import pandas as pd
import numpy as np
import statsmodels.api as sm
import seaborn as sns
import sklearn as sk

sns.set_style('whitegrid')
sns.set_palette('flare_r')
sns.color_palette('flare_r')

df_all = pd.read_csv('Dados Tratados/output_geral.csv', sep=';')

df_min = pd.read_csv('Dados Tratados/output_owners_min.csv', sep=';')

df_max = pd.read_csv('Dados Tratados/output_owners.csv', sep=';')

Colunas = ['appid','name','Year','english','platforms_windows','platforms_mac','platforms_linux','genres_Action',
           'genres_Free to Play', 'genres_Strategy','genres_Adventure', 'genres_Indie', 'genres_RPG',
           'genres_Casual','genres_Simulation', 'genres_Racing', 'genres_Violent','genres_Massively Multiplayer',
           'genres_Nudity', 'genres_Sports',       'genres_Early Access', 'genres_Gore', 'genres_Sexual Content',
           'categories_Multi-player', 'categories_Online Multi-Player','categories_Local Multi-Player',
           'categories_Valve Anti-Cheat enabled','categories_Single-player', 'categories_Steam Cloud',
           'categories_Steam Achievements', 'categories_Steam Trading Cards','categories_Captions available',
           'categories_Partial Controller Support','categories_Includes Source SDK','categories_Cross-Platform Multiplayer',
           'categories_Stats','categories_Commentary available', 'categories_Includes level editor',
           'categories_Steam Workshop', 'categories_In-App Purchases','categories_Co-op',
           'categories_Full controller support','categories_Steam Leaderboards', 'categories_SteamVR Collectibles',
           'categories_Online Co-op', 'categories_Shared/Split Screen','categories_Local Co-op', 'categories_MMO', 
           'categories_VR Support','categories_Mods', 'categories_Mods (require HL2)',
           'categories_Steam Turn Notifications','achievements','%_ratings','QTD_ratings','owners_mean',
           'average_playtime_>0','price','log_price','log_log_price']

Colunas_Tratada = ['Year','english','platforms_windows','platforms_mac','platforms_linux','genres_Action',
           'genres_Free to Play', 'genres_Strategy','genres_Adventure', 'genres_Indie', 'genres_RPG',
           'genres_Casual','genres_Simulation', 'genres_Racing', 'genres_Violent','genres_Massively Multiplayer',
           'genres_Nudity', 'genres_Sports',       'genres_Early Access', 'genres_Gore', 'genres_Sexual Content',
           'categories_Multi-player', 'categories_Online Multi-Player','categories_Local Multi-Player',
           'categories_Valve Anti-Cheat enabled','categories_Single-player', 'categories_Steam Cloud',
           'categories_Steam Achievements', 'categories_Steam Trading Cards','categories_Captions available',
           'categories_Partial Controller Support','categories_Includes Source SDK','categories_Cross-Platform Multiplayer',
           'categories_Stats','categories_Commentary available', 'categories_Includes level editor',
           'categories_Steam Workshop', 'categories_In-App Purchases','categories_Co-op',
           'categories_Full controller support','categories_Steam Leaderboards', 'categories_SteamVR Collectibles',
           'categories_Online Co-op', 'categories_Shared/Split Screen','categories_Local Co-op', 'categories_MMO', 
           'categories_VR Support','categories_Mods', 'categories_Mods (require HL2)',
           'categories_Steam Turn Notifications','achievements','%_ratings','QTD_ratings','owners_mean',
           'average_playtime_>0']

df_all.head()

df_min.head()

df_max.head()

df_all.describe()

df_min.describe()

df_max.describe()

df_all.shape

(26846, 61)

df_min.shape

(18433, 61)

df_max.shape

(8413, 61)

df_all.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 26846 entries, 0 to 26845
Data columns (total 61 columns):
 #   Column                                 Non-Null Count  Dtype  
---  ------                                 --------------  -----  
 0   Unnamed: 0                             26846 non-null  int64  
 1   appid                                  26846 non-null  int64  
 2   name                                   26846 non-null  object 
 3   Year                                   26846 non-null  int64  
 4   english                                26846 non-null  int64  
 5   platforms_windows                      26846 non-null  int64  
 6   platforms_mac                          26846 non-null  int64  
 7   platforms_linux                        26846 non-null  int64  
 8   genres_Action                          26846 non-null  int64  
 9   genres_Free to Play                    26846 non-null  int64  
 10  genres_Strategy                        26846 non-null  int64  
 11  genres_Adventure                       26846 non-null  int64  
 12  genres_Indie                           26846 non-null  int64  
 13  genres_RPG                             26846 non-null  int64  
 14  genres_Casual                          26846 non-null  int64  
 15  genres_Simulation                      26846 non-null  int64  
 16  genres_Racing                          26846 non-null  int64  
 17  genres_Violent                         26846 non-null  int64  
 18  genres_Massively Multiplayer           26846 non-null  int64  
 19  genres_Nudity                          26846 non-null  int64  
 20  genres_Sports                          26846 non-null  int64  
 21  genres_Early Access                    26846 non-null  int64  
 22  genres_Gore                            26846 non-null  int64  
 23  genres_Sexual Content                  26846 non-null  int64  
 24  categories_Multi-player                26846 non-null  int64  
 25  categories_Online Multi-Player         26846 non-null  int64  
 26  categories_Local Multi-Player          26846 non-null  int64  
 27  categories_Valve Anti-Cheat enabled    26846 non-null  int64  
 28  categories_Single-player               26846 non-null  int64  
 29  categories_Steam Cloud                 26846 non-null  int64  
 30  categories_Steam Achievements          26846 non-null  int64  
 31  categories_Steam Trading Cards         26846 non-null  int64  
 32  categories_Captions available          26846 non-null  int64  
 33  categories_Partial Controller Support  26846 non-null  int64  
 34  categories_Includes Source SDK         26846 non-null  int64  
 35  categories_Cross-Platform Multiplayer  26846 non-null  int64  
 36  categories_Stats                       26846 non-null  int64  
 37  categories_Commentary available        26846 non-null  int64  
 38  categories_Includes level editor       26846 non-null  int64  
 39  categories_Steam Workshop              26846 non-null  int64  
 40  categories_In-App Purchases            26846 non-null  int64  
 41  categories_Co-op                       26846 non-null  int64  
 42  categories_Full controller support     26846 non-null  int64  
 43  categories_Steam Leaderboards          26846 non-null  int64  
 44  categories_SteamVR Collectibles        26846 non-null  int64  
 45  categories_Online Co-op                26846 non-null  int64  
 46  categories_Shared/Split Screen         26846 non-null  int64  
 47  categories_Local Co-op                 26846 non-null  int64  
 48  categories_MMO                         26846 non-null  int64  
 49  categories_VR Support                  26846 non-null  int64  
 50  categories_Mods                        26846 non-null  int64  
 51  categories_Mods (require HL2)          26846 non-null  int64  
 52  categories_Steam Turn Notifications    26846 non-null  int64  
 53  achievements                           26846 non-null  int64  
 54  %_ratings                              26846 non-null  float64
 55  QTD_ratings                            26846 non-null  int64  
 56  owners_mean                            26846 non-null  float64
 57  average_playtime_>0                    26846 non-null  int64  
 58  price                                  26846 non-null  float64
 59  log_price                              26846 non-null  float64
 60  log_log_price                          26846 non-null  float64
dtypes: float64(5), int64(55), object(1)
memory usage: 12.5+ MB

df_min.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 18433 entries, 0 to 18432
Data columns (total 61 columns):
 #   Column                                 Non-Null Count  Dtype  
---  ------                                 --------------  -----  
 0   Unnamed: 0                             18433 non-null  int64  
 1   appid                                  18433 non-null  int64  
 2   name                                   18433 non-null  object 
 3   Year                                   18433 non-null  int64  
 4   english                                18433 non-null  int64  
 5   platforms_windows                      18433 non-null  int64  
 6   platforms_mac                          18433 non-null  int64  
 7   platforms_linux                        18433 non-null  int64  
 8   genres_Action                          18433 non-null  int64  
 9   genres_Free to Play                    18433 non-null  int64  
 10  genres_Strategy                        18433 non-null  int64  
 11  genres_Adventure                       18433 non-null  int64  
 12  genres_Indie                           18433 non-null  int64  
 13  genres_RPG                             18433 non-null  int64  
 14  genres_Casual                          18433 non-null  int64  
 15  genres_Simulation                      18433 non-null  int64  
 16  genres_Racing                          18433 non-null  int64  
 17  genres_Violent                         18433 non-null  int64  
 18  genres_Massively Multiplayer           18433 non-null  int64  
 19  genres_Nudity                          18433 non-null  int64  
 20  genres_Sports                          18433 non-null  int64  
 21  genres_Early Access                    18433 non-null  int64  
 22  genres_Gore                            18433 non-null  int64  
 23  genres_Sexual Content                  18433 non-null  int64  
 24  categories_Multi-player                18433 non-null  int64  
 25  categories_Online Multi-Player         18433 non-null  int64  
 26  categories_Local Multi-Player          18433 non-null  int64  
 27  categories_Valve Anti-Cheat enabled    18433 non-null  int64  
 28  categories_Single-player               18433 non-null  int64  
 29  categories_Steam Cloud                 18433 non-null  int64  
 30  categories_Steam Achievements          18433 non-null  int64  
 31  categories_Steam Trading Cards         18433 non-null  int64  
 32  categories_Captions available          18433 non-null  int64  
 33  categories_Partial Controller Support  18433 non-null  int64  
 34  categories_Includes Source SDK         18433 non-null  int64  
 35  categories_Cross-Platform Multiplayer  18433 non-null  int64  
 36  categories_Stats                       18433 non-null  int64  
 37  categories_Commentary available        18433 non-null  int64  
 38  categories_Includes level editor       18433 non-null  int64  
 39  categories_Steam Workshop              18433 non-null  int64  
 40  categories_In-App Purchases            18433 non-null  int64  
 41  categories_Co-op                       18433 non-null  int64  
 42  categories_Full controller support     18433 non-null  int64  
 43  categories_Steam Leaderboards          18433 non-null  int64  
 44  categories_SteamVR Collectibles        18433 non-null  int64  
 45  categories_Online Co-op                18433 non-null  int64  
 46  categories_Shared/Split Screen         18433 non-null  int64  
 47  categories_Local Co-op                 18433 non-null  int64  
 48  categories_MMO                         18433 non-null  int64  
 49  categories_VR Support                  18433 non-null  int64  
 50  categories_Mods                        18433 non-null  int64  
 51  categories_Mods (require HL2)          18433 non-null  int64  
 52  categories_Steam Turn Notifications    18433 non-null  int64  
 53  achievements                           18433 non-null  int64  
 54  %_ratings                              18433 non-null  float64
 55  QTD_ratings                            18433 non-null  int64  
 56  owners_mean                            18433 non-null  float64
 57  average_playtime_>0                    18433 non-null  int64  
 58  price                                  18433 non-null  float64
 59  log_price                              18433 non-null  float64
 60  log_log_price                          18433 non-null  float64
dtypes: float64(5), int64(55), object(1)
memory usage: 8.6+ MB

df_max.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 8413 entries, 0 to 8412
Data columns (total 61 columns):
 #   Column                                 Non-Null Count  Dtype  
---  ------                                 --------------  -----  
 0   Unnamed: 0                             8413 non-null   int64  
 1   appid                                  8413 non-null   int64  
 2   name                                   8413 non-null   object 
 3   Year                                   8413 non-null   int64  
 4   english                                8413 non-null   int64  
 5   platforms_windows                      8413 non-null   int64  
 6   platforms_mac                          8413 non-null   int64  
 7   platforms_linux                        8413 non-null   int64  
 8   genres_Action                          8413 non-null   int64  
 9   genres_Free to Play                    8413 non-null   int64  
 10  genres_Strategy                        8413 non-null   int64  
 11  genres_Adventure                       8413 non-null   int64  
 12  genres_Indie                           8413 non-null   int64  
 13  genres_RPG                             8413 non-null   int64  
 14  genres_Casual                          8413 non-null   int64  
 15  genres_Simulation                      8413 non-null   int64  
 16  genres_Racing                          8413 non-null   int64  
 17  genres_Violent                         8413 non-null   int64  
 18  genres_Massively Multiplayer           8413 non-null   int64  
 19  genres_Nudity                          8413 non-null   int64  
 20  genres_Sports                          8413 non-null   int64  
 21  genres_Early Access                    8413 non-null   int64  
 22  genres_Gore                            8413 non-null   int64  
 23  genres_Sexual Content                  8413 non-null   int64  
 24  categories_Multi-player                8413 non-null   int64  
 25  categories_Online Multi-Player         8413 non-null   int64  
 26  categories_Local Multi-Player          8413 non-null   int64  
 27  categories_Valve Anti-Cheat enabled    8413 non-null   int64  
 28  categories_Single-player               8413 non-null   int64  
 29  categories_Steam Cloud                 8413 non-null   int64  
 30  categories_Steam Achievements          8413 non-null   int64  
 31  categories_Steam Trading Cards         8413 non-null   int64  
 32  categories_Captions available          8413 non-null   int64  
 33  categories_Partial Controller Support  8413 non-null   int64  
 34  categories_Includes Source SDK         8413 non-null   int64  
 35  categories_Cross-Platform Multiplayer  8413 non-null   int64  
 36  categories_Stats                       8413 non-null   int64  
 37  categories_Commentary available        8413 non-null   int64  
 38  categories_Includes level editor       8413 non-null   int64  
 39  categories_Steam Workshop              8413 non-null   int64  
 40  categories_In-App Purchases            8413 non-null   int64  
 41  categories_Co-op                       8413 non-null   int64  
 42  categories_Full controller support     8413 non-null   int64  
 43  categories_Steam Leaderboards          8413 non-null   int64  
 44  categories_SteamVR Collectibles        8413 non-null   int64  
 45  categories_Online Co-op                8413 non-null   int64  
 46  categories_Shared/Split Screen         8413 non-null   int64  
 47  categories_Local Co-op                 8413 non-null   int64  
 48  categories_MMO                         8413 non-null   int64  
 49  categories_VR Support                  8413 non-null   int64  
 50  categories_Mods                        8413 non-null   int64  
 51  categories_Mods (require HL2)          8413 non-null   int64  
 52  categories_Steam Turn Notifications    8413 non-null   int64  
 53  achievements                           8413 non-null   int64  
 54  %_ratings                              8413 non-null   float64
 55  QTD_ratings                            8413 non-null   int64  
 56  owners_mean                            8413 non-null   float64
 57  average_playtime_>0                    8413 non-null   int64  
 58  price                                  8413 non-null   float64
 59  log_price                              8413 non-null   float64
 60  log_log_price                          8413 non-null   float64
dtypes: float64(5), int64(55), object(1)
memory usage: 3.9+ MB

Com isso, conseguimos dar uma boa olhada nos dados que temos a nossa disposição. Confirmamos, também, que a separação proposta no aquivo anterior realmente funcionou.

ax =sns.boxplot(data=df_all, y='price')
ax.figure.set_size_inches(15,6)

ax =sns.boxplot(data=df_all, y='log_price')
ax.figure.set_size_inches(15,6)

ax =sns.boxplot(data=df_all, y='log_log_price')
ax.figure.set_size_inches(15,6)

ax = sns.boxplot(data=df_min, y='price')
ax.figure.set_size_inches(15,6)

ax = sns.boxplot(data=df_min, y='log_price')
ax.figure.set_size_inches(15,6)

ax = sns.boxplot(data=df_min, y='log_log_price')
ax.figure.set_size_inches(15,6)

ax = sns.boxplot(data=df_max, y='price')
ax.figure.set_size_inches(15,6)

ax = sns.boxplot(data=df_max, y='log_price')
ax.figure.set_size_inches(15,6)

ax = sns.boxplot(data=df_max, y='log_log_price')
ax.figure.set_size_inches(15,6)

ax = sns.histplot(data=df_all['price'], kde=True)
ax.figure.set_size_inches(15,6)

ax = sns.histplot(data=df_all['log_price'], kde=True)
ax.figure.set_size_inches(15,6)

ax = sns.histplot(data=df_all['log_log_price'], kde=True)
ax.figure.set_size_inches(15,6)

ax = sns.histplot(data=df_min['price'], kde=True)
ax.figure.set_size_inches(15,6)

ax = sns.histplot(data=df_min['log_price'], kde=True)
ax.figure.set_size_inches(15,6)

ax = sns.histplot(data=df_min['log_log_price'], kde=True)
ax.figure.set_size_inches(15,6)

ax = sns.histplot(data=df_max['price'], kde=True)
ax.figure.set_size_inches(15,6)

ax = sns.histplot(data=df_max['log_price'], kde=True)
ax.figure.set_size_inches(15,6)

ax = sns.histplot(data=df_max['log_log_price'], kde=True)
ax.figure.set_size_inches(15,6)

É perceptível que nenhuma das distribuições de preço segue o formato de uma normal. Poderiamos utilizar um teste mais robusto, mas, só pela distribuição dos histogramas, já sabemos que nenhum dos formatos está próximo.

Como temos muitas variáveis, também fica um pouco difícil de se analisar o impacto de cada variável no preço, separadamente. Por isso, acho que é melhor seguir direto para a regressão linear, e utilizar os dados da própria pra refinar o modelo. Particularmente, prefiro a apresentação dos dados da biblioteca StatsModels, então, primeiro farei os testes nela, e depois construirei o modelo de machine learning com a biblioteca sklearn.
Também pra não gerar maiores confusões, vou primeiro usar o dataframe com todos os dados, depois com os dados cujo número médio de owners é 10 mil, e por fim, com o número médio de owners diferente de 10 mil.

Colunas_all = Colunas_Tratada.copy()

len(Colunas_all)

55

y_all = df_all['price']

X_all = sm.add_constant(df_all[Colunas_all])

regressão_all = sm.OLS(y_all, X_all).fit()

regressão_all.summary()

Rodada a primeira regressão, vemos que os números não foram muito animadores. As variáveis abaixo serão excluidas do modelo, e veremos se temos alguma melhora.

Retirar = ['english',
'platforms_windows',
'platforms_mac',
'genres_Racing',
'genres_Violent',
'genres_Gore',
'genres_Sexual Content',
'categories_Local Multi-Player',
'categories_Captions available',
'categories_Commentary available',
'categories_Includes level editor',
'categories_Online Co-op',
'categories_Shared/Split Screen',
'categories_Local Co-op',
'categories_MMO',
'categories_Mods',
'categories_Mods (require HL2)',
'categories_Steam Turn Notifications',
'achievements']

for i in Retirar:
    Colunas_all.remove(i)

len(Colunas_all)

36

X_all = sm.add_constant(df_all[Colunas_all])

regressão_all = sm.OLS(y_all, X_all).fit()

regressão_all.summary()

O baixo valor de R² indica que, de fato, essas variáveis sou pouco eficientes para explicar o preço dos jogos. Vou tentar fazer esses mesmos cálculos para log_price e log_log_price.

Colunas_all = Colunas_Tratada.copy()

len(Colunas_all)

55

y_all = df_all['log_price']
X_all = sm.add_constant(df_all[Colunas_all])
regressão_all = sm.OLS(y_all, X_all).fit()
regressão_all.summary()

Retirar = ['platforms_windows',
            'genres_Action',
            'genres_Racing',
            'genres_Violent',
            'genres_Gore',
            'categories_Local Multi-Player',
            'categories_Valve Anti-Cheat enabled',
            'categories_Captions available',
            'categories_Commentary available',
            'categories_Includes level editor',
            'categories_Online Co-op',
            'categories_Shared/Split Screen',
            'categories_Local Co-op',
            'categories_MMO',
            'categories_Mods',
            'categories_Mods (require HL2)',
            'categories_Steam Turn Notifications',
            'achievements',
            'average_playtime_>0']

for i in Retirar:
    Colunas_all.remove(i)

len(Colunas_all)

36

y_all = df_all['log_price']
X_all = sm.add_constant(df_all[Colunas_all])
regressão_all = sm.OLS(y_all, X_all).fit()
regressão_all.summary()

Apesar do valor de R² ter subido, ele ainda indica que as variáveis são pouco explicativas para o modelo. Vamos fazer uma última tentativa usando log_log_price.

Colunas_all = Colunas_Tratada.copy()
len(Colunas_all)

55

y_all = df_all['log_log_price']
X_all = sm.add_constant(df_all[Colunas_all])
regressão_all = sm.OLS(y_all, X_all).fit()
regressão_all.summary()

Retirar = ['platforms_windows',
'genres_Action',
'genres_Racing',
'genres_Violent',
'genres_Massively Multiplayer',
'genres_Gore',
'categories_Local Multi-Player',
'categories_Valve Anti-Cheat enabled',
'categories_Captions available',
'categories_Commentary available',
'categories_Includes level editor',
'categories_Includes Source SDK',
'categories_Steam Leaderboards',
'categories_Online Co-op',
'categories_Shared/Split Screen',
'categories_Local Co-op',
'categories_MMO',
'categories_Mods',
'categories_Mods (require HL2)',
'categories_Steam Turn Notifications',
'achievements']

for i in Retirar:
    Colunas_all.remove(i)

len(Colunas_all)

34

y_all = df_all['log_log_price']
X_all = sm.add_constant(df_all[Colunas_all])
regressão_all = sm.OLS(y_all, X_all).fit()
regressão_all.summary()

Os números não foram muito animadores. Como o maior valor de R² foi o encontrado na última regressão, vou utiliza-la de base para a análise. Podemos perceber que a variável que tem o maior coeficiente foi 'genres_Free to Play', que se refere ao fato de o jogo ser ou não gratuito para jogar. Podemos assumir que jogos Free to Play possuem um modelo diferente de agariar lucro. Usualmente, são vendidos a preços baixos. Faz sentido o seu coeficiente (beta) ser o maior e negativamente ligado.

regressão_all.params.round(3)

const                                    20.941
Year                                     -0.010
english                                   0.065
platforms_mac                             0.047
platforms_linux                          -0.025
genres_Free to Play                      -0.863
genres_Strategy                           0.070
genres_Adventure                          0.046
genres_Indie                             -0.133
genres_RPG                                0.035
genres_Casual                            -0.090
genres_Simulation                         0.069
genres_Nudity                             0.056
genres_Sports                             0.061
genres_Early Access                       0.111
genres_Sexual Content                     0.050
categories_Multi-player                   0.041
categories_Online Multi-Player            0.052
categories_Single-player                  0.061
categories_Steam Cloud                    0.094
categories_Steam Achievements             0.025
categories_Steam Trading Cards            0.045
categories_Partial Controller Support     0.038
categories_Cross-Platform Multiplayer    -0.039
categories_Stats                         -0.021
categories_Steam Workshop                 0.071
categories_In-App Purchases              -0.126
categories_Co-op                          0.043
categories_Full controller support        0.085
categories_SteamVR Collectibles           0.306
categories_VR Support                     0.050
%_ratings                                 0.090
QTD_ratings                               0.000
owners_mean                              -0.000
average_playtime_>0                      -0.021
dtype: float64

Vamos analisar agora o grupo com média de owners igual a 10 mil.

Colunas_Tratada_min = ['Year','english','platforms_windows','platforms_mac','platforms_linux','genres_Action',
           'genres_Free to Play', 'genres_Strategy','genres_Adventure', 'genres_Indie', 'genres_RPG',
           'genres_Casual','genres_Simulation', 'genres_Racing', 'genres_Violent','genres_Massively Multiplayer',
           'genres_Nudity', 'genres_Sports',       'genres_Early Access', 'genres_Gore', 'genres_Sexual Content',
           'categories_Multi-player', 'categories_Online Multi-Player','categories_Local Multi-Player',
           'categories_Valve Anti-Cheat enabled','categories_Single-player', 'categories_Steam Cloud',
           'categories_Steam Achievements', 'categories_Steam Trading Cards','categories_Captions available',
           'categories_Partial Controller Support','categories_Includes Source SDK','categories_Cross-Platform Multiplayer',
           'categories_Stats','categories_Commentary available', 'categories_Includes level editor',
           'categories_Steam Workshop', 'categories_In-App Purchases','categories_Co-op',
           'categories_Full controller support','categories_Steam Leaderboards', 'categories_SteamVR Collectibles',
           'categories_Online Co-op', 'categories_Shared/Split Screen','categories_Local Co-op', 'categories_MMO', 
           'categories_VR Support','categories_Mods', 'categories_Mods (require HL2)',
           'categories_Steam Turn Notifications','achievements','%_ratings','QTD_ratings',
           'average_playtime_>0']

Colunas_min = Colunas_Tratada_min.copy()

len(Colunas_min)

54

y_min = df_min['price']
X_min = sm.add_constant(df_min[Colunas_min])
regressão_min = sm.OLS(y_min, X_min).fit()
regressão_min.summary()

y_min = df_min['log_price']
X_min = sm.add_constant(df_min[Colunas_min])
regressão_min = sm.OLS(y_min, X_min).fit()
regressão_min.summary()

y_min = df_min['log_log_price']
X_min = sm.add_constant(df_min[Colunas_min])
regressão_min = sm.OLS(y_min, X_min).fit()
regressão_min.summary()

regressão_min.params.round(3)

const                                    22.261
Year                                     -0.011
english                                   0.073
platforms_windows                         0.241
platforms_mac                             0.046
platforms_linux                          -0.034
genres_Action                             0.005
genres_Free to Play                      -0.808
genres_Strategy                           0.073
genres_Adventure                          0.051
genres_Indie                             -0.126
genres_RPG                                0.022
genres_Casual                            -0.075
genres_Simulation                         0.051
genres_Racing                             0.005
genres_Violent                            0.030
genres_Massively Multiplayer             -0.045
genres_Nudity                             0.047
genres_Sports                             0.065
genres_Early Access                       0.111
genres_Gore                              -0.031
genres_Sexual Content                     0.033
categories_Multi-player                   0.053
categories_Online Multi-Player            0.025
categories_Local Multi-Player             0.025
categories_Valve Anti-Cheat enabled      -0.000
categories_Single-player                  0.071
categories_Steam Cloud                    0.081
categories_Steam Achievements             0.006
categories_Steam Trading Cards            0.066
categories_Captions available             0.010
categories_Partial Controller Support     0.023
categories_Includes Source SDK           -0.071
categories_Cross-Platform Multiplayer    -0.015
categories_Stats                         -0.008
categories_Commentary available          -0.092
categories_Includes level editor          0.007
categories_Steam Workshop                 0.025
categories_In-App Purchases              -0.167
categories_Co-op                          0.014
categories_Full controller support        0.060
categories_Steam Leaderboards            -0.005
categories_SteamVR Collectibles           0.183
categories_Online Co-op                   0.013
categories_Shared/Split Screen            0.002
categories_Local Co-op                    0.030
categories_MMO                            0.066
categories_VR Support                     0.068
categories_Mods                           0.000
categories_Mods (require HL2)            -0.000
categories_Steam Turn Notifications      -0.000
achievements                              0.000
%_ratings                                 0.059
QTD_ratings                               0.001
average_playtime_>0                      -0.043
dtype: float64

Podemos perceber que, no caso dos jogos com menos de 10 mil owners, os dados tem um potencial de explicação de preço ainda menor. Novamente, temos a variável "free to play" como principal contribuinte, provavelmente seguindo a mesma lógica que já foi elencada acima.

Por fim, vamos analizar o último grupo, com owners maiores que 10 mil em média.

Colunas_Tratada_max = ['Year','english','platforms_windows','platforms_mac','platforms_linux','genres_Action',
           'genres_Free to Play', 'genres_Strategy','genres_Adventure', 'genres_Indie', 'genres_RPG',
           'genres_Casual','genres_Simulation', 'genres_Racing', 'genres_Violent','genres_Massively Multiplayer',
           'genres_Nudity', 'genres_Sports',       'genres_Early Access', 'genres_Gore', 'genres_Sexual Content',
           'categories_Multi-player', 'categories_Online Multi-Player','categories_Local Multi-Player',
           'categories_Valve Anti-Cheat enabled','categories_Single-player', 'categories_Steam Cloud',
           'categories_Steam Achievements', 'categories_Steam Trading Cards','categories_Captions available',
           'categories_Partial Controller Support','categories_Includes Source SDK','categories_Cross-Platform Multiplayer',
           'categories_Stats','categories_Commentary available', 'categories_Includes level editor',
           'categories_Steam Workshop', 'categories_In-App Purchases','categories_Co-op',
           'categories_Full controller support','categories_Steam Leaderboards', 'categories_SteamVR Collectibles',
           'categories_Online Co-op', 'categories_Shared/Split Screen','categories_Local Co-op', 'categories_MMO', 
           'categories_VR Support','categories_Mods', 'categories_Mods (require HL2)',
           'categories_Steam Turn Notifications','achievements','%_ratings','QTD_ratings','owners_mean',
           'average_playtime_>0']

Colunas_max = Colunas_Tratada_max.copy()
len(Colunas_max)

55

y_max = df_max['price']
X_max = sm.add_constant(df_max[Colunas_max])
regressão_max = sm.OLS(y_max, X_max).fit()
regressão_max.summary()

y_max = df_max['log_price']
X_max = sm.add_constant(df_max[Colunas_max])
regressão_max = sm.OLS(y_max, X_max).fit()
regressão_max.summary()

y_max = df_max['log_log_price']
X_max = sm.add_constant(df_max[Colunas_max])
regressão_max = sm.OLS(y_max, X_max).fit()
regressão_max.summary()

regressão_max.params.round(3)

const                                    16.987
Year                                     -0.008
english                                   0.084
platforms_windows                        -0.177
platforms_mac                             0.038
platforms_linux                          -0.008
genres_Action                            -0.008
genres_Free to Play                      -0.898
genres_Strategy                           0.065
genres_Adventure                          0.029
genres_Indie                             -0.133
genres_RPG                                0.051
genres_Casual                            -0.115
genres_Simulation                         0.078
genres_Racing                            -0.002
genres_Violent                           -0.052
genres_Massively Multiplayer             -0.011
genres_Nudity                             0.048
genres_Sports                             0.031
genres_Early Access                       0.087
genres_Gore                               0.015
genres_Sexual Content                     0.086
categories_Multi-player                   0.029
categories_Online Multi-Player            0.060
categories_Local Multi-Player             0.020
categories_Valve Anti-Cheat enabled      -0.005
categories_Single-player                  0.025
categories_Steam Cloud                    0.098
categories_Steam Achievements             0.067
categories_Steam Trading Cards           -0.010
categories_Captions available             0.011
categories_Partial Controller Support     0.058
categories_Includes Source SDK           -0.130
categories_Cross-Platform Multiplayer    -0.061
categories_Stats                         -0.037
categories_Commentary available           0.038
categories_Includes level editor         -0.013
categories_Steam Workshop                 0.097
categories_In-App Purchases              -0.078
categories_Co-op                          0.044
categories_Full controller support        0.106
categories_Steam Leaderboards            -0.008
categories_SteamVR Collectibles           0.352
categories_Online Co-op                   0.012
categories_Shared/Split Screen            0.006
categories_Local Co-op                   -0.008
categories_MMO                           -0.038
categories_VR Support                     0.009
categories_Mods                          -0.048
categories_Mods (require HL2)            -0.063
categories_Steam Turn Notifications       0.091
achievements                             -0.000
%_ratings                                 0.170
QTD_ratings                               0.000
owners_mean                              -0.000
average_playtime_>0                      -0.009
dtype: float64

regressão_max.pvalues.round(3)

const                                    0.000
Year                                     0.000
english                                  0.007
platforms_windows                        0.528
platforms_mac                            0.000
platforms_linux                          0.416
genres_Action                            0.253
genres_Free to Play                      0.000
genres_Strategy                          0.000
genres_Adventure                         0.000
genres_Indie                             0.000
genres_RPG                               0.000
genres_Casual                            0.000
genres_Simulation                        0.000
genres_Racing                            0.905
genres_Violent                           0.087
genres_Massively Multiplayer             0.640
genres_Nudity                            0.242
genres_Sports                            0.078
genres_Early Access                      0.000
genres_Gore                              0.680
genres_Sexual Content                    0.045
categories_Multi-player                  0.003
categories_Online Multi-Player           0.000
categories_Local Multi-Player            0.311
categories_Valve Anti-Cheat enabled      0.868
categories_Single-player                 0.116
categories_Steam Cloud                   0.000
categories_Steam Achievements            0.000
categories_Steam Trading Cards           0.157
categories_Captions available            0.506
categories_Partial Controller Support    0.000
categories_Includes Source SDK           0.030
categories_Cross-Platform Multiplayer    0.000
categories_Stats                         0.002
categories_Commentary available          0.236
categories_Includes level editor         0.428
categories_Steam Workshop                0.000
categories_In-App Purchases              0.000
categories_Co-op                         0.002
categories_Full controller support       0.000
categories_Steam Leaderboards            0.404
categories_SteamVR Collectibles          0.000
categories_Online Co-op                  0.546
categories_Shared/Split Screen           0.676
categories_Local Co-op                   0.752
categories_MMO                           0.167
categories_VR Support                    0.766
categories_Mods                          0.867
categories_Mods (require HL2)            0.873
categories_Steam Turn Notifications      0.110
achievements                             0.000
%_ratings                                0.000
QTD_ratings                              0.003
owners_mean                              0.003
average_playtime_>0                      0.163
dtype: float64

type(regressão_max.pvalues.round(3))

pandas.core.series.Series

colunas = regressão_max.pvalues.round(3)

colunas[colunas >= 0.05].index.tolist()

['platforms_windows',
 'platforms_linux',
 'genres_Action',
 'genres_Racing',
 'genres_Violent',
 'genres_Massively Multiplayer',
 'genres_Nudity',
 'genres_Sports',
 'genres_Gore',
 'categories_Local Multi-Player',
 'categories_Valve Anti-Cheat enabled',
 'categories_Single-player',
 'categories_Steam Trading Cards',
 'categories_Captions available',
 'categories_Commentary available',
 'categories_Includes level editor',
 'categories_Steam Leaderboards',
 'categories_Online Co-op',
 'categories_Shared/Split Screen',
 'categories_Local Co-op',
 'categories_MMO',
 'categories_VR Support',
 'categories_Mods',
 'categories_Mods (require HL2)',
 'categories_Steam Turn Notifications',
 'average_playtime_>0']

for i in colunas[colunas >= 0.05].index.tolist():
    Colunas_max.remove(i)

Colunas_max

['Year',
 'english',
 'platforms_mac',
 'genres_Free to Play',
 'genres_Strategy',
 'genres_Adventure',
 'genres_Indie',
 'genres_RPG',
 'genres_Casual',
 'genres_Simulation',
 'genres_Early Access',
 'genres_Sexual Content',
 'categories_Multi-player',
 'categories_Online Multi-Player',
 'categories_Steam Cloud',
 'categories_Steam Achievements',
 'categories_Partial Controller Support',
 'categories_Includes Source SDK',
 'categories_Cross-Platform Multiplayer',
 'categories_Stats',
 'categories_Steam Workshop',
 'categories_In-App Purchases',
 'categories_Co-op',
 'categories_Full controller support',
 'categories_SteamVR Collectibles',
 'achievements',
 '%_ratings',
 'QTD_ratings',
 'owners_mean']

y_max = df_max['log_log_price']
X_max = sm.add_constant(df_max[Colunas_max])
regressão_max = sm.OLS(y_max, X_max).fit()
regressão_max.summary()

df_max[Colunas_max].corr()

ax = sns.heatmap(df_max[Colunas_max].corr(),xticklabels=True, yticklabels=True)
ax.figure.set_size_inches(15,15)

Os números do terceiro grupo (grupo com média de owners superior a 10 mil) parece mais animadores. Vale a pena estudar um pouco mais esse grupo.
Além disso, parece existir uma correlação alta entre a média de owners e a quantidade de ratings. Como o p-value de owners_mean é menor, vou descartar QTD_ratings, e vou rodar novamente a regressão.

Colunas_max.remove('QTD_ratings')
y_max = df_max['log_log_price']
X_max = sm.add_constant(df_max[Colunas_max])
regressão_max = sm.OLS(y_max, X_max).fit()
regressão_max.summary()

Aparentemente, isso não foi uma boa ideia, já que ambos R² e R² ajustado diminuiram. Vou voltar com a regressão anterior.

Colunas_max.append('QTD_ratings')
y_max = df_max['log_log_price']
X_max = sm.add_constant(df_max[Colunas_max])
regressão_max = sm.OLS(y_max, X_max).fit()
regressão_max.summary()

Bom, acho que não custa nada tentar criar um modelo no sklearn pra avaliar se essas variáveis são bons preditivos para o preço de um jogo na steam.

from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression

X_train, X_test, y_train, y_test = train_test_split(X_max, y_max, test_size=0.2)

modelo = LinearRegression().fit(X_train, y_train)

modelo.score(X_train, y_train)

0.6483608304355883

y_previsto = modelo.predict(X_test)

from sklearn import metrics
metrics.r2_score(y_test, y_previsto).round(3)

0.669

len(y_test)

1683

type(y_test)

pandas.core.series.Series

len(y_previsto)

1683

type(y_previsto)

numpy.ndarray

d = {'log_log_Y':y_test, 'log_log_Y^':y_previsto}

df_y = pd.DataFrame(d)

df_y

df_y['log_log_û'] = df_y['log_log_Y']-df_y['log_log_Y^']

df_y

df_y['Y'] = np.exp(np.exp(df_y['log_log_Y']))

df_y['Y^'] = np.exp(np.exp(df_y['log_log_Y^']))

df_y['û'] = df_y['Y']-df_y['Y^']

df_y

Bom, conseguimos observar que, esse, definitivamente, não é o melhor modelo para se prever os preços dos jogos da steam, porém, é visivel o efeito das variáveis sobre jogos mais populares. Dessa forma, podemos dizer que, se o jogo for mais popular do que uma média de detentores maior que 10 mil, o poder explicativo do modelo torna-se maior.

	Unnamed: 0	appid	name	Year	english	platforms_windows	platforms_mac	platforms_linux	genres_Action	...	%_ratings	QTD_ratings	owners_mean	average_playtime_>0	price	log_price	log_log_price
0	0	10	Counter-Strike	2000	1	1	1	1	1	...	0.973888	127873	15000000.0	1	7.19	2.102914	1.132342
1	1	20	Team Fortress Classic	1999	1	1	1	1	1	...	0.839787	3951	7500000.0	1	3.99	1.607436	0.958367
2	2	30	Day of Defeat	2003	1	1	1	1	1	...	0.895648	3814	7500000.0	1	3.99	1.607436	0.958367
3	3	40	Deathmatch Classic	2001	1	1	1	1	1	...	0.826623	1540	7500000.0	1	3.99	1.607436	0.958367
4	4	50	Half-Life: Opposing Force	1999	1	1	1	1	1	...	0.947996	5538	7500000.0	1	3.99	1.607436	0.958367

	Unnamed: 0	appid	name	Year	english	platforms_windows	...	%_ratings	QTD_ratings	owners_mean	price	log_price	log_log_price
0	122	4100	Poker Superstars II	2006	1	1	...	0.444444	9	10000.0	5.99	1.944481	1.079932
1	124	4290	RACE: Caterham Expansion	2007	1	1	...	0.666667	6	10000.0	3.99	1.607436	0.958367
2	145	4900	Zen of Sudoku	2006	1	1	...	0.877698	139	10000.0	0.00	0.000000	0.000000
3	188	7340	Azada	2010	1	1	...	0.666667	12	10000.0	6.99	2.078191	1.124342
4	248	9960	Haunted House™	2010	1	1	...	0.409091	22	10000.0	4.79	1.756132	1.013828

	Unnamed: 0	appid	name	Year	english	platforms_windows	platforms_mac	platforms_linux	genres_Action	...	%_ratings	QTD_ratings	owners_mean	average_playtime_>0	price	log_price	log_log_price
0	0	10	Counter-Strike	2000	1	1	1	1	1	...	0.973888	127873	15000000.0	1	7.19	2.102914	1.132342
1	1	20	Team Fortress Classic	1999	1	1	1	1	1	...	0.839787	3951	7500000.0	1	3.99	1.607436	0.958367
2	2	30	Day of Defeat	2003	1	1	1	1	1	...	0.895648	3814	7500000.0	1	3.99	1.607436	0.958367
3	3	40	Deathmatch Classic	2001	1	1	1	1	1	...	0.826623	1540	7500000.0	1	3.99	1.607436	0.958367
4	4	50	Half-Life: Opposing Force	1999	1	1	1	1	1	...	0.947996	5538	7500000.0	1	3.99	1.607436	0.958367

	Unnamed: 0	appid	Year	english	platforms_windows	platforms_mac	platforms_linux	genres_Action	genres_Free to Play	genres_Strategy	...	categories_Mods (require HL2)	categories_Steam Turn Notifications	achievements	%_ratings	QTD_ratings	owners_mean	average_playtime_>0	price	log_price	log_log_price
count	26846.000000	2.684600e+04	26846.000000	26846.000000	26846.000000	26846.000000	26846.000000	26846.000000	26846.000000	26846.000000	...	26846.000000	26846.000000	26846.000000	26846.000000	2.684600e+04	2.684600e+04	26846.000000	26846.000000	26846.000000	26846.000000
mean	13537.970834	5.961759e+05	2016.496908	0.981040	0.999814	0.299113	0.194256	0.443306	0.063175	0.195374	...	0.000037	0.002347	45.613536	0.714424	1.217097e+03	1.344908e+05	0.228600	5.999415	1.585724	0.882937
std	7817.936144	2.510454e+05	2.161338	0.136386	0.013646	0.457878	0.395634	0.496785	0.243282	0.396495	...	0.006103	0.048387	354.148334	0.233717	2.252065e+04	1.332872e+06	0.419939	7.244335	0.864164	0.387937
min	0.000000	1.000000e+01	1997.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	...	0.000000	0.000000	0.000000	0.000000	1.000000e+00	1.000000e+04	0.000000	0.000000	0.000000	0.000000
25%	6764.250000	4.011325e+05	2016.000000	1.000000	1.000000	0.000000	0.000000	0.000000	0.000000	0.000000	...	0.000000	0.000000	0.000000	0.583333	1.000000e+01	1.000000e+04	0.000000	1.690000	0.989541	0.687904
50%	13543.500000	5.992850e+05	2017.000000	1.000000	1.000000	0.000000	0.000000	0.000000	0.000000	0.000000	...	0.000000	0.000000	7.000000	0.760435	3.600000e+01	1.000000e+04	0.000000	3.990000	1.607436	0.958367
75%	20310.750000	7.989175e+05	2018.000000	1.000000	1.000000	1.000000	0.000000	1.000000	0.000000	0.000000	...	0.000000	0.000000	23.000000	0.893838	1.770000e+02	3.500000e+04	0.000000	7.190000	2.102914	1.132342
max	27074.000000	1.069460e+06	2019.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	...	1.000000	1.000000	9821.000000	1.000000	3.046717e+06	1.500000e+08	1.000000	421.990000	6.047349	1.952651

	Unnamed: 0	appid	Year	english	platforms_windows	platforms_mac	platforms_linux	genres_Action	genres_Free to Play	genres_Strategy	...	categories_Mods (require HL2)	categories_Steam Turn Notifications	achievements	%_ratings	QTD_ratings	owners_mean	average_playtime_>0	price	log_price	log_log_price
count	18433.000000	1.843300e+04	18433.000000	18433.000000	18433.000000	18433.000000	18433.000000	18433.000000	18433.000000	18433.000000	...	18433.0	18433.000000	18433.000000	18433.000000	18433.000000	18433.0	18433.000000	18433.000000	18433.000000	18433.000000
mean	16271.622525	6.847525e+05	2017.195682	0.976781	0.999783	0.259372	0.161395	0.435740	0.027776	0.182065	...	0.0	0.002062	46.889546	0.707029	40.729290	10000.0	0.041827	5.501475	1.570516	0.890951
std	6881.558945	2.120956e+05	1.388686	0.150603	0.014730	0.438302	0.367905	0.495867	0.164336	0.385908	...	0.0	0.045358	381.471008	0.255186	71.600204	0.0	0.200199	6.760558	0.778563	0.342277
min	122.000000	4.100000e+03	2006.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	...	0.0	0.000000	0.000000	0.000000	1.000000	10000.0	0.000000	0.000000	0.000000	0.000000
25%	10879.000000	5.254500e+05	2017.000000	1.000000	1.000000	0.000000	0.000000	0.000000	0.000000	0.000000	...	0.0	0.000000	0.000000	0.557692	6.000000	10000.0	0.000000	1.690000	0.989541	0.687904
50%	16973.000000	7.035100e+05	2017.000000	1.000000	1.000000	0.000000	0.000000	0.000000	0.000000	0.000000	...	0.0	0.000000	5.000000	0.750000	17.000000	10000.0	0.000000	3.990000	1.607436	0.958367
75%	22122.000000	8.544500e+05	2018.000000	1.000000	1.000000	1.000000	0.000000	1.000000	0.000000	0.000000	...	0.0	0.000000	20.000000	0.910256	42.000000	10000.0	0.000000	7.190000	2.102914	1.132342
max	27074.000000	1.069460e+06	2019.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	...	0.0	1.000000	5394.000000	1.000000	1880.000000	10000.0	1.000000	421.990000	6.047349	1.952651

	Unnamed: 0	appid	Year	english	platforms_windows	platforms_mac	platforms_linux	genres_Action	genres_Free to Play	genres_Strategy	...	categories_Mods (require HL2)	categories_Steam Turn Notifications	achievements	%_ratings	QTD_ratings	owners_mean	average_playtime_>0	price	log_price	log_log_price
count	8413.000000	8.413000e+03	8413.000000	8413.000000	8413.000000	8413.000000	8413.000000	8413.000000	8413.000000	8413.000000	...	8413.000000	8413.000000	8413.000000	8413.000000	8.413000e+03	8.413000e+03	8413.000000	8413.000000	8413.000000	8413.000000
mean	7548.501961	4.021034e+05	2014.965886	0.990372	0.999881	0.386188	0.266255	0.459884	0.140735	0.224533	...	0.000119	0.002972	42.817782	0.730627	3.794534e+03	4.072519e+05	0.637822	7.090409	1.619045	0.865379
std	6247.718107	2.183967e+05	2.695896	0.097654	0.010902	0.486903	0.442025	0.498418	0.347768	0.417300	...	0.010902	0.054434	285.279410	0.176774	4.011062e+04	2.358195e+06	0.480658	8.099292	1.026337	0.472357
min	0.000000	1.000000e+01	1997.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	...	0.000000	0.000000	0.000000	0.000000	1.000000e+00	3.500000e+04	0.000000	0.000000	0.000000	0.000000
25%	2381.000000	2.682600e+05	2014.000000	1.000000	1.000000	0.000000	0.000000	0.000000	0.000000	0.000000	...	0.000000	0.000000	0.000000	0.625569	1.360000e+02	3.500000e+04	0.000000	0.900000	0.641854	0.495826
50%	6021.000000	3.805600e+05	2016.000000	1.000000	1.000000	0.000000	0.000000	0.000000	0.000000	0.000000	...	0.000000	0.000000	13.000000	0.767386	3.980000e+02	7.500000e+04	1.000000	4.790000	1.756132	1.013828
75%	11299.000000	5.369300e+05	2017.000000	1.000000	1.000000	1.000000	1.000000	1.000000	0.000000	0.000000	...	0.000000	0.000000	33.000000	0.871795	1.386000e+03	3.500000e+05	1.000000	9.990000	2.396986	1.222888
max	27034.000000	1.057690e+06	2019.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	...	1.000000	1.000000	9821.000000	1.000000	3.046717e+06	1.500000e+08	1.000000	60.990000	4.126973	1.634515

Dep. Variable:	price	R-squared:	0.227
Model:	OLS	Adj. R-squared:	0.226
Method:	Least Squares	F-statistic:	143.4
Date:	Sun, 24 Oct 2021	Prob (F-statistic):	0.00
Time:	13:28:55	Log-Likelihood:	-87789.
No. Observations:	26846	AIC:	1.757e+05
Df Residuals:	26790	BIC:	1.761e+05
Df Model:	55
Covariance Type:	nonrobust

	coef	std err	t	P>\|t\|	[0.025	0.975]
const	-398.4477	43.768	-9.104	0.000	-484.235	-312.661
Year	0.1993	0.022	9.205	0.000	0.157	0.242
english	0.2238	0.291	0.769	0.442	-0.346	0.794
platforms_windows	1.0391	2.856	0.364	0.716	-4.560	6.638
platforms_mac	0.1497	0.112	1.338	0.181	-0.070	0.369
platforms_linux	-0.3864	0.129	-2.988	0.003	-0.640	-0.133
genres_Action	-0.3861	0.088	-4.373	0.000	-0.559	-0.213
genres_Free to Play	-6.1307	0.184	-33.382	0.000	-6.491	-5.771
genres_Strategy	0.9648	0.105	9.150	0.000	0.758	1.171
genres_Adventure	0.4093	0.086	4.744	0.000	0.240	0.578
genres_Indie	-3.7317	0.095	-39.285	0.000	-3.918	-3.546
genres_RPG	0.5923	0.113	5.252	0.000	0.371	0.813
genres_Casual	-2.1332	0.085	-24.955	0.000	-2.301	-1.966
genres_Simulation	1.5896	0.105	15.085	0.000	1.383	1.796
genres_Racing	-0.2558	0.215	-1.190	0.234	-0.677	0.166
genres_Violent	0.1569	0.300	0.523	0.601	-0.432	0.745
genres_Massively Multiplayer	-1.0994	0.361	-3.049	0.002	-1.806	-0.393
genres_Nudity	1.1908	0.496	2.400	0.016	0.218	2.163
genres_Sports	1.2100	0.193	6.259	0.000	0.831	1.589
genres_Early Access	1.3827	0.134	10.349	0.000	1.121	1.645
genres_Gore	-0.1369	0.369	-0.370	0.711	-0.861	0.587
genres_Sexual Content	0.9241	0.513	1.801	0.072	-0.081	1.930
categories_Multi-player	1.3980	0.152	9.198	0.000	1.100	1.696
categories_Online Multi-Player	1.8265	0.201	9.107	0.000	1.433	2.220
categories_Local Multi-Player	0.0646	0.228	0.284	0.776	-0.382	0.511
categories_Valve Anti-Cheat enabled	3.1379	0.707	4.440	0.000	1.753	4.523
categories_Single-player	1.3099	0.224	5.848	0.000	0.871	1.749
categories_Steam Cloud	1.7587	0.102	17.280	0.000	1.559	1.958
categories_Steam Achievements	0.6710	0.096	7.021	0.000	0.484	0.858
categories_Steam Trading Cards	0.5796	0.102	5.679	0.000	0.380	0.780
categories_Captions available	0.0765	0.249	0.307	0.759	-0.412	0.565
categories_Partial Controller Support	0.9660	0.117	8.289	0.000	0.738	1.194
categories_Includes Source SDK	-2.8936	1.175	-2.462	0.014	-5.197	-0.590
categories_Cross-Platform Multiplayer	-1.2881	0.229	-5.613	0.000	-1.738	-0.838
categories_Stats	-0.6329	0.166	-3.812	0.000	-0.958	-0.307
categories_Commentary available	-0.4946	0.540	-0.917	0.359	-1.552	0.563
categories_Includes level editor	-0.0701	0.240	-0.292	0.770	-0.540	0.400
categories_Steam Workshop	2.1671	0.262	8.259	0.000	1.653	2.681
categories_In-App Purchases	-1.2810	0.293	-4.378	0.000	-1.855	-0.708
categories_Co-op	1.1491	0.244	4.705	0.000	0.670	1.628
categories_Full controller support	1.9063	0.116	16.451	0.000	1.679	2.133
categories_Steam Leaderboards	-0.5609	0.132	-4.238	0.000	-0.820	-0.302
categories_SteamVR Collectibles	8.6050	1.049	8.205	0.000	6.549	10.660
categories_Online Co-op	0.0803	0.308	0.261	0.794	-0.523	0.684
categories_Shared/Split Screen	-0.1753	0.194	-0.904	0.366	-0.555	0.205
categories_Local Co-op	-0.5647	0.314	-1.796	0.073	-1.181	0.052
categories_MMO	0.3569	0.454	0.785	0.432	-0.534	1.248
categories_VR Support	1.4219	0.441	3.225	0.001	0.558	2.286
categories_Mods	-1.3181	6.512	-0.202	0.840	-14.082	11.446
categories_Mods (require HL2)	-0.6887	9.023	-0.076	0.939	-18.374	16.997
categories_Steam Turn Notifications	1.1034	0.816	1.353	0.176	-0.495	2.702
achievements	2.375e-06	0.000	0.021	0.983	-0.000	0.000
%_ratings	1.4823	0.174	8.504	0.000	1.141	1.824
QTD_ratings	1.007e-05	2.57e-06	3.913	0.000	5.03e-06	1.51e-05
owners_mean	-9.834e-08	4.51e-08	-2.180	0.029	-1.87e-07	-9.92e-09
average_playtime_>0	1.0625	0.110	9.634	0.000	0.846	1.279

Omnibus:	51073.102	Durbin-Watson:	1.908
Prob(Omnibus):	0.000	Jarque-Bera (JB):	575051620.740
Skew:	13.954	Prob(JB):	0.00
Kurtosis:	719.457	Cond. No.	1.51e+09

Omnibus:	51057.600	Durbin-Watson:	1.908
Prob(Omnibus):	0.000	Jarque-Bera (JB):	573664514.219
Skew:	13.945	Prob(JB):	0.00
Kurtosis:	718.592	Cond. No.	1.49e+09

Omnibus:	377.283	Durbin-Watson:	1.867
Prob(Omnibus):	0.000	Jarque-Bera (JB):	532.838
Skew:	-0.177	Prob(JB):	1.98e-116
Kurtosis:	3.592	Cond. No.	1.51e+09

Omnibus:	373.288	Durbin-Watson:	1.867
Prob(Omnibus):	0.000	Jarque-Bera (JB):	523.825
Skew:	-0.178	Prob(JB):	1.79e-114
Kurtosis:	3.585	Cond. No.	1.42e+09

Omnibus:	4473.999	Durbin-Watson:	1.884
Prob(Omnibus):	0.000	Jarque-Bera (JB):	9342.587
Skew:	-0.998	Prob(JB):	0.00
Kurtosis:	5.090	Cond. No.	1.51e+09

Omnibus:	4469.682	Durbin-Watson:	1.884
Prob(Omnibus):	0.000	Jarque-Bera (JB):	9292.591
Skew:	-0.999	Prob(JB):	0.00
Kurtosis:	5.077	Cond. No.	1.49e+09

Omnibus:	42026.115	Durbin-Watson:	1.973
Prob(Omnibus):	0.000	Jarque-Bera (JB):	1094610824.774
Skew:	21.328	Prob(JB):	0.00
Kurtosis:	1196.054	Cond. No.	1.00e+16

	coef	std err	t	P>\|t\|	[0.025	0.975]
const	-389.9933	43.131	-9.042	0.000	-474.533	-305.454
Year	0.1957	0.021	9.148	0.000	0.154	0.238
platforms_linux	-0.2884	0.106	-2.732	0.006	-0.495	-0.081
genres_Action	-0.3976	0.087	-4.558	0.000	-0.569	-0.227
genres_Free to Play	-6.1063	0.183	-33.422	0.000	-6.464	-5.748
genres_Strategy	0.9723	0.105	9.269	0.000	0.767	1.178
genres_Adventure	0.4258	0.086	4.975	0.000	0.258	0.594
genres_Indie	-3.7323	0.095	-39.449	0.000	-3.918	-3.547
genres_RPG	0.6105	0.111	5.492	0.000	0.393	0.828
genres_Casual	-2.1394	0.085	-25.234	0.000	-2.306	-1.973
genres_Simulation	1.5934	0.105	15.177	0.000	1.388	1.799
genres_Massively Multiplayer	-0.8851	0.285	-3.104	0.002	-1.444	-0.326
genres_Nudity	1.7458	0.394	4.430	0.000	0.973	2.518
genres_Sports	1.1259	0.187	6.009	0.000	0.759	1.493
genres_Early Access	1.3809	0.133	10.347	0.000	1.119	1.642
categories_Multi-player	1.3906	0.145	9.564	0.000	1.106	1.676
categories_Online Multi-Player	1.8707	0.178	10.535	0.000	1.523	2.219
categories_Valve Anti-Cheat enabled	3.1420	0.700	4.488	0.000	1.770	4.514
categories_Single-player	1.3157	0.222	5.936	0.000	0.881	1.750
categories_Steam Cloud	1.7538	0.101	17.298	0.000	1.555	1.953
categories_Steam Achievements	0.6959	0.094	7.392	0.000	0.511	0.880
categories_Steam Trading Cards	0.5861	0.102	5.755	0.000	0.386	0.786
categories_Partial Controller Support	0.9309	0.115	8.085	0.000	0.705	1.157
categories_Includes Source SDK	-3.0793	1.136	-2.712	0.007	-5.305	-0.854
categories_Cross-Platform Multiplayer	-1.1902	0.226	-5.265	0.000	-1.633	-0.747
categories_Stats	-0.6367	0.165	-3.848	0.000	-0.961	-0.312
categories_Steam Workshop	2.1350	0.231	9.224	0.000	1.681	2.589
categories_In-App Purchases	-1.2358	0.291	-4.251	0.000	-1.806	-0.666
categories_Co-op	0.8958	0.151	5.935	0.000	0.600	1.192
categories_Full controller support	1.8488	0.113	16.425	0.000	1.628	2.069
categories_Steam Leaderboards	-0.5677	0.132	-4.304	0.000	-0.826	-0.309
categories_SteamVR Collectibles	8.6575	1.048	8.261	0.000	6.603	10.712
categories_VR Support	1.4336	0.440	3.255	0.001	0.570	2.297
%_ratings	1.4765	0.173	8.513	0.000	1.137	1.816
QTD_ratings	1.005e-05	2.57e-06	3.908	0.000	5.01e-06	1.51e-05
owners_mean	-9.592e-08	4.5e-08	-2.131	0.033	-1.84e-07	-7.69e-09
average_playtime_>0	1.0790	0.110	9.802	0.000	0.863	1.295

	coef	std err	t	P>\|t\|	[0.025	0.975]
const	31.4903	4.593	6.856	0.000	22.487	40.493
Year	-0.0151	0.002	-6.657	0.000	-0.020	-0.011
english	0.1190	0.031	3.898	0.000	0.059	0.179
platforms_windows	0.2571	0.300	0.858	0.391	-0.330	0.845
platforms_mac	0.0959	0.012	8.173	0.000	0.073	0.119
platforms_linux	-0.0572	0.014	-4.211	0.000	-0.084	-0.031
genres_Action	-0.0174	0.009	-1.872	0.061	-0.036	0.001
genres_Free to Play	-1.5431	0.019	-80.062	0.000	-1.581	-1.505
genres_Strategy	0.1629	0.011	14.719	0.000	0.141	0.185
genres_Adventure	0.1056	0.009	11.668	0.000	0.088	0.123
genres_Indie	-0.3806	0.010	-38.175	0.000	-0.400	-0.361
genres_RPG	0.0889	0.012	7.509	0.000	0.066	0.112
genres_Casual	-0.2525	0.009	-28.148	0.000	-0.270	-0.235
genres_Simulation	0.1882	0.011	17.018	0.000	0.167	0.210
genres_Racing	-0.0223	0.023	-0.989	0.322	-0.067	0.022
genres_Violent	0.0463	0.032	1.469	0.142	-0.015	0.108
genres_Massively Multiplayer	-0.1053	0.038	-2.783	0.005	-0.179	-0.031
genres_Nudity	0.1440	0.052	2.765	0.006	0.042	0.246
genres_Sports	0.1560	0.020	7.691	0.000	0.116	0.196
genres_Early Access	0.2744	0.014	19.570	0.000	0.247	0.302
genres_Gore	-0.0612	0.039	-1.578	0.115	-0.137	0.015
genres_Sexual Content	0.1221	0.054	2.268	0.023	0.017	0.228
categories_Multi-player	0.1231	0.016	7.719	0.000	0.092	0.154
categories_Online Multi-Player	0.1608	0.021	7.638	0.000	0.120	0.202
categories_Local Multi-Player	0.0399	0.024	1.672	0.095	-0.007	0.087
categories_Valve Anti-Cheat enabled	0.1034	0.074	1.394	0.163	-0.042	0.249
categories_Single-player	0.1271	0.024	5.405	0.000	0.081	0.173
categories_Steam Cloud	0.2369	0.011	22.175	0.000	0.216	0.258
categories_Steam Achievements	0.0697	0.010	6.954	0.000	0.050	0.089
categories_Steam Trading Cards	0.0983	0.011	9.182	0.000	0.077	0.119
categories_Captions available	0.0163	0.026	0.623	0.534	-0.035	0.068
categories_Partial Controller Support	0.1001	0.012	8.182	0.000	0.076	0.124
categories_Includes Source SDK	-0.2945	0.123	-2.388	0.017	-0.536	-0.053
categories_Cross-Platform Multiplayer	-0.1068	0.024	-4.435	0.000	-0.154	-0.060
categories_Stats	-0.0536	0.017	-3.076	0.002	-0.088	-0.019
categories_Commentary available	-0.0449	0.057	-0.792	0.428	-0.156	0.066
categories_Includes level editor	-0.0112	0.025	-0.445	0.657	-0.061	0.038
categories_Steam Workshop	0.2219	0.028	8.058	0.000	0.168	0.276
categories_In-App Purchases	-0.2507	0.031	-8.165	0.000	-0.311	-0.191

	coef	std err	t	P>\|t\|	[0.025	0.975]
const	21.5461	1.948	11.062	0.000	17.728	25.364
Year	-0.0104	0.001	-10.789	0.000	-0.012	-0.009
english	0.0641	0.013	4.951	0.000	0.039	0.089
platforms_windows	0.1471	0.127	1.157	0.247	-0.102	0.396
platforms_mac	0.0462	0.005	9.282	0.000	0.036	0.056
platforms_linux	-0.0247	0.006	-4.291	0.000	-0.036	-0.013
genres_Action	7.322e-05	0.004	0.019	0.985	-0.008	0.008
genres_Free to Play	-0.8592	0.008	-105.134	0.000	-0.875	-0.843
genres_Strategy	0.0695	0.005	14.803	0.000	0.060	0.079
genres_Adventure	0.0467	0.004	12.172	0.000	0.039	0.054
genres_Indie	-0.1332	0.004	-31.516	0.000	-0.142	-0.125
genres_RPG	0.0358	0.005	7.137	0.000	0.026	0.046
genres_Casual	-0.0906	0.004	-23.808	0.000	-0.098	-0.083
genres_Simulation	0.0697	0.005	14.860	0.000	0.060	0.079
genres_Racing	-0.0006	0.010	-0.067	0.947	-0.019	0.018
genres_Violent	0.0210	0.013	1.574	0.115	-0.005	0.047
genres_Massively Multiplayer	-0.0271	0.016	-1.687	0.092	-0.059	0.004
genres_Nudity	0.0552	0.022	2.499	0.012	0.012	0.098
genres_Sports	0.0595	0.009	6.910	0.000	0.043	0.076
genres_Early Access	0.1111	0.006	18.685	0.000	0.099	0.123
genres_Gore	-0.0263	0.016	-1.600	0.110	-0.059	0.006
genres_Sexual Content	0.0488	0.023	2.137	0.033	0.004	0.094
categories_Multi-player	0.0393	0.007	5.817	0.000	0.026	0.053
categories_Online Multi-Player	0.0487	0.009	5.456	0.000	0.031	0.066
categories_Local Multi-Player	0.0199	0.010	1.961	0.050	6.55e-06	0.040
categories_Valve Anti-Cheat enabled	0.0124	0.031	0.394	0.693	-0.049	0.074
categories_Single-player	0.0549	0.010	5.510	0.000	0.035	0.074
categories_Steam Cloud	0.0936	0.005	20.661	0.000	0.085	0.102
categories_Steam Achievements	0.0273	0.004	6.410	0.000	0.019	0.036
categories_Steam Trading Cards	0.0444	0.005	9.772	0.000	0.035	0.053
categories_Captions available	0.0092	0.011	0.833	0.405	-0.012	0.031
categories_Partial Controller Support	0.0370	0.005	7.136	0.000	0.027	0.047
categories_Includes Source SDK	-0.1004	0.052	-1.920	0.055	-0.203	0.002
categories_Cross-Platform Multiplayer	-0.0372	0.010	-3.647	0.000	-0.057	-0.017
categories_Stats	-0.0190	0.007	-2.572	0.010	-0.033	-0.005
categories_Commentary available	-0.0148	0.024	-0.617	0.537	-0.062	0.032
categories_Includes level editor	-0.0046	0.011	-0.432	0.665	-0.026	0.016
categories_Steam Workshop	0.0743	0.012	6.364	0.000	0.051	0.097
categories_In-App Purchases	-0.1205	0.013	-9.253	0.000	-0.146	-0.095

	coef	std err	t	P>\|t\|	[0.025	0.975]
const	-311.8648	72.437	-4.305	0.000	-453.848	-169.881
Year	0.1557	0.036	4.339	0.000	0.085	0.226
english	0.4209	0.310	1.357	0.175	-0.187	1.029
platforms_windows	1.9260	3.095	0.622	0.534	-4.141	7.993
platforms_mac	0.1136	0.132	0.862	0.389	-0.145	0.372
platforms_linux	-0.5594	0.158	-3.551	0.000	-0.868	-0.251
genres_Action	-0.2527	0.103	-2.458	0.014	-0.454	-0.051
genres_Free to Play	-5.0359	0.289	-17.441	0.000	-5.602	-4.470
genres_Strategy	0.9118	0.125	7.296	0.000	0.667	1.157
genres_Adventure	0.4790	0.101	4.767	0.000	0.282	0.676
genres_Indie	-2.9808	0.114	-26.218	0.000	-3.204	-2.758
genres_RPG	0.1408	0.138	1.022	0.307	-0.129	0.411
genres_Casual	-1.6170	0.097	-16.642	0.000	-1.807	-1.427
genres_Simulation	1.1744	0.122	9.625	0.000	0.935	1.414
genres_Racing	-0.2796	0.250	-1.117	0.264	-0.770	0.211
genres_Violent	-0.0032	0.323	-0.010	0.992	-0.637	0.631
genres_Massively Multiplayer	-1.2348	0.458	-2.696	0.007	-2.133	-0.337
genres_Nudity	0.7567	0.571	1.325	0.185	-0.362	1.876
genres_Sports	1.2458	0.214	5.826	0.000	0.827	1.665
genres_Early Access	1.3856	0.143	9.700	0.000	1.106	1.666
genres_Gore	0.0050	0.402	0.012	0.990	-0.783	0.793
genres_Sexual Content	0.6300	0.585	1.078	0.281	-0.516	1.776
categories_Multi-player	1.4576	0.208	6.998	0.000	1.049	1.866
categories_Online Multi-Player	1.1737	0.251	4.669	0.000	0.681	1.666
categories_Local Multi-Player	0.2564	0.263	0.974	0.330	-0.260	0.772
categories_Valve Anti-Cheat enabled	-4.454e-12	4.4e-12	-1.011	0.312	-1.31e-11	4.18e-12
categories_Single-player	1.3736	0.281	4.880	0.000	0.822	1.925
categories_Steam Cloud	1.2682	0.124	10.195	0.000	1.024	1.512
categories_Steam Achievements	0.1300	0.110	1.182	0.237	-0.086	0.346
categories_Steam Trading Cards	0.7725	0.137	5.658	0.000	0.505	1.040
categories_Captions available	-0.3222	0.314	-1.025	0.305	-0.938	0.294
categories_Partial Controller Support	0.5106	0.139	3.665	0.000	0.238	0.784
categories_Includes Source SDK	-2.5364	2.350	-1.079	0.281	-7.143	2.070
categories_Cross-Platform Multiplayer	-0.9633	0.316	-3.046	0.002	-1.583	-0.343
categories_Stats	-0.1566	0.203	-0.771	0.441	-0.555	0.241
categories_Commentary available	-1.7112	0.786	-2.178	0.029	-3.251	-0.171
categories_Includes level editor	0.5018	0.313	1.601	0.109	-0.112	1.116
categories_Steam Workshop	0.5315	0.377	1.409	0.159	-0.208	1.271
categories_In-App Purchases	-1.4337	0.496	-2.892	0.004	-2.406	-0.462

Omnibus:	164.007	Durbin-Watson:	1.904
Prob(Omnibus):	0.000	Jarque-Bera (JB):	236.478
Skew:	-0.103	Prob(JB):	4.46e-52
Kurtosis:	3.516	Cond. No.	1.00e+16

Omnibus:	2481.648	Durbin-Watson:	1.908
Prob(Omnibus):	0.000	Jarque-Bera (JB):	4471.626
Skew:	-0.882	Prob(JB):	0.00
Kurtosis:	4.647	Cond. No.	1.00e+16

Omnibus:	3263.985	Durbin-Watson:	1.831
Prob(Omnibus):	0.000	Jarque-Bera (JB):	18777.182
Skew:	1.767	Prob(JB):	0.00
Kurtosis:	9.410	Cond. No.	2.27e+09

Omnibus:	483.183	Durbin-Watson:	1.821
Prob(Omnibus):	0.000	Jarque-Bera (JB):	736.072
Skew:	-0.491	Prob(JB):	1.46e-160
Kurtosis:	4.066	Cond. No.	2.27e+09

Omnibus:	2275.705	Durbin-Watson:	1.835
Prob(Omnibus):	0.000	Jarque-Bera (JB):	6998.792
Skew:	-1.388	Prob(JB):	0.00
Kurtosis:	6.501	Cond. No.	2.27e+09

Omnibus:	2244.723	Durbin-Watson:	1.835
Prob(Omnibus):	0.000	Jarque-Bera (JB):	6788.798
Skew:	-1.376	Prob(JB):	0.00
Kurtosis:	6.435	Cond. No.	2.18e+09

	Year	english	platforms_mac	genres_Free to Play	genres_Strategy	genres_Adventure	genres_Indie	genres_RPG	genres_Casual	genres_Simulation	...	categories_Stats	categories_Steam Workshop	categories_In-App Purchases	categories_Co-op	categories_Full controller support	categories_SteamVR Collectibles	achievements	%_ratings	QTD_ratings	owners_mean
Year	1.000000	-0.082978	0.015472	0.236272	-0.043806	0.104617	0.271935	0.043699	0.140550	0.118410	...	0.010357	0.040704	0.184621	0.045730	0.113789	0.034240	0.067032	-0.071347	-0.034609	-0.110494
english	-0.082978	1.000000	0.050706	-0.047607	-0.008205	-0.005878	0.019551	-0.057199	0.004411	0.000797	...	0.016513	0.019417	-0.021621	0.035900	0.036415	0.005595	0.006466	-0.013599	0.006797	0.011206
platforms_mac	0.015472	0.050706	1.000000	-0.040892	0.059965	0.067276	0.217872	-0.008779	0.060104	0.021443	...	0.073569	0.104577	-0.016235	-0.008482	0.090161	-0.040691	-0.005986	0.197562	0.031426	0.040690
genres_Free to Play	0.236272	-0.047607	-0.040892	1.000000	0.032072	-0.079276	-0.018441	0.045413	0.068011	0.010515	...	0.000427	-0.052947	0.464180	0.079062	-0.134629	0.001210	-0.022465	-0.065258	0.037751	0.075699
genres_Strategy	-0.043806	-0.008205	0.059965	0.032072	1.000000	-0.203391	-0.024716	0.060289	-0.030255	0.147153	...	0.030511	0.093756	0.104867	0.030191	-0.155202	-0.005351	0.019209	-0.039162	-0.013012	-0.004210
genres_Adventure	0.104617	-0.005878	0.067276	-0.079276	-0.203391	1.000000	0.114411	0.117141	0.004457	-0.137481	...	-0.056062	-0.073111	-0.069771	-0.037174	0.087080	0.000475	-0.018926	0.027102	-0.005821	-0.023324
genres_Indie	0.271935	0.019551	0.217872	-0.018441	-0.024716	0.114411	1.000000	0.000797	0.168210	-0.002334	...	0.088599	0.044996	-0.128760	-0.018569	0.107005	0.000336	0.033502	0.040181	-0.050968	-0.086617
genres_RPG	0.043699	-0.057199	-0.008779	0.045413	0.060289	0.117141	0.000797	1.000000	-0.126580	-0.039991	...	-0.011186	-0.019813	0.077305	0.066478	0.011069	-0.016932	0.010250	0.007115	0.005591	0.001766
genres_Casual	0.140550	0.004411	0.060104	0.068011	-0.030255	0.004457	0.168210	-0.126580	1.000000	0.035898	...	0.011685	-0.059453	-0.001554	-0.095298	-0.096994	0.002146	0.075496	-0.026894	-0.038824	-0.054940
genres_Simulation	0.118410	0.000797	0.021443	0.010515	0.147153	-0.137481	-0.002334	-0.039991	0.035898	1.000000	...	0.010936	0.157201	0.026719	0.009901	-0.121232	0.012420	-0.013809	-0.056964	-0.005281	-0.015097
genres_Early Access	0.156809	-0.008173	-0.053678	0.117839	0.035959	-0.006464	0.070170	0.043867	-0.022757	0.115386	...	0.027013	0.055001	0.078209	0.128405	-0.067567	0.013909	-0.007789	-0.041432	-0.004820	-0.012992
genres_Sexual Content	0.054906	-0.003900	0.012657	0.028475	-0.034986	-0.007296	0.027150	-0.012959	0.056012	-0.002834	...	-0.028207	-0.017885	-0.018067	-0.033698	-0.017601	-0.005309	0.015317	0.035679	-0.003583	-0.008454
categories_Multi-player	-0.129843	0.037421	-0.056713	0.114288	0.155933	-0.217761	-0.172798	-0.016796	-0.158229	0.039178	...	0.113883	0.126697	0.155165	0.427217	-0.005881	0.003247	-0.008059	-0.041550	0.078673	0.112265
categories_Online Multi-Player	0.238129	-0.008404	-0.030163	0.267235	0.084508	-0.108480	-0.056573	0.035293	-0.065092	0.042011	...	0.077435	0.112956	0.397258	0.345696	-0.004689	0.024209	-0.008671	-0.046856	0.029614	0.045289
categories_Steam Cloud	0.036612	-0.013761	0.149301	-0.198136	0.032948	0.050398	0.019819	0.054046	-0.063034	-0.017554	...	0.128826	0.150431	-0.107761	0.046337	0.309192	-0.003722	0.016706	0.238371	0.012285	0.006290
categories_Steam Achievements	0.198357	0.028044	0.224662	-0.142167	-0.005507	0.050325	0.225157	0.035279	0.017605	-0.029639	...	0.204219	0.119656	-0.048793	0.054982	0.331717	-0.004717	0.106578	0.183885	0.025047	0.001920
categories_Partial Controller Support	-0.023010	0.007794	-0.029121	-0.024322	-0.123526	0.008459	0.014906	-0.015327	-0.065926	-0.005751	...	0.041487	0.025170	-0.021067	0.067571	-0.257041	-0.026442	-0.013671	0.000122	0.007791	0.012629
categories_Includes Source SDK	-0.072379	0.005490	0.030609	0.057522	-0.004300	-0.029001	-0.014593	-0.027096	-0.020345	-0.020101	...	0.083944	0.077283	0.004151	0.039845	-0.016815	-0.003159	0.001995	0.031617	0.031046	0.109474
categories_Cross-Platform Multiplayer	0.051877	0.021563	0.212020	0.177166	0.157598	-0.087415	0.037836	0.025366	-0.021760	0.012211	...	0.096315	0.111195	0.230484	0.258109	-0.003721	0.009999	0.009512	-0.001590	0.020451	0.027436
categories_Stats	0.010357	0.016513	0.073569	0.000427	0.030511	-0.056062	0.088599	-0.011186	0.011685	0.010936	...	1.000000	0.151841	0.028080	0.088999	0.063991	-0.001899	0.034449	0.039899	0.056706	0.051619
categories_Steam Workshop	0.040704	0.019417	0.104577	-0.052947	0.093756	-0.073111	0.044996	-0.019813	-0.059453	0.157201	...	0.151841	1.000000	-0.013372	0.120398	0.042400	0.003738	0.012106	0.103074	0.112367	0.109260
categories_In-App Purchases	0.184621	-0.021621	-0.016235	0.464180	0.104867	-0.069771	-0.128760	0.077305	-0.001554	0.026719	...	0.028080	-0.013372	1.000000	0.118510	-0.087035	-0.005351	-0.000845	-0.117775	0.087137	0.112300
categories_Co-op	0.045730	0.035900	-0.008482	0.079062	0.030191	-0.037174	-0.018569	0.066478	-0.095298	0.009901	...	0.088999	0.120398	0.118510	1.000000	0.113303	0.032167	0.007310	0.013091	0.056475	0.087425
categories_Full controller support	0.113789	0.036415	0.090161	-0.134629	-0.155202	0.087080	0.107005	0.011069	-0.096994	-0.121232	...	0.063991	0.042400	-0.087035	0.113303	1.000000	-0.017700	-0.006013	0.170011	0.038892	0.012989
categories_SteamVR Collectibles	0.034240	0.005595	-0.040691	0.001210	-0.005351	0.000475	0.000336	-0.016932	0.002146	0.012420	...	-0.001899	0.003738	-0.005351	0.032167	-0.017700	1.000000	-0.004413	0.043450	0.049613	0.127850
achievements	0.067032	0.006466	-0.005986	-0.022465	0.019209	-0.018926	0.033502	0.010250	0.075496	-0.013809	...	0.034449	0.012106	-0.000845	0.007310	-0.006013	-0.004413	1.000000	-0.025386	0.013696	0.009161
%_ratings	-0.071347	-0.013599	0.197562	-0.065258	-0.039162	0.027102	0.040181	0.007115	-0.026894	-0.056964	...	0.039899	0.103074	-0.117775	0.013091	0.170011	0.043450	-0.025386	1.000000	0.051687	0.067987
QTD_ratings	-0.034609	0.006797	0.031426	0.037751	-0.013012	-0.005821	-0.050968	0.005591	-0.038824	-0.005281	...	0.056706	0.112367	0.087137	0.056475	0.038892	0.049613	0.013696	0.051687	1.000000	0.734385
owners_mean	-0.110494	0.011206	0.040690	0.075699	-0.004210	-0.023324	-0.086617	0.001766	-0.054940	-0.015097	...	0.051619	0.109260	0.112300	0.087425	0.012989	0.127850	0.009161	0.067987	0.734385	1.000000

Omnibus:	2243.426	Durbin-Watson:	1.837
Prob(Omnibus):	0.000	Jarque-Bera (JB):	6792.928
Skew:	-1.374	Prob(JB):	0.00
Kurtosis:	6.439	Cond. No.	2.18e+09

	log_log_Y	log_log_Y^
8208	0.000000	-0.232962
2093	1.124342	1.041000
6425	1.079932	1.102279
4802	0.000000	-0.065669
924	1.257577	0.915709
...	...	...
4719	0.668679	1.026345
2831	0.846883	0.840389
2938	1.489226	1.015788
1375	1.026074	0.910699
3259	0.000000	1.078248