Seleção de modelos
Gian Lima
Vamos usar a base de dados EURO4PlayerSkillsSep11 do pacote SportsAnalytics. O objetivo é modelar a precisão em passes de longa distância de jogadores de futebol em função de covariáveis referentes a características dos jogadores.
## Name League Team
## Length:1851 Bundesliga :434 Manchester United FC: 30
## Class :character LaLiga :454 QPR : 29
## Mode :character PremierLeague:496 SS Lazio : 29
## SerieA :467 Stoke City FC : 29
## Arsenal FC : 28
## AS Roma : 28
## (Other) :1678
## Number Position Positions Birthday
## Min. : 0.0 Goalkeeper:191 Length:1851 Length:1851
## 1st Qu.: 7.0 Defender :592 Class :character Class :character
## Median :15.0 Midfielder:657 Mode :character Mode :character
## Mean :17.1 Forward :411
## 3rd Qu.:23.0
## Max. :99.0
##
## Nationality Age Height Weight
## Spanish :305 Min. :17.0 Min. :160.0 Min. : 55.00
## Italian :239 1st Qu.:23.0 1st Qu.:178.0 1st Qu.: 72.00
## German :216 Median :26.0 Median :183.0 Median : 76.00
## English :179 Mean :26.5 Mean :182.3 Mean : 76.67
## Argentinian: 97 3rd Qu.:30.0 3rd Qu.:187.0 3rd Qu.: 81.00
## Brazilian : 85 Max. :42.0 Max. :203.0 Max. :100.00
## (Other) :730 NA's :37
## InjuryTolerance Foot Side Attack Defence
## A : 55 L: 412 B:1402 Min. : 0.00 Min. : 0.00
## B :1643 R:1439 L: 237 1st Qu.:65.00 1st Qu.:48.00
## C : 150 R: 212 Median :73.00 Median :67.00
## NA's: 3 Mean :68.33 Mean :63.51
## 3rd Qu.:77.00 3rd Qu.:78.00
## Max. :95.00 Max. :94.00
##
## Balance Stamina TopSpeed Acceleration
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.00
## 1st Qu.:78.00 1st Qu.:82.00 1st Qu.:78.00 1st Qu.:77.50
## Median :82.00 Median :83.00 Median :81.00 Median :81.00
## Mean :81.53 Mean :82.08 Mean :80.05 Mean :80.35
## 3rd Qu.:85.00 3rd Qu.:85.00 3rd Qu.:83.00 3rd Qu.:84.00
## Max. :96.00 Max. :96.00 Max. :97.00 Max. :98.00
##
## Response Agility DribbleAccuracy DribbleSpeed
## Min. : 0.00 Min. : 0.0 Min. : 0.00 Min. : 0.00
## 1st Qu.:79.00 1st Qu.:77.0 1st Qu.:74.00 1st Qu.:76.00
## Median :81.00 Median :80.0 Median :78.00 Median :79.00
## Mean :80.97 Mean :80.1 Mean :75.77 Mean :77.35
## 3rd Qu.:83.00 3rd Qu.:83.0 3rd Qu.:81.00 3rd Qu.:83.00
## Max. :98.00 Max. :97.0 Max. :97.00 Max. :97.00
##
## ShortPassAccuracy ShortPassSpeed LongPassAccuracy LongPassSpeed
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.00
## 1st Qu.:72.00 1st Qu.:73.00 1st Qu.:72.00 1st Qu.:73.00
## Median :74.00 Median :75.00 Median :75.00 Median :76.00
## Mean :73.43 Mean :74.67 Mean :74.32 Mean :75.91
## 3rd Qu.:78.00 3rd Qu.:78.00 3rd Qu.:78.00 3rd Qu.:79.00
## Max. :96.00 Max. :96.00 Max. :96.00 Max. :96.00
##
## ShotAccuracy ShotPower ShotTechnique FreeKickAccuracy
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.00
## 1st Qu.:66.00 1st Qu.:81.00 1st Qu.:66.00 1st Qu.:65.00
## Median :70.00 Median :82.00 Median :72.00 Median :68.00
## Mean :68.71 Mean :82.22 Mean :70.18 Mean :67.18
## 3rd Qu.:75.00 3rd Qu.:84.00 3rd Qu.:77.00 3rd Qu.:73.00
## Max. :94.00 Max. :96.00 Max. :95.00 Max. :89.00
##
## Curling Header Jump Technique
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.00
## 1st Qu.:69.00 1st Qu.:70.00 1st Qu.:76.00 1st Qu.:75.00
## Median :74.00 Median :75.00 Median :79.00 Median :78.00
## Mean :72.18 Mean :72.74 Mean :79.05 Mean :76.44
## 3rd Qu.:78.00 3rd Qu.:80.00 3rd Qu.:82.00 3rd Qu.:82.00
## Max. :95.00 Max. :95.00 Max. :96.00 Max. :97.00
##
## Aggression Mentality KeeperSkills Teamwork
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.0
## 1st Qu.:68.00 1st Qu.:77.00 1st Qu.:50.00 1st Qu.:77.0
## Median :78.00 Median :79.00 Median :50.00 Median :78.0
## Mean :75.85 Mean :79.66 Mean :53.33 Mean :78.8
## 3rd Qu.:83.00 3rd Qu.:82.00 3rd Qu.:50.00 3rd Qu.:81.0
## Max. :99.00 Max. :95.00 Max. :93.00 Max. :98.0
##
## ConditionFitness WeakFootAccuracy WeakFootFrequency
## Min. :3.000 Min. :2.000 Min. :2.00
## 1st Qu.:6.000 1st Qu.:4.000 1st Qu.:4.00
## Median :6.000 Median :5.000 Median :5.00
## Mean :6.143 Mean :5.063 Mean :4.78
## 3rd Qu.:7.000 3rd Qu.:6.000 3rd Qu.:5.00
## Max. :8.000 Max. :8.000 Max. :8.00
## Selecionando as covariáveis para análise
dados <- EURO4PlayerSkillsSep11[-1166,c('Agility' , 'Acceleration' , 'TopSpeed'
,'Balance', 'Jump', 'Teamwork', 'Mentality',
'ConditionFitness','Height', 'Age', 'Weight',
'LongPassAccuracy')]
dados <- na.omit(dados)O jogador da linha 1166 foi excluído pois os dados correspondentes, sua maioria, eram iguais a zero (provavelmente dados missing). Além disso, 37 jogadores foram excluídos da base por não terem todas as informações disponíveis. A base final para análise tem
Antes de usar a função step para selecionar covariáveis via testes de hipóteses usando os algoritmos backward, forward e stepwise, vamos fazer isso no braço.
Algoritmo backward
Ajuste com todas as covariáveis
## Single term deletions
##
## Model:
## LongPassAccuracy ~ Agility + Acceleration + TopSpeed + Balance +
## Jump + Teamwork + Mentality + ConditionFitness + Height +
## Age + Weight
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 22069 4555.1
## Agility 1 565.1 22634 4598.9 46.1140 1.510e-11 ***
## Acceleration 1 3.1 22073 4553.3 0.2570 0.6123
## TopSpeed 1 2075.2 24145 4716.0 169.3476 < 2.2e-16 ***
## Balance 1 349.8 22419 4581.6 28.5475 1.031e-07 ***
## Jump 1 2805.9 24875 4770.0 228.9751 < 2.2e-16 ***
## Teamwork 1 9996.6 32066 5230.4 815.7837 < 2.2e-16 ***
## Mentality 1 5.0 22074 4553.5 0.4097 0.5222
## ConditionFitness 1 2.9 22072 4553.3 0.2334 0.6291
## Height 1 201.6 22271 4569.5 16.4500 5.208e-05 ***
## Age 1 0.0 22069 4553.1 0.0014 0.9698
## Weight 1 5.3 22075 4553.5 0.4320 0.5111
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1A função drop1 apresenta os resultados do teste F produzidos mediante extração das covariáveis do modelo (uma a uma). A variável Age tem maior p-valor (p = 0.9698) e será eliminada do modelo.
Modelo ajustado sem a variável Age
## Single term deletions
##
## Model:
## LongPassAccuracy ~ Agility + Acceleration + TopSpeed + Balance +
## Jump + Teamwork + Mentality + ConditionFitness + Height +
## Weight
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 22069 4553.1
## Agility 1 569.6 22639 4597.3 46.5090 1.241e-11 ***
## Acceleration 1 3.2 22073 4551.3 0.2602 0.6100
## TopSpeed 1 2079.0 24148 4714.3 169.7527 < 2.2e-16 ***
## Balance 1 351.9 22421 4579.7 28.7361 9.363e-08 ***
## Jump 1 2813.0 24882 4768.6 229.6847 < 2.2e-16 ***
## Teamwork 1 10296.6 32366 5245.3 840.7321 < 2.2e-16 ***
## Mentality 1 5.0 22074 4551.5 0.4095 0.5223
## ConditionFitness 1 2.9 22072 4551.3 0.2329 0.6295
## Height 1 213.8 22283 4568.5 17.4566 3.080e-05 ***
## Weight 1 5.3 22075 4551.5 0.4321 0.5111
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1A variável ConditionFitness tem maior p-valor (p = 0.6295) e será eliminada do modelo.
Modelo ajustado sem a variável ConditionFitness
## Single term deletions
##
## Model:
## LongPassAccuracy ~ Agility + Acceleration + TopSpeed + Balance +
## Jump + Teamwork + Mentality + Height + Weight
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 22072 4551.3
## Agility 1 585.0 22657 4596.7 47.7851 6.576e-12 ***
## Acceleration 1 3.5 22076 4549.6 0.2829 0.5949
## TopSpeed 1 2096.4 24169 4713.8 171.2511 < 2.2e-16 ***
## Balance 1 359.5 22432 4578.6 29.3663 6.797e-08 ***
## Jump 1 2847.4 24920 4769.3 232.5919 < 2.2e-16 ***
## Teamwork 1 10762.7 32835 5269.4 879.1644 < 2.2e-16 ***
## Mentality 1 3.9 22076 4549.6 0.3162 0.5740
## Height 1 213.4 22286 4566.7 17.4301 3.123e-05 ***
## Weight 1 5.7 22078 4549.8 0.4666 0.4946
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1A variável Acceleration tem maior p-valor (p = 0.5949) e será eliminada do modelo.
Modelo ajustado sem a variável Acceleration
## Single term deletions
##
## Model:
## LongPassAccuracy ~ Agility + TopSpeed + Balance + Jump + Teamwork +
## Mentality + Height + Weight
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 22076 4549.6
## Agility 1 746.4 22822 4607.9 60.9913 9.649e-15 ***
## TopSpeed 1 9292.0 31368 5184.5 759.3277 < 2.2e-16 ***
## Balance 1 356.5 22432 4576.6 29.1290 7.667e-08 ***
## Jump 1 2856.3 24932 4768.2 233.4136 < 2.2e-16 ***
## Teamwork 1 10769.0 32845 5267.9 880.0302 < 2.2e-16 ***
## Mentality 1 4.2 22080 4547.9 0.3412 0.5592
## Height 1 209.9 22286 4564.7 17.1549 3.604e-05 ***
## Weight 1 5.7 22081 4548.1 0.4682 0.4939
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1A variável Mentality tem maior p-valor (p = 0.5592) e será eliminada do modelo.
Modelo ajustado sem a variável Mentality
## Single term deletions
##
## Model:
## LongPassAccuracy ~ Agility + TopSpeed + Balance + Jump + Teamwork +
## Height + Weight
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 22080 4547.9
## Agility 1 781.2 22861 4609.0 63.860 2.360e-15 ***
## TopSpeed 1 9645.8 31726 5203.1 788.535 < 2.2e-16 ***
## Balance 1 360.1 22440 4575.3 29.438 6.552e-08 ***
## Jump 1 2897.6 24977 4769.5 236.876 < 2.2e-16 ***
## Teamwork 1 15066.7 37147 5489.1 1231.681 < 2.2e-16 ***
## Height 1 228.4 22308 4564.6 18.671 1.638e-05 ***
## Weight 1 6.0 22086 4546.4 0.494 0.4822
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1A variável Weight tem maior p-valor (p = 0.4822) e será eliminada do modelo.
Modelo ajustado sem a variável Weight
## Single term deletions
##
## Model:
## LongPassAccuracy ~ Agility + TopSpeed + Balance + Jump + Teamwork +
## Height
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 22086 4546.4
## Agility 1 780.1 22866 4607.4 63.789 2.443e-15 ***
## TopSpeed 1 9780.3 31866 5209.1 799.752 < 2.2e-16 ***
## Balance 1 449.8 22536 4581.0 36.785 1.603e-09 ***
## Jump 1 2895.8 24982 4767.8 236.793 < 2.2e-16 ***
## Teamwork 1 15311.1 37397 5499.2 1252.012 < 2.2e-16 ***
## Height 1 356.9 22443 4573.5 29.188 7.439e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Todas as variáveis remanescentes têm efeito significativo. O processo é encerrado com o modelo atual, sem excluir novas covariáveis.
Resumo do modelo final
##
## Call:
## lm(formula = LongPassAccuracy ~ Agility + TopSpeed + Balance +
## Jump + Teamwork + Height, data = dados)
##
## Residuals:
## Min 1Q Median 3Q Max
## -12.4177 -2.2009 -0.0368 2.2641 12.1375
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 39.52347 5.48863 7.201 8.74e-13 ***
## Agility -0.22568 0.02826 -7.987 2.44e-15 ***
## TopSpeed 0.56021 0.01981 28.280 < 2e-16 ***
## Balance -0.20783 0.03427 -6.065 1.60e-09 ***
## Jump -0.38166 0.02480 -15.388 < 2e-16 ***
## Teamwork 0.94919 0.02683 35.384 < 2e-16 ***
## Height -0.10775 0.01994 -5.403 7.44e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.497 on 1806 degrees of freedom
## Multiple R-squared: 0.6743, Adjusted R-squared: 0.6732
## F-statistic: 623.2 on 6 and 1806 DF, p-value: < 2.2e-16Algoritmo forward
Modelo nulo (só com intercepto)
add1(ajuste0, scope=~Agility + Acceleration + TopSpeed
+ Balance + Jump + Teamwork + Mentality + ConditionFitness
+ Height + Age + Weight, test = 'F')## Single term additions
##
## Model:
## LongPassAccuracy ~ 1
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 67812 6568.2
## Agility 1 6975.4 60837 6373.5 207.6443 < 2.2e-16 ***
## Acceleration 1 19573.6 48238 5952.8 734.8443 < 2.2e-16 ***
## TopSpeed 1 21923.9 45888 5862.2 865.2358 < 2.2e-16 ***
## Balance 1 12055.7 55756 6215.4 391.5779 < 2.2e-16 ***
## Jump 1 10694.1 57118 6259.1 339.0700 < 2.2e-16 ***
## Teamwork 1 16772.5 51040 6055.1 595.1288 < 2.2e-16 ***
## Mentality 1 3223.9 64588 6481.9 90.3944 < 2.2e-16 ***
## ConditionFitness 1 346.2 67466 6561.0 9.2921 0.002335 **
## Height 1 15781.5 52031 6090.0 549.2977 < 2.2e-16 ***
## Age 1 244.7 67567 6563.7 6.5586 0.010518 *
## Weight 1 13834.9 53977 6156.6 464.1797 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1A função add1 apresenta os resultados do teste F produzidos mediante inclusão das covariáveis do modelo (uma a uma). A variável TopSpeed tem maior valor para a estatística F (F = 865.2358), e p-valor extremamente baixo, e será incluída ao modelo.
Nota: neste caso avaliar menor p-valor e maior valor da estatística F é equivalente apenas porque todas as covariáveis têm um grau de liberdade associado.
Modelo com a inclusão de TopSpeed
add1(ajuste2, scope=~Agility + Acceleration + TopSpeed
+ Balance + Jump + Teamwork + Mentality + ConditionFitness
+ Height + Age + Weight, test = 'F')## Single term additions
##
## Model:
## LongPassAccuracy ~ TopSpeed
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 45888 5862.2
## Agility 1 11.6 45877 5863.8 0.4561 0.49952
## Acceleration 1 72.0 45816 5861.4 2.8424 0.09198 .
## Balance 1 2356.7 43531 5768.6 97.9904 < 2.2e-16 ***
## Jump 1 5816.7 40071 5618.5 262.7380 < 2.2e-16 ***
## Teamwork 1 15663.7 30224 5107.2 938.0251 < 2.2e-16 ***
## Mentality 1 2458.9 43429 5764.4 102.4788 < 2.2e-16 ***
## ConditionFitness 1 648.1 45240 5838.4 25.9276 3.913e-07 ***
## Height 1 3518.7 42369 5719.6 150.3176 < 2.2e-16 ***
## Age 1 801.1 45087 5832.3 32.1600 1.649e-08 ***
## Weight 1 2848.3 43040 5748.0 119.7806 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1A inclusão da variável Teamwork produziu maior valor para a estatística F (e p-valor extremamente baixo) e será incluída ao modelo.
Modelo com a inclusão de Teamwork
ajuste3 <- lm(LongPassAccuracy ~ TopSpeed + Teamwork, data = dados)
add1(ajuste3, scope=~Agility + Acceleration + TopSpeed
+ Balance + Jump + Teamwork + Mentality + ConditionFitness
+ Height + Age + Weight, test = 'F')## Single term additions
##
## Model:
## LongPassAccuracy ~ TopSpeed + Teamwork
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 30225 5107.2
## Agility 1 0.0 30224 5109.2 0.0026 0.95916
## Acceleration 1 98.2 30126 5103.3 5.8949 0.01528 *
## Balance 1 3956.5 26268 4854.8 272.4738 < 2.2e-16 ***
## Jump 1 6419.2 23805 4676.3 487.8011 < 2.2e-16 ***
## Mentality 1 493.1 29731 5079.4 30.0042 4.915e-08 ***
## ConditionFitness 1 553.3 29671 5075.7 33.7350 7.445e-09 ***
## Height 1 1997.7 28227 4985.2 128.0309 < 2.2e-16 ***
## Age 1 59.2 30165 5105.6 3.5485 0.05976 .
## Weight 1 1752.2 28472 5000.9 111.3281 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Modelo com a inclusão de Jump
ajuste4 <- lm(LongPassAccuracy ~ TopSpeed + Teamwork + Jump, data = dados)
add1(ajuste4, scope=~Agility + Acceleration + TopSpeed
+ Balance + Jump + Teamwork + Mentality + ConditionFitness
+ Height + Age + Weight, test = 'F')## Single term additions
##
## Model:
## LongPassAccuracy ~ TopSpeed + Teamwork + Jump
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 23805 4676.3
## Agility 1 65.78 23740 4673.3 5.0099 0.02532 *
## Acceleration 1 2.62 23803 4678.1 0.1991 0.65552
## Balance 1 780.21 23025 4617.9 61.2648 8.427e-15 ***
## Mentality 1 3.51 23802 4678.1 0.2668 0.60552
## ConditionFitness 1 49.02 23756 4674.6 3.7307 0.05358 .
## Height 1 738.51 23067 4621.2 57.8851 4.443e-14 ***
## Age 1 4.80 23801 4678.0 0.3647 0.54598
## Weight 1 591.99 23213 4632.7 46.1082 1.513e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Modelo com a inclusão de Balance
ajuste5 <- lm(LongPassAccuracy ~ TopSpeed + Teamwork + Jump + Balance, data = dados)
add1(ajuste5, scope=~Agility + Acceleration + TopSpeed
+ Balance + Jump + Teamwork + Mentality + ConditionFitness
+ Height + Age + Weight, test = 'F')## Single term additions
##
## Model:
## LongPassAccuracy ~ TopSpeed + Teamwork + Jump + Balance
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 23025 4617.9
## Agility 1 582.24 22443 4573.5 46.8793 1.031e-11 ***
## Acceleration 1 101.33 22924 4611.9 7.9873 0.0047625 **
## Mentality 1 74.78 22950 4614.0 5.8875 0.0153463 *
## ConditionFitness 1 14.33 23011 4618.8 1.1254 0.2889064
## Height 1 159.10 22866 4607.4 12.5733 0.0004013 ***
## Age 1 23.85 23001 4618.0 1.8737 0.1712262
## Weight 1 70.37 22955 4614.4 5.5393 0.0187009 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Modelo com a inclusão de Agility
ajuste6 <- lm(LongPassAccuracy ~ TopSpeed + Teamwork +
Jump + Balance + Agility, data = dados)
add1(ajuste6, scope=~Agility + Acceleration + TopSpeed
+ Balance + Jump + Teamwork + Mentality + ConditionFitness
+ Height + Age + Weight, test = 'F') ## Single term additions
##
## Model:
## LongPassAccuracy ~ TopSpeed + Teamwork + Jump + Balance + Agility
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 22443 4573.5
## Acceleration 1 0.72 22442 4575.4 0.0577 0.8101457
## Mentality 1 40.06 22403 4572.3 3.2293 0.0724971 .
## ConditionFitness 1 0.87 22442 4575.4 0.0702 0.7910046
## Height 1 356.95 22086 4546.4 29.1882 7.439e-08 ***
## Age 1 12.76 22430 4574.5 1.0274 0.3109095
## Weight 1 134.59 22308 4564.6 10.8963 0.0009824 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Modelo com a inclusão de Height
ajuste7 <- lm(LongPassAccuracy ~ TopSpeed + Teamwork +
Jump + Balance + Agility + Height, data = dados)
add1(ajuste7, scope=~Agility + Acceleration + TopSpeed
+ Balance + Jump + Teamwork + Mentality + ConditionFitness
+ Height + Age + Weight, test = 'F') ## Single term additions
##
## Model:
## LongPassAccuracy ~ TopSpeed + Teamwork + Jump + Balance + Agility +
## Height
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 22086 4546.4
## Acceleration 1 3.7991 22082 4548.1 0.3105 0.5774
## Mentality 1 4.4891 22081 4548.1 0.3670 0.5447
## ConditionFitness 1 2.2037 22084 4548.2 0.1801 0.6713
## Age 1 0.0608 22086 4548.4 0.0050 0.9438
## Weight 1 6.0430 22080 4547.9 0.4940 0.4822As variáveis que ainda não foram incluídas no modelo não apresentam efeito significativo, segundo o teste F. O processo é encerrado com o modelo atual, sem adicionar novas covariáveis.
Usando a função step do R
Seleção backward
## Start: AIC=4555.06
## LongPassAccuracy ~ Agility + Acceleration + TopSpeed + Balance +
## Jump + Teamwork + Mentality + ConditionFitness + Height +
## Age + Weight
##
## Df Sum of Sq RSS AIC F value Pr(>F)
## - Age 1 0.0 22069 4553.1 0.0014 0.9698
## - ConditionFitness 1 2.9 22072 4553.3 0.2334 0.6291
## - Acceleration 1 3.1 22073 4553.3 0.2570 0.6123
## - Mentality 1 5.0 22074 4553.5 0.4097 0.5222
## - Weight 1 5.3 22075 4553.5 0.4320 0.5111
## <none> 22069 4555.1
## - Height 1 201.6 22271 4569.5 16.4500 5.208e-05 ***
## - Balance 1 349.8 22419 4581.6 28.5475 1.031e-07 ***
## - Agility 1 565.1 22634 4598.9 46.1140 1.510e-11 ***
## - TopSpeed 1 2075.2 24145 4716.0 169.3476 < 2.2e-16 ***
## - Jump 1 2805.9 24875 4770.0 228.9751 < 2.2e-16 ***
## - Teamwork 1 9996.6 32066 5230.4 815.7837 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=4553.07
## LongPassAccuracy ~ Agility + Acceleration + TopSpeed + Balance +
## Jump + Teamwork + Mentality + ConditionFitness + Height +
## Weight
##
## Df Sum of Sq RSS AIC F value Pr(>F)
## - ConditionFitness 1 2.9 22072 4551.3 0.2329 0.6295
## - Acceleration 1 3.2 22073 4551.3 0.2602 0.6100
## - Mentality 1 5.0 22074 4551.5 0.4095 0.5223
## - Weight 1 5.3 22075 4551.5 0.4321 0.5111
## <none> 22069 4553.1
## - Height 1 213.8 22283 4568.5 17.4566 3.080e-05 ***
## - Balance 1 351.9 22421 4579.7 28.7361 9.363e-08 ***
## - Agility 1 569.6 22639 4597.3 46.5090 1.241e-11 ***
## - TopSpeed 1 2079.0 24148 4714.3 169.7527 < 2.2e-16 ***
## - Jump 1 2813.0 24882 4768.6 229.6847 < 2.2e-16 ***
## - Teamwork 1 10296.6 32366 5245.3 840.7321 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=4551.3
## LongPassAccuracy ~ Agility + Acceleration + TopSpeed + Balance +
## Jump + Teamwork + Mentality + Height + Weight
##
## Df Sum of Sq RSS AIC F value Pr(>F)
## - Acceleration 1 3.5 22076 4549.6 0.2829 0.5949
## - Mentality 1 3.9 22076 4549.6 0.3162 0.5740
## - Weight 1 5.7 22078 4549.8 0.4666 0.4946
## <none> 22072 4551.3
## - Height 1 213.4 22286 4566.7 17.4301 3.123e-05 ***
## - Balance 1 359.5 22432 4578.6 29.3663 6.797e-08 ***
## - Agility 1 585.0 22657 4596.7 47.7851 6.576e-12 ***
## - TopSpeed 1 2096.4 24169 4713.8 171.2511 < 2.2e-16 ***
## - Jump 1 2847.4 24920 4769.3 232.5919 < 2.2e-16 ***
## - Teamwork 1 10762.7 32835 5269.4 879.1644 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=4549.58
## LongPassAccuracy ~ Agility + TopSpeed + Balance + Jump + Teamwork +
## Mentality + Height + Weight
##
## Df Sum of Sq RSS AIC F value Pr(>F)
## - Mentality 1 4.2 22080 4547.9 0.3412 0.5592
## - Weight 1 5.7 22081 4548.1 0.4682 0.4939
## <none> 22076 4549.6
## - Height 1 209.9 22286 4564.7 17.1549 3.604e-05 ***
## - Balance 1 356.5 22432 4576.6 29.1290 7.667e-08 ***
## - Agility 1 746.4 22822 4607.9 60.9913 9.649e-15 ***
## - Jump 1 2856.3 24932 4768.2 233.4136 < 2.2e-16 ***
## - TopSpeed 1 9292.0 31368 5184.5 759.3277 < 2.2e-16 ***
## - Teamwork 1 10769.0 32845 5267.9 880.0302 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=4547.93
## LongPassAccuracy ~ Agility + TopSpeed + Balance + Jump + Teamwork +
## Height + Weight
##
## Df Sum of Sq RSS AIC F value Pr(>F)
## - Weight 1 6.0 22086 4546.4 0.494 0.4822
## <none> 22080 4547.9
## - Height 1 228.4 22308 4564.6 18.671 1.638e-05 ***
## - Balance 1 360.1 22440 4575.3 29.438 6.552e-08 ***
## - Agility 1 781.2 22861 4609.0 63.860 2.360e-15 ***
## - Jump 1 2897.6 24977 4769.5 236.876 < 2.2e-16 ***
## - TopSpeed 1 9645.8 31726 5203.1 788.535 < 2.2e-16 ***
## - Teamwork 1 15066.7 37147 5489.1 1231.681 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=4546.42
## LongPassAccuracy ~ Agility + TopSpeed + Balance + Jump + Teamwork +
## Height
##
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 22086 4546.4
## - Height 1 356.9 22443 4573.5 29.188 7.439e-08 ***
## - Balance 1 449.8 22536 4581.0 36.785 1.603e-09 ***
## - Agility 1 780.1 22866 4607.4 63.789 2.443e-15 ***
## - Jump 1 2895.8 24982 4767.8 236.793 < 2.2e-16 ***
## - TopSpeed 1 9780.3 31866 5209.1 799.752 < 2.2e-16 ***
## - Teamwork 1 15311.1 37397 5499.2 1252.012 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Seleção forward
mod_for <- step(ajuste0, scope=~Agility + Acceleration + TopSpeed
+ Balance + Jump + Teamwork + Mentality + ConditionFitness
+ Height + Age + Weight, direction = 'forward', test = 'F')## Start: AIC=6568.25
## LongPassAccuracy ~ 1
##
## Df Sum of Sq RSS AIC F value Pr(>F)
## + TopSpeed 1 21923.9 45888 5862.2 865.2358 < 2.2e-16 ***
## + Acceleration 1 19573.6 48238 5952.8 734.8443 < 2.2e-16 ***
## + Teamwork 1 16772.5 51040 6055.1 595.1288 < 2.2e-16 ***
## + Height 1 15781.5 52031 6090.0 549.2977 < 2.2e-16 ***
## + Weight 1 13834.9 53977 6156.6 464.1797 < 2.2e-16 ***
## + Balance 1 12055.7 55756 6215.4 391.5779 < 2.2e-16 ***
## + Jump 1 10694.1 57118 6259.1 339.0700 < 2.2e-16 ***
## + Agility 1 6975.4 60837 6373.5 207.6443 < 2.2e-16 ***
## + Mentality 1 3223.9 64588 6481.9 90.3944 < 2.2e-16 ***
## + ConditionFitness 1 346.2 67466 6561.0 9.2921 0.002335 **
## + Age 1 244.7 67567 6563.7 6.5586 0.010518 *
## <none> 67812 6568.2
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=5862.21
## LongPassAccuracy ~ TopSpeed
##
## Df Sum of Sq RSS AIC F value Pr(>F)
## + Teamwork 1 15663.7 30224 5107.2 938.0251 < 2.2e-16 ***
## + Jump 1 5816.7 40071 5618.5 262.7380 < 2.2e-16 ***
## + Height 1 3518.7 42369 5719.6 150.3176 < 2.2e-16 ***
## + Weight 1 2848.3 43040 5748.0 119.7806 < 2.2e-16 ***
## + Mentality 1 2458.9 43429 5764.4 102.4788 < 2.2e-16 ***
## + Balance 1 2356.7 43531 5768.6 97.9904 < 2.2e-16 ***
## + Age 1 801.1 45087 5832.3 32.1600 1.649e-08 ***
## + ConditionFitness 1 648.1 45240 5838.4 25.9276 3.913e-07 ***
## + Acceleration 1 72.0 45816 5861.4 2.8424 0.09198 .
## <none> 45888 5862.2
## + Agility 1 11.6 45877 5863.8 0.4561 0.49952
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=5107.18
## LongPassAccuracy ~ TopSpeed + Teamwork
##
## Df Sum of Sq RSS AIC F value Pr(>F)
## + Jump 1 6419.2 23805 4676.3 487.8011 < 2.2e-16 ***
## + Balance 1 3956.5 26268 4854.8 272.4738 < 2.2e-16 ***
## + Height 1 1997.7 28227 4985.2 128.0309 < 2.2e-16 ***
## + Weight 1 1752.2 28472 5000.9 111.3281 < 2.2e-16 ***
## + ConditionFitness 1 553.3 29671 5075.7 33.7350 7.445e-09 ***
## + Mentality 1 493.1 29731 5079.4 30.0042 4.915e-08 ***
## + Acceleration 1 98.2 30126 5103.3 5.8949 0.01528 *
## + Age 1 59.2 30165 5105.6 3.5485 0.05976 .
## <none> 30225 5107.2
## + Agility 1 0.0 30224 5109.2 0.0026 0.95916
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=4676.34
## LongPassAccuracy ~ TopSpeed + Teamwork + Jump
##
## Df Sum of Sq RSS AIC F value Pr(>F)
## + Balance 1 780.21 23025 4617.9 61.2648 8.427e-15 ***
## + Height 1 738.51 23067 4621.2 57.8851 4.443e-14 ***
## + Weight 1 591.99 23213 4632.7 46.1082 1.513e-11 ***
## + Agility 1 65.78 23740 4673.3 5.0099 0.02532 *
## + ConditionFitness 1 49.02 23756 4674.6 3.7307 0.05358 .
## <none> 23805 4676.3
## + Age 1 4.80 23801 4678.0 0.3647 0.54598
## + Mentality 1 3.51 23802 4678.1 0.2668 0.60552
## + Acceleration 1 2.62 23803 4678.1 0.1991 0.65552
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=4617.93
## LongPassAccuracy ~ TopSpeed + Teamwork + Jump + Balance
##
## Df Sum of Sq RSS AIC F value Pr(>F)
## + Agility 1 582.24 22443 4573.5 46.8793 1.031e-11 ***
## + Height 1 159.10 22866 4607.4 12.5733 0.0004013 ***
## + Acceleration 1 101.33 22924 4611.9 7.9873 0.0047625 **
## + Mentality 1 74.78 22950 4614.0 5.8875 0.0153463 *
## + Weight 1 70.37 22955 4614.4 5.5393 0.0187009 *
## <none> 23025 4617.9
## + Age 1 23.85 23001 4618.0 1.8737 0.1712262
## + ConditionFitness 1 14.33 23011 4618.8 1.1254 0.2889064
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=4573.49
## LongPassAccuracy ~ TopSpeed + Teamwork + Jump + Balance + Agility
##
## Df Sum of Sq RSS AIC F value Pr(>F)
## + Height 1 356.95 22086 4546.4 29.1882 7.439e-08 ***
## + Weight 1 134.59 22308 4564.6 10.8963 0.0009824 ***
## + Mentality 1 40.06 22403 4572.3 3.2293 0.0724971 .
## <none> 22443 4573.5
## + Age 1 12.76 22430 4574.5 1.0274 0.3109095
## + ConditionFitness 1 0.87 22442 4575.4 0.0702 0.7910046
## + Acceleration 1 0.72 22442 4575.4 0.0577 0.8101457
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=4546.42
## LongPassAccuracy ~ TopSpeed + Teamwork + Jump + Balance + Agility +
## Height
##
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 22086 4546.4
## + Weight 1 6.0430 22080 4547.9 0.4940 0.4822
## + Mentality 1 4.4891 22081 4548.1 0.3670 0.5447
## + Acceleration 1 3.7991 22082 4548.1 0.3105 0.5774
## + ConditionFitness 1 2.2037 22084 4548.2 0.1801 0.6713
## + Age 1 0.0608 22086 4548.4 0.0050 0.9438Seleção stepwise
## Start: AIC=4555.06
## LongPassAccuracy ~ Agility + Acceleration + TopSpeed + Balance +
## Jump + Teamwork + Mentality + ConditionFitness + Height +
## Age + Weight
##
## Df Sum of Sq RSS AIC F value Pr(>F)
## - Age 1 0.0 22069 4553.1 0.0014 0.9698
## - ConditionFitness 1 2.9 22072 4553.3 0.2334 0.6291
## - Acceleration 1 3.1 22073 4553.3 0.2570 0.6123
## - Mentality 1 5.0 22074 4553.5 0.4097 0.5222
## - Weight 1 5.3 22075 4553.5 0.4320 0.5111
## <none> 22069 4555.1
## - Height 1 201.6 22271 4569.5 16.4500 5.208e-05 ***
## - Balance 1 349.8 22419 4581.6 28.5475 1.031e-07 ***
## - Agility 1 565.1 22634 4598.9 46.1140 1.510e-11 ***
## - TopSpeed 1 2075.2 24145 4716.0 169.3476 < 2.2e-16 ***
## - Jump 1 2805.9 24875 4770.0 228.9751 < 2.2e-16 ***
## - Teamwork 1 9996.6 32066 5230.4 815.7837 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=4553.07
## LongPassAccuracy ~ Agility + Acceleration + TopSpeed + Balance +
## Jump + Teamwork + Mentality + ConditionFitness + Height +
## Weight
##
## Df Sum of Sq RSS AIC F value Pr(>F)
## - ConditionFitness 1 2.9 22072 4551.3 0.2329 0.6295
## - Acceleration 1 3.2 22073 4551.3 0.2602 0.6100
## - Mentality 1 5.0 22074 4551.5 0.4095 0.5223
## - Weight 1 5.3 22075 4551.5 0.4321 0.5111
## <none> 22069 4553.1
## + Age 1 0.0 22069 4555.1 0.0014 0.9698
## - Height 1 213.8 22283 4568.5 17.4566 3.080e-05 ***
## - Balance 1 351.9 22421 4579.7 28.7361 9.363e-08 ***
## - Agility 1 569.6 22639 4597.3 46.5090 1.241e-11 ***
## - TopSpeed 1 2079.0 24148 4714.3 169.7527 < 2.2e-16 ***
## - Jump 1 2813.0 24882 4768.6 229.6847 < 2.2e-16 ***
## - Teamwork 1 10296.6 32366 5245.3 840.7321 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=4551.3
## LongPassAccuracy ~ Agility + Acceleration + TopSpeed + Balance +
## Jump + Teamwork + Mentality + Height + Weight
##
## Df Sum of Sq RSS AIC F value Pr(>F)
## - Acceleration 1 3.5 22076 4549.6 0.2829 0.5949
## - Mentality 1 3.9 22076 4549.6 0.3162 0.5740
## - Weight 1 5.7 22078 4549.8 0.4666 0.4946
## <none> 22072 4551.3
## + ConditionFitness 1 2.9 22069 4553.1 0.2329 0.6295
## + Age 1 0.0 22072 4553.3 0.0008 0.9778
## - Height 1 213.4 22286 4566.7 17.4301 3.123e-05 ***
## - Balance 1 359.5 22432 4578.6 29.3663 6.797e-08 ***
## - Agility 1 585.0 22657 4596.7 47.7851 6.576e-12 ***
## - TopSpeed 1 2096.4 24169 4713.8 171.2511 < 2.2e-16 ***
## - Jump 1 2847.4 24920 4769.3 232.5919 < 2.2e-16 ***
## - Teamwork 1 10762.7 32835 5269.4 879.1644 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=4549.58
## LongPassAccuracy ~ Agility + TopSpeed + Balance + Jump + Teamwork +
## Mentality + Height + Weight
##
## Df Sum of Sq RSS AIC F value Pr(>F)
## - Mentality 1 4.2 22080 4547.9 0.3412 0.5592
## - Weight 1 5.7 22081 4548.1 0.4682 0.4939
## <none> 22076 4549.6
## + Acceleration 1 3.5 22072 4551.3 0.2829 0.5949
## + ConditionFitness 1 3.1 22073 4551.3 0.2555 0.6133
## + Age 1 0.0 22076 4551.6 0.0000 0.9999
## - Height 1 209.9 22286 4564.7 17.1549 3.604e-05 ***
## - Balance 1 356.5 22432 4576.6 29.1290 7.667e-08 ***
## - Agility 1 746.4 22822 4607.9 60.9913 9.649e-15 ***
## - Jump 1 2856.3 24932 4768.2 233.4136 < 2.2e-16 ***
## - TopSpeed 1 9292.0 31368 5184.5 759.3277 < 2.2e-16 ***
## - Teamwork 1 10769.0 32845 5267.9 880.0302 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=4547.93
## LongPassAccuracy ~ Agility + TopSpeed + Balance + Jump + Teamwork +
## Height + Weight
##
## Df Sum of Sq RSS AIC F value Pr(>F)
## - Weight 1 6.0 22086 4546.4 0.4940 0.4822
## <none> 22080 4547.9
## + Mentality 1 4.2 22076 4549.6 0.3412 0.5592
## + Acceleration 1 3.8 22076 4549.6 0.3080 0.5790
## + ConditionFitness 1 1.9 22078 4549.8 0.1546 0.6943
## + Age 1 0.0 22080 4549.9 0.0001 0.9914
## - Height 1 228.4 22308 4564.6 18.6712 1.638e-05 ***
## - Balance 1 360.1 22440 4575.3 29.4384 6.552e-08 ***
## - Agility 1 781.2 22861 4609.0 63.8603 2.360e-15 ***
## - Jump 1 2897.6 24977 4769.5 236.8765 < 2.2e-16 ***
## - TopSpeed 1 9645.8 31726 5203.1 788.5349 < 2.2e-16 ***
## - Teamwork 1 15066.7 37147 5489.1 1231.6807 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=4546.42
## LongPassAccuracy ~ Agility + TopSpeed + Balance + Jump + Teamwork +
## Height
##
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 22086 4546.4
## + Weight 1 6.0 22080 4547.9 0.4940 0.4822
## + Mentality 1 4.5 22081 4548.1 0.3670 0.5447
## + Acceleration 1 3.8 22082 4548.1 0.3105 0.5774
## + ConditionFitness 1 2.2 22084 4548.2 0.1801 0.6713
## + Age 1 0.1 22086 4548.4 0.0050 0.9438
## - Height 1 356.9 22443 4573.5 29.1882 7.439e-08 ***
## - Balance 1 449.8 22536 4581.0 36.7846 1.603e-09 ***
## - Agility 1 780.1 22866 4607.4 63.7887 2.443e-15 ***
## - Jump 1 2895.8 24982 4767.8 236.7933 < 2.2e-16 ***
## - TopSpeed 1 9780.3 31866 5209.1 799.7516 < 2.2e-16 ***
## - Teamwork 1 15311.1 37397 5499.2 1252.0120 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Calls:
## 1: lm(formula = LongPassAccuracy ~ Agility + TopSpeed + Balance + Jump
## + Teamwork + Height, data = dados)
## 2: lm(formula = LongPassAccuracy ~ TopSpeed + Teamwork + Jump +
## Balance + Agility + Height, data = dados)
## 3: lm(formula = LongPassAccuracy ~ Agility + TopSpeed + Balance + Jump
## + Teamwork + Height, data = dados)
##
## Model 1 Model 2 Model 3
## (Intercept) 39.52 39.52 39.52
## SE 5.49 5.49 5.49
##
## Agility -0.2257 -0.2257 -0.2257
## SE 0.0283 0.0283 0.0283
##
## TopSpeed 0.5602 0.5602 0.5602
## SE 0.0198 0.0198 0.0198
##
## Balance -0.2078 -0.2078 -0.2078
## SE 0.0343 0.0343 0.0343
##
## Jump -0.3817 -0.3817 -0.3817
## SE 0.0248 0.0248 0.0248
##
## Teamwork 0.9492 0.9492 0.9492
## SE 0.0268 0.0268 0.0268
##
## Height -0.1078 -0.1078 -0.1078
## SE 0.0199 0.0199 0.0199
## Os três métodos produziram o mesmo modelo (mesmo conjunto de covariáveis selecionadas). Isso não acontece sempre, é plenamente possível obter modelos diferentes usando métodos de seleção diferentes.
Análise baseada em critérios de ajuste
require(leaps)
all_reg <- regsubsets(LongPassAccuracy ~ Agility + Acceleration + TopSpeed
+ Balance + Jump + Teamwork + Mentality + ConditionFitness
+ Height + Age + Weight, method = "exhaustive",
nvmax = 11, data = dados)A função regsubsets vai ajustar todos os modelos de regressão possíveis, e armazenar os valores dos critérios de qualidade para os melhores ajustes com j = 1, j = 2, …, j = k covariáveis.
BICs para os modelos ótimos para cada número de covariáveis.
## Subset selection object
## Call: regsubsets.formula(LongPassAccuracy ~ Agility + Acceleration +
## TopSpeed + Balance + Jump + Teamwork + Mentality + ConditionFitness +
## Height + Age + Weight, method = "exhaustive", nvmax = 11,
## data = dados)
## 11 Variables (and intercept)
## Forced in Forced out
## Agility FALSE FALSE
## Acceleration FALSE FALSE
## TopSpeed FALSE FALSE
## Balance FALSE FALSE
## Jump FALSE FALSE
## Teamwork FALSE FALSE
## Mentality FALSE FALSE
## ConditionFitness FALSE FALSE
## Height FALSE FALSE
## Age FALSE FALSE
## Weight FALSE FALSE
## 1 subsets of each size up to 11
## Selection Algorithm: exhaustive
## Agility Acceleration TopSpeed Balance Jump Teamwork Mentality
## 1 ( 1 ) FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## 2 ( 1 ) FALSE FALSE TRUE FALSE FALSE TRUE FALSE
## 3 ( 1 ) FALSE FALSE TRUE FALSE TRUE TRUE FALSE
## 4 ( 1 ) FALSE FALSE TRUE TRUE TRUE TRUE FALSE
## 5 ( 1 ) TRUE FALSE TRUE TRUE TRUE TRUE FALSE
## 6 ( 1 ) TRUE FALSE TRUE TRUE TRUE TRUE FALSE
## 7 ( 1 ) TRUE FALSE TRUE TRUE TRUE TRUE FALSE
## 8 ( 1 ) TRUE FALSE TRUE TRUE TRUE TRUE TRUE
## 9 ( 1 ) TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 10 ( 1 ) TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 11 ( 1 ) TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## ConditionFitness Height Age Weight
## 1 ( 1 ) FALSE FALSE FALSE FALSE
## 2 ( 1 ) FALSE FALSE FALSE FALSE
## 3 ( 1 ) FALSE FALSE FALSE FALSE
## 4 ( 1 ) FALSE FALSE FALSE FALSE
## 5 ( 1 ) FALSE FALSE FALSE FALSE
## 6 ( 1 ) FALSE TRUE FALSE FALSE
## 7 ( 1 ) FALSE TRUE FALSE TRUE
## 8 ( 1 ) FALSE TRUE FALSE TRUE
## 9 ( 1 ) FALSE TRUE FALSE TRUE
## 10 ( 1 ) TRUE TRUE FALSE TRUE
## 11 ( 1 ) TRUE TRUE TRUE TRUECada linha da matriz lógica apresenta o melhor modelo para um particular número de covariáveis. Neste caso TRUE indica que a variável é incluída no modelo e FALSE que ela não é incluída.
Assim, a título de exemplo, o melhor modelo com uma covariável tem TopSpeed como regressora; o melhor modelo com duas covariáveis é ajustado por TopSpeed e Teamwork e assim por diante.
Como nesse primeiro momento apenas são comparados modelos com igual número de parâmetros, qualquer critério de qualidade de ajuste vai indicar a seleção do mesmo modelo.
Para comparar a sequência de modelos obtidos para diferentes números de covariáveis, podemos recorrer aos critérios de qualidade de ajuste estudados.
\(R^2\)
## [1] 0.3233033 0.5542904 0.6489515 0.6604570 0.6690431 0.6743069 0.6743960
## [8] 0.6744576 0.6745087 0.6745507 0.6745510\(R^2\) ajustado
## [1] 0.3229296 0.5537979 0.6483693 0.6597058 0.6681274 0.6732249 0.6731333
## [8] 0.6730140 0.6728839 0.6727447 0.6725632Cp de Mallows
## [1] 1935.767261 659.509053 137.664863 75.994409 30.479972
## [6] 3.350739 4.857589 6.516812 8.234189 10.001433
## [11] 12.000000BIC
## [1] -693.0292 -1442.5548 -1867.8934 -1920.8070 -1959.7395 -1981.3038
## [7] -1974.2972 -1967.1374 -1959.9191 -1952.6506 -1945.1493## [1] 6O modelo com seis covariáveis produziu maior valor de \(R^2\) ajustado.
## [1] 6O modelo com seis covariáveis produziu menor valor de BIC.
## [1] 11O modelo com onze covariáveis produziu menor valor de \(R^2\) (obviamente).
Vamos produzir gráficos
n_cov <- 1:11
plot(n_cov, s1$rsq, type = 'b', xlab = 'Número de covariáveis', ylab = 'R2', las = 1, pch = 20)
Agora a análise do Cp de Mallows
Os elevados valores de Cp para modelos com uma a três covariáveis dificulta a visualização dos resultados.
plot(n_cov[3:11], s1$cp[3:11], xlab = 'Número de covariáveis', ylab = 'Cp', las = 1, pch = 20)
abline(0,1)
O modelo com menor Cp próximo à reta identidade é o modelo com seis covariáveis.
Minimização dos critérios AIC e BIC
Agora vamos repetir a análise usando os algoritmos backward, forward e stepwise com base na minimização dos critérios AIC e BIC. Primeiro usando AIC (k=2 é a constante de penalização).
Seleção backward, critério AIC
## Start: AIC=4555.06
## LongPassAccuracy ~ Agility + Acceleration + TopSpeed + Balance +
## Jump + Teamwork + Mentality + ConditionFitness + Height +
## Age + Weight
##
## Df Sum of Sq RSS AIC
## - Age 1 0.0 22069 4553.1
## - ConditionFitness 1 2.9 22072 4553.3
## - Acceleration 1 3.1 22073 4553.3
## - Mentality 1 5.0 22074 4553.5
## - Weight 1 5.3 22075 4553.5
## <none> 22069 4555.1
## - Height 1 201.6 22271 4569.5
## - Balance 1 349.8 22419 4581.6
## - Agility 1 565.1 22634 4598.9
## - TopSpeed 1 2075.2 24145 4716.0
## - Jump 1 2805.9 24875 4770.0
## - Teamwork 1 9996.6 32066 5230.4
##
## Step: AIC=4553.07
## LongPassAccuracy ~ Agility + Acceleration + TopSpeed + Balance +
## Jump + Teamwork + Mentality + ConditionFitness + Height +
## Weight
##
## Df Sum of Sq RSS AIC
## - ConditionFitness 1 2.9 22072 4551.3
## - Acceleration 1 3.2 22073 4551.3
## - Mentality 1 5.0 22074 4551.5
## - Weight 1 5.3 22075 4551.5
## <none> 22069 4553.1
## - Height 1 213.8 22283 4568.5
## - Balance 1 351.9 22421 4579.7
## - Agility 1 569.6 22639 4597.3
## - TopSpeed 1 2079.0 24148 4714.3
## - Jump 1 2813.0 24882 4768.6
## - Teamwork 1 10296.6 32366 5245.3
##
## Step: AIC=4551.3
## LongPassAccuracy ~ Agility + Acceleration + TopSpeed + Balance +
## Jump + Teamwork + Mentality + Height + Weight
##
## Df Sum of Sq RSS AIC
## - Acceleration 1 3.5 22076 4549.6
## - Mentality 1 3.9 22076 4549.6
## - Weight 1 5.7 22078 4549.8
## <none> 22072 4551.3
## - Height 1 213.4 22286 4566.7
## - Balance 1 359.5 22432 4578.6
## - Agility 1 585.0 22657 4596.7
## - TopSpeed 1 2096.4 24169 4713.8
## - Jump 1 2847.4 24920 4769.3
## - Teamwork 1 10762.7 32835 5269.4
##
## Step: AIC=4549.58
## LongPassAccuracy ~ Agility + TopSpeed + Balance + Jump + Teamwork +
## Mentality + Height + Weight
##
## Df Sum of Sq RSS AIC
## - Mentality 1 4.2 22080 4547.9
## - Weight 1 5.7 22081 4548.1
## <none> 22076 4549.6
## - Height 1 209.9 22286 4564.7
## - Balance 1 356.5 22432 4576.6
## - Agility 1 746.4 22822 4607.9
## - Jump 1 2856.3 24932 4768.2
## - TopSpeed 1 9292.0 31368 5184.5
## - Teamwork 1 10769.0 32845 5267.9
##
## Step: AIC=4547.93
## LongPassAccuracy ~ Agility + TopSpeed + Balance + Jump + Teamwork +
## Height + Weight
##
## Df Sum of Sq RSS AIC
## - Weight 1 6.0 22086 4546.4
## <none> 22080 4547.9
## - Height 1 228.4 22308 4564.6
## - Balance 1 360.1 22440 4575.3
## - Agility 1 781.2 22861 4609.0
## - Jump 1 2897.6 24977 4769.5
## - TopSpeed 1 9645.8 31726 5203.1
## - Teamwork 1 15066.7 37147 5489.1
##
## Step: AIC=4546.42
## LongPassAccuracy ~ Agility + TopSpeed + Balance + Jump + Teamwork +
## Height
##
## Df Sum of Sq RSS AIC
## <none> 22086 4546.4
## - Height 1 356.9 22443 4573.5
## - Balance 1 449.8 22536 4581.0
## - Agility 1 780.1 22866 4607.4
## - Jump 1 2895.8 24982 4767.8
## - TopSpeed 1 9780.3 31866 5209.1
## - Teamwork 1 15311.1 37397 5499.2##
## Call:
## lm(formula = LongPassAccuracy ~ Agility + TopSpeed + Balance +
## Jump + Teamwork + Height, data = dados)
##
## Residuals:
## Min 1Q Median 3Q Max
## -12.4177 -2.2009 -0.0368 2.2641 12.1375
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 39.52347 5.48863 7.201 8.74e-13 ***
## Agility -0.22568 0.02826 -7.987 2.44e-15 ***
## TopSpeed 0.56021 0.01981 28.280 < 2e-16 ***
## Balance -0.20783 0.03427 -6.065 1.60e-09 ***
## Jump -0.38166 0.02480 -15.388 < 2e-16 ***
## Teamwork 0.94919 0.02683 35.384 < 2e-16 ***
## Height -0.10775 0.01994 -5.403 7.44e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.497 on 1806 degrees of freedom
## Multiple R-squared: 0.6743, Adjusted R-squared: 0.6732
## F-statistic: 623.2 on 6 and 1806 DF, p-value: < 2.2e-16Seleção forward, critério AIC
mod_for <- step(ajuste0, scope=~Agility + Acceleration + TopSpeed
+ Balance + Jump + Teamwork + Mentality + ConditionFitness
+ Height + Age + Weight, direction = 'forward', k = 2)## Start: AIC=6568.25
## LongPassAccuracy ~ 1
##
## Df Sum of Sq RSS AIC
## + TopSpeed 1 21923.9 45888 5862.2
## + Acceleration 1 19573.6 48238 5952.8
## + Teamwork 1 16772.5 51040 6055.1
## + Height 1 15781.5 52031 6090.0
## + Weight 1 13834.9 53977 6156.6
## + Balance 1 12055.7 55756 6215.4
## + Jump 1 10694.1 57118 6259.1
## + Agility 1 6975.4 60837 6373.5
## + Mentality 1 3223.9 64588 6481.9
## + ConditionFitness 1 346.2 67466 6561.0
## + Age 1 244.7 67567 6563.7
## <none> 67812 6568.2
##
## Step: AIC=5862.21
## LongPassAccuracy ~ TopSpeed
##
## Df Sum of Sq RSS AIC
## + Teamwork 1 15663.7 30224 5107.2
## + Jump 1 5816.7 40071 5618.5
## + Height 1 3518.7 42369 5719.6
## + Weight 1 2848.3 43040 5748.0
## + Mentality 1 2458.9 43429 5764.4
## + Balance 1 2356.7 43531 5768.6
## + Age 1 801.1 45087 5832.3
## + ConditionFitness 1 648.1 45240 5838.4
## + Acceleration 1 72.0 45816 5861.4
## <none> 45888 5862.2
## + Agility 1 11.6 45877 5863.8
##
## Step: AIC=5107.18
## LongPassAccuracy ~ TopSpeed + Teamwork
##
## Df Sum of Sq RSS AIC
## + Jump 1 6419.2 23805 4676.3
## + Balance 1 3956.5 26268 4854.8
## + Height 1 1997.7 28227 4985.2
## + Weight 1 1752.2 28472 5000.9
## + ConditionFitness 1 553.3 29671 5075.7
## + Mentality 1 493.1 29731 5079.4
## + Acceleration 1 98.2 30126 5103.3
## + Age 1 59.2 30165 5105.6
## <none> 30225 5107.2
## + Agility 1 0.0 30224 5109.2
##
## Step: AIC=4676.34
## LongPassAccuracy ~ TopSpeed + Teamwork + Jump
##
## Df Sum of Sq RSS AIC
## + Balance 1 780.21 23025 4617.9
## + Height 1 738.51 23067 4621.2
## + Weight 1 591.99 23213 4632.7
## + Agility 1 65.78 23740 4673.3
## + ConditionFitness 1 49.02 23756 4674.6
## <none> 23805 4676.3
## + Age 1 4.80 23801 4678.0
## + Mentality 1 3.51 23802 4678.1
## + Acceleration 1 2.62 23803 4678.1
##
## Step: AIC=4617.93
## LongPassAccuracy ~ TopSpeed + Teamwork + Jump + Balance
##
## Df Sum of Sq RSS AIC
## + Agility 1 582.24 22443 4573.5
## + Height 1 159.10 22866 4607.4
## + Acceleration 1 101.33 22924 4611.9
## + Mentality 1 74.78 22950 4614.0
## + Weight 1 70.37 22955 4614.4
## <none> 23025 4617.9
## + Age 1 23.85 23001 4618.0
## + ConditionFitness 1 14.33 23011 4618.8
##
## Step: AIC=4573.49
## LongPassAccuracy ~ TopSpeed + Teamwork + Jump + Balance + Agility
##
## Df Sum of Sq RSS AIC
## + Height 1 356.95 22086 4546.4
## + Weight 1 134.59 22308 4564.6
## + Mentality 1 40.06 22403 4572.3
## <none> 22443 4573.5
## + Age 1 12.76 22430 4574.5
## + ConditionFitness 1 0.87 22442 4575.4
## + Acceleration 1 0.72 22442 4575.4
##
## Step: AIC=4546.42
## LongPassAccuracy ~ TopSpeed + Teamwork + Jump + Balance + Agility +
## Height
##
## Df Sum of Sq RSS AIC
## <none> 22086 4546.4
## + Weight 1 6.0430 22080 4547.9
## + Mentality 1 4.4891 22081 4548.1
## + Acceleration 1 3.7991 22082 4548.1
## + ConditionFitness 1 2.2037 22084 4548.2
## + Age 1 0.0608 22086 4548.4##
## Call:
## lm(formula = LongPassAccuracy ~ TopSpeed + Teamwork + Jump +
## Balance + Agility + Height, data = dados)
##
## Residuals:
## Min 1Q Median 3Q Max
## -12.4177 -2.2009 -0.0368 2.2641 12.1375
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 39.52347 5.48863 7.201 8.74e-13 ***
## TopSpeed 0.56021 0.01981 28.280 < 2e-16 ***
## Teamwork 0.94919 0.02683 35.384 < 2e-16 ***
## Jump -0.38166 0.02480 -15.388 < 2e-16 ***
## Balance -0.20783 0.03427 -6.065 1.60e-09 ***
## Agility -0.22568 0.02826 -7.987 2.44e-15 ***
## Height -0.10775 0.01994 -5.403 7.44e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.497 on 1806 degrees of freedom
## Multiple R-squared: 0.6743, Adjusted R-squared: 0.6732
## F-statistic: 623.2 on 6 and 1806 DF, p-value: < 2.2e-16Seleção stepwise, critério AIC
## Start: AIC=4621.1
## LongPassAccuracy ~ Agility + Acceleration + TopSpeed + Balance +
## Jump + Teamwork + Mentality + ConditionFitness + Height +
## Age + Weight
##
## Df Sum of Sq RSS AIC
## - Age 1 0.0 22069 4613.6
## - ConditionFitness 1 2.9 22072 4613.8
## - Acceleration 1 3.1 22073 4613.9
## - Mentality 1 5.0 22074 4614.0
## - Weight 1 5.3 22075 4614.0
## <none> 22069 4621.1
## - Height 1 201.6 22271 4630.1
## - Balance 1 349.8 22419 4642.1
## - Agility 1 565.1 22634 4659.4
## - TopSpeed 1 2075.2 24145 4776.5
## - Jump 1 2805.9 24875 4830.6
## - Teamwork 1 9996.6 32066 5290.9
##
## Step: AIC=4613.6
## LongPassAccuracy ~ Agility + Acceleration + TopSpeed + Balance +
## Jump + Teamwork + Mentality + ConditionFitness + Height +
## Weight
##
## Df Sum of Sq RSS AIC
## - ConditionFitness 1 2.9 22072 4606.3
## - Acceleration 1 3.2 22073 4606.4
## - Mentality 1 5.0 22074 4606.5
## - Weight 1 5.3 22075 4606.5
## <none> 22069 4613.6
## + Age 1 0.0 22069 4621.1
## - Height 1 213.8 22283 4623.6
## - Balance 1 351.9 22421 4634.8
## - Agility 1 569.6 22639 4652.3
## - TopSpeed 1 2079.0 24148 4769.3
## - Jump 1 2813.0 24882 4823.6
## - Teamwork 1 10296.6 32366 5300.3
##
## Step: AIC=4606.33
## LongPassAccuracy ~ Agility + Acceleration + TopSpeed + Balance +
## Jump + Teamwork + Mentality + Height + Weight
##
## Df Sum of Sq RSS AIC
## - Acceleration 1 3.5 22076 4599.1
## - Mentality 1 3.9 22076 4599.1
## - Weight 1 5.7 22078 4599.3
## <none> 22072 4606.3
## + ConditionFitness 1 2.9 22069 4613.6
## + Age 1 0.0 22072 4613.8
## - Height 1 213.4 22286 4616.3
## - Balance 1 359.5 22432 4628.1
## - Agility 1 585.0 22657 4646.2
## - TopSpeed 1 2096.4 24169 4763.3
## - Jump 1 2847.4 24920 4818.8
## - Teamwork 1 10762.7 32835 5318.9
##
## Step: AIC=4599.11
## LongPassAccuracy ~ Agility + TopSpeed + Balance + Jump + Teamwork +
## Mentality + Height + Weight
##
## Df Sum of Sq RSS AIC
## - Mentality 1 4.2 22080 4591.9
## - Weight 1 5.7 22081 4592.1
## <none> 22076 4599.1
## + Acceleration 1 3.5 22072 4606.3
## + ConditionFitness 1 3.1 22073 4606.4
## + Age 1 0.0 22076 4606.6
## - Height 1 209.9 22286 4608.8
## - Balance 1 356.5 22432 4620.6
## - Agility 1 746.4 22822 4651.9
## - Jump 1 2856.3 24932 4812.2
## - TopSpeed 1 9292.0 31368 5228.5
## - Teamwork 1 10769.0 32845 5311.9
##
## Step: AIC=4591.95
## LongPassAccuracy ~ Agility + TopSpeed + Balance + Jump + Teamwork +
## Height + Weight
##
## Df Sum of Sq RSS AIC
## - Weight 1 6.0 22086 4584.9
## <none> 22080 4591.9
## + Mentality 1 4.2 22076 4599.1
## + Acceleration 1 3.8 22076 4599.1
## + ConditionFitness 1 1.9 22078 4599.3
## + Age 1 0.0 22080 4599.5
## - Height 1 228.4 22308 4603.1
## - Balance 1 360.1 22440 4613.8
## - Agility 1 781.2 22861 4647.5
## - Jump 1 2897.6 24977 4808.0
## - TopSpeed 1 9645.8 31726 5241.6
## - Teamwork 1 15066.7 37147 5527.6
##
## Step: AIC=4584.94
## LongPassAccuracy ~ Agility + TopSpeed + Balance + Jump + Teamwork +
## Height
##
## Df Sum of Sq RSS AIC
## <none> 22086 4584.9
## + Weight 1 6.0 22080 4591.9
## + Mentality 1 4.5 22081 4592.1
## + Acceleration 1 3.8 22082 4592.1
## + ConditionFitness 1 2.2 22084 4592.3
## + Age 1 0.1 22086 4592.4
## - Height 1 356.9 22443 4606.5
## - Balance 1 449.8 22536 4614.0
## - Agility 1 780.1 22866 4640.4
## - Jump 1 2895.8 24982 4800.8
## - TopSpeed 1 9780.3 31866 5242.1
## - Teamwork 1 15311.1 37397 5532.3##
## Call:
## lm(formula = LongPassAccuracy ~ Agility + TopSpeed + Balance +
## Jump + Teamwork + Height, data = dados)
##
## Residuals:
## Min 1Q Median 3Q Max
## -12.4177 -2.2009 -0.0368 2.2641 12.1375
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 39.52347 5.48863 7.201 8.74e-13 ***
## Agility -0.22568 0.02826 -7.987 2.44e-15 ***
## TopSpeed 0.56021 0.01981 28.280 < 2e-16 ***
## Balance -0.20783 0.03427 -6.065 1.60e-09 ***
## Jump -0.38166 0.02480 -15.388 < 2e-16 ***
## Teamwork 0.94919 0.02683 35.384 < 2e-16 ***
## Height -0.10775 0.01994 -5.403 7.44e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.497 on 1806 degrees of freedom
## Multiple R-squared: 0.6743, Adjusted R-squared: 0.6732
## F-statistic: 623.2 on 6 and 1806 DF, p-value: < 2.2e-16usando BIC (k=log(n) é a constante de penalização).
Seleção backward, critério BIC
## Start: AIC=4621.1
## LongPassAccuracy ~ Agility + Acceleration + TopSpeed + Balance +
## Jump + Teamwork + Mentality + ConditionFitness + Height +
## Age + Weight
##
## Df Sum of Sq RSS AIC
## - Age 1 0.0 22069 4613.6
## - ConditionFitness 1 2.9 22072 4613.8
## - Acceleration 1 3.1 22073 4613.9
## - Mentality 1 5.0 22074 4614.0
## - Weight 1 5.3 22075 4614.0
## <none> 22069 4621.1
## - Height 1 201.6 22271 4630.1
## - Balance 1 349.8 22419 4642.1
## - Agility 1 565.1 22634 4659.4
## - TopSpeed 1 2075.2 24145 4776.5
## - Jump 1 2805.9 24875 4830.6
## - Teamwork 1 9996.6 32066 5290.9
##
## Step: AIC=4613.6
## LongPassAccuracy ~ Agility + Acceleration + TopSpeed + Balance +
## Jump + Teamwork + Mentality + ConditionFitness + Height +
## Weight
##
## Df Sum of Sq RSS AIC
## - ConditionFitness 1 2.9 22072 4606.3
## - Acceleration 1 3.2 22073 4606.4
## - Mentality 1 5.0 22074 4606.5
## - Weight 1 5.3 22075 4606.5
## <none> 22069 4613.6
## - Height 1 213.8 22283 4623.6
## - Balance 1 351.9 22421 4634.8
## - Agility 1 569.6 22639 4652.3
## - TopSpeed 1 2079.0 24148 4769.3
## - Jump 1 2813.0 24882 4823.6
## - Teamwork 1 10296.6 32366 5300.3
##
## Step: AIC=4606.33
## LongPassAccuracy ~ Agility + Acceleration + TopSpeed + Balance +
## Jump + Teamwork + Mentality + Height + Weight
##
## Df Sum of Sq RSS AIC
## - Acceleration 1 3.5 22076 4599.1
## - Mentality 1 3.9 22076 4599.1
## - Weight 1 5.7 22078 4599.3
## <none> 22072 4606.3
## - Height 1 213.4 22286 4616.3
## - Balance 1 359.5 22432 4628.1
## - Agility 1 585.0 22657 4646.2
## - TopSpeed 1 2096.4 24169 4763.3
## - Jump 1 2847.4 24920 4818.8
## - Teamwork 1 10762.7 32835 5318.9
##
## Step: AIC=4599.11
## LongPassAccuracy ~ Agility + TopSpeed + Balance + Jump + Teamwork +
## Mentality + Height + Weight
##
## Df Sum of Sq RSS AIC
## - Mentality 1 4.2 22080 4591.9
## - Weight 1 5.7 22081 4592.1
## <none> 22076 4599.1
## - Height 1 209.9 22286 4608.8
## - Balance 1 356.5 22432 4620.6
## - Agility 1 746.4 22822 4651.9
## - Jump 1 2856.3 24932 4812.2
## - TopSpeed 1 9292.0 31368 5228.5
## - Teamwork 1 10769.0 32845 5311.9
##
## Step: AIC=4591.95
## LongPassAccuracy ~ Agility + TopSpeed + Balance + Jump + Teamwork +
## Height + Weight
##
## Df Sum of Sq RSS AIC
## - Weight 1 6.0 22086 4584.9
## <none> 22080 4591.9
## - Height 1 228.4 22308 4603.1
## - Balance 1 360.1 22440 4613.8
## - Agility 1 781.2 22861 4647.5
## - Jump 1 2897.6 24977 4808.0
## - TopSpeed 1 9645.8 31726 5241.6
## - Teamwork 1 15066.7 37147 5527.6
##
## Step: AIC=4584.94
## LongPassAccuracy ~ Agility + TopSpeed + Balance + Jump + Teamwork +
## Height
##
## Df Sum of Sq RSS AIC
## <none> 22086 4584.9
## - Height 1 356.9 22443 4606.5
## - Balance 1 449.8 22536 4614.0
## - Agility 1 780.1 22866 4640.4
## - Jump 1 2895.8 24982 4800.8
## - TopSpeed 1 9780.3 31866 5242.1
## - Teamwork 1 15311.1 37397 5532.3##
## Call:
## lm(formula = LongPassAccuracy ~ Agility + TopSpeed + Balance +
## Jump + Teamwork + Height, data = dados)
##
## Residuals:
## Min 1Q Median 3Q Max
## -12.4177 -2.2009 -0.0368 2.2641 12.1375
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 39.52347 5.48863 7.201 8.74e-13 ***
## Agility -0.22568 0.02826 -7.987 2.44e-15 ***
## TopSpeed 0.56021 0.01981 28.280 < 2e-16 ***
## Balance -0.20783 0.03427 -6.065 1.60e-09 ***
## Jump -0.38166 0.02480 -15.388 < 2e-16 ***
## Teamwork 0.94919 0.02683 35.384 < 2e-16 ***
## Height -0.10775 0.01994 -5.403 7.44e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.497 on 1806 degrees of freedom
## Multiple R-squared: 0.6743, Adjusted R-squared: 0.6732
## F-statistic: 623.2 on 6 and 1806 DF, p-value: < 2.2e-16Seleção forward, critério BIC
mod_for <- step(ajuste0, scope=~Agility + Acceleration + TopSpeed
+ Balance + Jump + Teamwork + Mentality + ConditionFitness
+ Height + Age + Weight, direction = 'forward', k = log(n))## Start: AIC=6573.75
## LongPassAccuracy ~ 1
##
## Df Sum of Sq RSS AIC
## + TopSpeed 1 21923.9 45888 5873.2
## + Acceleration 1 19573.6 48238 5963.8
## + Teamwork 1 16772.5 51040 6066.1
## + Height 1 15781.5 52031 6101.0
## + Weight 1 13834.9 53977 6167.6
## + Balance 1 12055.7 55756 6226.4
## + Jump 1 10694.1 57118 6270.1
## + Agility 1 6975.4 60837 6384.5
## + Mentality 1 3223.9 64588 6492.9
## + ConditionFitness 1 346.2 67466 6572.0
## <none> 67812 6573.7
## + Age 1 244.7 67567 6574.7
##
## Step: AIC=5873.22
## LongPassAccuracy ~ TopSpeed
##
## Df Sum of Sq RSS AIC
## + Teamwork 1 15663.7 30224 5123.7
## + Jump 1 5816.7 40071 5635.0
## + Height 1 3518.7 42369 5736.1
## + Weight 1 2848.3 43040 5764.5
## + Mentality 1 2458.9 43429 5780.9
## + Balance 1 2356.7 43531 5785.1
## + Age 1 801.1 45087 5848.8
## + ConditionFitness 1 648.1 45240 5854.9
## <none> 45888 5873.2
## + Acceleration 1 72.0 45816 5877.9
## + Agility 1 11.6 45877 5880.3
##
## Step: AIC=5123.69
## LongPassAccuracy ~ TopSpeed + Teamwork
##
## Df Sum of Sq RSS AIC
## + Jump 1 6419.2 23805 4698.4
## + Balance 1 3956.5 26268 4876.8
## + Height 1 1997.7 28227 5007.2
## + Weight 1 1752.2 28472 5022.9
## + ConditionFitness 1 553.3 29671 5097.7
## + Mentality 1 493.1 29731 5101.4
## <none> 30225 5123.7
## + Acceleration 1 98.2 30126 5125.3
## + Age 1 59.2 30165 5127.6
## + Agility 1 0.0 30224 5131.2
##
## Step: AIC=4698.35
## LongPassAccuracy ~ TopSpeed + Teamwork + Jump
##
## Df Sum of Sq RSS AIC
## + Balance 1 780.21 23025 4645.4
## + Height 1 738.51 23067 4648.7
## + Weight 1 591.99 23213 4660.2
## <none> 23805 4698.4
## + Agility 1 65.78 23740 4700.8
## + ConditionFitness 1 49.02 23756 4702.1
## + Age 1 4.80 23801 4705.5
## + Mentality 1 3.51 23802 4705.6
## + Acceleration 1 2.62 23803 4705.7
##
## Step: AIC=4645.44
## LongPassAccuracy ~ TopSpeed + Teamwork + Jump + Balance
##
## Df Sum of Sq RSS AIC
## + Agility 1 582.24 22443 4606.5
## + Height 1 159.10 22866 4640.4
## + Acceleration 1 101.33 22924 4644.9
## <none> 23025 4645.4
## + Mentality 1 74.78 22950 4647.0
## + Weight 1 70.37 22955 4647.4
## + Age 1 23.85 23001 4651.1
## + ConditionFitness 1 14.33 23011 4651.8
##
## Step: AIC=4606.51
## LongPassAccuracy ~ TopSpeed + Teamwork + Jump + Balance + Agility
##
## Df Sum of Sq RSS AIC
## + Height 1 356.95 22086 4584.9
## + Weight 1 134.59 22308 4603.1
## <none> 22443 4606.5
## + Mentality 1 40.06 22403 4610.8
## + Age 1 12.76 22430 4613.0
## + ConditionFitness 1 0.87 22442 4613.9
## + Acceleration 1 0.72 22442 4614.0
##
## Step: AIC=4584.94
## LongPassAccuracy ~ TopSpeed + Teamwork + Jump + Balance + Agility +
## Height
##
## Df Sum of Sq RSS AIC
## <none> 22086 4584.9
## + Weight 1 6.0430 22080 4591.9
## + Mentality 1 4.4891 22081 4592.1
## + Acceleration 1 3.7991 22082 4592.1
## + ConditionFitness 1 2.2037 22084 4592.3
## + Age 1 0.0608 22086 4592.4##
## Call:
## lm(formula = LongPassAccuracy ~ TopSpeed + Teamwork + Jump +
## Balance + Agility + Height, data = dados)
##
## Residuals:
## Min 1Q Median 3Q Max
## -12.4177 -2.2009 -0.0368 2.2641 12.1375
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 39.52347 5.48863 7.201 8.74e-13 ***
## TopSpeed 0.56021 0.01981 28.280 < 2e-16 ***
## Teamwork 0.94919 0.02683 35.384 < 2e-16 ***
## Jump -0.38166 0.02480 -15.388 < 2e-16 ***
## Balance -0.20783 0.03427 -6.065 1.60e-09 ***
## Agility -0.22568 0.02826 -7.987 2.44e-15 ***
## Height -0.10775 0.01994 -5.403 7.44e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.497 on 1806 degrees of freedom
## Multiple R-squared: 0.6743, Adjusted R-squared: 0.6732
## F-statistic: 623.2 on 6 and 1806 DF, p-value: < 2.2e-16Seleção stepwise, critério BIC
## Start: AIC=4621.1
## LongPassAccuracy ~ Agility + Acceleration + TopSpeed + Balance +
## Jump + Teamwork + Mentality + ConditionFitness + Height +
## Age + Weight
##
## Df Sum of Sq RSS AIC
## - Age 1 0.0 22069 4613.6
## - ConditionFitness 1 2.9 22072 4613.8
## - Acceleration 1 3.1 22073 4613.9
## - Mentality 1 5.0 22074 4614.0
## - Weight 1 5.3 22075 4614.0
## <none> 22069 4621.1
## - Height 1 201.6 22271 4630.1
## - Balance 1 349.8 22419 4642.1
## - Agility 1 565.1 22634 4659.4
## - TopSpeed 1 2075.2 24145 4776.5
## - Jump 1 2805.9 24875 4830.6
## - Teamwork 1 9996.6 32066 5290.9
##
## Step: AIC=4613.6
## LongPassAccuracy ~ Agility + Acceleration + TopSpeed + Balance +
## Jump + Teamwork + Mentality + ConditionFitness + Height +
## Weight
##
## Df Sum of Sq RSS AIC
## - ConditionFitness 1 2.9 22072 4606.3
## - Acceleration 1 3.2 22073 4606.4
## - Mentality 1 5.0 22074 4606.5
## - Weight 1 5.3 22075 4606.5
## <none> 22069 4613.6
## + Age 1 0.0 22069 4621.1
## - Height 1 213.8 22283 4623.6
## - Balance 1 351.9 22421 4634.8
## - Agility 1 569.6 22639 4652.3
## - TopSpeed 1 2079.0 24148 4769.3
## - Jump 1 2813.0 24882 4823.6
## - Teamwork 1 10296.6 32366 5300.3
##
## Step: AIC=4606.33
## LongPassAccuracy ~ Agility + Acceleration + TopSpeed + Balance +
## Jump + Teamwork + Mentality + Height + Weight
##
## Df Sum of Sq RSS AIC
## - Acceleration 1 3.5 22076 4599.1
## - Mentality 1 3.9 22076 4599.1
## - Weight 1 5.7 22078 4599.3
## <none> 22072 4606.3
## + ConditionFitness 1 2.9 22069 4613.6
## + Age 1 0.0 22072 4613.8
## - Height 1 213.4 22286 4616.3
## - Balance 1 359.5 22432 4628.1
## - Agility 1 585.0 22657 4646.2
## - TopSpeed 1 2096.4 24169 4763.3
## - Jump 1 2847.4 24920 4818.8
## - Teamwork 1 10762.7 32835 5318.9
##
## Step: AIC=4599.11
## LongPassAccuracy ~ Agility + TopSpeed + Balance + Jump + Teamwork +
## Mentality + Height + Weight
##
## Df Sum of Sq RSS AIC
## - Mentality 1 4.2 22080 4591.9
## - Weight 1 5.7 22081 4592.1
## <none> 22076 4599.1
## + Acceleration 1 3.5 22072 4606.3
## + ConditionFitness 1 3.1 22073 4606.4
## + Age 1 0.0 22076 4606.6
## - Height 1 209.9 22286 4608.8
## - Balance 1 356.5 22432 4620.6
## - Agility 1 746.4 22822 4651.9
## - Jump 1 2856.3 24932 4812.2
## - TopSpeed 1 9292.0 31368 5228.5
## - Teamwork 1 10769.0 32845 5311.9
##
## Step: AIC=4591.95
## LongPassAccuracy ~ Agility + TopSpeed + Balance + Jump + Teamwork +
## Height + Weight
##
## Df Sum of Sq RSS AIC
## - Weight 1 6.0 22086 4584.9
## <none> 22080 4591.9
## + Mentality 1 4.2 22076 4599.1
## + Acceleration 1 3.8 22076 4599.1
## + ConditionFitness 1 1.9 22078 4599.3
## + Age 1 0.0 22080 4599.5
## - Height 1 228.4 22308 4603.1
## - Balance 1 360.1 22440 4613.8
## - Agility 1 781.2 22861 4647.5
## - Jump 1 2897.6 24977 4808.0
## - TopSpeed 1 9645.8 31726 5241.6
## - Teamwork 1 15066.7 37147 5527.6
##
## Step: AIC=4584.94
## LongPassAccuracy ~ Agility + TopSpeed + Balance + Jump + Teamwork +
## Height
##
## Df Sum of Sq RSS AIC
## <none> 22086 4584.9
## + Weight 1 6.0 22080 4591.9
## + Mentality 1 4.5 22081 4592.1
## + Acceleration 1 3.8 22082 4592.1
## + ConditionFitness 1 2.2 22084 4592.3
## + Age 1 0.1 22086 4592.4
## - Height 1 356.9 22443 4606.5
## - Balance 1 449.8 22536 4614.0
## - Agility 1 780.1 22866 4640.4
## - Jump 1 2895.8 24982 4800.8
## - TopSpeed 1 9780.3 31866 5242.1
## - Teamwork 1 15311.1 37397 5532.3##
## Call:
## lm(formula = LongPassAccuracy ~ Agility + TopSpeed + Balance +
## Jump + Teamwork + Height, data = dados)
##
## Residuals:
## Min 1Q Median 3Q Max
## -12.4177 -2.2009 -0.0368 2.2641 12.1375
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 39.52347 5.48863 7.201 8.74e-13 ***
## Agility -0.22568 0.02826 -7.987 2.44e-15 ***
## TopSpeed 0.56021 0.01981 28.280 < 2e-16 ***
## Balance -0.20783 0.03427 -6.065 1.60e-09 ***
## Jump -0.38166 0.02480 -15.388 < 2e-16 ***
## Teamwork 0.94919 0.02683 35.384 < 2e-16 ***
## Height -0.10775 0.01994 -5.403 7.44e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.497 on 1806 degrees of freedom
## Multiple R-squared: 0.6743, Adjusted R-squared: 0.6732
## F-statistic: 623.2 on 6 and 1806 DF, p-value: < 2.2e-16