slide0022.htm",1,-1,1),new hrefList("slide0038.htm",1,= -1,1),new hrefList("slide0041.htm",1,-1,1),new hrefList("slide0055.htm",1,-= 1,1),new hrefList("slide0024.htm",1,-1,1),new hrefList("slide0060.htm",1,-1= ,1),new hrefList("slide0039.htm",1,-1,1),new hrefList("slide0042.htm",1,-1,= 1),new hrefList("slide0026.htm",1,-1,1),new hrefList("slide0056.htm",1,-1,1= ),new hrefList("slide0025.htm",1,-1,1),new hrefList("slide0027.htm",1,-1,1)= ,new hrefList("slide0028.htm",1,-1,1),new hrefList("slide0030.htm",1,-1,1),= new hrefList("slide0058.htm",1,-1,1),new hrefList("slide0057.htm",1,-1,1),n= ew hrefList("slide0029.htm",1,-1,1),new hrefList("slide0063.htm",1,-1,1),ne= w hrefList("slide0064.htm",1,-1,1),new hrefList("slide0043.htm",1,-1,1),new= hrefList("slide0048.htm",1,-1,1),new hrefList("slide0031.htm",1,-1,1),new = hrefList("slide0032.htm",1,-1,1)); /********************************************* Frameset functions These functions control slide navigation and state of the frameset. **********************************************/ function RemoveFilePrefixFromHref(href) { var regExp =3D /^file:\/\/\//i; return href.replace(regExp, "") } function FullScrInit() { g_allowAdvOnClick =3D GetCurSld().mAdvOnClk document.body.style.backgroundColor=3D"black" document.oncontextmenu=3Dparent._CM; document.onkeydown =3D _KDH; document.ondragstart=3DCancel document.onselectstart=3DCancel self.focus() } function Redirect( frmId ) {=09 var str=3Ddocument.location.hash,idx=3Dstr.indexOf('#'), sId=3DGetSldId() if(idx>=3D0) str=3Dstr.substr(1); if( window.name !=3D frmId && ( sId !=3D str) ) { obj =3D GetObj("Main-File") window.location.href=3Dobj.href+"#"+sId return 1 } return 0 } var MHTMLPrefix =3D CalculateMHTMLPrefix();=20 function CalculateMHTMLPrefix() { if ( document.location.protocol =3D=3D 'mhtml:') {=20 href=3Dnew String(document.location.href)=20 Start=3Dhref.indexOf('!')+1=20 End=3Dhref.lastIndexOf('/')+1=20 if (End < Start)=20 return href.substring(0, Start)=20 else=20 return href.substring(0, End)=20 } return ''; } function GetTags(base,tag) { if(g_supportsPPTHTML) return base.all.tags(tag); else return base.getElementsByTagName(tag); } function UpdNtsPane(){ if(frames["PPTNts"]) PPTNts.location.replace( MHTMLP= refix+GetHrefObj( gCurSld ).mNtsHref ) } function UpdNavPane( sldIndex ){ if(gNavLoaded) PPTNav.UpdNav() } function UpdOtNavPane(){ if(gOtlNavLoaded) PPTOtlNav.UpdOtlNav() } function UpdOtlPane(){ if(gOtlLoaded) PPTOtl.UpdOtl() } function SetHasNts( fVal ) { if( gHasNts !=3D fVal ) { gHasNts=3DfVal UpdNavPane() } } function ToggleOtlText() { gOtlTxtExp=3D!gOtlTxtExp UpdOtlPane() } function ClearMedia() { // Clear any sounds playing before launching another browser window. Other= wise, // in fullscreen mode, you'll continue to hear the sound in the frames mod= e. if (PPTSld.pptSound) PPTSld.pptSound.loop =3D 0; } function FullScreen() {=20 if ( PPTSld.g_animUseRuntime ) PPTSld.document.body.pause(); ClearMedia(); var href =3D ( document.location.protocol =3D=3D 'mhtml:') ? FULLSCR_HREF = : FULLSCR_HREF+"#"+GetHrefObj(gCurSld).mSldHref; if (MHTMLPrefix !=3D "") href =3D RemoveFilePrefixFromHref(href) if(PPTNav.event.ctrlKey) { var w =3D (window.screen.availWidth * 1.0) / 2.0 var h =3D w * (PPTSld.g_origH * 1.0) / PPTSld.g_origW win =3D window.open( MHTMLPrefix+href,null,"toolbar=3D0,resizable=3D1,top= =3D0,left=3D0," + "width=3D"+ w + ",height=3D" + h ); if( win.document.body && PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } else { win =3D window.open( MHTMLPrefix+href,null,"fullscreen=3Dyes" ); if( win.document.body && PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } } function ToggleVNarration() { rObj=3DPPTSld.document.all("NSPlay") if( rObj && !PPTSld.g_animUseRuntime ) { if( (rObj.playState =3D=3D 1)||(rObj.playState =3D=3D 0) ) rObj.Play() else if( rObj.playState =3D=3D 2 ) rObj.Pause() else return; } else if( PPTSld.g_animUseRuntime ) { narObj =3D PPTSld.document.all("narrationID") if( narObj ) narObj.togglePause() } } function GetCurSldNum() { =20 obj=3DGetHrefObj(gCurSld) if( obj.mOrigVis =3D=3D 1 ) return obj.mSldIdx else =20 return gCurSld } function GetNumSlds() { =20 if( GetHrefObj(gCurSld).mOrigVis =3D=3D 1 ) return GetSldList().mNumVisSlds; else return GetSldList().mList.length } function GetSldNum( href ) { for(ii=3D0; ii 1 ) PopSldList(); else if( !IsFramesMode() ) { if( gLoopCont ) GoToFirst() else EndShow() } } function GoToPrevSld() { ii=3DgCurSld-1 if( ii > 0 ) { obj=3DGetHrefObj(ii) while ( obj && ( obj.mVis =3D=3D 0 ) && ( ii>0 ) ) obj=3DGetHrefObj(--ii) if( ii =3D=3D 0 ) ii=3D1 GoToSldNum(ii) } } function GoToFirst(){ GoToSld( GetHrefObj(1).mSldHref ) } function GoToLast() { ii=3DGetSldList().mList.length if( ii !=3D gCurSld ) GoToSld( GetHrefObj(ii).mSldHref ) } function GoToSldNum( num ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue obj =3D GetHrefObj( num ) obj.mVis=3D1 gPrevSld=3DgCurSld gCurSld =3D num; =09 if (MHTMLPrefix !=3D "") PPTSld.location.replace(MHTMLPrefix+RemoveFilePrefixFromHref(obj.mSldHref= )) else PPTSld.location.replace(obj.mSldHref) =09 if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function GoToSld( href ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue GetHrefObj( GetSldNum(href) ).mVis=3D1 if (MHTMLPrefix !=3D "") PPTSld.location.replace(MHTMLPrefix+RemoveFilePrefixFromHref(href)) else PPTSld.location.replace(href) } function SldUpdated( id ) { if( id =3D=3D GetHrefObj(gCurSld).mSldHref ) return gPrevSld=3DgCurSld gCurSld=3DGetSldNum(id) if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function PrevSldViewed(){ GoToSld( GetHrefObj(gPrevSld).mSldHref ) } function HasPrevSld() { return ( gIsEndShow || ( gCurSld !=3D 1 && GetHrefO= bj( gCurSld-1 ).mVis =3D=3D 1 )||( GetCurSldNum() > 1 ) ) } function HasNextSld() { return (GetCurSldNum() !=3D GetNumSlds()) } function CloseWindow() { if( HideMenu() ) return; =09 var event =3D PPTSld.event; if( !IsFramesMode() && event && (event.keyCode=3D=3D27 || event.keyCode=3D= =3D32 || event.type=3D=3D"click" ) ) window.close( self ); CatchNumKeys( self, event ); } function Unload() { gIsEndShow=3D0; } function SetupEndShow() { gIsEndShow=3D1; PPTSld.document.body.scroll=3D"no"; PPTSld.document.onkeypress=3DCloseWindow; PPTSld.document.onclick=3DCloseWindow; PPTSld.document.oncontextmenu=3D_CM; } function EndShow() { if( IsFramesMode() ) return if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue doc=3DPPTSld.document var dir =3D doc.body.dir if( dir !=3D "rtl" ) dir =3D "ltr"; doc.open() doc.writeln('


' + ENDSHOW_MESG + '

') doc.close() } function SetSldVisited(){ GetSldList().mList[gCurSld-1].mVisited=3Dtrue } function IsSldVisited(){ return GetSldList().mList[gCurSld-1].mVisited } function hrefList( sldHref, visible, advDelay, advClk ) { this.mSldHref=3D this.mNtsHref =3D sldHref this.mOrigVis=3D this.mVis =3D visible this.mVisited=3D false this.mAdvDelay=3D advDelay this.mAdvOnClk=3D advClk } function SldList(arr,curSld,fEnd) { this.mCurSld =3D curSld; this.mList =3D new Array(); var idx =3D 1; for(ii=3D0;ii 0) { PushSldList(sldList,fEnd); gCurSld =3D 1; } else if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue } function PushSldList(arr,fEnd) { var ii =3D gSldStack.length; gSldStack[ii] =3D new SldList(arr,gCurSld,fEnd); GoToSld( gSldStack[ii].mList[0].mSldHref ); } function PopSldList() { if (gSldStack[gSldStack.length-1].fEndShow) EndShow() else { gCurSld =3D gSldStack[gSldStack.length-1].mCurSld; gSldStack[gSldStack.length-1] =3D null; gSldStack.length--; var sldList =3D gSldStack[gSldStack.length-1]; GoToSld( sldList.mList[gCurSld - 1].mSldHref ); } } var custShowList=3Dnew Array(); /********************************************* Navigation button implementation There are 2 types of buttons: ImgBtn, TxtBtn implemented as function objects. They share a similiar interface so the event handlers can call SetActive, for example, on a button=20 object without needing to know exactly=20 what type of button it is. **********************************************/ //---------------------------------- function ImgBtn( oId,bId,w,action ) //---------------------------------- { var t=3Dthis t.Perform =3D _IBP t.SetActive =3D _IBSetA t.SetInactive=3D _IBSetI t.SetPressed =3D _IBSetP t.SetDisabled=3D _IBSetD t.Enabled =3D _IBSetE t.ChangeIcon =3D null t.UserAction =3D action t.ChgState =3D _IBUI t.mObjId =3D oId t.mBorderId=3D bId t.mWidth =3D w t.mIsOn =3D t.mCurState =3D 0 } function _IBSetA() { if( this.mIsOn ) { obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 ) obj.style.posTop=3D0 } } function _IBSetI() { if( this.mIsOn ) { obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 ) obj.style.posTop=3D0=20 } } function _IBSetP() { if( this.mIsOn ) { obj=3Dthis.ChgState( gShadowClr,gHiliteClr,2 ) obj.style.posLeft+=3D1; obj.style.posTop+=3D1 } } function _IBSetD() { =20 obj=3Dthis.ChgState( gFaceClr,gFaceClr,0 ) obj.style.posTop=3D0=20 } function _IBSetE( state ) { var t=3Dthis GetObj( t.mBorderId ).style.visibility=3D"visible" if( state !=3D t.mIsOn ) { t.mIsOn=3Dstate if( state ) t.SetInactive() else t.SetDisabled() } } function _IBP() { var t=3Dthis if( t.mIsOn ) { if( t.UserAction !=3D null ) t.UserAction() if( t.ChangeIcon ) { obj=3DGetObj(t.mObjId) if( t.ChangeIcon() ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-4)*t.mWidth else obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-0)*t.mWidth } t.SetActive() } =20 } function _IBUI( clr1,clr2,nextState ) { var t=3Dthis SetBorder( GetObj( t.mBorderId ),clr1,clr2 ) obj=3DGetObj( t.mObjId ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-nextState)*t.mWidth-obj= .style.posTop t.mCurState=3DnextState return obj } //----------------------------------------- function TxtBtn( oId,oeId,action,chkState ) //----------------------------------------- { var t=3Dthis t.Perform =3D _TBP t.SetActive =3D _TBSetA t.SetInactive=3D _TBSetI t.SetPressed =3D _TBSetP t.SetDisabled=3D _TBSetD t.SetEnabled =3D _TBSetE t.GetState =3D chkState t.UserAction =3D action t.ChgState =3D _TBUI t.mObjId =3D oId t.m_elementsId=3D oeId t.mIsOn =3D 1 } function _TBSetA() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gHiliteClr,gShadowClr,0,0 ) } function _TBSetI() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) } function _TBSetP() { if( this.mIsOn ) this.ChgState( gShadowClr,gHiliteClr,1,1 ) } function _TBSetD() { =20 this.ChgState( gFaceClr,gFaceClr,0,0 ) this.mIsOn =3D 0 } function _TBSetE() { var t=3Dthis if( !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) else t.ChgState( gShadowClr,gHiliteClr,1,1 ) t.mIsOn =3D 1 } function _TBP() { var t=3Dthis if( t.mIsOn ) {=20 if( t.UserAction !=3D null ) t.UserAction() if( !t.GetState ) return if( t.GetState() ) t.SetPressed() else t.SetActive() } =20 } function _TBUI( clr1,clr2,lOffset,tOffset ) { SetBorder( GetObj( this.mObjId ),clr1,clr2 ) Offset( GetObj( this.m_elementsId ),lOffset,tOffset ) } function Offset( obj, top, left ){ obj.style.top=3Dtop; obj.style.left=3Dle= ft } function SetBorder( obj, upperLeft, lowerRight ) { s=3Dobj.style; s.borderStyle =3D "solid" s.borderWidth =3D 1=20 s.borderLeftColor =3D s.borderTopColor =3D upperLeft s.borderBottomColor=3D s.borderRightColor =3D lowerRight } function GetBtnObj(){ return gBtnArr[window.event.srcElement.id] } function BtnOnOver(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetActive() } function BtnOnDown(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetPressed() } function BtnOnOut(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetInactive() } function BtnOnUp() { b=3DGetBtnObj() if( b !=3D null ) b.Perform() else Upd() } function GetNtsState(){ return parent.gNtsOpen } function GetOtlState(){ return parent.gOtlOpen } function GetOtlTxtState(){ return parent.gOtlTxtExp } function NtsBtnSetFlag( fVal ) { s=3Ddocument.all.item( this.m_flagId ).style s.display=3D"none" if( fVal ) s.display=3D"" else s.display=3D"none" } function _BSetA_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etActive() } function _BSetI_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etInactive() } function _BSetP_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etPressed() } function _BSetA_BorderImg() {=20 b =3D gBtnArr[this.mBorderId]=20 if( b !=3D null && this.mIsOn && !b.GetState() ) { obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 ) obj.style.posTop=3D0 } } function _BSetI_BorderImg() {=20 b =3D gBtnArr[this.mBorderId] if( b !=3D null && this.mIsOn && !b.GetState() ) { obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 ) obj.style.posTop=3D0 } } var gHiliteClr=3D"THREEDHIGHLIGHT",gShadowClr=3D"THREEDSHADOW",gFaceClr=3D"= THREEDFACE" var gBtnArr =3D new Array() gBtnArr["nb_otl"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOtlPan= e,GetOtlState ) gBtnArr["nb_otlElem"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOt= lPane,GetOtlState ) gBtnArr["nb_nts"] =3D new ImgBtn( "nb_nts","nb_ntsBorder",10,parent.ToggleN= tsPane ) gBtnArr["nb_nts"].SetActive =3D _BSetA_BorderImg; gBtnArr["nb_nts"].SetInactive =3D _BSetI_BorderImg; gBtnArr["nb_ntsBorder"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.= ToggleNtsPane,GetNtsState ) gBtnArr["nb_ntsElem"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.To= ggleNtsPane,GetNtsState ) gBtnArr["nb_prevBorder"] =3D gBtnArr["nb_prev"]=3D new ImgBtn( "nb_prev","n= b_prevBorder",30,parent.GoToPrevSld ) gBtnArr["nb_nextBorder"] =3D gBtnArr["nb_next"]=3D new ImgBtn( "nb_next","n= b_nextBorder",30,parent.GoToNextSld ) gBtnArr["nb_sldshw"]=3D new ImgBtn( "nb_sldshw","nb_sldshwBorder",18,parent= .FullScreen ) gBtnArr["nb_sldshwBorder"] =3D new TxtBtn( "nb_sldshw","nb_sldshwBorder",pa= rent.FullScreen,null ) gBtnArr["nb_sldshwBorder"].SetActive =3D _BSetA_Border; gBtnArr["nb_sldshwBorder"].SetInactive =3D _BSetI_Border; gBtnArr["nb_sldshwText"] =3D new TxtBtn( "nb_sldshw","nb_sldshwText",parent= .FullScreen,null ) gBtnArr["nb_sldshwText"].SetActive =3D _BSetA_Border; gBtnArr["nb_sldshwText"].SetInactive =3D _BSetI_Border; gBtnArr["nb_voice"] =3D gBtnArr["nb_voiceBorder"] =3D new ImgBtn( "nb_voice= ","nb_voiceBorder",18,parent.ToggleVNarration ) gBtnArr["nb_otlTxtBorder"] =3D gBtnArr["nb_otlTxt"]=3D new ImgBtn( "nb_otlT= xt","nb_otlTxtBorder",23,parent.ToggleOtlText ) gBtnArr["nb_ntsBorder"].m_flagId=3D "nb_nts" gBtnArr["nb_ntsBorder"].SetFlag =3D NtsBtnSetFlag gBtnArr["nb_otlTxt"].ChangeIcon=3D GetOtlTxtState /********************************************* Context menu implementation _CM() is the function that's hooked up to the oncontextmenu event. Once we're asked to show the menu, we first build it by creating DIVs on-the-fly. Then we position it=20 within the screen area so it doesn't get clipped. Creating the DIVs using createElement() means we don't have to write out any extra HTML into the slide HTML files. **********************************************/ var sNext=3D"次へ",sPrev=3D"前へ",sEnd=3D"スライド ショーの終了",sFont=3D"= lＳ 明朝",sArrow=3D"矢印",sFreeform=3D"フリーフォーム",sRect=3D"四角形",sOv= al=3D"楕円" function ShowMenu() { BuildMenu(); var doc=3DPPTSld.document.body,x=3DPPTSld.event.clientX+doc.scrollLeft,y= =3DPPTSld.event.clientY+doc.scrollTop m =3D PPTSld.document.all.item("ctxtmenu") m.style.pixelLeft=3Dx if( (x+m.scrollWidth > doc.clientWidth)&&(x-m.scrollWidth > 0) ) m.style.pixelLeft=3Dx-m.scrollWidth m.style.pixelTop=3Dy if( (y+m.scrollHeight > doc.clientHeight)&&(y-m.scrollHeight > 0) ) m.style.pixelTop=3Dy-m.scrollHeight m.style.display=3D"" } function _CM() { if( !parent.IsFullScrMode() ) return; if(!PPTSld.event.ctrlKey) { ShowMenu() return false } else HideMenu() } function BuildMenu() { if( PPTSld.document.all.item("ctxtmenu") ) return var mObj=3DCreateItem( PPTSld.document.body ) mObj.id=3D"ctxtmenu" mObj.style.visibility=3D"hidden" var s=3DmObj.style s.position=3D"absolute" s.cursor=3D"default" s.width=3D"120px" SetCMBorder(mObj,"menu","black") var iObj=3DCreateItem( mObj ) SetCMBorder( iObj, "threedhighlight","threedshadow" ) iObj.style.padding=3D2 CreateMenuItem( iObj,sNext,M_GoNextSld,M_True ) CreateMenuItem( iObj,sPrev,M_GoPrevSld,M_HasPrevSld ) =09 CreateSeparator( iObj ) CreateMenuItem( iObj,sEnd,M_End,M_True ) mObj.style.visibility=3D"visible" } function Cancel() { window.event.cancelBubble=3Dtrue; window.event.returnVa= lue=3Dfalse } function Highlight() { ChangeClr("activecaption","threedhighlight") } function Deselect() { ChangeClr("threedface","menutext") } function Perform() { e=3DPPTSld.event.srcElement if( e.type=3D=3D"menuitem" && e.IsActive() ) e.Action() else PPTSld.event.cancelBubble=3Dtrue } function ChangeClr( bg,clr ) { e=3DPPTSld.event.srcElement if( e.type=3D=3D"menuitem" && e.IsActive() ) { e.style.backgroundColor=3Dbg e.style.color=3Dclr } } function M_HasPrevSld() { return( parent.HasPrevSld() ) } function M_GoNextSld() { if( gIsEndShow ) M_End(); else GoToNextSld() } function M_GoPrevSld() { if( gIsEndShow ) { gIsEndShow=3D0; history.back();= PPTSld.event.cancelBubble=3Dtrue; } else GoToPrevSld() } function M_True() { return true } function M_End() { window.close( self ) } function CreateMenuItem( node,text,action,eval ) { var e=3DCreateItem( node ) e.type=3D"menuitem" e.Action=3Daction e.IsActive=3Deval e.innerHTML=3Dtext if( !e.IsActive() ) e.style.color=3D"threedshadow" e.onclick=3DPerform e.onmouseover=3DHighlight e.onmouseout=3DDeselect s=3De.style; 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 ノ= ート
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アウトライン
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