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<h1 class="title toc-ignore">statistical test</h1>
<h4 class="author">Jiawen Zhao</h4>
<h4 class="date">12/5/2022</h4>
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<p>Correlation matrix between predictor variables</p>
<pre class="r"><code>data <- read.csv("./data/worldcup_final.csv") %>%
na.omit() %>%
select(-country)
#hist.data.frame(data, nclass = 8)
num = data[2:14] %>%
select(-gd, -player)
#summary(num)
corrplot(cor(num), diag = FALSE)</code></pre>
<p><img src="statistical-analysis_files/figure-html/unnamed-chunk-2-1.png" width="672" /></p>
<p>Model selection: stepwise method</p>
<p>Model selection that didn’t work.</p>
<pre class="r"><code>model_step_wise = step(glm(w ~ ., data = data), direction = "both")</code></pre>
<pre><code>## Start: AIC=-4704.92
## w ~ X.1 + X + part + pld + d + l + gf + ga + gd + pts + rank +
## player + goals + land_area_km + confederation
##
##
## Step: AIC=-4704.92
## w ~ X.1 + X + part + pld + d + l + gf + ga + gd + pts + rank +
## player + goals + land_area_km
##
##
## Step: AIC=-4704.92
## w ~ X.1 + X + part + pld + d + l + gf + ga + gd + pts + rank +
## player + goals
##
##
## Step: AIC=-4704.92
## w ~ X.1 + X + part + pld + d + l + gf + ga + gd + pts + rank +
## player
##
##
## Step: AIC=-4684.83
## w ~ X.1 + X + part + pld + d + l + gf + ga + gd + pts + player</code></pre>
<pre class="r"><code>model_forward = step(glm(w ~ 1, data = data), direction = "forward", scope = formula(lm(gf ~ ., data = data)), test = "F")</code></pre>
<pre><code>## Start: AIC=650.5
## w ~ 1</code></pre>
<pre><code>## Warning in model.matrix.default(Terms, m, contrasts.arg = object$contrasts): the
## response appeared on the right-hand side and was dropped</code></pre>
<pre><code>## Warning in model.matrix.default(Terms, m, contrasts.arg = object$contrasts):
## problem with term 5 in model.matrix: no columns are assigned</code></pre>
<pre><code>## Warning in pf(q = q, df1 = df1, ...): NaNs produced</code></pre>
<pre><code>## Df Deviance AIC F value Pr(>F)
## + player 78 0.0 -4516.4 0.0000 NaN
## + pts 1 55.7 202.6 22819.5964 < 0.00000000000000022 ***
## + pld 1 1239.9 447.7 951.8644 < 0.00000000000000022 ***
## + gd 42 1119.1 521.6 11.8313 0.000000000007697 ***
## + part 1 3427.4 528.0 295.1918 < 0.00000000000000022 ***
## + d 1 4404.6 547.8 212.6190 < 0.00000000000000022 ***
## + ga 1 4618.6 551.6 199.1985 < 0.00000000000000022 ***
## + l 1 8151.2 596.5 79.4979 0.000000000000174 ***
## + rank 1 11472.2 623.5 34.1943 0.000000114141983 ***
## + confederation 5 13045.7 641.6 3.9407 0.003219 **
## + goals 1 14688.0 643.0 9.8496 0.002408 **
## + land_area_km 1 16106.7 650.3 2.1997 0.142115
## <none> 16566.8 650.5
## + X.1 1 16279.9 651.1 1.3569 0.247668
## + X 1 16279.9 651.1 1.3569 0.247668
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=-4516.41
## w ~ player</code></pre>
<pre><code>## Warning in model.matrix.default(Terms, m, contrasts.arg = object$contrasts): the
## response appeared on the right-hand side and was dropped</code></pre>
<pre><code>## Warning in model.matrix.default(Terms, m, contrasts.arg = object$contrasts):
## problem with term 6 in model.matrix: no columns are assigned</code></pre>
<pre><code>## Df Deviance AIC F value Pr(>F)
## <none> 0.000000000000000000000000090583 -4516.4</code></pre>
<pre class="r"><code>model_backward = step(glm(w ~ ., data = data), direction = "backward", test = "F")</code></pre>
<pre><code>## Start: AIC=-4704.92
## w ~ X.1 + X + part + pld + d + l + gf + ga + gd + pts + rank +
## player + goals + land_area_km + confederation</code></pre>
<pre><code>## Warning in pf(q = q, df1 = df1, ...): NaNs produced</code></pre>
<pre><code>##
## Step: AIC=-4704.92
## w ~ X.1 + X + part + pld + d + l + gf + ga + gd + pts + rank +
## player + goals + land_area_km</code></pre>
<pre><code>## Warning in pf(q = q, df1 = df1, ...): NaNs produced</code></pre>
<pre><code>##
## Step: AIC=-4704.92
## w ~ X.1 + X + part + pld + d + l + gf + ga + gd + pts + rank +
## player + goals</code></pre>
<pre><code>## Warning in pf(q = q, df1 = df1, ...): NaNs produced</code></pre>
<pre><code>##
## Step: AIC=-4704.92
## w ~ X.1 + X + part + pld + d + l + gf + ga + gd + pts + rank +
## player</code></pre>
<pre><code>## Warning in pf(q = q, df1 = df1, ...): NaNs produced</code></pre>
<pre><code>##
## Step: AIC=-4684.83
## w ~ X.1 + X + part + pld + d + l + gf + ga + gd + pts + player</code></pre>
<pre class="r"><code>model_step_wise</code></pre>
<pre><code>##
## Call: glm(formula = w ~ X.1 + X + part + pld + d + l + gf + ga + gd +
## pts + player, data = data)
##
## Coefficients:
## (Intercept)
## 0.0000000000000024134
## X.1
## 0.0000000000000004817
## X
## NA
## part
## 0.0000000000000083960
## pld
## 0.9999999999999913403
## d
## -0.9999999999999983347
## l
## -1.0000000000000031086
## gf
## 0.0000000000000362729
## ga
## -0.0000000000000307581
## gd−1
## 0.0000000000000177528
## gd−10
## 0.0000000000003069281
## gd−11
## 0.0000000000003785680
## gd−12
## 0.0000000000003667302
## gd−13
## 0.0000000000003487008
## gd−14
## 0.0000000000004558264
## gd−15
## 0.0000000000005008951
## gd−16
## 0.0000000000004779476
## gd−17
## 0.0000000000005499038
## gd−18
## 0.0000000000005984908
## gd−19
## 0.0000000000006229132
## gd−2
## 0.0000000000000354397
## gd−20
## 0.0000000000006497331
## gd−21
## 0.0000000000006871761
## gd−25
## 0.0000000000008286075
## gd−26
## 0.0000000000008034887
## gd−3
## 0.0000000000000928784
## gd−30
## 0.0000000000009636107
## gd−31
## 0.0000000000010274547
## gd−39
## 0.0000000000012549277
## gd−4
## 0.0000000000001115257
## gd−5
## 0.0000000000001426738
## gd−6
## 0.0000000000001793904
## gd−7
## 0.0000000000002275724
## gd−8
## 0.0000000000002329129
## gd−9
## 0.0000000000002707476
## gd+102
## -0.0000000000036121206
## gd+12
## -0.0000000000003983960
## gd+129
## -0.0000000000044634136
## gd+13
## -0.0000000000005108038
## gd+16
## -0.0000000000005829673
## gd+2
## -0.0000000000000762114
## gd+23
## -0.0000000000008362256
## gd+3
## -0.0000000000001591636
## gd+30
## -0.0000000000011808189
## gd+33
## -0.0000000000011897718
## gd+37
## -0.0000000000012117531
## gd+44
## -0.0000000000015134993
## gd+48
## -0.0000000000017058081
## gd+51
## -0.0000000000017294916
## gd+7
## -0.0000000000003246887
## gd0
## NA
## pts
## NA
## playerAdrian Mutu & Gheorghe Hagi
## -0.0000000000000298358
## playerAhmed Faras
## 0.0000000000000226185
## playerAkwá
## 0.0000000000000416509
## playerAleksandar Mitrović
## -0.0000000000000649159
## playerAlexander Frei
## NA
## playerAlexander Kerzhakov & Artem Dzyuba
## NA
## playerAlexis Sánchez
## 0.0000000000000237378
## playerAli Daei
## NA
## playerAli Mabkhout
## -0.0000000000000149395
## playerAndriy Shevchenko
## 0.0000000000000035207
## playerAsamoah Gyan
## 0.0000000000000154620
## playerBashar Abdullah
## 0.0000000000000084313
## playerBenni McCarthy
## -0.0000000000000246940
## playerCarlos Pavón
## NA
## playerCha Bum-kun
## -0.0000000000000276173
## playerChris Wood
## 0.0000000000000004658
## playerClint Dempsey & Landon Donovan
## NA
## playerCristiano Ronaldo
## NA
## playerCyle Larin
## 0.0000000000000428103
## playerDavid Healy
## NA
## playerDavid Villa
## NA
## playerDavor Šuker
## NA
## playerDenis Law & Kenny Dalglish
## NA
## playerDidier Drogba
## -0.0000000000000063227
## playerDieumerci Mbokani
## NA
## playerDimitar Berbatov & Hristo Bonev
## NA
## playerEdin Džeko
## 0.0000000000000080834
## playerEmmanuel Adebayor
## 0.0000000000000019908
## playerEmmanuel Sanon
## 0.0000000000000081302
## playerEnner Valencia
## 0.0000000000000105829
## playerEran Zahavi
## 0.0000000000000285122
## playerFerenc Puskás
## NA
## playerGareth Bale
## 0.0000000000000007082
## playerGigi Riva
## NA
## playerHakan Şükür
## NA
## playerHao Haidong
## 0.0000000000000336063
## playerHossam Hassan
## 0.0000000000000009971
## playerHussein Saeed
## 0.0000000000000102416
## playerIslam Slimani
## 0.0000000000000464244
## playerIssam Jemâa
## 0.0000000000000152079
## playerJan Koller
## 0.0000000000000074672
## playerJavier Hernández
## NA
## playerJong Il-gwan
## -0.0000000000000345507
## playerJørgen Juve
## 0.0000000000000026634
## playerKolbeinn Sigþórsson & Eiður Guðjohnsen
## NA
## playerKunishige Kamamoto
## 0.0000000000000380785
## playerLester Moré
## -0.0000000000000217666
## playerLionel Messi
## NA
## playerLuis Suárez
## NA
## playerLuis Tejada
## NA
## playerLuton Shelton
## NA
## playerMajed Abdullah
## NA
## playerMansour Muftah
## NA
## playerMarcelo Moreno
## NA
## playerMarek Hamšík
## NA
## playerMiroslav Klose
## NA
## playerNikos Anastopoulos
## NA
## playerOlivier Giroud
## NA
## playerPaolo Guerrero
## NA
## playerPelé
## NA
## playerPoul Nielsen & Jon Dahl Tomasson
## NA
## playerRadamel Falcao
## NA
## playerRashidi Yekini
## NA
## playerRaúl Díaz Arce
## NA
## playerRobbie Keane
## NA
## playerRobert Lewandowski
## NA
## playerRobin van Persie
## NA
## playerRolando Fonseca
## NA
## playerRomelu Lukaku
## NA
## playerRoque Santa Cruz
## NA
## playerSadio Mané
## NA
## playerSamuel Eto'o
## NA
## playerStern John
## NA
## playerTim Cahill
## NA
## playerToni Polster
## NA
## playerWayne Rooney
## NA
## playerZlatan Ibrahimović
## NA
## playerZlatko Zahovič
## NA
##
## Degrees of Freedom: 78 Total (i.e. Null); 0 Residual
## Null Deviance: 16570
## Residual Deviance: 0.00000000000000000000000001075 AIC: -4685</code></pre>
<pre class="r"><code>model_forward</code></pre>
<pre><code>##
## Call: glm(formula = w ~ player, data = data)
##
## Coefficients:
## (Intercept)
## 0.00000000000000344751
## playerAdrian Mutu & Gheorghe Hagi
## 7.99999999999998934186
## playerAhmed Faras
## 3.99999999999993605115
## playerAkwá
## 0.00000000000002693183
## playerAleksandar Mitrović
## 18.00000000000000355271
## playerAlexander Frei
## 14.00000000000000355271
## playerAlexander Kerzhakov & Artem Dzyuba
## 19.00000000000000355271
## playerAlexis Sánchez
## 11.00000000000006572520
## playerAli Daei
## 2.99999999999991429078
## playerAli Mabkhout
## -0.00000000000001553844
## playerAndriy Shevchenko
## 2.00000000000000577316
## playerAsamoah Gyan
## 5.00000000000001421085
## playerBashar Abdullah
## -0.00000000000000347427
## playerBenni McCarthy
## 1.99999999999999555911
## playerCarlos Pavón
## 0.00000000000002873739
## playerCha Bum-kun
## 7.00000000000000444089
## playerChris Wood
## 0.00000000000001675702
## playerClint Dempsey & Landon Donovan
## 8.99999999999999822364
## playerCristiano Ronaldo
## 16.00000000000001065814
## playerCyle Larin
## -0.00000000000001726031
## playerDavid Healy
## 2.99999999999999733546
## playerDavid Villa
## 31.00000000000000355271
## playerDavor Šuker
## 12.00000000000001421085
## playerDenis Law & Kenny Dalglish
## 4.00000000000000177636
## playerDidier Drogba
## 2.99999999999991873167
## playerDieumerci Mbokani
## 0.00000000000011476268
## playerDimitar Berbatov & Hristo Bonev
## 3.00000000000007771561
## playerEdin Džeko
## 0.99999999999993227640
## playerEmmanuel Adebayor
## 0.00000000000000321772
## playerEmmanuel Sanon
## -0.00000000000002528465
## playerEnner Valencia
## 4.99999999999999822364
## playerEran Zahavi
## -0.00000000000001559202
## playerFerenc Puskás
## 15.00000000000000532907
## playerGareth Bale
## 0.99999999999999733546
## playerGigi Riva
## 44.99999999999996447286
## playerHakan Şükür
## 4.99999999999999911182
## playerHao Haidong
## -0.00000000000000001508
## playerHossam Hassan
## 0.00000000000005256390
## playerHussein Saeed
## -0.00000000000001337180
## playerIslam Slimani
## 2.99999999999999777955
## playerIssam Jemâa
## 3.00000000000000088818
## playerJan Koller
## 11.99999999999998756550
## playerJavier Hernández
## 17.00000000000003552714
## playerJong Il-gwan
## 0.99999999999999222844
## playerJørgen Juve
## 1.99999999999998867573
## playerKolbeinn Sigþórsson & Eiður Guðjohnsen
## -0.00000000000002773838
## playerKunishige Kamamoto
## 7.00000000000001421085
## playerLester Moré
## 0.99999999999997324363
## playerLionel Messi
## 46.00000000000002842171
## playerLuis Suárez
## 25.00000000000003907985
## playerLuis Tejada
## -0.00000000000001185663
## playerLuton Shelton
## 0.99999999999999433786
## playerMajed Abdullah
## 3.99999999999999511502
## playerMansour Muftah
## -0.00000000000000724354
## playerMarcelo Moreno
## -0.00000000000001110273
## playerMarek Hamšík
## 0.99999999999999711342
## playerMiroslav Klose
## 67.99999999999992894573
## playerNikos Anastopoulos
## 2.00000000000000222045
## playerOlivier Giroud
## 36.99999999999993605115
## playerPaolo Guerrero
## 4.99999999999999200639
## playerPelé
## 76.00000000000007105427
## playerPoul Nielsen & Jon Dahl Tomasson
## 9.00000000000000000000
## playerRadamel Falcao
## 8.99999999999995559108
## playerRashidi Yekini
## 5.99999999999999023004
## playerRaúl Díaz Arce
## -0.00000000000000280925
## playerRobbie Keane
## 2.00000000000000976996
## playerRobert Lewandowski
## 17.00000000000001776357
## playerRobin van Persie
## 29.99999999999997513100
## playerRolando Fonseca
## 5.99999999999998312461
## playerRomelu Lukaku
## 20.99999999999999644729
## playerRoque Santa Cruz
## 7.00000000000000888178
## playerSadio Mané
## 5.00000000000001421085
## playerSamuel Eto'o
## 4.99999999999999911182
## playerStern John
## -0.00000000000000779466
## playerTim Cahill
## 3.99999999999996447286
## playerToni Polster
## 11.99999999999999467093
## playerWayne Rooney
## 32.00000000000009947598
## playerZlatan Ibrahimović
## 19.00000000000002486900
## playerZlatko Zahovič
## 0.99999999999999611422
##
## Degrees of Freedom: 78 Total (i.e. Null); 0 Residual
## Null Deviance: 16570
## Residual Deviance: 0.00000000000000000000000009058 AIC: -4516</code></pre>
<pre class="r"><code>model_backward</code></pre>
<pre><code>##
## Call: glm(formula = w ~ X.1 + X + part + pld + d + l + gf + ga + gd +
## pts + player, data = data)
##
## Coefficients:
## (Intercept)
## 0.0000000000000024134
## X.1
## 0.0000000000000004817
## X
## NA
## part
## 0.0000000000000083960
## pld
## 0.9999999999999913403
## d
## -0.9999999999999983347
## l
## -1.0000000000000031086
## gf
## 0.0000000000000362729
## ga
## -0.0000000000000307581
## gd−1
## 0.0000000000000177528
## gd−10
## 0.0000000000003069281
## gd−11
## 0.0000000000003785680
## gd−12
## 0.0000000000003667302
## gd−13
## 0.0000000000003487008
## gd−14
## 0.0000000000004558264
## gd−15
## 0.0000000000005008951
## gd−16
## 0.0000000000004779476
## gd−17
## 0.0000000000005499038
## gd−18
## 0.0000000000005984908
## gd−19
## 0.0000000000006229132
## gd−2
## 0.0000000000000354397
## gd−20
## 0.0000000000006497331
## gd−21
## 0.0000000000006871761
## gd−25
## 0.0000000000008286075
## gd−26
## 0.0000000000008034887
## gd−3
## 0.0000000000000928784
## gd−30
## 0.0000000000009636107
## gd−31
## 0.0000000000010274547
## gd−39
## 0.0000000000012549277
## gd−4
## 0.0000000000001115257
## gd−5
## 0.0000000000001426738
## gd−6
## 0.0000000000001793904
## gd−7
## 0.0000000000002275724
## gd−8
## 0.0000000000002329129
## gd−9
## 0.0000000000002707476
## gd+102
## -0.0000000000036121206
## gd+12
## -0.0000000000003983960
## gd+129
## -0.0000000000044634136
## gd+13