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_images/ec4f4d50cd0c997098dfa7ca95e35c189d991140714af9ecec7731a27a7b3197.png delete mode 100644 _images/ec9847e39ead686f4dc173d2ad13e16624331178191cac4d14af61ee6dedca28.png create mode 100644 _images/ef988a027c4686c408f09780dbc78f9f538afcb4660dc7f9987e0307f1a9af93.png create mode 100644 _images/ef98d22859b6d75822e704be96391a2a8358a81b4cc37a6c0a78d4a073377f5d.png delete mode 100644 _images/f134b403a21d2005e77925fa9743a8bc08c765d16f75c823967f730acaa99128.png create mode 100644 _images/f3ad962c236dbf9bebc6288d6d456f0f14d0b98abbc527ead677abb307f604cc.png create mode 100644 _images/f4478338633ce64c9c74e4b71ec3b9aecde068095689ffe7b86190623e5c84bf.png delete mode 100644 _images/f7363c88c53a190d02b4343c5bda358caacad2058812e56363ff268a40a3f7b0.png create mode 100644 _images/fbdb1c89a04138e1f8363ff7c2efbe8171193fe8cfdf8643caf87a27432c2cf9.png delete mode 100644 _images/fca7950b90a1463ba5da889cb89a9817a86be84c03329cbd100583643359d1c3.png delete mode 100644 _images/fd3a758d064e24cd70dbacf4eef8b9bd80a23b94b93a9f73394cdd1808ad1a6c.png create mode 100644 _images/fe3e5e90eaab242090ce3907ed8009675290f14afdad761a2889472ac6a5e784.png diff --git a/10_Residuals.html b/10_Residuals.html index 348db5d9..e1bcc3c4 100644 --- a/10_Residuals.html +++ b/10_Residuals.html @@ -600,8 +600,8 @@

説明#
-
決定係数が高いケース: 0.897
-決定係数が高いケース: 0.503
+
決定係数が高いケース: 0.916
+決定係数が高いケース: 0.573
@@ -638,7 +638,7 @@

散布図と回帰直線 -_images/8c6770d7095822a4c57beaa37b75ce52176642bc7f48981b35eedaa1896f6814.png +_images/5d9a61329744e67a0ec7500fd0f08f59110a3a6392efe2f83d65819620f764fa.png

回帰直線のフィット感ははっきりと決定係数の値に現れている。

@@ -671,7 +671,7 @@

残差#
-_images/abd7f0809136447ea8fd136127961bdb236c7186a737301be6558ee6805a70de.png +_images/6839c6145d81304003749e98c5a4c88127bdbd6331010a127694dbfc4f1115f5.png

ここでも決定係数の値との関係がハッキリとわかる。

@@ -704,7 +704,7 @@

標準化残差 -_images/5dfa02cd82241804090eb214fc98c6fb554a68366622cbc5b14f8333edbc319c.png +_images/04b0535cf48506430ba126aaae3183340ee9e7d088df9a14d4f44fc8cf41215e.png

左右ともに散らばりの差はあまりない。もちろん，理由は平均0，分散1になるように「標準化」されているためである。

@@ -753,7 +753,7 @@

「理想的な」残差の分布 -_images/2206f233d43df96047bdf3e5708f4ed3602bf4fdf631dd7a36ecf964647f4050.png +_images/3ec3f03eca313b45e1e4ac28b0f06419a82fad66feb23f2de471a08738b6939e.png

0の周りに均等に分散しているのが確認できる。

@@ -766,7 +766,7 @@

「理想的な」残差の分布 -_images/6c66fcd166292db8e452effac16c637159cae51fa3f0f5c671b604be5bcddcb4.png +_images/94e5342a691a533d60d93e248fe3bc73b011a2bb514fd59ecc4890d3ce72e06f.png

観測値の間隔は少し広がっているが，シミュレーションによっては\(n=2000\)と比べて大きな変化は見られない場合もあれば，「外れ値」が気になる場合もあるかも知れない。

@@ -779,7 +779,7 @@

「理想的な」残差の分布 -_images/36b588cf00331758eb035d9c509197fc4f0f2bd2057ddb92f8bd923d9fb5675a.png +_images/750744c3aff1e1e9c9c2986c7cf519418d4e053501e0bd49cfaab77834752fc4.png

さらに隙間が広くなっている。シミュレーションによっては，少し偏りがあるように見える場合も発生するため，上の例と比べると，GM仮定1,4,5に関して自信を持って判断しづらくなる。

@@ -792,7 +792,7 @@

「理想的な」残差の分布 -_images/3fb3edec2c370b5404dd213e7a99cf5a1cf350ec9ecaab5ac766497a74f0a60d.png +_images/ef988a027c4686c408f09780dbc78f9f538afcb4660dc7f9987e0307f1a9af93.png

正規分布と分かって眺めるとそう見えるかも知れないが，実際の実証分析を行う上でこの図だけでGM仮定1,4,5が満たされているかどうかを判断するのは難しい。

@@ -805,7 +805,7 @@

「理想的な」残差の分布 -_images/ec4f4d50cd0c997098dfa7ca95e35c189d991140714af9ecec7731a27a7b3197.png +_images/a566b98b5773d36633eddb0c70a2fe1fb5d0c58dd75631d13c635b74fecb268b.png

標本の大きさが小さい場合，観測数が10少なくなると図が大きく違うように見える。

@@ -857,7 +857,7 @@

resid_fit()
-_images/5a99d378409a2f606bfbe03877588925d9725dc42c3d940d06ee750cfb807742.png +_images/fbdb1c89a04138e1f8363ff7c2efbe8171193fe8cfdf8643caf87a27432c2cf9.png

回帰分析結果の「健康状態」を診断する上でこの図は最もよく使われる。この図について以下の点を覚えておこう。

@@ -893,7 +893,7 @@

q_q()
-_images/b1a94b37c44712dd7f58dff886168328c7449b374382ea1578a2af0cd055a621.png +_images/2cca4410f188f96c06cd74f0f32082d7c3030a63b39e51860c2ce66101374142.png
@@ -925,7 +925,7 @@

scale_loc()
-_images/79c4e24475f9bcd1efae791493e9f6228c0837e9b6ea7933778f3d0dd9d642a4.png +_images/12483f85c0b7bce6d0d6590993ab6ec7aca11af6dcfac4bc206aa8f1c201543d.png
@@ -984,7 +984,7 @@

resid_lev()
-_images/c7ac5124b6952ad74475f9d20dfb20362f9875d569cc79c3b52d4281ba2b8754.png +_images/d97782afce474f0956daf61ad604fc7fcd1180e95ca2d2646299ae141757a776.png
@@ -999,7 +999,7 @@

plot()
-_images/dd509db883bdb535d58c506effa221781dab89beb8844de69e2edcd60385e613.png +_images/41003f3f915aedda0037ce74b9c9239e8cf4d2452998a9a5189cd2d25006151c.png
@@ -1025,7 +1025,7 @@

qq
-_images/889883ca911f20d89cda6533dc3cc27aae804cc550f9d9020c2ea267652bf2fe.png +_images/fe3e5e90eaab242090ce3907ed8009675290f14afdad761a2889472ac6a5e784.png
@@ -1068,7 +1068,7 @@

ケース１：被説明変数の変換が必要な回帰式 -_images/fca7950b90a1463ba5da889cb89a9817a86be84c03329cbd100583643359d1c3.png +_images/d7d2aea8d367e961e527a654d8378b6fcc395917eac7aaf419af03cc48d46714.png

lmdiagパッケージを使う。

@@ -1081,7 +1081,7 @@

ケース１：被説明変数の変換が必要な回帰式 -_images/4f450169a90919e80d734dbb25c2c9424e052222d5f1953159f1d8d71d5f93dd.png +_images/ec1a6ddeca5c531bae2ea15a471bae7664c9b717c577b133269ba28fea3dd4bc.png @@ -1121,7 +1121,7 @@

ケース２：説明変数の２乗項の欠落 -_images/539dfcc42dd0af1a83d79304ac1ff1bc0834fc4a6002b5797fe4216198ad473c.png +_images/4a5574bad646440c723988338f6efd6af00f20414c210c5e9cfd1d0975066673.png

lmdiagパッケージを使う。

@@ -1134,7 +1134,7 @@

ケース２：説明変数の２乗項の欠落 -_images/a250a0206ca426a14765e76d784430cd4d5c1679e4e0d9f8af4d41bb8bea4254.png +_images/ec367371d39f4c322bf447389c1b36e2b2ee64bc9f82bacc40c8e065245f1f1f.png @@ -1184,7 +1184,7 @@

ケース３：定数項がある条件により変化する場合 -_images/a55987f72e48595c2890a946b31bed807c3a3359900c782dffcb70ed7d05318e.png +_images/14ea2eb74f63a44ad2f79a118c41850389651c44d11c7e9fb381da083e4bbd60.png

lmdiagパッケージを使う。

@@ -1197,7 +1197,7 @@

ケース３：定数項がある条件により変化する場合 -_images/fd3a758d064e24cd70dbacf4eef8b9bd80a23b94b93a9f73394cdd1808ad1a6c.png +_images/d509a8a7a726490cc121541a20363c58e55f3b67cae1e4daa0fc792f8d99a92a.png @@ -1250,7 +1250,7 @@

ケース４：不均一分散 -_images/683e1f5aa1cfe7be7ce6c2c06bc651303b3cf98f82c1001e9a6f68a4fffa7c5a.png +_images/827c9ee16b4db0124279f3b37da638ce6acb5d339400380c4e280551ebab3e21.png

lmdiagパッケージを使う。

@@ -1263,7 +1263,7 @@

ケース４：不均一分散 -_images/099fbbf21ae6e28c9e53efc604a5dcb4d8a6f30d00ab38ae2be17e3c666df7d6.png +_images/13e8353644c12228d3871d1037263e24697feebae130290214c79574f8def095.png diff --git a/11_Inference.html b/11_Inference.html index 00dcbaed..a823e794 100644 --- a/11_Inference.html +++ b/11_Inference.html @@ -1366,7 +1366,7 @@

例２#< Model: OLS Adj. R-squared: 0.622 Method: Least Squares F-statistic: 117.1 Date: Fri, 26 Apr 2024 Prob (F-statistic): 2.94e-72 -Time: 01:07:44 Log-Likelihood: -385.11 +Time: 01:22:49 Log-Likelihood: -385.11 No. Observations: 353 AIC: 782.2 Df Residuals: 347 BIC: 805.4 Df Model: 5 diff --git a/12_Asymptotics.html b/12_Asymptotics.html index cf48493a..191d6359 100644 --- a/12_Asymptotics.html +++ b/12_Asymptotics.html @@ -623,8 +623,8 @@

誤差項のプロット -
array([-0.05009079,  0.0529165 , -0.15018024, -0.68668332, -0.63185186,
-       -0.60238598,  0.34450712,  0.4914732 ,  2.02892046, -0.21149635])
+
array([-0.58755397, -0.6923631 , -0.65175023, -0.58854049, -0.57294096,
+        1.83644576, -0.53638275,  0.08298528,  0.50667047, -0.70576722])
@@ -641,7 +641,7 @@

誤差項のプロット -_images/22d2361d09e89e74d53472e5c4488e3a2b713a6d6a00a89a50a2413b6197925f.png +_images/53f6f990c916e20e8b551e8959cb5e6bc269a7ca5c2a749f7b7b174a064fabe4.png

確認のために、生成されたn個のランダム変数（誤差項）の平均を計算してみる。

@@ -652,7 +652,7 @@

誤差項のプロット -
0.011008358073635097
+
-0.0008650462833405683
@@ -764,8 +764,8 @@

一致性#

-
array([ 0.46223136,  0.25710557,  0.1312048 , ...,  0.36277218,
-       -0.03453762,  0.74689937])
+
array([ 0.61278042,  1.10006178, -0.04201085, ...,  0.48081694,
+        0.74138616,  1.14906769])
@@ -803,7 +803,7 @@

一致性#

-_images/e56ffe7d16c329e245e4caac7e52b26d00c69b2de9f2c06b090f5aab3f74831b.png +_images/233a33e118a3f215e32283ee1b34cfe1631457ec2da4c486dab3faab580f6e31.png

上のコードには同じような行が複数あり，単純な間違いの可能性が高くなる。。forループを使うとよりコンパクトに書くことが可能となり，間違いも少なくなる。

@@ -835,7 +835,7 @@

一致性#
-_images/e56ffe7d16c329e245e4caac7e52b26d00c69b2de9f2c06b090f5aab3f74831b.png +_images/233a33e118a3f215e32283ee1b34cfe1631457ec2da4c486dab3faab580f6e31.png

＜コードの説明＞

@@ -1040,7 +1040,7 @@

誤差項の正規性が満たされる場合 -_images/8089312c8f7c83c6c40768243ee9f262e005b1b682797971c5f3b8834a7fe494.png +_images/7c18543a5ffa0e836255dbc799ba3c9d59b4b51ee8121041921e08765d560a07.png

（結果：小標本特性）

@@ -1140,7 +1140,7 @@

誤差項の正規性が満たされない場合 -_images/591737bd0207bc4320db690fd9166e6c73f56d06b990b13ac81902ea71fc1ff0.png +_images/bbc006fe84faa452b4dba59bffee0ef0ab19982553deed405ef2dd181c345a21.png

（結果：大標本特性）

@@ -1169,7 +1169,7 @@

qqプロット
-_images/d093015d6a631585c8b9152d9f900359648d5ac772fafaed0ce0f8ae839e0291.png +_images/5cc52add4988df777cc90ae2ebf1f14c54db82d1c7c3219e35686894797b1048.png

一様分布から生成したデータの場合。45度線から乖離しているのが分かる。

@@ -1182,7 +1182,7 @@

qqプロット
-_images/ada2ec8e0707ccd27d9fe47c8a32fbe1e0b44102561775335f8ac178b507e62a.png +_images/60571ddfeeb176e2e5033d31ebf4e5d4342caea617032e11f71b199743f44ec0.png

wooldridgeパッケージにあるwage1のデータを使ってみる。

@@ -1236,10 +1236,10 @@

Jarque-Bera検定 -
(1.2221850531550185,
- 0.5427575679667518,
- -0.08420142033403416,
- 2.8259156359509388)
+
(0.1286611984361572,
+ 0.937694947065706,
+ -0.03488944656828683,
+ 3.036147525469528)
@@ -1262,10 +1262,10 @@

Jarque-Bera検定 -
(28.47510877308583,
- 6.557053001323347e-07,
- -0.031199528500363383,
- 1.8325619593342266)
+
(26.25343977788888,
+ 1.991305928581544e-06,
+ -0.04500843378441752,
+ 1.881044204227995)
@@ -1347,7 +1347,7 @@

Omnibus検定 -
NormaltestResult(statistic=1.1331437150723616, pvalue=0.5674674673438247)
+
NormaltestResult(statistic=0.20934069198621627, pvalue=0.9006213670979423)
@@ -1363,7 +1363,7 @@

Omnibus検定 -
NormaltestResult(statistic=253.85225892609765, pvalue=7.5280477452466725e-56)
+
NormaltestResult(statistic=188.733148762597, pvalue=1.0402014865514322e-41)
diff --git a/15_Pooling.html b/15_Pooling.html index ed434e2a..e86f023f 100644 --- a/15_Pooling.html +++ b/15_Pooling.html @@ -1302,7 +1302,7 @@

１階差分推定の準備：

-
<pandas.core.groupby.generic.DataFrameGroupBy object at 0x1038ec9a0>
+
<pandas.core.groupby.generic.DataFrameGroupBy object at 0x12f1aa1d0>
diff --git a/17_Panel.html b/17_Panel.html index 60718f8a..6bcf7b29 100644 --- a/17_Panel.html +++ b/17_Panel.html @@ -1174,7 +1174,7 @@

EntityEffects#< Estimator: RandomEffects R-squared (Between): 0.0967 No. Observations: 4360 R-squared (Within): 0.1806 Date: Fri, Apr 26 2024 R-squared (Overall): 0.1355 -Time: 01:08:13 Log-likelihood -1609.8 +Time: 01:23:11 Log-likelihood -1609.8 Cov. Estimator: Unadjusted F-statistic: 69.027 Entities: 545 P-value 0.0000 @@ -1687,7 +1687,7 @@

FE対RE検定

@@ -1770,7 +1770,7 @@

一定な変数を含める#

==============================================================================

+

+
+
@@ -2097,32 +2100,32 @@

推定値の計算0 2000 - -0.151936 - 0.087116 + 2.543866 + 0.744371 0.0 2001 - -0.873052 - -0.813811 + -2.503718 + -1.072235 0.0 2002 - 3.474612 - 0.485697 + 1.136667 + 0.038189 0.0 2003 - 1.735614 - 0.038616 + 2.137807 + -0.094892 0.0 2004 - 4.058849 - 1.496551 + 1.137354 + 0.451932 0.0 @@ -2145,7 +2148,7 @@

推定値の計算 -_images/4bfcbfe9e4826d25585512870516b15a472db9d3c3a72f67cc7aa1900531212d.png +_images/d6893f4c93555ad26975787013c8c2a588b9f0b56c66308db5d33b626a7bf2e3.png diff --git a/18_Zero_Conditional_Mean.html b/18_Zero_Conditional_Mean.html index acd42db6..1fdb8344 100644 --- a/18_Zero_Conditional_Mean.html +++ b/18_Zero_Conditional_Mean.html @@ -557,7 +557,7 @@

仮定４が満たされる場合： -_images/bffb5c5b8da1a7a5765a4ff7e3c501ae40fefea2e9be017ec73b22bafcdacd37.png +_images/6befbb57c863a7e3f35e4601e29d347e6c97edb17158ed8d716d6df17224754b.png

共分散を計算してみよう。

@@ -568,8 +568,8 @@

仮定４が満たされる場合： -
array([[1.        , 0.16548808],
-       [0.16548808, 1.        ]])
+
array([[1.       , 0.1090939],
+       [0.1090939, 1.       ]])
@@ -588,7 +588,7 @@

仮定４が満たされる場合： -_images/13bfd8a0c248ddd78d72e7c96ce6f6b1f5e684d7c2cc3a303a04a80623573f87.png +_images/cf94e7a5444b65dde718614ce928b6c6b94b383f51dde9a662db40107c92ad1f.png

推定量が不偏性を満たしているため両方は殆ど同じである。

@@ -612,7 +612,7 @@

仮定４が満たされない場合： -_images/6ecd831d3e6d6400c0b5c50f64dea1c037b416f37fa2354e0e662e610a27fa1f.png +_images/ef98d22859b6d75822e704be96391a2a8358a81b4cc37a6c0a78d4a073377f5d.png
@@ -622,8 +622,8 @@

仮定４が満たされない場合： -
array([[1.        , 0.77959644],
-       [0.77959644, 1.        ]])
+
array([[1.        , 0.81183185],
+       [0.81183185, 1.        ]])
@@ -642,7 +642,7 @@

仮定４が満たされない場合： -_images/53f942639da81effc5a3b3550b504fa734b72fae7418541617b4fc54410163e8.png +_images/e0320e7b903230cb606b642ea526423371e931838249ed5f790769e6f868b3f4.png

明らかに異なる。GM仮定４が満たされず，推定量の不偏性が満たされないためである。この場合，一致性も満たされない。標本の大きさnを100000にして確かめてみる。

@@ -661,7 +661,7 @@

仮定４が満たされない場合： -_images/f134b403a21d2005e77925fa9743a8bc08c765d16f75c823967f730acaa99128.png +_images/2ff9b281f5a011163eb9bb5729dbc64f4dcb36fcfb2de9ad96aa90598a8ae330.png

上から３行目にalpha=0.1とあるが，散布図のマーカーの透明度をしている引数であり0~1の値をとる。デフォルトは1であり，0は透明になる。

@@ -744,9 +744,9 @@

シミュレーション１：推定値の計算 -
Intercept    1.634411
-X1           3.096871
-X2           0.990375
+
Intercept    2.145330
+X1           2.948788
+X2           1.003965
 dtype: float64
 

 

@@ -834,7 +834,7 @@ 
シミュレーション２：推定値の分布
-_images/3f87833bffb1e66dcfd89c0796c2eb8a0c7224064835b2d287c1745f7295193e.png
+_images/5f54091308d6f2b0b2aa5b1d671106bc03f36e6c458309aa10b0254ebe39cb5d.png

\(\hat{\beta}_1\)の分布

@@ -847,7 +847,7 @@

シミュレーション２：推定値の分布 -_images/4ee457e0fa2c02e52d9c71097f5f5aaf5904f1c92b7dc54b2e2feddfbeae4d8e.png +_images/40ac86fe19642b27ac056e5dd5ba89efb78e00335a6580c94564b60dae1a992e.png

\(\hat{\beta}_2\)の分布

@@ -860,7 +860,7 @@

シミュレーション２：推定値の分布 -_images/0150eac657dda3f7418ec0e321d0f5770a6b470319080ec1a76e37e48a6abf05.png +_images/f3ad962c236dbf9bebc6288d6d456f0f14d0b98abbc527ead677abb307f604cc.png @@ -926,8 +926,8 @@

シミュレーション１：推定値の計算 -
Intercept    4.449084
-X            0.373601
+
Intercept    4.140016
+X            0.379328
 dtype: float64
 

 

@@ -998,7 +998,7 @@ 
シミュレーション２：推定値の分布
-_images/54fb0ff60fbceb52fdd9858938813f844c64fbc449ad8f30f70db45190d6d1e4.png
+_images/910b8d39332eb9278e7d7a832cd933be41f7799a97fa2d517d2c4d20c6fc559b.png

\(\hat{\beta}_1\)の分布

@@ -1011,7 +1011,7 @@

シミュレーション２：推定値の分布 -_images/d44f2cf63720801259b31cc663ef6bc185b294083e35f5bacf171ade202b4975.png +_images/f4478338633ce64c9c74e4b71ec3b9aecde068095689ffe7b86190623e5c84bf.png @@ -1141,9 +1141,9 @@

シミュレーション１：推定値の計算 -
Intercept    1.331037
-L           -0.828044
-Xd           2.545579
+
Intercept    1.306970
+L           -0.831754
+Xd           2.553262
 dtype: float64
 

 

@@ -1159,9 +1159,9 @@ 
シミュレーション１：推定値の計算
-
d0の真の値：1.5		d0の推定量：1.331036798884476
-d1の真の値：-1		d1の推定量：-0.8280438756717954
-d2の真の値：2.0		d2の推定量：2.545578785974058
+
d0の真の値：1.5		d0の推定量：1.3069698094125497
+d1の真の値：-1		d1の推定量：-0.8317536172667027
+d2の真の値：2.0		d2の推定量：2.553261797516754
 

 

 

@@ -1251,7 +1251,7 @@ 
シミュレーション２：推定値の分布
-_images/561e484b6efbd697ad1f581a400a1666cd19740637d2382de65af7330d373109.png
+_images/a48def7eb07626f07fca88672a4ad75aa8ba336879b70b433eb3eafe4cd64bbf.png

\(\hat{\beta}_1\)の分布

@@ -1264,7 +1264,7 @@

シミュレーション２：推定値の分布 -_images/153c79456986b4c8885e8fe04cabdcefcead218102f95faf4125b07f25a9c355.png +_images/c240990b9f2dc775f18bf5d614adaad31480a7e18d0c1a073c25acc2e665aa89.png

\(\hat{\beta}_2\)の分布

@@ -1277,7 +1277,7 @@

シミュレーション２：推定値の分布 -_images/69a33a64e5d353a849180eff362028709c0ff1102861dbc99a465dd2b9877631.png +_images/1df6d4efbd1eaabf17b20aac9343719ed39237981c26adb93e0d37031211e6ab.png diff --git a/19_IV2SLS.html b/19_IV2SLS.html index 4955b4d4..ebd9314a 100644 --- a/19_IV2SLS.html +++ b/19_IV2SLS.html @@ -939,7 +939,7 @@

educデータの作成 ============================================================================== Parameter Std. Err. T-stat P-value Lower CI Upper CI ------------------------------------------------------------------------------ -Intercept 1.0069 0.0173 58.225 0.0000 0.9730 1.0408 -x3 1.0021 0.0172 58.176 0.0000 0.9683 1.0358 -w1 1.0067 0.0214 47.150 0.0000 0.9649 1.0486 -w2 0.9877 0.0213 46.286 0.0000 0.9459 1.0295 +Intercept 1.0041 0.0173 57.976 0.0000 0.9701 1.0380 +x3 0.9961 0.0176 56.678 0.0000 0.9616 1.0305 +w1 0.9799 0.0215 45.530 0.0000 0.9377 1.0221 +w2 0.9920 0.0217 45.674 0.0000 0.9495 1.0346 ============================================================================== @@ -1549,7 +1549,7 @@

一致性#
-_images/a647a1d7f2271e082e8fae97dade46b573d493ef38a11cfb22e306b232939475.png +_images/6129567095e854432d76f346ed369cb0ac0ceba8d778984189a74bd6a33153ef.png