Psychology or Good Moves?
Akshat Jain
10/8/2020
Introduction
This study is to find the various factors affecting the result of chess games. Chess primarily being a game of patterns, and as data science is all about detecting patterns in data, which is why chess has been one of the most invested in areas of AI in the past. On top of it, Chess being an indoor game, it was quick to get online. There are number of websites which stores a comprehnsive amount of data on each game.
The datset for this study is also sourced from one such website named Lichess. The dataset is collected by Kaggle user Mitchell J.. The dataset collects all of the information available from 20,000 games. We will try to explore
- How much out-of-game factors like rated game, increment type , - duration, piece colore etc. affect a game outcome i.e draw or W/L
- The relationship between openings, rating difference, number of moves etc. and victory for black and white
Describing the Data
Datafields
- Game ID: Item ID
- Rated (T/F): Weight of the Item
- Start Time: The Fat content in item categorized as Low Fat and Regular
- End Time: Visibility on a scale of 0-1
- Number of Turns: Type of the Item categorized as Dairy, Soft drinks, Baking goods, breads, frozen foods etc.
- Game Status: Maximum Retail Price of the Item
- Winner: Outlet ID
- Time Increment: V/S
- White Player ID:
- White Player Rating: T
- Black Player ID
- Black Player Rating:
- Moves:
- Opening Eco: T
- Opening Name
- Opening Ply :
Data Loading
library(ggplot2)
library(tidyverse)## -- Attaching packages ------------------------------------ tidyverse 1.3.0 --## v tibble 3.0.1 v dplyr 1.0.0
## v tidyr 1.1.0 v stringr 1.4.0
## v readr 1.3.1 v forcats 0.5.0
## v purrr 0.3.4## -- Conflicts --------------------------------------- tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()library(fastDummies)
library(car)## Loading required package: carData##
## Attaching package: 'car'## The following object is masked from 'package:dplyr':
##
## recode## The following object is masked from 'package:purrr':
##
## somelibrary(caTools)
library(InformationValue)
chessDS <-read.csv("chess.csv",header = T, strip.white=T)
str(chessDS)## 'data.frame': 20058 obs. of 16 variables:
## $ id : chr "TZJHLljE" "l1NXvwaE" "mIICvQHh" "kWKvrqYL" ...
## $ rated : chr "FALSE" "TRUE" "TRUE" "TRUE" ...
## $ created_at : num 1.5e+12 1.5e+12 1.5e+12 1.5e+12 1.5e+12 ...
## $ last_move_at : num 1.5e+12 1.5e+12 1.5e+12 1.5e+12 1.5e+12 ...
## $ turns : int 13 16 61 61 95 5 33 9 66 119 ...
## $ victory_status: chr "outoftime" "resign" "mate" "mate" ...
## $ winner : chr "white" "black" "white" "white" ...
## $ increment_code: chr "15+2" "5+10" "5+10" "20+0" ...
## $ white_id : chr "bourgris" "a-00" "ischia" "daniamurashov" ...
## $ white_rating : int 1500 1322 1496 1439 1523 1250 1520 1413 1439 1381 ...
## $ black_id : chr "a-00" "skinnerua" "a-00" "adivanov2009" ...
## $ black_rating : int 1191 1261 1500 1454 1469 1002 1423 2108 1392 1209 ...
## $ moves : chr "d4 d5 c4 c6 cxd5 e6 dxe6 fxe6 Nf3 Bb4+ Nc3 Ba5 Bf4" "d4 Nc6 e4 e5 f4 f6 dxe5 fxe5 fxe5 Nxe5 Qd4 Nc6 Qe5+ Nxe5 c4 Bb4+" "e4 e5 d3 d6 Be3 c6 Be2 b5 Nd2 a5 a4 c5 axb5 Nc6 bxc6 Ra6 Nc4 a4 c3 a3 Nxa3 Rxa3 Rxa3 c4 dxc4 d5 cxd5 Qxd5 exd5 "| __truncated__ "d4 d5 Nf3 Bf5 Nc3 Nf6 Bf4 Ng4 e3 Nc6 Be2 Qd7 O-O O-O-O Nb5 Nb4 Rc1 Nxa2 Ra1 Nb4 Nxa7+ Kb8 Nb5 Bxc2 Bxc7+ Kc8 Qd"| __truncated__ ...
## $ opening_eco : chr "D10" "B00" "C20" "D02" ...
## $ opening_name : chr "Slav Defense: Exchange Variation" "Nimzowitsch Defense: Kennedy Variation" "King's Pawn Game: Leonardis Variation" "Queen's Pawn Game: Zukertort Variation" ...
## $ opening_ply : int 5 4 3 3 5 4 10 5 6 4 ...head(chessDS)## id rated created_at last_move_at turns victory_status winner
## 1 TZJHLljE FALSE 1.50421e+12 1.50421e+12 13 outoftime white
## 2 l1NXvwaE TRUE 1.50413e+12 1.50413e+12 16 resign black
## 3 mIICvQHh TRUE 1.50413e+12 1.50413e+12 61 mate white
## 4 kWKvrqYL TRUE 1.50411e+12 1.50411e+12 61 mate white
## 5 9tXo1AUZ TRUE 1.50403e+12 1.50403e+12 95 mate white
## 6 MsoDV9wj FALSE 1.50424e+12 1.50424e+12 5 draw draw
## increment_code white_id white_rating black_id black_rating
## 1 15+2 bourgris 1500 a-00 1191
## 2 5+10 a-00 1322 skinnerua 1261
## 3 5+10 ischia 1496 a-00 1500
## 4 20+0 daniamurashov 1439 adivanov2009 1454
## 5 30+3 nik221107 1523 adivanov2009 1469
## 6 10+0 trelynn17 1250 franklin14532 1002
## moves
## 1 d4 d5 c4 c6 cxd5 e6 dxe6 fxe6 Nf3 Bb4+ Nc3 Ba5 Bf4
## 2 d4 Nc6 e4 e5 f4 f6 dxe5 fxe5 fxe5 Nxe5 Qd4 Nc6 Qe5+ Nxe5 c4 Bb4+
## 3 e4 e5 d3 d6 Be3 c6 Be2 b5 Nd2 a5 a4 c5 axb5 Nc6 bxc6 Ra6 Nc4 a4 c3 a3 Nxa3 Rxa3 Rxa3 c4 dxc4 d5 cxd5 Qxd5 exd5 Be6 Ra8+ Ke7 Bc5+ Kf6 Bxf8 Kg6 Bxg7 Kxg7 dxe6 Kh6 exf7 Nf6 Rxh8 Nh5 Bxh5 Kg5 Rxh7 Kf5 Qf3+ Ke6 Bg4+ Kd6 Rh6+ Kc5 Qe3+ Kb5 c4+ Kb4 Qc3+ Ka4 Bd1#
## 4 d4 d5 Nf3 Bf5 Nc3 Nf6 Bf4 Ng4 e3 Nc6 Be2 Qd7 O-O O-O-O Nb5 Nb4 Rc1 Nxa2 Ra1 Nb4 Nxa7+ Kb8 Nb5 Bxc2 Bxc7+ Kc8 Qd2 Qc6 Na7+ Kd7 Nxc6 bxc6 Bxd8 Kxd8 Qxb4 e5 Qb8+ Ke7 dxe5 Be4 Ra7+ Ke6 Qe8+ Kf5 Qxf7+ Nf6 Nh4+ Kg5 g3 Ng4 Qf4+ Kh5 Qxg4+ Kh6 Qf4+ g5 Qf6+ Bg6 Nxg6 Bg7 Qxg7#
## 5 e4 e5 Nf3 d6 d4 Nc6 d5 Nb4 a3 Na6 Nc3 Be7 b4 Nf6 Bg5 O-O b5 Nc5 Bxf6 Bxf6 Bd3 Qd7 O-O Nxd3 Qxd3 c6 a4 cxd5 Nxd5 Qe6 Nc7 Qg4 Nxa8 Bd7 Nc7 Rc8 Nd5 Qg6 Nxf6+ Qxf6 Rfd1 Re8 Qxd6 Bg4 Qxf6 gxf6 Rd3 Bxf3 Rxf3 Rd8 Rxf6 Kg7 Rf3 Rd2 Rg3+ Kf8 c3 Re2 f3 Rc2 Rg5 f6 Rh5 Kg7 Rd1 Kg6 Rh3 Rxc3 Rd7 Rc1+ Kf2 Rc2+ Kg3 h5 Rxb7 Kg5 Rxa7 h4+ Rxh4 Rxg2+ Kxg2 Kxh4 b6 Kg5 b7 f5 exf5 Kxf5 b8=Q e4 Rf7+ Kg5 Qg8+ Kh6 Rh7#
## 6 e4 c5 Nf3 Qa5 a3
## opening_eco opening_name opening_ply
## 1 D10 Slav Defense: Exchange Variation 5
## 2 B00 Nimzowitsch Defense: Kennedy Variation 4
## 3 C20 King's Pawn Game: Leonardis Variation 3
## 4 D02 Queen's Pawn Game: Zukertort Variation 3
## 5 C41 Philidor Defense 5
## 6 B27 Sicilian Defense: Mongoose Variation 4Columns<-colnames(chessDS)Data Cleaning
After exploring the data we found out that there were some columns with different coding for same output. Also, we found out that there was a need to introduce some new variables. The modification we did to dataset are as follows: 1. Rated column was transformed to contain only ‘True’ and ‘False’ value. 2. A new column as ‘outcome’ which contained the transformed result of ‘winner’ column by transforming ‘white’, ‘black’, and ‘draw’ to ‘W’, ‘L’, and ‘D’ 3. A new column ‘result’ with value ‘y’ if the game had outcome and ‘n’ if it did not. 4. A new column ’ opening10’ with top 10 most played chess openings in dataset. 5. Two new column ‘duration’ to show the time duration of the game and ‘increment’ to indicate weather there was increment or not. 6. A new column ‘rating differnece with difference in ratings of the players 7. Two new columns ’titleW’ and ‘titleB’ with categorical data of four categories based on the ratings of player as follws 1. GM: >2400 2. Pro: <2400 & >1800 3. Exp: <1800 & >1200 4. N: <1200
for (i in 1:16)
print (length(unique(chessDS[,i])))## [1] 19113
## [1] 4
## [1] 13151
## [1] 13186
## [1] 211
## [1] 4
## [1] 3
## [1] 400
## [1] 9438
## [1] 1516
## [1] 9331
## [1] 1521
## [1] 18920
## [1] 365
## [1] 1477
## [1] 23unique(chessDS$rated)## [1] "FALSE" "TRUE" "True" "False"unique(chessDS$turns)## [1] 13 16 61 95 5 33 9 66 119 39 38 60 31 43 52 101 25 14
## [19] 3 17 36 69 54 53 64 21 11 19 28 22 37 34 32 71 30 41
## [37] 49 7 35 8 44 29 40 57 78 62 87 50 131 48 47 51 58 114
## [55] 20 85 113 75 135 81 46 70 91 137 18 111 90 59 26 23 118 120
## [73] 24 2 97 12 72 156 77 65 73 125 76 63 107 100 80 105 144 158
## [91] 117 110 178 136 124 96 10 106 15 42 159 74 112 104 150 88 55 103
## [109] 177 82 99 67 6 115 83 89 116 27 102 45 98 108 92 56 123 129
## [127] 4 163 130 121 94 79 148 195 122 128 84 86 93 161 133 68 153 154
## [145] 160 141 132 204 140 168 127 109 174 157 142 143 170 1 138 171 145 151
## [163] 179 149 173 208 139 134 169 155 164 147 126 146 190 167 255 210 176 172
## [181] 188 152 182 184 162 221 189 166 196 165 193 175 349 198 218 205 207 216
## [199] 206 200 181 180 183 222 209 185 259 226 212 187 201unique(chessDS$victory_status)## [1] "outoftime" "resign" "mate" "draw"unique(chessDS$winner)## [1] "white" "black" "draw"unique(chessDS$increment_code)## [1] "15+2" "5+10" "20+0" "30+3" "10+0" "15+30" "15+0"
## [8] "20+60" "5+40" "8+0" "15+15" "15+16" "11+0" "30+60"
## [15] "15+5" "10+10" "15+3" "18+0" "30+30" "20+25" "5+5"
## [22] "30+0" "40+40" "16+0" "6+10" "8+10" "8+12" "7+12"
## [29] "15+10" "20+5" "20+10" "45+0" "5+8" "30+2" "25+0"
## [36] "10+2" "7+2" "25+25" "7+8" "6+6" "10+4" "12+0"
## [43] "15+1" "2+10" "9+0" "10+9" "6+7" "30+10" "30+15"
## [50] "10+3" "45+30" "9+2" "7+3" "6+5" "25+5" "5+7"
## [57] "8+2" "20+8" "30+5" "25+15" "15+7" "8+8" "5+9"
## [64] "16+7" "10+7" "7+5" "40+20" "10+5" "11+5" "10+15"
## [71] "180+0" "17+5" "8+5" "3+8" "60+120" "90+120" "15+8"
## [78] "9+1" "9+3" "2+15" "10+1" "5+12" "60+10" "5+60"
## [85] "8+15" "30+25" "12+1" "14+0" "60+20" "10+8" "20+3"
## [92] "14+12" "7+7" "60+0" "45+45" "4+15" "5+6" "180+180"
## [99] "8+3" "4+6" "10+25" "3+10" "7+4" "6+3" "5+15"
## [106] "45+15" "15+20" "6+8" "6+9" "14+8" "6+4" "15+4"
## [113] "9+20" "20+15" "20+2" "9+10" "8+7" "13+1" "150+180"
## [120] "3+12" "7+10" "10+60" "5+30" "20+30" "14+10" "25+10"
## [127] "8+1" "19+0" "9+12" "20+1" "0+25" "0+15" "15+6"
## [134] "8+6" "10+6" "25+8" "15+14" "20+20" "13+10" "3+9"
## [141] "17+11" "12+5" "12+2" "7+25" "20+7" "12+6" "25+30"
## [148] "15+45" "25+3" "17+1" "30+1" "17+8" "17+3" "45+10"
## [155] "8+25" "19+19" "12+8" "9+9" "15+60" "5+20" "30+6"
## [162] "12+12" "30+12" "25+2" "40+10" "16+2" "90+0" "30+11"
## [169] "4+10" "12+13" "11+8" "60+4" "10+30" "60+3" "20+6"
## [176] "1+30" "90+30" "4+8" "40+0" "17+2" "180+8" "12+10"
## [183] "16+1" "1+10" "7+14" "3+15" "60+60" "13+3" "45+4"
## [190] "45+5" "10+180" "120+0" "30+7" "14+4" "13+2" "6+20"
## [197] "180+60" "60+30" "40+30" "30+35" "10+11" "1+12" "11+11"
## [204] "18+5" "8+9" "15+11" "9+5" "19+17" "14+14" "17+15"
## [211] "7+6" "40+2" "10+20" "12+9" "14+17" "14+20" "10+13"
## [218] "30+8" "30+9" "30+4" "30+20" "5+180" "7+9" "5+13"
## [225] "30+45" "25+4" "25+1" "12+4" "11+4" "13+0" "60+5"
## [232] "9+11" "1+15" "12+3" "2+16" "13+5" "20+4" "40+1"
## [239] "17+16" "11+10" "1+19" "40+60" "7+35" "16+10" "9+17"
## [246] "15+12" "10+12" "35+10" "18+20" "6+15" "19+20" "11+1"
## [253] "30+150" "35+3" "17+0" "40+15" "14+6" "20+40" "13+14"
## [260] "8+4" "180+25" "2+20" "12+11" "13+13" "16+8" "60+7"
## [267] "45+1" "20+11" "150+8" "20+180" "90+5" "9+6" "45+8"
## [274] "17+90" "18+19" "0+12" "9+4" "35+0" "7+15" "1+25"
## [281] "11+3" "17+13" "9+8" "13+12" "16+4" "19+8" "11+7"
## [288] "0+180" "14+5" "19+2" "10+35" "4+7" "6+12" "19+30"
## [295] "12+20" "29+30" "15+9" "120+1" "180+5" "12+7" "8+180"
## [302] "35+15" "17+17" "150+60" "18+18" "18+10" "150+3" "1+13"
## [309] "0+16" "5+17" "5+25" "25+17" "18+8" "180+45" "1+45"
## [316] "10+45" "20+9" "25+9" "13+20" "1+20" "0+40" "0+20"
## [323] "14+9" "40+9" "25+20" "180+150" "180+120" "20+12" "30+16"
## [330] "20+120" "2+40" "19+5" "18+15" "19+45" "11+2" "5+21"
## [337] "19+4" "4+180" "5+11" "60+13" "40+8" "4+18" "4+12"
## [344] "21+0" "90+8" "13+7" "9+7" "14+2" "20+13" "19+3"
## [351] "60+15" "3+35" "7+11" "2+12" "8+30" "120+10" "150+0"
## [358] "5+14" "16+20" "15+25" "120+180" "60+40" "180+3" "10+40"
## [365] "30+40" "3+30" "2+9" "7+18" "35+2" "8+11" "12+15"
## [372] "1+18" "20+90" "4+20" "35+1" "7+30" "25+12" "45+2"
## [379] "13+15" "14+1" "25+6" "16+3" "0+13" "60+1" "11+9"
## [386] "19+18" "120+5" "9+15" "0+30" "6+30" "35+35" "3+20"
## [393] "4+9" "10+14" "35+8" "13+40" "16+15" "60+180" "8+45"
## [400] "14+15"sum(is.na(chessDS))## [1] 0sum(complete.cases(chessDS))## [1] 20058sum(chessDS[,2]=="FALSE")## [1] 1855chessDS[which(chessDS[,2]=="FALSE"),2]<- "False"
sum(chessDS[,2]=="FALSE")## [1] 0sum(chessDS[,2]=="TRUE")## [1] 7432chessDS[which(chessDS[,2]=="TRUE"),2]<- "True"
sum(chessDS[,2]=="TRUE")## [1] 0sum(chessDS[,2]=="True")## [1] 16155sum(chessDS[,2]=="False")## [1] 3903summary(chessDS$turns)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.00 37.00 55.00 60.47 79.00 349.00summary(chessDS$white_rating)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 784 1398 1567 1597 1793 2700summary(chessDS$black_rating)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 789 1391 1562 1589 1784 2723outcome<-chessDS$winner
outcome[which(outcome=="white")]<- "W"
outcome[which(outcome=="black")]<- "L"
outcome[which(outcome=="draw")]<- "D"
chessDS<-cbind(chessDS,outcome)
str(chessDS)## 'data.frame': 20058 obs. of 17 variables:
## $ id : chr "TZJHLljE" "l1NXvwaE" "mIICvQHh" "kWKvrqYL" ...
## $ rated : chr "False" "True" "True" "True" ...
## $ created_at : num 1.5e+12 1.5e+12 1.5e+12 1.5e+12 1.5e+12 ...
## $ last_move_at : num 1.5e+12 1.5e+12 1.5e+12 1.5e+12 1.5e+12 ...
## $ turns : int 13 16 61 61 95 5 33 9 66 119 ...
## $ victory_status: chr "outoftime" "resign" "mate" "mate" ...
## $ winner : chr "white" "black" "white" "white" ...
## $ increment_code: chr "15+2" "5+10" "5+10" "20+0" ...
## $ white_id : chr "bourgris" "a-00" "ischia" "daniamurashov" ...
## $ white_rating : int 1500 1322 1496 1439 1523 1250 1520 1413 1439 1381 ...
## $ black_id : chr "a-00" "skinnerua" "a-00" "adivanov2009" ...
## $ black_rating : int 1191 1261 1500 1454 1469 1002 1423 2108 1392 1209 ...
## $ moves : chr "d4 d5 c4 c6 cxd5 e6 dxe6 fxe6 Nf3 Bb4+ Nc3 Ba5 Bf4" "d4 Nc6 e4 e5 f4 f6 dxe5 fxe5 fxe5 Nxe5 Qd4 Nc6 Qe5+ Nxe5 c4 Bb4+" "e4 e5 d3 d6 Be3 c6 Be2 b5 Nd2 a5 a4 c5 axb5 Nc6 bxc6 Ra6 Nc4 a4 c3 a3 Nxa3 Rxa3 Rxa3 c4 dxc4 d5 cxd5 Qxd5 exd5 "| __truncated__ "d4 d5 Nf3 Bf5 Nc3 Nf6 Bf4 Ng4 e3 Nc6 Be2 Qd7 O-O O-O-O Nb5 Nb4 Rc1 Nxa2 Ra1 Nb4 Nxa7+ Kb8 Nb5 Bxc2 Bxc7+ Kc8 Qd"| __truncated__ ...
## $ opening_eco : chr "D10" "B00" "C20" "D02" ...
## $ opening_name : chr "Slav Defense: Exchange Variation" "Nimzowitsch Defense: Kennedy Variation" "King's Pawn Game: Leonardis Variation" "Queen's Pawn Game: Zukertort Variation" ...
## $ opening_ply : int 5 4 3 3 5 4 10 5 6 4 ...
## $ outcome : chr "W" "L" "W" "W" ...result<-chessDS$outcome
result[which(result=="L")]<- "y"
result[which(result=="W")]<- "y"
result[which(result=="D")]<- "n"
chessDS<-cbind(chessDS,result)
openingDF<-table(chessDS$opening_name)
openingDF<-sort(openingDF)
openingDF50<-openingDF[which(openingDF>50)]
barplot(openingDF50)
length(openingDF50)## [1] 81head(sort(openingDF50,decreasing=T))##
## Van't Kruijs Opening
## 368
## Sicilian Defense
## 358
## Sicilian Defense: Bowdler Attack
## 296
## French Defense: Knight Variation
## 271
## Scotch Game
## 271
## Scandinavian Defense: Mieses-Kotroc Variation
## 259topOpenings<-names(head(sort(openingDF50,decreasing=T),10))
openingsOutcome<-chessDS[chessDS$opening_name %in% topOpenings ,]
openingDF10<-openingDF[which(openingDF>200)]
openings10<-chessDS$opening_name
openings10[!chessDS$opening_name %in% topOpenings ]<-"Others"
unique(openings10)## [1] "Others"
## [2] "Scandinavian Defense: Mieses-Kotroc Variation"
## [3] "Van't Kruijs Opening"
## [4] "French Defense: Knight Variation"
## [5] "Horwitz Defense"
## [6] "Sicilian Defense: Bowdler Attack"
## [7] "Queen's Pawn Game: Chigorin Variation"
## [8] "Sicilian Defense"
## [9] "Scandinavian Defense"
## [10] "Scotch Game"
## [11] "Queen's Pawn Game: Mason Attack"chessDS<-cbind(chessDS,openings10)
incrementsplit<-unlist(strsplit(chessDS$increment_code, "\\+"))
length(incrementsplit)## [1] 40116duration<-incrementsplit[c(TRUE, FALSE)]
length(duration)## [1] 20058increment<-incrementsplit[c( FALSE,TRUE)]
length(increment)## [1] 20058chessDS<-cbind(chessDS,duration)
increment[which(increment>0)]<- 1
unique(increment)## [1] "1" "0"chessDS<-cbind(chessDS,increment)
ratingDifference<-chessDS$white_rating-chessDS$black_rating
chessDS<-cbind(chessDS,ratingDifference)
#binning
length<-ifelse(chessDS$turns>55,"Long","Short")
titleW <- ifelse(chessDS$white_rating>2400,"GM",ifelse(chessDS$white_rating>1800,"EXP",ifelse(chessDS$white_rating>1200,"PRO","N")))
titleB <- ifelse(chessDS$black_rating >2400,"GM",ifelse(chessDS$black_rating>1800,"EXP",ifelse(chessDS$black_rating>1200,"PRO","N")))
chessDS<-cbind(chessDS,length)
chessDS<-cbind(chessDS,titleW)
chessDS<-cbind(chessDS,titleB)
hist(chessDS$turns,breaks=30,xlim=c(0,350),col="blue",border = "black", ylim = c(0,5000),xlab="Turns",ylab="Counts", main="Histogram of Number of Turns")
which(chessDS$turns > 300)## [1] 11555 13860chessDS[11555,]## id rated created_at last_move_at turns victory_status winner
## 11555 pN0ioHNr True 1.503084e+12 1.503086e+12 349 outoftime white
## increment_code white_id white_rating black_id black_rating
## 11555 10+0 shiwen 2194 kijek 2240
## moves
## 11555 d4 d5 c4 c6 Nf3 Nf6 Nc3 e6 Bg5 h6 Bxf6 Qxf6 Qb3 Qd8 e4 dxe4 Nxe4 Nd7 Bd3 Be7 O-O Nf6 Rfd1 O-O Qc2 Qc7 Qe2 b6 Rac1 Bb7 Nxf6+ Bxf6 d5 exd5 cxd5 c5 Qe4 g6 b3 Qd6 Bc4 Rfe8 Qg4 a6 a4 Kg7 Nd2 Bc8 Qf3 Bf5 h3 h5 Bd3 Bxd3 Qxd3 Qe5 Nc4 Qb8 d6 b5 axb5 axb5 Ne3 Bd4 Nc2 Qxd6 Nxd4 cxd4 Qxd4+ Qxd4 Rxd4 Red8 Rxd8 Rxd8 Rc5 Rd1+ Kh2 Rd2 f3 b4 Rc4 Rb2 Rxb4 h4 Rxh4 Rxb3 Kg3 g5 Rc4 Kg6 h4 gxh4+ Rxh4 Rb2 Rc4 f6 Rc5 Rb4 Kh3 Rd4 Kh2 Rb4 Kh1 Rb1+ Kh2 Rb4 Kg1 Rb2 Kf1 Ra2 Rb5 Rc2 Rd5 Ra2 Kg1 Rb2 Kh1 Rb1+ Kh2 Rb4 Kh3 Rc4 Ra5 Rb4 Kg3 Rc4 Kf2 Rc3 Kf1 Rc2 Kg1 Rb2 Kh1 Rc2 Kh2 Rb2 Kh3 Rb4 Kg3 Rc4 Ra8 Rb4 Rc8 Rd4 Rc7 Rb4 Kh2 Rd4 Kh3 Rb4 Kg3 Rd4 Kf2 Rd3 Kf1 Rd2 Kg1 Rb2 Kh1 Rd2 Kh2 Rb2 Kh3 Rb4 Kg3 Rd4 Rc8 Rb4 Rd8 Rc4 Kh3 Rb4 Rg8+ Kf7 Rh8 Kg6 Rd8 Rc4 Rd1 Rb4 Kh2 Rc4 Kh1 Rb4 Kg1 Rb2 Kh2 Rb4 Kh3 Rc4 Re1 Rb4 g3 Rc4 Rf1 Rb4 Rf2 Rc4 Re2 Rb4 Kg2 Rc4 Kf2 Rc3 Rd2 Rb3 Ra2 Rc3 Rb2 Ra3 Rd2 Rc3 Kg2 Rb3 Rd8 Rc3 Ra8 Rb3 Ra7 Rc3 Ra6 Rb3 Ra5 Rc3 Ra4 Rb3 Ra2 Rc3 Ra1 Rb3 Rc1 Rd3 Re1 Rc3 Re8 Rd3 Rg8+ Kf7 Rh8 Kg7 Rh4 Kg6 Rg4+ Kf7 Ra4 Kg6 Kf2 Rc3 Rh4 Rb3 Rh1 Rc3 Rg1 Rb3 Rf1 Rc3 Re1 Rb3 Rd1 Rc3 Ke2 Rb3 Rc1 Ra3 Rb1 Rc3 Kf2 Ra3 Rb2 Rc3 Kg2 Ra3 g4 Rc3 Kg3 Rc4 Rb3 Ra4 Rc3 Rb4 Rd3 Rc4 Re3 Rb4 Re2 Rc4 Rf2 Rb4 Rg2 Rc4 Rh2 Rb4 Rh1 Rc4 Rg1 Rb4 Rc1 Ra4 Rb1 Rc4 Re1 Rb4 Rc1 Rd4 Kf2 Rd3 Ke2 Ra3 Rb1 Ra2+ Ke3 Ra3+ Kf4 Ra4+ Kg3 Ra3 Rb8 Ra4 Rg8+ Kf7 Rh8 Kg7 Rb8 Kg6 Rg8+ Kf7 Rc8 Kg6 Rc7 Ra5 Kh4 Ra4 Rc6 Rc4 Kg3 Ra4 Rb6 Rc4 Rb5 Ra4 f4 Ra3+ Kh4 Ra1 f5+ Kg7 Rb7+ Kh6 Kg3
## opening_eco opening_name opening_ply
## 11555 D30 Queen's Gambit Declined: Hastings Variation 13
## outcome result openings10 duration increment ratingDifference length
## 11555 W y Others 10 0 -46 Long
## titleW titleB
## 11555 EXP EXPchessDS[13860,]## id rated created_at last_move_at turns victory_status winner
## 13860 pN0ioHNr True 1.503084e+12 1.503086e+12 349 outoftime white
## increment_code white_id white_rating black_id black_rating
## 13860 10+0 shiwen 2194 kijek 2240
## moves
## 13860 d4 d5 c4 c6 Nf3 Nf6 Nc3 e6 Bg5 h6 Bxf6 Qxf6 Qb3 Qd8 e4 dxe4 Nxe4 Nd7 Bd3 Be7 O-O Nf6 Rfd1 O-O Qc2 Qc7 Qe2 b6 Rac1 Bb7 Nxf6+ Bxf6 d5 exd5 cxd5 c5 Qe4 g6 b3 Qd6 Bc4 Rfe8 Qg4 a6 a4 Kg7 Nd2 Bc8 Qf3 Bf5 h3 h5 Bd3 Bxd3 Qxd3 Qe5 Nc4 Qb8 d6 b5 axb5 axb5 Ne3 Bd4 Nc2 Qxd6 Nxd4 cxd4 Qxd4+ Qxd4 Rxd4 Red8 Rxd8 Rxd8 Rc5 Rd1+ Kh2 Rd2 f3 b4 Rc4 Rb2 Rxb4 h4 Rxh4 Rxb3 Kg3 g5 Rc4 Kg6 h4 gxh4+ Rxh4 Rb2 Rc4 f6 Rc5 Rb4 Kh3 Rd4 Kh2 Rb4 Kh1 Rb1+ Kh2 Rb4 Kg1 Rb2 Kf1 Ra2 Rb5 Rc2 Rd5 Ra2 Kg1 Rb2 Kh1 Rb1+ Kh2 Rb4 Kh3 Rc4 Ra5 Rb4 Kg3 Rc4 Kf2 Rc3 Kf1 Rc2 Kg1 Rb2 Kh1 Rc2 Kh2 Rb2 Kh3 Rb4 Kg3 Rc4 Ra8 Rb4 Rc8 Rd4 Rc7 Rb4 Kh2 Rd4 Kh3 Rb4 Kg3 Rd4 Kf2 Rd3 Kf1 Rd2 Kg1 Rb2 Kh1 Rd2 Kh2 Rb2 Kh3 Rb4 Kg3 Rd4 Rc8 Rb4 Rd8 Rc4 Kh3 Rb4 Rg8+ Kf7 Rh8 Kg6 Rd8 Rc4 Rd1 Rb4 Kh2 Rc4 Kh1 Rb4 Kg1 Rb2 Kh2 Rb4 Kh3 Rc4 Re1 Rb4 g3 Rc4 Rf1 Rb4 Rf2 Rc4 Re2 Rb4 Kg2 Rc4 Kf2 Rc3 Rd2 Rb3 Ra2 Rc3 Rb2 Ra3 Rd2 Rc3 Kg2 Rb3 Rd8 Rc3 Ra8 Rb3 Ra7 Rc3 Ra6 Rb3 Ra5 Rc3 Ra4 Rb3 Ra2 Rc3 Ra1 Rb3 Rc1 Rd3 Re1 Rc3 Re8 Rd3 Rg8+ Kf7 Rh8 Kg7 Rh4 Kg6 Rg4+ Kf7 Ra4 Kg6 Kf2 Rc3 Rh4 Rb3 Rh1 Rc3 Rg1 Rb3 Rf1 Rc3 Re1 Rb3 Rd1 Rc3 Ke2 Rb3 Rc1 Ra3 Rb1 Rc3 Kf2 Ra3 Rb2 Rc3 Kg2 Ra3 g4 Rc3 Kg3 Rc4 Rb3 Ra4 Rc3 Rb4 Rd3 Rc4 Re3 Rb4 Re2 Rc4 Rf2 Rb4 Rg2 Rc4 Rh2 Rb4 Rh1 Rc4 Rg1 Rb4 Rc1 Ra4 Rb1 Rc4 Re1 Rb4 Rc1 Rd4 Kf2 Rd3 Ke2 Ra3 Rb1 Ra2+ Ke3 Ra3+ Kf4 Ra4+ Kg3 Ra3 Rb8 Ra4 Rg8+ Kf7 Rh8 Kg7 Rb8 Kg6 Rg8+ Kf7 Rc8 Kg6 Rc7 Ra5 Kh4 Ra4 Rc6 Rc4 Kg3 Ra4 Rb6 Rc4 Rb5 Ra4 f4 Ra3+ Kh4 Ra1 f5+ Kg7 Rb7+ Kh6 Kg3
## opening_eco opening_name opening_ply
## 13860 D30 Queen's Gambit Declined: Hastings Variation 13
## outcome result openings10 duration increment ratingDifference length
## 13860 W y Others 10 0 -46 Long
## titleW titleB
## 13860 EXP EXPExploartory Data Analysis
#EDA
#Categorical variables
# Outcome Vs Rated
counts <- table(chessDS$outcome,chessDS$rated,dnn=c("Outcome","Rated"))
sumtable <- addmargins(counts,2)
prop.table(counts)## Rated
## Outcome False True
## D 0.01151660 0.03584605
## L 0.08590089 0.36813242
## W 0.09716821 0.40143584col.margin <- prop.table(counts, margin = 2)
round_col <- round(col.margin,4)*100
#Normalized bar chart
barplot(round_col,legend = rownames(counts),col=c("grey","white","black"),xlab="Rated",ylab="perc",ylim=c(0,100))
par(mar = rep(2, 4))
# Outcome Vs Result
countResult <- table(chessDS$rated,chessDS$result,dnn=c("Rated","Outcome"))
sumtable.Result <- addmargins(countResult,2)
col.margin.Result <- prop.table(countResult, margin = 2)
round_col_result <- round(col.margin.Result,4)*100
barplot(round_col_result,legend = rownames(countResult),col=c("white","black"),xlab="Result",ylab="perc",ylim=c(0,100))
# Outcome vs Victstat
victStat<-(chessDS$victory_status[which(chessDS$result=="y")])
outcomerVictstat<-chessDS$outcome[which(chessDS$result=="y")]
countvictStat <- table(victStat,outcomerVictstat,dnn=c("Victory Type","Outcome"))
sumtable.victStat <- addmargins(countvictStat,2)
col.margin.victStat <- prop.table(countvictStat, margin = 2)
round_col_victStat <- round(col.margin.victStat,4)*100
barplot(round_col_victStat,legend = rownames(countvictStat),col=c("grey","white","black"),xlab="Rated",ylab="Victory Type",ylim=c(0,100))
#Opening type
openingDF<-table(chessDS$opening_name)
openingDF<-sort(openingDF)
openingDF10<-openingDF[which(openingDF>200)]
sort(openingDF10)##
## Horwitz Defense
## 209
## Scandinavian Defense
## 223
## Queen's Pawn Game: Chigorin Variation
## 229
## Queen's Pawn Game: Mason Attack
## 232
## Scandinavian Defense: Mieses-Kotroc Variation
## 259
## French Defense: Knight Variation
## 271
## Scotch Game
## 271
## Sicilian Defense: Bowdler Attack
## 296
## Sicilian Defense
## 358
## Van't Kruijs Opening
## 368barplot(openingDF10)
#Opening Name vs Outcome
countOpeningOutcome <- table(openingsOutcome$outcome,openingsOutcome$opening_name,dnn=c("Opening Outcome","Opening Name"))
sumtable.OpeningOutcome <- addmargins(countOpeningOutcome,2)
col.margin.OpeningOutcome <- prop.table(countOpeningOutcome, margin = 2)
round_col_OpeningOutcome <- round(col.margin.OpeningOutcome,4)*100
barplot(round_col_OpeningOutcome,legend = rownames(countOpeningOutcome),horiz=F)
#Numerical Variable
ggplot(chessDS,aes(ratingDifference))+geom_bar(aes(fill=outcome),position="fill")+scale_y_continuous("Percent")
ggplot(chessDS,aes(turns))+geom_bar(aes(fill=outcome),position="fill")+scale_y_continuous("Percent")
ggplot(chessDS,aes(white_rating))+geom_bar(aes(fill=outcome),position="fill")+scale_y_continuous("Percent")
ggplot(chessDS,aes(black_rating))+geom_bar(aes(fill=outcome),position="fill")+scale_y_continuous("Percent")
par(mfrow=c(2,2))
outComeF <- as.factor(chessDS$outcome)
plot(outComeF, ratingDifference,xlab="Churn", ylab="Day Minutes",col="red")
plot(outComeF, chessDS$turns,xlab="Churn", ylab="Eve Minutes",col="blue")
plot(outComeF, chessDS$white_rating,xlab="Churn", ylab="Night Minutes",col="green")
plot(outComeF, chessDS$black_rating,xlab="Churn", ylab="Intl Minutes",col="yellow")
plot(chessDS$white_rating,chessDS$black_rating,col=ifelse(chessDS$outcome =="W","green",ifelse(chessDS$outcome =="L","red","blue")))
Models Slection
We here will try to study two models i.e. 1. The impact of variables created on getting a win i.e. given there is a outcome what factors will contribute towards the victory for player with white pieces 2. The impact of variables created on getting a result i.e. to get a win or loss vs. getting a draw ### Generating Dummy variable and preparing final datset for both the models
str(chessDS)## 'data.frame': 20058 obs. of 25 variables:
## $ id : chr "TZJHLljE" "l1NXvwaE" "mIICvQHh" "kWKvrqYL" ...
## $ rated : chr "False" "True" "True" "True" ...
## $ created_at : num 1.5e+12 1.5e+12 1.5e+12 1.5e+12 1.5e+12 ...
## $ last_move_at : num 1.5e+12 1.5e+12 1.5e+12 1.5e+12 1.5e+12 ...
## $ turns : int 13 16 61 61 95 5 33 9 66 119 ...
## $ victory_status : chr "outoftime" "resign" "mate" "mate" ...
## $ winner : chr "white" "black" "white" "white" ...
## $ increment_code : chr "15+2" "5+10" "5+10" "20+0" ...
## $ white_id : chr "bourgris" "a-00" "ischia" "daniamurashov" ...
## $ white_rating : int 1500 1322 1496 1439 1523 1250 1520 1413 1439 1381 ...
## $ black_id : chr "a-00" "skinnerua" "a-00" "adivanov2009" ...
## $ black_rating : int 1191 1261 1500 1454 1469 1002 1423 2108 1392 1209 ...
## $ moves : chr "d4 d5 c4 c6 cxd5 e6 dxe6 fxe6 Nf3 Bb4+ Nc3 Ba5 Bf4" "d4 Nc6 e4 e5 f4 f6 dxe5 fxe5 fxe5 Nxe5 Qd4 Nc6 Qe5+ Nxe5 c4 Bb4+" "e4 e5 d3 d6 Be3 c6 Be2 b5 Nd2 a5 a4 c5 axb5 Nc6 bxc6 Ra6 Nc4 a4 c3 a3 Nxa3 Rxa3 Rxa3 c4 dxc4 d5 cxd5 Qxd5 exd5 "| __truncated__ "d4 d5 Nf3 Bf5 Nc3 Nf6 Bf4 Ng4 e3 Nc6 Be2 Qd7 O-O O-O-O Nb5 Nb4 Rc1 Nxa2 Ra1 Nb4 Nxa7+ Kb8 Nb5 Bxc2 Bxc7+ Kc8 Qd"| __truncated__ ...
## $ opening_eco : chr "D10" "B00" "C20" "D02" ...
## $ opening_name : chr "Slav Defense: Exchange Variation" "Nimzowitsch Defense: Kennedy Variation" "King's Pawn Game: Leonardis Variation" "Queen's Pawn Game: Zukertort Variation" ...
## $ opening_ply : int 5 4 3 3 5 4 10 5 6 4 ...
## $ outcome : chr "W" "L" "W" "W" ...
## $ result : chr "y" "y" "y" "y" ...
## $ openings10 : chr "Others" "Others" "Others" "Others" ...
## $ duration : chr "15" "5" "5" "20" ...
## $ increment : chr "1" "1" "1" "0" ...
## $ ratingDifference: int 309 61 -4 -15 54 248 97 -695 47 172 ...
## $ length : chr "Short" "Short" "Long" "Long" ...
## $ titleW : chr "PRO" "PRO" "PRO" "PRO" ...
## $ titleB : chr "N" "PRO" "PRO" "PRO" ...chessDS$duration<-as.numeric( chessDS$duration)
#chessDS<-chess
chess<-chessDS
str(chess)## 'data.frame': 20058 obs. of 25 variables:
## $ id : chr "TZJHLljE" "l1NXvwaE" "mIICvQHh" "kWKvrqYL" ...
## $ rated : chr "False" "True" "True" "True" ...
## $ created_at : num 1.5e+12 1.5e+12 1.5e+12 1.5e+12 1.5e+12 ...
## $ last_move_at : num 1.5e+12 1.5e+12 1.5e+12 1.5e+12 1.5e+12 ...
## $ turns : int 13 16 61 61 95 5 33 9 66 119 ...
## $ victory_status : chr "outoftime" "resign" "mate" "mate" ...
## $ winner : chr "white" "black" "white" "white" ...
## $ increment_code : chr "15+2" "5+10" "5+10" "20+0" ...
## $ white_id : chr "bourgris" "a-00" "ischia" "daniamurashov" ...
## $ white_rating : int 1500 1322 1496 1439 1523 1250 1520 1413 1439 1381 ...
## $ black_id : chr "a-00" "skinnerua" "a-00" "adivanov2009" ...
## $ black_rating : int 1191 1261 1500 1454 1469 1002 1423 2108 1392 1209 ...
## $ moves : chr "d4 d5 c4 c6 cxd5 e6 dxe6 fxe6 Nf3 Bb4+ Nc3 Ba5 Bf4" "d4 Nc6 e4 e5 f4 f6 dxe5 fxe5 fxe5 Nxe5 Qd4 Nc6 Qe5+ Nxe5 c4 Bb4+" "e4 e5 d3 d6 Be3 c6 Be2 b5 Nd2 a5 a4 c5 axb5 Nc6 bxc6 Ra6 Nc4 a4 c3 a3 Nxa3 Rxa3 Rxa3 c4 dxc4 d5 cxd5 Qxd5 exd5 "| __truncated__ "d4 d5 Nf3 Bf5 Nc3 Nf6 Bf4 Ng4 e3 Nc6 Be2 Qd7 O-O O-O-O Nb5 Nb4 Rc1 Nxa2 Ra1 Nb4 Nxa7+ Kb8 Nb5 Bxc2 Bxc7+ Kc8 Qd"| __truncated__ ...
## $ opening_eco : chr "D10" "B00" "C20" "D02" ...
## $ opening_name : chr "Slav Defense: Exchange Variation" "Nimzowitsch Defense: Kennedy Variation" "King's Pawn Game: Leonardis Variation" "Queen's Pawn Game: Zukertort Variation" ...
## $ opening_ply : int 5 4 3 3 5 4 10 5 6 4 ...
## $ outcome : chr "W" "L" "W" "W" ...
## $ result : chr "y" "y" "y" "y" ...
## $ openings10 : chr "Others" "Others" "Others" "Others" ...
## $ duration : num 15 5 5 20 30 10 10 15 15 10 ...
## $ increment : chr "1" "1" "1" "0" ...
## $ ratingDifference: int 309 61 -4 -15 54 248 97 -695 47 172 ...
## $ length : chr "Short" "Short" "Long" "Long" ...
## $ titleW : chr "PRO" "PRO" "PRO" "PRO" ...
## $ titleB : chr "N" "PRO" "PRO" "PRO" ...Columns<-colnames(chessDS)
Columns## [1] "id" "rated" "created_at" "last_move_at"
## [5] "turns" "victory_status" "winner" "increment_code"
## [9] "white_id" "white_rating" "black_id" "black_rating"
## [13] "moves" "opening_eco" "opening_name" "opening_ply"
## [17] "outcome" "result" "openings10" "duration"
## [21] "increment" "ratingDifference" "length" "titleW"
## [25] "titleB"chessData<-chessDS[,-c(1,3,4,9,11)]
chessData<-chessData[,-c(3,4,5,6,7,8,9,11,10,18)]
Columns<-colnames(chessData)
Columns## [1] "rated" "turns" "outcome" "result"
## [5] "openings10" "duration" "increment" "ratingDifference"
## [9] "titleW" "titleB"chessData <- dummy_cols(chessData,select_columns = "rated",remove_first_dummy = TRUE)
chessData <- dummy_cols(chessData,select_columns = "result",remove_first_dummy = TRUE)
chessData <- dummy_cols(chessData,select_columns = "openings10",remove_first_dummy = TRUE)
chessData <- dummy_cols(chessData,select_columns = "titleW",remove_first_dummy = TRUE)
chessData <- dummy_cols(chessData,select_columns = "titleB",remove_first_dummy = TRUE)
chessData <- dummy_cols(chessData,select_columns = "increment",remove_first_dummy = TRUE)
#chessData <- dummy_cols(chessData,select_columns = "result,openings10,titleW,titleB,increment",remove_first_dummy = TRUE)
Columns<-colnames(chessData)
Columns## [1] "rated"
## [2] "turns"
## [3] "outcome"
## [4] "result"
## [5] "openings10"
## [6] "duration"
## [7] "increment"
## [8] "ratingDifference"
## [9] "titleW"
## [10] "titleB"
## [11] "rated_True"
## [12] "result_y"
## [13] "openings10_Horwitz Defense"
## [14] "openings10_Others"
## [15] "openings10_Queen's Pawn Game: Chigorin Variation"
## [16] "openings10_Queen's Pawn Game: Mason Attack"
## [17] "openings10_Scandinavian Defense"
## [18] "openings10_Scandinavian Defense: Mieses-Kotroc Variation"
## [19] "openings10_Scotch Game"
## [20] "openings10_Sicilian Defense"
## [21] "openings10_Sicilian Defense: Bowdler Attack"
## [22] "openings10_Van't Kruijs Opening"
## [23] "titleW_GM"
## [24] "titleW_N"
## [25] "titleW_PRO"
## [26] "titleB_GM"
## [27] "titleB_N"
## [28] "titleB_PRO"
## [29] "increment_1"chessData<-chessData[,-c(1,4,5,7,9,10)]
chessData_1<-chessData[which(chessData$result_y=="1"),]
which(chessData_1$result_y=="0")## integer(0)chessData_1 <- dummy_cols(chessData_1,select_columns = "outcome",remove_first_dummy = TRUE)
chessData_1<-chessData_1[,-c(2,6)]
Columns<-colnames(chessData_1)
Columns## [1] "turns"
## [2] "duration"
## [3] "ratingDifference"
## [4] "rated_True"
## [5] "openings10_Horwitz Defense"
## [6] "openings10_Others"
## [7] "openings10_Queen's Pawn Game: Chigorin Variation"
## [8] "openings10_Queen's Pawn Game: Mason Attack"
## [9] "openings10_Scandinavian Defense"
## [10] "openings10_Scandinavian Defense: Mieses-Kotroc Variation"
## [11] "openings10_Scotch Game"
## [12] "openings10_Sicilian Defense"
## [13] "openings10_Sicilian Defense: Bowdler Attack"
## [14] "openings10_Van't Kruijs Opening"
## [15] "titleW_GM"
## [16] "titleW_N"
## [17] "titleW_PRO"
## [18] "titleB_GM"
## [19] "titleB_N"
## [20] "titleB_PRO"
## [21] "increment_1"
## [22] "outcome_W"chessData_2<-chessData[,-c(2)]
Columns<-colnames(chessData_2)
Columns## [1] "turns"
## [2] "duration"
## [3] "ratingDifference"
## [4] "rated_True"
## [5] "result_y"
## [6] "openings10_Horwitz Defense"
## [7] "openings10_Others"
## [8] "openings10_Queen's Pawn Game: Chigorin Variation"
## [9] "openings10_Queen's Pawn Game: Mason Attack"
## [10] "openings10_Scandinavian Defense"
## [11] "openings10_Scandinavian Defense: Mieses-Kotroc Variation"
## [12] "openings10_Scotch Game"
## [13] "openings10_Sicilian Defense"
## [14] "openings10_Sicilian Defense: Bowdler Attack"
## [15] "openings10_Van't Kruijs Opening"
## [16] "titleW_GM"
## [17] "titleW_N"
## [18] "titleW_PRO"
## [19] "titleB_GM"
## [20] "titleB_N"
## [21] "titleB_PRO"
## [22] "increment_1"Since our target variables are binary, we will use logit regression here. We will use step-wise Regression for selection of variables. The model with these variable will be the optimal model.
###Model 1 - Defining Functional Form of model
reg_1<- lm(outcome_W~.,chessData_1)
summary(reg_1)##
## Call:
## lm(formula = outcome_W ~ ., data = chessData_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.18729 -0.46847 0.09536 0.44334 1.25314
##
## Coefficients:
## Estimate
## (Intercept) 5.552e-01
## turns -5.195e-04
## duration 1.184e-04
## ratingDifference 7.619e-04
## rated_True 4.919e-03
## `openings10_Horwitz Defense` -2.231e-02
## openings10_Others -1.359e-02
## `openings10_Queen's Pawn Game: Chigorin Variation` -2.334e-02
## `openings10_Queen's Pawn Game: Mason Attack` -3.214e-02
## `openings10_Scandinavian Defense` -9.983e-02
## `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 5.352e-02
## `openings10_Scotch Game` -2.484e-02
## `openings10_Sicilian Defense` -6.994e-02
## `openings10_Sicilian Defense: Bowdler Attack` -8.246e-02
## `openings10_Van't Kruijs Opening` -1.191e-01
## titleW_GM -2.347e-01
## titleW_N 2.275e-02
## titleW_PRO 3.455e-02
## titleB_GM 1.053e-01
## titleB_N -8.034e-03
## titleB_PRO -2.452e-02
## increment_1 -2.972e-03
## Std. Error t value
## (Intercept) 3.189e-02 17.410
## turns 1.055e-04 -4.922
## duration 2.042e-04 0.580
## ratingDifference 2.037e-05 37.392
## rated_True 8.680e-03 0.567
## `openings10_Horwitz Defense` 4.353e-02 -0.513
## openings10_Others 2.922e-02 -0.465
## `openings10_Queen's Pawn Game: Chigorin Variation` 4.259e-02 -0.548
## `openings10_Queen's Pawn Game: Mason Attack` 4.270e-02 -0.753
## `openings10_Scandinavian Defense` 4.312e-02 -2.315
## `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 4.113e-02 1.301
## `openings10_Scotch Game` 4.084e-02 -0.608
## `openings10_Sicilian Defense` 3.830e-02 -1.826
## `openings10_Sicilian Defense: Bowdler Attack` 3.999e-02 -2.062
## `openings10_Van't Kruijs Opening` 3.828e-02 -3.112
## titleW_GM 4.669e-02 -5.026
## titleW_N 2.066e-02 1.101
## titleW_PRO 1.179e-02 2.931
## titleB_GM 6.025e-02 1.748
## titleB_N 2.055e-02 -0.391
## titleB_PRO 1.188e-02 -2.064
## increment_1 6.799e-03 -0.437
## Pr(>|t|)
## (Intercept) < 2e-16 ***
## turns 8.63e-07 ***
## duration 0.56206
## ratingDifference < 2e-16 ***
## rated_True 0.57096
## `openings10_Horwitz Defense` 0.60830
## openings10_Others 0.64186
## `openings10_Queen's Pawn Game: Chigorin Variation` 0.58372
## `openings10_Queen's Pawn Game: Mason Attack` 0.45158
## `openings10_Scandinavian Defense` 0.02063 *
## `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 0.19316
## `openings10_Scotch Game` 0.54300
## `openings10_Sicilian Defense` 0.06782 .
## `openings10_Sicilian Defense: Bowdler Attack` 0.03924 *
## `openings10_Van't Kruijs Opening` 0.00186 **
## titleW_GM 5.04e-07 ***
## titleW_N 0.27070
## titleW_PRO 0.00339 **
## titleB_GM 0.08039 .
## titleB_N 0.69585
## titleB_PRO 0.03905 *
## increment_1 0.66206
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4635 on 19086 degrees of freedom
## Multiple R-squared: 0.1397, Adjusted R-squared: 0.1387
## F-statistic: 147.5 on 21 and 19086 DF, p-value: < 2.2e-16#step-wise regression
reg_1_i <- lm(outcome_W~1,data=chessData_1)
summary(reg_1_i)##
## Call:
## lm(formula = outcome_W ~ 1, data = chessData_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.5234 -0.5234 0.4766 0.4766 0.4766
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.523393 0.003613 144.9 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4995 on 19107 degrees of freedomreg_1_f<- lm(outcome_W~.,chessData_1)
summary(reg_1_f)##
## Call:
## lm(formula = outcome_W ~ ., data = chessData_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.18729 -0.46847 0.09536 0.44334 1.25314
##
## Coefficients:
## Estimate
## (Intercept) 5.552e-01
## turns -5.195e-04
## duration 1.184e-04
## ratingDifference 7.619e-04
## rated_True 4.919e-03
## `openings10_Horwitz Defense` -2.231e-02
## openings10_Others -1.359e-02
## `openings10_Queen's Pawn Game: Chigorin Variation` -2.334e-02
## `openings10_Queen's Pawn Game: Mason Attack` -3.214e-02
## `openings10_Scandinavian Defense` -9.983e-02
## `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 5.352e-02
## `openings10_Scotch Game` -2.484e-02
## `openings10_Sicilian Defense` -6.994e-02
## `openings10_Sicilian Defense: Bowdler Attack` -8.246e-02
## `openings10_Van't Kruijs Opening` -1.191e-01
## titleW_GM -2.347e-01
## titleW_N 2.275e-02
## titleW_PRO 3.455e-02
## titleB_GM 1.053e-01
## titleB_N -8.034e-03
## titleB_PRO -2.452e-02
## increment_1 -2.972e-03
## Std. Error t value
## (Intercept) 3.189e-02 17.410
## turns 1.055e-04 -4.922
## duration 2.042e-04 0.580
## ratingDifference 2.037e-05 37.392
## rated_True 8.680e-03 0.567
## `openings10_Horwitz Defense` 4.353e-02 -0.513
## openings10_Others 2.922e-02 -0.465
## `openings10_Queen's Pawn Game: Chigorin Variation` 4.259e-02 -0.548
## `openings10_Queen's Pawn Game: Mason Attack` 4.270e-02 -0.753
## `openings10_Scandinavian Defense` 4.312e-02 -2.315
## `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 4.113e-02 1.301
## `openings10_Scotch Game` 4.084e-02 -0.608
## `openings10_Sicilian Defense` 3.830e-02 -1.826
## `openings10_Sicilian Defense: Bowdler Attack` 3.999e-02 -2.062
## `openings10_Van't Kruijs Opening` 3.828e-02 -3.112
## titleW_GM 4.669e-02 -5.026
## titleW_N 2.066e-02 1.101
## titleW_PRO 1.179e-02 2.931
## titleB_GM 6.025e-02 1.748
## titleB_N 2.055e-02 -0.391
## titleB_PRO 1.188e-02 -2.064
## increment_1 6.799e-03 -0.437
## Pr(>|t|)
## (Intercept) < 2e-16 ***
## turns 8.63e-07 ***
## duration 0.56206
## ratingDifference < 2e-16 ***
## rated_True 0.57096
## `openings10_Horwitz Defense` 0.60830
## openings10_Others 0.64186
## `openings10_Queen's Pawn Game: Chigorin Variation` 0.58372
## `openings10_Queen's Pawn Game: Mason Attack` 0.45158
## `openings10_Scandinavian Defense` 0.02063 *
## `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 0.19316
## `openings10_Scotch Game` 0.54300
## `openings10_Sicilian Defense` 0.06782 .
## `openings10_Sicilian Defense: Bowdler Attack` 0.03924 *
## `openings10_Van't Kruijs Opening` 0.00186 **
## titleW_GM 5.04e-07 ***
## titleW_N 0.27070
## titleW_PRO 0.00339 **
## titleB_GM 0.08039 .
## titleB_N 0.69585
## titleB_PRO 0.03905 *
## increment_1 0.66206
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4635 on 19086 degrees of freedom
## Multiple R-squared: 0.1397, Adjusted R-squared: 0.1387
## F-statistic: 147.5 on 21 and 19086 DF, p-value: < 2.2e-16x <- step(reg_1_i,scope=list(lower=reg_1_i,upper=reg_1_f),direction = "forward",test="F",trace=TRUE)## Start: AIC=-26529.19
## outcome_W ~ 1
##
## Df Sum of Sq
## + ratingDifference 1 642.78
## + titleB_N 1 60.30
## + titleW_N 1 46.30
## + `openings10_Van't Kruijs Opening` 1 9.82
## + turns 1 9.81
## + titleW_GM 1 9.22
## + titleB_GM 1 8.16
## + openings10_Others 1 4.18
## + titleB_PRO 1 4.06
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 1 4.00
## + `openings10_Sicilian Defense: Bowdler Attack` 1 3.04
## + `openings10_Sicilian Defense` 1 2.77
## + `openings10_Scandinavian Defense` 1 2.19
## + titleW_PRO 1 2.12
## <none>
## + `openings10_Scotch Game` 1 0.31
## + rated_True 1 0.25
## + duration 1 0.17
## + increment_1 1 0.10
## + `openings10_Queen's Pawn Game: Chigorin Variation` 1 0.06
## + `openings10_Horwitz Defense` 1 0.05
## + `openings10_Queen's Pawn Game: Mason Attack` 1 0.01
## RSS AIC
## + ratingDifference 4123.8 -29295
## + titleB_N 4706.2 -26770
## + titleW_N 4720.2 -26714
## + `openings10_Van't Kruijs Opening` 4756.7 -26567
## + turns 4756.7 -26567
## + titleW_GM 4757.3 -26564
## + titleB_GM 4758.4 -26560
## + openings10_Others 4762.4 -26544
## + titleB_PRO 4762.5 -26544
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 4762.5 -26543
## + `openings10_Sicilian Defense: Bowdler Attack` 4763.5 -26539
## + `openings10_Sicilian Defense` 4763.8 -26538
## + `openings10_Scandinavian Defense` 4764.4 -26536
## + titleW_PRO 4764.4 -26536
## <none> 4766.5 -26529
## + `openings10_Scotch Game` 4766.2 -26528
## + rated_True 4766.3 -26528
## + duration 4766.4 -26528
## + increment_1 4766.4 -26528
## + `openings10_Queen's Pawn Game: Chigorin Variation` 4766.5 -26527
## + `openings10_Horwitz Defense` 4766.5 -26527
## + `openings10_Queen's Pawn Game: Mason Attack` 4766.5 -26527
## F value
## + ratingDifference 2978.0823
## + titleB_N 244.7917
## + titleW_N 187.3892
## + `openings10_Van't Kruijs Opening` 39.4234
## + turns 39.3886
## + titleW_GM 37.0455
## + titleB_GM 32.7474
## + openings10_Others 16.7543
## + titleB_PRO 16.2833
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 16.0274
## + `openings10_Sicilian Defense: Bowdler Attack` 12.1991
## + `openings10_Sicilian Defense` 11.0936
## + `openings10_Scandinavian Defense` 8.7869
## + titleW_PRO 8.5056
## <none>
## + `openings10_Scotch Game` 1.2430
## + rated_True 0.9924
## + duration 0.6690
## + increment_1 0.3957
## + `openings10_Queen's Pawn Game: Chigorin Variation` 0.2471
## + `openings10_Horwitz Defense` 0.2069
## + `openings10_Queen's Pawn Game: Mason Attack` 0.0351
## Pr(>F)
## + ratingDifference < 2.2e-16 ***
## + titleB_N < 2.2e-16 ***
## + titleW_N < 2.2e-16 ***
## + `openings10_Van't Kruijs Opening` 3.485e-10 ***
## + turns 3.548e-10 ***
## + titleW_GM 1.176e-09 ***
## + titleB_GM 1.065e-08 ***
## + openings10_Others 4.272e-05 ***
## + titleB_PRO 5.475e-05 ***
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 6.267e-05 ***
## + `openings10_Sicilian Defense: Bowdler Attack` 0.0004792 ***
## + `openings10_Sicilian Defense` 0.0008679 ***
## + `openings10_Scandinavian Defense` 0.0030378 **
## + titleW_PRO 0.0035446 **
## <none>
## + `openings10_Scotch Game` 0.2649029
## + rated_True 0.3191652
## + duration 0.4133941
## + increment_1 0.5293424
## + `openings10_Queen's Pawn Game: Chigorin Variation` 0.6191002
## + `openings10_Horwitz Defense` 0.6491968
## + `openings10_Queen's Pawn Game: Mason Attack` 0.8513882
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=-29295.07
## outcome_W ~ ratingDifference
##
## Df Sum of Sq
## + titleW_GM 1 5.5598
## + turns 1 4.9987
## + `openings10_Van't Kruijs Opening` 1 3.2880
## + openings10_Others 1 2.0189
## + titleW_PRO 1 1.8240
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 1 1.2680
## + `openings10_Sicilian Defense: Bowdler Attack` 1 1.2177
## + `openings10_Scandinavian Defense` 1 1.0958
## + `openings10_Sicilian Defense` 1 0.8932
## + titleB_N 1 0.8801
## + titleB_GM 1 0.4428
## <none>
## + titleB_PRO 1 0.1615
## + titleW_N 1 0.1487
## + `openings10_Queen's Pawn Game: Mason Attack` 1 0.0567
## + rated_True 1 0.0517
## + increment_1 1 0.0448
## + duration 1 0.0151
## + `openings10_Scotch Game` 1 0.0060
## + `openings10_Queen's Pawn Game: Chigorin Variation` 1 0.0053
## + `openings10_Horwitz Defense` 1 0.0011
## RSS AIC
## + titleW_GM 4118.2 -29319
## + turns 4118.8 -29316
## + `openings10_Van't Kruijs Opening` 4120.5 -29308
## + openings10_Others 4121.7 -29302
## + titleW_PRO 4121.9 -29302
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 4122.5 -29299
## + `openings10_Sicilian Defense: Bowdler Attack` 4122.5 -29299
## + `openings10_Scandinavian Defense` 4122.7 -29298
## + `openings10_Sicilian Defense` 4122.9 -29297
## + titleB_N 4122.9 -29297
## + titleB_GM 4123.3 -29295
## <none> 4123.8 -29295
## + titleB_PRO 4123.6 -29294
## + titleW_N 4123.6 -29294
## + `openings10_Queen's Pawn Game: Mason Attack` 4123.7 -29293
## + rated_True 4123.7 -29293
## + increment_1 4123.7 -29293
## + duration 4123.8 -29293
## + `openings10_Scotch Game` 4123.8 -29293
## + `openings10_Queen's Pawn Game: Chigorin Variation` 4123.8 -29293
## + `openings10_Horwitz Defense` 4123.8 -29293
## F value Pr(>F)
## + titleW_GM 25.7929 3.837e-07
## + turns 23.1867 1.481e-06
## + `openings10_Van't Kruijs Opening` 15.2452 9.474e-05
## + openings10_Others 9.3581 0.002223
## + titleW_PRO 8.4540 0.003647
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 5.8764 0.015355
## + `openings10_Sicilian Defense: Bowdler Attack` 5.6432 0.017533
## + `openings10_Scandinavian Defense` 5.0779 0.024244
## + `openings10_Sicilian Defense` 4.1391 0.041916
## + titleB_N 4.0785 0.043447
## + titleB_GM 2.0516 0.152060
## <none>
## + titleB_PRO 0.7484 0.386994
## + titleW_N 0.6887 0.406604
## + `openings10_Queen's Pawn Game: Mason Attack` 0.2627 0.608288
## + rated_True 0.2395 0.624573
## + increment_1 0.2074 0.648804
## + duration 0.0699 0.791492
## + `openings10_Scotch Game` 0.0276 0.868051
## + `openings10_Queen's Pawn Game: Chigorin Variation` 0.0247 0.875225
## + `openings10_Horwitz Defense` 0.0052 0.942356
##
## + titleW_GM ***
## + turns ***
## + `openings10_Van't Kruijs Opening` ***
## + openings10_Others **
## + titleW_PRO **
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` *
## + `openings10_Sicilian Defense: Bowdler Attack` *
## + `openings10_Scandinavian Defense` *
## + `openings10_Sicilian Defense` *
## + titleB_N *
## + titleB_GM
## <none>
## + titleB_PRO
## + titleW_N
## + `openings10_Queen's Pawn Game: Mason Attack`
## + rated_True
## + increment_1
## + duration
## + `openings10_Scotch Game`
## + `openings10_Queen's Pawn Game: Chigorin Variation`
## + `openings10_Horwitz Defense`
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=-29318.85
## outcome_W ~ ratingDifference + titleW_GM
##
## Df Sum of Sq
## + turns 1 5.2044
## + `openings10_Van't Kruijs Opening` 1 3.2822
## + openings10_Others 1 2.0920
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 1 1.3144
## + titleW_PRO 1 1.3082
## + `openings10_Sicilian Defense: Bowdler Attack` 1 1.2387
## + `openings10_Scandinavian Defense` 1 1.1181
## + `openings10_Sicilian Defense` 1 0.8885
## + titleB_N 1 0.6227
## + titleB_GM 1 0.6192
## <none>
## + titleB_PRO 1 0.3047
## + titleW_N 1 0.0949
## + `openings10_Queen's Pawn Game: Mason Attack` 1 0.0699
## + duration 1 0.0209
## + increment_1 1 0.0087
## + `openings10_Queen's Pawn Game: Chigorin Variation` 1 0.0079
## + `openings10_Scotch Game` 1 0.0068
## + `openings10_Horwitz Defense` 1 0.0033
## + rated_True 1 0.0002
## RSS AIC
## + turns 4113.0 -29341
## + `openings10_Van't Kruijs Opening` 4114.9 -29332
## + openings10_Others 4116.1 -29327
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 4116.9 -29323
## + titleW_PRO 4116.9 -29323
## + `openings10_Sicilian Defense: Bowdler Attack` 4117.0 -29323
## + `openings10_Scandinavian Defense` 4117.1 -29322
## + `openings10_Sicilian Defense` 4117.3 -29321
## + titleB_N 4117.6 -29320
## + titleB_GM 4117.6 -29320
## <none> 4118.2 -29319
## + titleB_PRO 4117.9 -29318
## + titleW_N 4118.1 -29317
## + `openings10_Queen's Pawn Game: Mason Attack` 4118.1 -29317
## + duration 4118.2 -29317
## + increment_1 4118.2 -29317
## + `openings10_Queen's Pawn Game: Chigorin Variation` 4118.2 -29317
## + `openings10_Scotch Game` 4118.2 -29317
## + `openings10_Horwitz Defense` 4118.2 -29317
## + rated_True 4118.2 -29317
## F value Pr(>F)
## + turns 24.1735 8.877e-07
## + `openings10_Van't Kruijs Opening` 15.2382 9.509e-05
## + openings10_Others 9.7095 0.001836
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 6.0993 0.013533
## + titleW_PRO 6.0704 0.013755
## + `openings10_Sicilian Defense: Bowdler Attack` 5.7479 0.016518
## + `openings10_Scandinavian Defense` 5.1883 0.022750
## + `openings10_Sicilian Defense` 4.1226 0.042327
## + titleB_N 2.8891 0.089198
## + titleB_GM 2.8730 0.090090
## <none>
## + titleB_PRO 1.4138 0.234446
## + titleW_N 0.4404 0.506945
## + `openings10_Queen's Pawn Game: Mason Attack` 0.3242 0.569094
## + duration 0.0969 0.755608
## + increment_1 0.0403 0.840848
## + `openings10_Queen's Pawn Game: Chigorin Variation` 0.0368 0.847797
## + `openings10_Scotch Game` 0.0313 0.859496
## + `openings10_Horwitz Defense` 0.0155 0.901067
## + rated_True 0.0012 0.972928
##
## + turns ***
## + `openings10_Van't Kruijs Opening` ***
## + openings10_Others **
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` *
## + titleW_PRO *
## + `openings10_Sicilian Defense: Bowdler Attack` *
## + `openings10_Scandinavian Defense` *
## + `openings10_Sicilian Defense` *
## + titleB_N .
## + titleB_GM .
## <none>
## + titleB_PRO
## + titleW_N
## + `openings10_Queen's Pawn Game: Mason Attack`
## + duration
## + increment_1
## + `openings10_Queen's Pawn Game: Chigorin Variation`
## + `openings10_Scotch Game`
## + `openings10_Horwitz Defense`
## + rated_True
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=-29341.01
## outcome_W ~ ratingDifference + titleW_GM + turns
##
## Df Sum of Sq
## + `openings10_Van't Kruijs Opening` 1 3.5092
## + openings10_Others 1 2.1851
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 1 1.3471
## + `openings10_Scandinavian Defense` 1 1.3264
## + `openings10_Sicilian Defense: Bowdler Attack` 1 1.1467
## + titleW_PRO 1 1.1414
## + `openings10_Sicilian Defense` 1 0.9069
## + titleB_GM 1 0.6114
## <none>
## + titleB_PRO 1 0.4070
## + titleB_N 1 0.3399
## + titleW_N 1 0.2819
## + `openings10_Queen's Pawn Game: Mason Attack` 1 0.0481
## + increment_1 1 0.0388
## + rated_True 1 0.0339
## + `openings10_Scotch Game` 1 0.0114
## + `openings10_Queen's Pawn Game: Chigorin Variation` 1 0.0070
## + `openings10_Horwitz Defense` 1 0.0040
## + duration 1 0.0001
## RSS AIC
## + `openings10_Van't Kruijs Opening` 4109.5 -29355
## + openings10_Others 4110.8 -29349
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 4111.7 -29345
## + `openings10_Scandinavian Defense` 4111.7 -29345
## + `openings10_Sicilian Defense: Bowdler Attack` 4111.9 -29344
## + titleW_PRO 4111.9 -29344
## + `openings10_Sicilian Defense` 4112.1 -29343
## + titleB_GM 4112.4 -29342
## <none> 4113.0 -29341
## + titleB_PRO 4112.6 -29341
## + titleB_N 4112.7 -29341
## + titleW_N 4112.7 -29340
## + `openings10_Queen's Pawn Game: Mason Attack` 4113.0 -29339
## + increment_1 4113.0 -29339
## + rated_True 4113.0 -29339
## + `openings10_Scotch Game` 4113.0 -29339
## + `openings10_Queen's Pawn Game: Chigorin Variation` 4113.0 -29339
## + `openings10_Horwitz Defense` 4113.0 -29339
## + duration 4113.0 -29339
## F value Pr(>F)
## + `openings10_Van't Kruijs Opening` 16.3127 5.391e-05
## + openings10_Others 10.1540 0.001442
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 6.2589 0.012365
## + `openings10_Scandinavian Defense` 6.1626 0.013056
## + `openings10_Sicilian Defense: Bowdler Attack` 5.3274 0.021003
## + titleW_PRO 5.3030 0.021300
## + `openings10_Sicilian Defense` 4.2129 0.040131
## + titleB_GM 2.8401 0.091952
## <none>
## + titleB_PRO 1.8904 0.169168
## + titleB_N 1.5790 0.208926
## + titleW_N 1.3094 0.252513
## + `openings10_Queen's Pawn Game: Mason Attack` 0.2232 0.636599
## + increment_1 0.1804 0.671008
## + rated_True 0.1574 0.691588
## + `openings10_Scotch Game` 0.0527 0.818387
## + `openings10_Queen's Pawn Game: Chigorin Variation` 0.0325 0.856854
## + `openings10_Horwitz Defense` 0.0188 0.891079
## + duration 0.0006 0.980807
##
## + `openings10_Van't Kruijs Opening` ***
## + openings10_Others **
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` *
## + `openings10_Scandinavian Defense` *
## + `openings10_Sicilian Defense: Bowdler Attack` *
## + titleW_PRO *
## + `openings10_Sicilian Defense` *
## + titleB_GM .
## <none>
## + titleB_PRO
## + titleB_N
## + titleW_N
## + `openings10_Queen's Pawn Game: Mason Attack`
## + increment_1
## + rated_True
## + `openings10_Scotch Game`
## + `openings10_Queen's Pawn Game: Chigorin Variation`
## + `openings10_Horwitz Defense`
## + duration
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=-29355.32
## outcome_W ~ ratingDifference + titleW_GM + turns + `openings10_Van't Kruijs Opening`
##
## Df Sum of Sq
## + `openings10_Scandinavian Defense` 1 1.39927
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 1 1.28743
## + `openings10_Sicilian Defense: Bowdler Attack` 1 1.21902
## + titleW_PRO 1 1.14529
## + `openings10_Sicilian Defense` 1 0.98060
## + openings10_Others 1 0.78854
## + titleB_GM 1 0.56745
## + titleB_N 1 0.47449
## <none>
## + titleB_PRO 1 0.35310
## + titleW_N 1 0.14855
## + `openings10_Queen's Pawn Game: Mason Attack` 1 0.05986
## + duration 1 0.04814
## + rated_True 1 0.04231
## + increment_1 1 0.03035
## + `openings10_Scotch Game` 1 0.01818
## + `openings10_Queen's Pawn Game: Chigorin Variation` 1 0.01256
## + `openings10_Horwitz Defense` 1 0.00799
## RSS AIC
## + `openings10_Scandinavian Defense` 4108.1 -29360
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 4108.2 -29359
## + `openings10_Sicilian Defense: Bowdler Attack` 4108.3 -29359
## + titleW_PRO 4108.3 -29359
## + `openings10_Sicilian Defense` 4108.5 -29358
## + openings10_Others 4108.7 -29357
## + titleB_GM 4108.9 -29356
## + titleB_N 4109.0 -29356
## <none> 4109.5 -29355
## + titleB_PRO 4109.1 -29355
## + titleW_N 4109.3 -29354
## + `openings10_Queen's Pawn Game: Mason Attack` 4109.4 -29354
## + duration 4109.4 -29354
## + rated_True 4109.4 -29354
## + increment_1 4109.5 -29354
## + `openings10_Scotch Game` 4109.5 -29353
## + `openings10_Queen's Pawn Game: Chigorin Variation` 4109.5 -29353
## + `openings10_Horwitz Defense` 4109.5 -29353
## F value Pr(>F)
## + `openings10_Scandinavian Defense` 6.5064 0.01076 *
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 5.9862 0.01443 *
## + `openings10_Sicilian Defense: Bowdler Attack` 5.6680 0.01729 *
## + titleW_PRO 5.3251 0.02103 *
## + `openings10_Sicilian Defense` 4.5592 0.03276 *
## + openings10_Others 3.6660 0.05555 .
## + titleB_GM 2.6380 0.10435
## + titleB_N 2.2058 0.13751
## <none>
## + titleB_PRO 1.6414 0.20014
## + titleW_N 0.6905 0.40600
## + `openings10_Queen's Pawn Game: Mason Attack` 0.2782 0.59787
## + duration 0.2238 0.63618
## + rated_True 0.1967 0.65742
## + increment_1 0.1411 0.70722
## + `openings10_Scotch Game` 0.0845 0.77126
## + `openings10_Queen's Pawn Game: Chigorin Variation` 0.0584 0.80907
## + `openings10_Horwitz Defense` 0.0371 0.84722
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=-29359.83
## outcome_W ~ ratingDifference + titleW_GM + turns + `openings10_Van't Kruijs Opening` +
## `openings10_Scandinavian Defense`
##
## Df Sum of Sq
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 1 1.25647
## + `openings10_Sicilian Defense: Bowdler Attack` 1 1.25350
## + titleW_PRO 1 1.13001
## + `openings10_Sicilian Defense` 1 1.01718
## + titleB_N 1 0.62835
## + titleB_GM 1 0.55219
## <none>
## + titleB_PRO 1 0.37798
## + openings10_Others 1 0.32414
## + titleW_N 1 0.09542
## + `openings10_Queen's Pawn Game: Mason Attack` 1 0.06621
## + duration 1 0.06269
## + rated_True 1 0.04622
## + increment_1 1 0.02856
## + `openings10_Scotch Game` 1 0.02249
## + `openings10_Queen's Pawn Game: Chigorin Variation` 1 0.01589
## + `openings10_Horwitz Defense` 1 0.01054
## RSS AIC
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 4106.8 -29364
## + `openings10_Sicilian Defense: Bowdler Attack` 4106.8 -29364
## + titleW_PRO 4107.0 -29363
## + `openings10_Sicilian Defense` 4107.1 -29363
## + titleB_N 4107.5 -29361
## + titleB_GM 4107.5 -29360
## <none> 4108.1 -29360
## + titleB_PRO 4107.7 -29360
## + openings10_Others 4107.8 -29359
## + titleW_N 4108.0 -29358
## + `openings10_Queen's Pawn Game: Mason Attack` 4108.0 -29358
## + duration 4108.0 -29358
## + rated_True 4108.0 -29358
## + increment_1 4108.1 -29358
## + `openings10_Scotch Game` 4108.1 -29358
## + `openings10_Queen's Pawn Game: Chigorin Variation` 4108.1 -29358
## + `openings10_Horwitz Defense` 4108.1 -29358
## F value Pr(>F)
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 5.8439 0.01564 *
## + `openings10_Sicilian Defense: Bowdler Attack` 5.8300 0.01576 *
## + titleW_PRO 5.2555 0.02189 *
## + `openings10_Sicilian Defense` 4.7306 0.02964 *
## + titleB_N 2.9220 0.08739 .
## + titleB_GM 2.5678 0.10907
## <none>
## + titleB_PRO 1.7576 0.18494
## + openings10_Others 1.5072 0.21958
## + titleW_N 0.4437 0.50536
## + `openings10_Queen's Pawn Game: Mason Attack` 0.3079 0.57900
## + duration 0.2915 0.58929
## + rated_True 0.2149 0.64295
## + increment_1 0.1328 0.71556
## + `openings10_Scotch Game` 0.1046 0.74643
## + `openings10_Queen's Pawn Game: Chigorin Variation` 0.0739 0.78579
## + `openings10_Horwitz Defense` 0.0490 0.82478
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=-29363.67
## outcome_W ~ ratingDifference + titleW_GM + turns + `openings10_Van't Kruijs Opening` +
## `openings10_Scandinavian Defense` + `openings10_Scandinavian Defense: Mieses-Kotroc Variation`
##
## Df Sum of Sq RSS AIC
## + `openings10_Sicilian Defense: Bowdler Attack` 1 1.21925 4105.6 -29367
## + titleW_PRO 1 1.08057 4105.8 -29367
## + openings10_Others 1 1.00546 4105.8 -29366
## + `openings10_Sicilian Defense` 1 0.98343 4105.9 -29366
## + titleB_N 1 0.61515 4106.2 -29365
## + titleB_GM 1 0.55653 4106.3 -29364
## <none> 4106.8 -29364
## + titleB_PRO 1 0.40320 4106.4 -29364
## + titleW_N 1 0.10167 4106.7 -29362
## + duration 1 0.06111 4106.8 -29362
## + `openings10_Queen's Pawn Game: Mason Attack` 1 0.05878 4106.8 -29362
## + rated_True 1 0.04680 4106.8 -29362
## + increment_1 1 0.02649 4106.8 -29362
## + `openings10_Scotch Game` 1 0.01780 4106.8 -29362
## + `openings10_Queen's Pawn Game: Chigorin Variation` 1 0.01253 4106.8 -29362
## + `openings10_Horwitz Defense` 1 0.00784 4106.8 -29362
## F value Pr(>F)
## + `openings10_Sicilian Defense: Bowdler Attack` 5.6722 0.01725 *
## + titleW_PRO 5.0268 0.02497 *
## + openings10_Others 4.6773 0.03058 *
## + `openings10_Sicilian Defense` 4.5748 0.03246 *
## + titleB_N 2.8614 0.09075 .
## + titleB_GM 2.5887 0.10765
## <none>
## + titleB_PRO 1.8754 0.17088
## + titleW_N 0.4729 0.49168
## + duration 0.2842 0.59395
## + `openings10_Queen's Pawn Game: Mason Attack` 0.2734 0.60108
## + rated_True 0.2176 0.64084
## + increment_1 0.1232 0.72557
## + `openings10_Scotch Game` 0.0828 0.77355
## + `openings10_Queen's Pawn Game: Chigorin Variation` 0.0583 0.80928
## + `openings10_Horwitz Defense` 0.0365 0.84858
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=-29367.35
## outcome_W ~ ratingDifference + titleW_GM + turns + `openings10_Van't Kruijs Opening` +
## `openings10_Scandinavian Defense` + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` +
## `openings10_Sicilian Defense: Bowdler Attack`
##
## Df Sum of Sq RSS AIC
## + titleW_PRO 1 1.15547 4104.5 -29371
## + `openings10_Sicilian Defense` 1 1.02359 4104.6 -29370
## + titleB_N 1 0.60800 4105.0 -29368
## + titleB_GM 1 0.53894 4105.1 -29368
## <none> 4105.6 -29367
## + openings10_Others 1 0.39646 4105.2 -29367
## + titleB_PRO 1 0.37423 4105.2 -29367
## + titleW_N 1 0.11407 4105.5 -29366
## + `openings10_Queen's Pawn Game: Mason Attack` 1 0.06645 4105.6 -29366
## + duration 1 0.06507 4105.6 -29366
## + rated_True 1 0.04957 4105.6 -29366
## + increment_1 1 0.02861 4105.6 -29366
## + `openings10_Scotch Game` 1 0.02225 4105.6 -29366
## + `openings10_Queen's Pawn Game: Chigorin Variation` 1 0.01626 4105.6 -29365
## + `openings10_Horwitz Defense` 1 0.01060 4105.6 -29365
## F value Pr(>F)
## + titleW_PRO 5.3766 0.02042 *
## + `openings10_Sicilian Defense` 4.7629 0.02909 *
## + titleB_N 2.8288 0.09261 .
## + titleB_GM 2.5075 0.11333
## <none>
## + openings10_Others 1.8445 0.17444
## + titleB_PRO 1.7410 0.18702
## + titleW_N 0.5306 0.46634
## + `openings10_Queen's Pawn Game: Mason Attack` 0.3091 0.57822
## + duration 0.3027 0.58221
## + rated_True 0.2306 0.63108
## + increment_1 0.1331 0.71524
## + `openings10_Scotch Game` 0.1035 0.74767
## + `openings10_Queen's Pawn Game: Chigorin Variation` 0.0756 0.78329
## + `openings10_Horwitz Defense` 0.0493 0.82427
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=-29370.73
## outcome_W ~ ratingDifference + titleW_GM + turns + `openings10_Van't Kruijs Opening` +
## `openings10_Scandinavian Defense` + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` +
## `openings10_Sicilian Defense: Bowdler Attack` + titleW_PRO
##
## Df Sum of Sq RSS AIC
## + titleB_PRO 1 1.38376 4103.1 -29375
## + `openings10_Sicilian Defense` 1 1.06799 4103.4 -29374
## + titleB_N 1 0.67682 4103.8 -29372
## + titleB_GM 1 0.63977 4103.8 -29372
## + openings10_Others 1 0.45726 4104.0 -29371
## <none> 4104.5 -29371
## + duration 1 0.07164 4104.4 -29369
## + `openings10_Queen's Pawn Game: Mason Attack` 1 0.07027 4104.4 -29369
## + rated_True 1 0.04847 4104.4 -29369
## + titleW_N 1 0.04537 4104.4 -29369
## + `openings10_Scotch Game` 1 0.03378 4104.4 -29369
## + increment_1 1 0.03290 4104.4 -29369
## + `openings10_Queen's Pawn Game: Chigorin Variation` 1 0.01736 4104.4 -29369
## + `openings10_Horwitz Defense` 1 0.01026 4104.5 -29369
## F value Pr(>F)
## + titleB_PRO 6.4408 0.01116 *
## + `openings10_Sicilian Defense` 4.9706 0.02579 *
## + titleB_N 3.1498 0.07595 .
## + titleB_GM 2.9773 0.08446 .
## + openings10_Others 2.1279 0.14466
## <none>
## + duration 0.3333 0.56370
## + `openings10_Queen's Pawn Game: Mason Attack` 0.3270 0.56745
## + rated_True 0.2255 0.63487
## + titleW_N 0.2111 0.64592
## + `openings10_Scotch Game` 0.1572 0.69176
## + increment_1 0.1531 0.69560
## + `openings10_Queen's Pawn Game: Chigorin Variation` 0.0808 0.77625
## + `openings10_Horwitz Defense` 0.0477 0.82704
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=-29375.17
## outcome_W ~ ratingDifference + titleW_GM + turns + `openings10_Van't Kruijs Opening` +
## `openings10_Scandinavian Defense` + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` +
## `openings10_Sicilian Defense: Bowdler Attack` + titleW_PRO +
## titleB_PRO
##
## Df Sum of Sq RSS AIC
## + `openings10_Sicilian Defense` 1 1.05588 4102.0 -29378
## + titleB_GM 1 0.55515 4102.5 -29376
## + openings10_Others 1 0.43109 4102.6 -29375
## <none> 4103.1 -29375
## + titleW_N 1 0.21214 4102.9 -29374
## + duration 1 0.06632 4103.0 -29374
## + `openings10_Queen's Pawn Game: Mason Attack` 1 0.06492 4103.0 -29374
## + titleB_N 1 0.04753 4103.0 -29373
## + rated_True 1 0.03990 4103.0 -29373
## + increment_1 1 0.03191 4103.0 -29373
## + `openings10_Scotch Game` 1 0.02369 4103.1 -29373
## + `openings10_Queen's Pawn Game: Chigorin Variation` 1 0.01371 4103.1 -29373
## + `openings10_Horwitz Defense` 1 0.01041 4103.1 -29373
## F value Pr(>F)
## + `openings10_Sicilian Defense` 4.9157 0.02663 *
## + titleB_GM 2.5842 0.10795
## + openings10_Others 2.0066 0.15663
## <none>
## + titleW_N 0.9874 0.32039
## + duration 0.3087 0.57850
## + `openings10_Queen's Pawn Game: Mason Attack` 0.3022 0.58254
## + titleB_N 0.2212 0.63813
## + rated_True 0.1857 0.66652
## + increment_1 0.1485 0.69994
## + `openings10_Scotch Game` 0.1103 0.73983
## + `openings10_Queen's Pawn Game: Chigorin Variation` 0.0638 0.80059
## + `openings10_Horwitz Defense` 0.0484 0.82579
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=-29378.09
## outcome_W ~ ratingDifference + titleW_GM + turns + `openings10_Van't Kruijs Opening` +
## `openings10_Scandinavian Defense` + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` +
## `openings10_Sicilian Defense: Bowdler Attack` + titleW_PRO +
## titleB_PRO + `openings10_Sicilian Defense`
##
## Df Sum of Sq RSS AIC
## + titleB_GM 1 0.54891 4101.5 -29379
## <none> 4102.0 -29378
## + titleW_N 1 0.21305 4101.8 -29377
## + duration 1 0.07335 4101.9 -29376
## + `openings10_Queen's Pawn Game: Mason Attack` 1 0.07313 4101.9 -29376
## + titleB_N 1 0.05317 4102.0 -29376
## + openings10_Others 1 0.04223 4102.0 -29376
## + rated_True 1 0.03910 4102.0 -29376
## + increment_1 1 0.03308 4102.0 -29376
## + `openings10_Scotch Game` 1 0.02939 4102.0 -29376
## + `openings10_Queen's Pawn Game: Chigorin Variation` 1 0.01781 4102.0 -29376
## + `openings10_Horwitz Defense` 1 0.01370 4102.0 -29376
## F value Pr(>F)
## + titleB_GM 2.5557 0.1099
## <none>
## + titleW_N 0.9919 0.3193
## + duration 0.3414 0.5590
## + `openings10_Queen's Pawn Game: Mason Attack` 0.3405 0.5596
## + titleB_N 0.2475 0.6188
## + openings10_Others 0.1966 0.6575
## + rated_True 0.1820 0.6697
## + increment_1 0.1540 0.6947
## + `openings10_Scotch Game` 0.1368 0.7115
## + `openings10_Queen's Pawn Game: Chigorin Variation` 0.0829 0.7734
## + `openings10_Horwitz Defense` 0.0638 0.8006
##
## Step: AIC=-29378.64
## outcome_W ~ ratingDifference + titleW_GM + turns + `openings10_Van't Kruijs Opening` +
## `openings10_Scandinavian Defense` + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` +
## `openings10_Sicilian Defense: Bowdler Attack` + titleW_PRO +
## titleB_PRO + `openings10_Sicilian Defense` + titleB_GM
##
## Df Sum of Sq RSS AIC
## <none> 4101.5 -29379
## + titleW_N 1 0.273754 4101.2 -29378
## + duration 1 0.075403 4101.4 -29377
## + `openings10_Queen's Pawn Game: Mason Attack` 1 0.075262 4101.4 -29377
## + titleB_N 1 0.053972 4101.4 -29377
## + rated_True 1 0.053351 4101.4 -29377
## + openings10_Others 1 0.040301 4101.4 -29377
## + increment_1 1 0.040092 4101.4 -29377
## + `openings10_Scotch Game` 1 0.029218 4101.4 -29377
## + `openings10_Queen's Pawn Game: Chigorin Variation` 1 0.016518 4101.5 -29377
## + `openings10_Horwitz Defense` 1 0.012897 4101.5 -29377
## F value Pr(>F)
## <none>
## + titleW_N 1.2746 0.2589
## + duration 0.3511 0.5535
## + `openings10_Queen's Pawn Game: Mason Attack` 0.3504 0.5539
## + titleB_N 0.2513 0.6162
## + rated_True 0.2484 0.6182
## + openings10_Others 0.1876 0.6649
## + increment_1 0.1867 0.6657
## + `openings10_Scotch Game` 0.1360 0.7123
## + `openings10_Queen's Pawn Game: Chigorin Variation` 0.0769 0.7815
## + `openings10_Horwitz Defense` 0.0600 0.8064After running step function we have concluded that model with variables ‘ratingDifference’, ‘titleW_GM’, ‘turns’, ‘openings10_Van't Kruijs Opening’, ‘openings10_Scandinavian Defense’,‘openings10_Scandinavian Defense: Mieses-Kotroc Variation’, & ‘openings10_Sicilian Defense: Bowdler Attack’ are significantly contributing to the model.
#Estiimating Regression Model Now before doing further analysis let us first split database in training and testing datasets in ratio of 3:1.
reg_1<- lm(outcome_W ~ ratingDifference + titleW_GM + turns + `openings10_Van't Kruijs Opening` +
`openings10_Scandinavian Defense` + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` +
`openings10_Sicilian Defense: Bowdler Attack` + titleW_PRO +
titleB_PRO + `openings10_Sicilian Defense` + titleB_GM,chessData_1)
summary(reg_1)##
## Call:
## lm(formula = outcome_W ~ ratingDifference + titleW_GM + turns +
## `openings10_Van't Kruijs Opening` + `openings10_Scandinavian Defense` +
## `openings10_Scandinavian Defense: Mieses-Kotroc Variation` +
## `openings10_Sicilian Defense: Bowdler Attack` + titleW_PRO +
## titleB_PRO + `openings10_Sicilian Defense` + titleB_GM, data = chessData_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.19129 -0.46811 0.09386 0.44358 1.24627
##
## Coefficients:
## Estimate
## (Intercept) 0.5495236
## ratingDifference 0.0007499
## titleW_GM -0.2356428
## turns -0.0005290
## `openings10_Van't Kruijs Opening` -0.1013070
## `openings10_Scandinavian Defense` -0.0831981
## `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 0.0683205
## `openings10_Sicilian Defense: Bowdler Attack` -0.0683824
## titleW_PRO 0.0262328
## titleB_PRO -0.0196295
## `openings10_Sicilian Defense` -0.0558910
## titleB_GM 0.0955885
## Std. Error t value
## (Intercept) 0.0094091 58.403
## ratingDifference 0.0000141 53.175
## titleW_GM 0.0460120 -5.121
## turns 0.0001041 -5.082
## `openings10_Van't Kruijs Opening` 0.0250017 -4.052
## `openings10_Scandinavian Defense` 0.0319844 -2.601
## `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 0.0293702 2.326
## `openings10_Sicilian Defense: Bowdler Attack` 0.0277993 -2.460
## titleW_PRO 0.0080397 3.263
## titleB_PRO 0.0080162 -2.449
## `openings10_Sicilian Defense` 0.0252825 -2.211
## titleB_GM 0.0597934 1.599
## Pr(>|t|)
## (Intercept) < 2e-16 ***
## ratingDifference < 2e-16 ***
## titleW_GM 3.06e-07 ***
## turns 3.78e-07 ***
## `openings10_Van't Kruijs Opening` 5.10e-05 ***
## `openings10_Scandinavian Defense` 0.0093 **
## `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 0.0200 *
## `openings10_Sicilian Defense: Bowdler Attack` 0.0139 *
## titleW_PRO 0.0011 **
## titleB_PRO 0.0143 *
## `openings10_Sicilian Defense` 0.0271 *
## titleB_GM 0.1099
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4634 on 19096 degrees of freedom
## Multiple R-squared: 0.1395, Adjusted R-squared: 0.139
## F-statistic: 281.5 on 11 and 19096 DF, p-value: < 2.2e-16# Partition the data set
set.seed(1610)
# Split the dataset
split <- sample.split(chessData_1[,22],SplitRatio=0.75)
training <- subset(chessData_1,split=="TRUE")
testing <- subset(chessData_1,split=="FALSE")
str(training);str(testing)## 'data.frame': 14331 obs. of 22 variables:
## $ turns : int 13 16 61 95 9 66 39 38 60 31 ...
## $ duration : num 15 5 5 30 15 15 20 20 5 15 ...
## $ ratingDifference : int 309 61 -4 54 -695 47 109 -486 -555 -47 ...
## $ rated_True : int 0 1 1 1 0 1 0 0 0 0 ...
## $ openings10_Horwitz Defense : int 0 0 0 0 0 0 0 0 0 0 ...
## $ openings10_Others : int 1 1 1 1 1 1 0 1 0 1 ...
## $ openings10_Queen's Pawn Game: Chigorin Variation : int 0 0 0 0 0 0 0 0 0 0 ...
## $ openings10_Queen's Pawn Game: Mason Attack : int 0 0 0 0 0 0 0 0 0 0 ...
## $ openings10_Scandinavian Defense : int 0 0 0 0 0 0 0 0 0 0 ...
## $ openings10_Scandinavian Defense: Mieses-Kotroc Variation: int 0 0 0 0 0 0 0 0 0 0 ...
## $ openings10_Scotch Game : int 0 0 0 0 0 0 0 0 0 0 ...
## $ openings10_Sicilian Defense : int 0 0 0 0 0 0 0 0 0 0 ...
## $ openings10_Sicilian Defense: Bowdler Attack : int 0 0 0 0 0 0 0 0 0 0 ...
## $ openings10_Van't Kruijs Opening : int 0 0 0 0 0 0 1 0 0 0 ...
## $ titleW_GM : int 0 0 0 0 0 0 0 0 0 0 ...
## $ titleW_N : int 0 0 0 0 0 0 0 0 0 1 ...
## $ titleW_PRO : int 1 1 1 1 1 1 1 1 1 0 ...
## $ titleB_GM : int 0 0 0 0 0 0 0 0 0 0 ...
## $ titleB_N : int 1 0 0 0 0 0 0 0 0 1 ...
## $ titleB_PRO : int 0 1 1 1 0 1 1 0 0 0 ...
## $ increment_1 : int 1 1 1 1 1 0 1 1 1 1 ...
## $ outcome_W : int 1 0 1 1 0 0 1 0 0 1 ...## 'data.frame': 4777 obs. of 22 variables:
## $ turns : int 61 33 119 31 43 52 36 13 69 54 ...
## $ duration : num 20 10 10 8 15 15 10 10 10 10 ...
## $ ratingDifference : int -15 97 172 -226 47 -47 201 -310 -141 290 ...
## $ rated_True : int 1 1 1 0 0 0 1 1 1 1 ...
## $ openings10_Horwitz Defense : int 0 0 0 0 0 0 0 0 0 0 ...
## $ openings10_Others : int 1 1 0 1 1 1 1 1 0 0 ...
## $ openings10_Queen's Pawn Game: Chigorin Variation : int 0 0 0 0 0 0 0 0 1 1 ...
## $ openings10_Queen's Pawn Game: Mason Attack : int 0 0 0 0 0 0 0 0 0 0 ...
## $ openings10_Scandinavian Defense : int 0 0 0 0 0 0 0 0 0 0 ...
## $ openings10_Scandinavian Defense: Mieses-Kotroc Variation: int 0 0 1 0 0 0 0 0 0 0 ...
## $ openings10_Scotch Game : int 0 0 0 0 0 0 0 0 0 0 ...
## $ openings10_Sicilian Defense : int 0 0 0 0 0 0 0 0 0 0 ...
## $ openings10_Sicilian Defense: Bowdler Attack : int 0 0 0 0 0 0 0 0 0 0 ...
## $ openings10_Van't Kruijs Opening : int 0 0 0 0 0 0 0 0 0 0 ...
## $ titleW_GM : int 0 0 0 0 0 0 0 0 0 0 ...
## $ titleW_N : int 0 0 0 0 1 1 0 1 1 0 ...
## $ titleW_PRO : int 1 1 1 1 0 0 1 0 0 1 ...
## $ titleB_GM : int 0 0 0 0 0 0 0 0 0 0 ...
## $ titleB_N : int 0 0 0 0 1 1 1 0 0 1 ...
## $ titleB_PRO : int 1 1 1 1 0 0 0 1 1 0 ...
## $ increment_1 : int 0 0 0 0 1 1 0 0 1 1 ...
## $ outcome_W : int 1 1 1 0 0 0 1 0 1 0 ...prop.table(table(chessData_1$outcome_W))##
## 0 1
## 0.4766067 0.5233933prop.table(table(training$outcome_W))##
## 0 1
## 0.4765892 0.5234108prop.table(table(testing$outcome_W))##
## 0 1
## 0.476659 0.523341model <- glm(outcome_W ~ ratingDifference + titleW_GM + turns + `openings10_Van't Kruijs Opening` +
`openings10_Scandinavian Defense` + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` +
`openings10_Sicilian Defense: Bowdler Attack` + titleW_PRO + titleB_PRO + `openings10_Sicilian Defense` + titleB_GM,training,family=binomial)
summary(model)##
## Call:
## glm(formula = outcome_W ~ ratingDifference + titleW_GM + turns +
## `openings10_Van't Kruijs Opening` + `openings10_Scandinavian Defense` +
## `openings10_Scandinavian Defense: Mieses-Kotroc Variation` +
## `openings10_Sicilian Defense: Bowdler Attack` + titleW_PRO +
## titleB_PRO + `openings10_Sicilian Defense` + titleB_GM, family = binomial,
## data = training)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.5431 -1.1052 0.4695 1.0655 2.8450
##
## Coefficients:
## Estimate
## (Intercept) 0.2177480
## ratingDifference 0.0038254
## titleW_GM -0.7581523
## turns -0.0022050
## `openings10_Van't Kruijs Opening` -0.5280239
## `openings10_Scandinavian Defense` -0.4583319
## `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 0.4719704
## `openings10_Sicilian Defense: Bowdler Attack` -0.1827203
## titleW_PRO 0.1181613
## titleB_PRO -0.1003448
## `openings10_Sicilian Defense` -0.1791304
## titleB_GM 0.3152878
## Std. Error z value
## (Intercept) 0.0509894 4.270
## ratingDifference 0.0000984 38.876
## titleW_GM 0.3182515 -2.382
## turns 0.0005575 -3.955
## `openings10_Van't Kruijs Opening` 0.1436032 -3.677
## `openings10_Scandinavian Defense` 0.1787085 -2.565
## `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 0.1692782 2.788
## `openings10_Sicilian Defense: Bowdler Attack` 0.1502074 -1.216
## titleW_PRO 0.0464597 2.543
## titleB_PRO 0.0464845 -2.159
## `openings10_Sicilian Defense` 0.1399744 -1.280
## titleB_GM 0.4120121 0.765
## Pr(>|z|)
## (Intercept) 1.95e-05 ***
## ratingDifference < 2e-16 ***
## titleW_GM 0.017208 *
## turns 7.66e-05 ***
## `openings10_Van't Kruijs Opening` 0.000236 ***
## `openings10_Scandinavian Defense` 0.010327 *
## `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 0.005301 **
## `openings10_Sicilian Defense: Bowdler Attack` 0.223812
## titleW_PRO 0.010981 *
## titleB_PRO 0.030876 *
## `openings10_Sicilian Defense` 0.200638
## titleB_GM 0.444129
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 19836 on 14330 degrees of freedom
## Residual deviance: 17627 on 14319 degrees of freedom
## AIC: 17651
##
## Number of Fisher Scoring iterations: 4vif(model)## ratingDifference
## 1.057801
## titleW_GM
## 1.029998
## turns
## 1.006239
## `openings10_Van't Kruijs Opening`
## 1.002739
## `openings10_Scandinavian Defense`
## 1.003253
## `openings10_Scandinavian Defense: Mieses-Kotroc Variation`
## 1.001300
## `openings10_Sicilian Defense: Bowdler Attack`
## 1.003604
## titleW_PRO
## 1.402827
## titleB_PRO
## 1.400529
## `openings10_Sicilian Defense`
## 1.002409
## titleB_GM
## 1.016910We have ran logistictic regression on the training dataset and the logit of model is as follows: =b00.2177480 + ratingDifference0.0038254+ titleW_GM-0.7581523+ turns-0.0022050+ openings10_Van't Kruijs Opening-0.5280239+ openings10_Scandinavian Defense-0.4583319+ openings10_Scandinavian Defense: Mieses-Kotroc Variation0.4719704+ openings10_Sicilian Defense: Bowdler Attack-0.1827203+ titleW_PRO0.1181613+ titleB_PRO-0.1003448+ openings10_Sicilian Defense-0.1791304+ titleB_GM 0.3152878
We also tested multi collinearity and found there is no severe multicollinearity in the model
#Testing Assumptions for the model
#Checking linearity assumptions
# predict
res_train <- predict(model,training,type="response")
length(res_train)## [1] 14331logit_train <- log(res_train/(1-res_train))
plot(logit_train,training$age)
# Check for influential points
plot(model,5)
# Model Significance
with(model,null.deviance-deviance)## [1] 2208.8with(model,df.null-df.residual)## [1] 11#p-value of the test
with(model,pchisq(null.deviance-deviance,df.null-df.residual,lower.tail=FALSE))## [1] 0We tested for the linearity and did not observed any linearity. There were no influential points as well. To check the overall significance of model we ran chi-square test and found that is significant. We also observed that the individual predictors are also significant at 95% confidence interval.
Validating the Model
# predicting probabilities on test data from logistic model
res_test <- predict(model,testing,type="response")
length(res_test)## [1] 4777# Performance on test data
# Confusion matrix with threshold 0.5
Predicted_type <- ifelse(res_test>0.5, "Positive","Negative")
p <- table(ActualValue = testing$outcome_W, PredictedValue = Predicted_type)
accuracy <- (p[1,1]+p[2,2])/sum(p)
# Confusion matrix with threshold 0.3
Predicted_type <- res_test>0.3
p <- table(ActualValue = testing$outcome_W, PredictedValue = Predicted_type)
p## PredictedValue
## ActualValue FALSE TRUE
## 0 484 1793
## 1 110 2390accuracy <- (p[1,1]+p[2,2])/sum(p)
# ROC curve and AUC
plotROC(actuals =testing$outcome_W , predictedScores = res_test)
# Binary Classification
# cut off value while minimizing mis-classification error
optimalCutoff(actuals =testing$outcome_W , predictedScores = res_test,optimiseFor = "misclasserror")## [1] 0.5462903# Confusion matrix with threshold 0.5462
Predicted_type <- ifelse(res_test>0.5462, "Positive","Negative")
p <- table(ActualValue = testing$outcome_W, PredictedValue = Predicted_type)
accuracy <- (p[1,1]+p[2,2])/sum(p)
plotROC(actuals =testing$outcome_W , predictedScores = res_test) After verification of assumption we validated the model using test dataset. The optimal cut-off value came 0.5462 The model accuracy is 65.54%. The area under the ROC curve came out to be 0.7261
Getting functional form of model
#Result or Not Prediction Model
reg_2<- lm(result_y~.,chessData_2)
summary(reg_2)##
## Call:
## lm(formula = result_y ~ ., data = chessData_2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.03183 0.01503 0.03842 0.06521 0.36847
##
## Coefficients:
## Estimate
## (Intercept) 9.974e-01
## turns -1.115e-03
## duration -5.568e-04
## ratingDifference -2.328e-07
## rated_True 1.817e-02
## `openings10_Horwitz Defense` 2.958e-02
## openings10_Others 1.075e-02
## `openings10_Queen's Pawn Game: Chigorin Variation` 2.228e-02
## `openings10_Queen's Pawn Game: Mason Attack` 9.128e-03
## `openings10_Scandinavian Defense` -5.894e-04
## `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 3.579e-02
## `openings10_Scotch Game` 1.339e-02
## `openings10_Sicilian Defense` 1.497e-02
## `openings10_Sicilian Defense: Bowdler Attack` 1.646e-02
## `openings10_Van't Kruijs Opening` 1.425e-02
## titleW_GM -1.979e-02
## titleW_N 1.394e-02
## titleW_PRO 1.719e-02
## titleB_GM -8.353e-02
## titleB_N -7.062e-03
## titleB_PRO -2.783e-03
## increment_1 -1.230e-02
## Std. Error t value
## (Intercept) 1.395e-02 71.501
## turns 4.467e-05 -24.969
## duration 8.727e-05 -6.381
## ratingDifference 8.975e-06 -0.026
## rated_True 3.798e-03 4.784
## `openings10_Horwitz Defense` 1.922e-02 1.539
## openings10_Others 1.279e-02 0.841
## `openings10_Queen's Pawn Game: Chigorin Variation` 1.874e-02 1.189
## `openings10_Queen's Pawn Game: Mason Attack` 1.868e-02 0.489
## `openings10_Scandinavian Defense` 1.893e-02 -0.031
## `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 1.815e-02 1.972
## `openings10_Scotch Game` 1.794e-02 0.746
## `openings10_Sicilian Defense` 1.681e-02 0.891
## `openings10_Sicilian Defense: Bowdler Attack` 1.755e-02 0.938
## `openings10_Van't Kruijs Opening` 1.679e-02 0.849
## titleW_GM 2.012e-02 -0.983
## titleW_N 9.084e-03 1.535
## titleW_PRO 5.175e-03 3.322
## titleB_GM 2.502e-02 -3.339
## titleB_N 9.045e-03 -0.781
## titleB_PRO 5.219e-03 -0.533
## increment_1 2.986e-03 -4.118
## Pr(>|t|)
## (Intercept) < 2e-16 ***
## turns < 2e-16 ***
## duration 1.80e-10 ***
## ratingDifference 0.979304
## rated_True 1.73e-06 ***
## `openings10_Horwitz Defense` 0.123814
## openings10_Others 0.400632
## `openings10_Queen's Pawn Game: Chigorin Variation` 0.234445
## `openings10_Queen's Pawn Game: Mason Attack` 0.625050
## `openings10_Scandinavian Defense` 0.975161
## `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 0.048614 *
## `openings10_Scotch Game` 0.455449
## `openings10_Sicilian Defense` 0.373042
## `openings10_Sicilian Defense: Bowdler Attack` 0.348375
## `openings10_Van't Kruijs Opening` 0.396090
## titleW_GM 0.325480
## titleW_N 0.124917
## titleW_PRO 0.000894 ***
## titleB_GM 0.000842 ***
## titleB_N 0.434957
## titleB_PRO 0.593862
## increment_1 3.83e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2087 on 20036 degrees of freedom
## Multiple R-squared: 0.03596, Adjusted R-squared: 0.03495
## F-statistic: 35.59 on 21 and 20036 DF, p-value: < 2.2e-16#step-wise regression
reg_2_i <- lm(result_y~1,data=chessData_2)
summary(reg_2_i)##
## Call:
## lm(formula = result_y ~ 1, data = chessData_2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.95264 0.04736 0.04736 0.04736 0.04736
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.9526 0.0015 635.2 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2124 on 20057 degrees of freedomreg_2_f<- lm(result_y~.,chessData_2)
summary(reg_2_f)##
## Call:
## lm(formula = result_y ~ ., data = chessData_2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.03183 0.01503 0.03842 0.06521 0.36847
##
## Coefficients:
## Estimate
## (Intercept) 9.974e-01
## turns -1.115e-03
## duration -5.568e-04
## ratingDifference -2.328e-07
## rated_True 1.817e-02
## `openings10_Horwitz Defense` 2.958e-02
## openings10_Others 1.075e-02
## `openings10_Queen's Pawn Game: Chigorin Variation` 2.228e-02
## `openings10_Queen's Pawn Game: Mason Attack` 9.128e-03
## `openings10_Scandinavian Defense` -5.894e-04
## `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 3.579e-02
## `openings10_Scotch Game` 1.339e-02
## `openings10_Sicilian Defense` 1.497e-02
## `openings10_Sicilian Defense: Bowdler Attack` 1.646e-02
## `openings10_Van't Kruijs Opening` 1.425e-02
## titleW_GM -1.979e-02
## titleW_N 1.394e-02
## titleW_PRO 1.719e-02
## titleB_GM -8.353e-02
## titleB_N -7.062e-03
## titleB_PRO -2.783e-03
## increment_1 -1.230e-02
## Std. Error t value
## (Intercept) 1.395e-02 71.501
## turns 4.467e-05 -24.969
## duration 8.727e-05 -6.381
## ratingDifference 8.975e-06 -0.026
## rated_True 3.798e-03 4.784
## `openings10_Horwitz Defense` 1.922e-02 1.539
## openings10_Others 1.279e-02 0.841
## `openings10_Queen's Pawn Game: Chigorin Variation` 1.874e-02 1.189
## `openings10_Queen's Pawn Game: Mason Attack` 1.868e-02 0.489
## `openings10_Scandinavian Defense` 1.893e-02 -0.031
## `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 1.815e-02 1.972
## `openings10_Scotch Game` 1.794e-02 0.746
## `openings10_Sicilian Defense` 1.681e-02 0.891
## `openings10_Sicilian Defense: Bowdler Attack` 1.755e-02 0.938
## `openings10_Van't Kruijs Opening` 1.679e-02 0.849
## titleW_GM 2.012e-02 -0.983
## titleW_N 9.084e-03 1.535
## titleW_PRO 5.175e-03 3.322
## titleB_GM 2.502e-02 -3.339
## titleB_N 9.045e-03 -0.781
## titleB_PRO 5.219e-03 -0.533
## increment_1 2.986e-03 -4.118
## Pr(>|t|)
## (Intercept) < 2e-16 ***
## turns < 2e-16 ***
## duration 1.80e-10 ***
## ratingDifference 0.979304
## rated_True 1.73e-06 ***
## `openings10_Horwitz Defense` 0.123814
## openings10_Others 0.400632
## `openings10_Queen's Pawn Game: Chigorin Variation` 0.234445
## `openings10_Queen's Pawn Game: Mason Attack` 0.625050
## `openings10_Scandinavian Defense` 0.975161
## `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 0.048614 *
## `openings10_Scotch Game` 0.455449
## `openings10_Sicilian Defense` 0.373042
## `openings10_Sicilian Defense: Bowdler Attack` 0.348375
## `openings10_Van't Kruijs Opening` 0.396090
## titleW_GM 0.325480
## titleW_N 0.124917
## titleW_PRO 0.000894 ***
## titleB_GM 0.000842 ***
## titleB_N 0.434957
## titleB_PRO 0.593862
## increment_1 3.83e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2087 on 20036 degrees of freedom
## Multiple R-squared: 0.03596, Adjusted R-squared: 0.03495
## F-statistic: 35.59 on 21 and 20036 DF, p-value: < 2.2e-16x <- step(reg_2_i,scope=list(lower=reg_2_i,upper=reg_2_f),direction = "both",test="F",trace=TRUE)## Start: AIC=-62146.56
## result_y ~ 1
##
## Df Sum of Sq
## + turns 1 26.3546
## + duration 1 1.3342
## + titleW_PRO 1 1.2516
## + titleB_GM 1 0.7822
## + rated_True 1 0.6773
## + increment_1 1 0.5802
## + titleB_PRO 1 0.4740
## + titleW_GM 1 0.1659
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 1 0.1536
## + openings10_Others 1 0.1179
## + `openings10_Horwitz Defense` 1 0.1160
## <none>
## + titleB_N 1 0.0879
## + titleW_N 1 0.0822
## + `openings10_Queen's Pawn Game: Chigorin Variation` 1 0.0358
## + ratingDifference 1 0.0311
## + `openings10_Queen's Pawn Game: Mason Attack` 1 0.0177
## + `openings10_Scotch Game` 1 0.0126
## + `openings10_Sicilian Defense` 1 0.0109
## + `openings10_Van't Kruijs Opening` 1 0.0057
## + `openings10_Sicilian Defense: Bowdler Attack` 1 0.0036
## + `openings10_Scandinavian Defense` 1 0.0014
## RSS AIC
## + turns 878.65 -62737
## + duration 903.67 -62174
## + titleW_PRO 903.75 -62172
## + titleB_GM 904.22 -62162
## + rated_True 904.33 -62160
## + increment_1 904.43 -62157
## + titleB_PRO 904.53 -62155
## + titleW_GM 904.84 -62148
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 904.85 -62148
## + openings10_Others 904.89 -62147
## + `openings10_Horwitz Defense` 904.89 -62147
## <none> 905.01 -62147
## + titleB_N 904.92 -62147
## + titleW_N 904.92 -62146
## + `openings10_Queen's Pawn Game: Chigorin Variation` 904.97 -62145
## + ratingDifference 904.97 -62145
## + `openings10_Queen's Pawn Game: Mason Attack` 904.99 -62145
## + `openings10_Scotch Game` 904.99 -62145
## + `openings10_Sicilian Defense` 904.99 -62145
## + `openings10_Van't Kruijs Opening` 905.00 -62145
## + `openings10_Sicilian Defense: Bowdler Attack` 905.00 -62145
## + `openings10_Scandinavian Defense` 905.00 -62145
## F value Pr(>F)
## + turns 601.5666 < 2.2e-16
## + duration 29.6100 5.345e-08
## + titleW_PRO 27.7764 1.376e-07
## + titleB_GM 17.3485 3.124e-05
## + rated_True 15.0218 0.0001066
## + increment_1 12.8657 0.0003355
## + titleB_PRO 10.5106 0.0011888
## + titleW_GM 3.6768 0.0551894
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 3.4050 0.0650128
## + openings10_Others 2.6125 0.1060404
## + `openings10_Horwitz Defense` 2.5718 0.1088027
## <none>
## + titleB_N 1.9478 0.1628436
## + titleW_N 1.8218 0.1771103
## + `openings10_Queen's Pawn Game: Chigorin Variation` 0.7929 0.3732204
## + ratingDifference 0.6895 0.4063349
## + `openings10_Queen's Pawn Game: Mason Attack` 0.3912 0.5316929
## + `openings10_Scotch Game` 0.2792 0.5972210
## + `openings10_Sicilian Defense` 0.2411 0.6234178
## + `openings10_Van't Kruijs Opening` 0.1254 0.7233047
## + `openings10_Sicilian Defense: Bowdler Attack` 0.0790 0.7787161
## + `openings10_Scandinavian Defense` 0.0317 0.8586319
##
## + turns ***
## + duration ***
## + titleW_PRO ***
## + titleB_GM ***
## + rated_True ***
## + increment_1 ***
## + titleB_PRO **
## + titleW_GM .
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` .
## + openings10_Others
## + `openings10_Horwitz Defense`
## <none>
## + titleB_N
## + titleW_N
## + `openings10_Queen's Pawn Game: Chigorin Variation`
## + ratingDifference
## + `openings10_Queen's Pawn Game: Mason Attack`
## + `openings10_Scotch Game`
## + `openings10_Sicilian Defense`
## + `openings10_Van't Kruijs Opening`
## + `openings10_Sicilian Defense: Bowdler Attack`
## + `openings10_Scandinavian Defense`
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=-62737.34
## result_y ~ turns
##
## Df Sum of Sq
## + duration 1 2.1376
## + rated_True 1 1.6743
## + increment_1 1 0.9868
## + titleW_PRO 1 0.9087
## + titleB_GM 1 0.7016
## + titleW_GM 1 0.2817
## + titleB_PRO 1 0.2164
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 1 0.1674
## + ratingDifference 1 0.1298
## + `openings10_Horwitz Defense` 1 0.0981
## <none>
## + openings10_Others 1 0.0726
## + titleB_N 1 0.0442
## + `openings10_Queen's Pawn Game: Chigorin Variation` 1 0.0359
## + `openings10_Scandinavian Defense` 1 0.0339
## + titleW_N 1 0.0240
## + `openings10_Sicilian Defense: Bowdler Attack` 1 0.0193
## + `openings10_Sicilian Defense` 1 0.0072
## + `openings10_Scotch Game` 1 0.0035
## + `openings10_Van't Kruijs Opening` 1 0.0011
## + `openings10_Queen's Pawn Game: Mason Attack` 1 0.0008
## - turns 1 26.3546
## RSS AIC
## + duration 876.51 -62784
## + rated_True 876.98 -62774
## + increment_1 877.66 -62758
## + titleW_PRO 877.74 -62756
## + titleB_GM 877.95 -62751
## + titleW_GM 878.37 -62742
## + titleB_PRO 878.43 -62740
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 878.48 -62739
## + ratingDifference 878.52 -62738
## + `openings10_Horwitz Defense` 878.55 -62738
## <none> 878.65 -62737
## + openings10_Others 878.58 -62737
## + titleB_N 878.61 -62736
## + `openings10_Queen's Pawn Game: Chigorin Variation` 878.62 -62736
## + `openings10_Scandinavian Defense` 878.62 -62736
## + titleW_N 878.63 -62736
## + `openings10_Sicilian Defense: Bowdler Attack` 878.63 -62736
## + `openings10_Sicilian Defense` 878.64 -62736
## + `openings10_Scotch Game` 878.65 -62735
## + `openings10_Van't Kruijs Opening` 878.65 -62735
## + `openings10_Queen's Pawn Game: Mason Attack` 878.65 -62735
## - turns 905.01 -62147
## F value Pr(>F)
## + duration 48.9087 2.766e-12
## + rated_True 38.2887 6.220e-10
## + increment_1 22.5483 2.063e-06
## + titleW_PRO 20.7615 5.233e-06
## + titleB_GM 16.0256 6.272e-05
## + titleW_GM 6.4319 0.01122
## + titleB_PRO 4.9415 0.02623
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 3.8224 0.05058
## + ratingDifference 2.9636 0.08517
## + `openings10_Horwitz Defense` 2.2404 0.13446
## <none>
## + openings10_Others 1.6581 0.19788
## + titleB_N 1.0097 0.31498
## + `openings10_Queen's Pawn Game: Chigorin Variation` 0.8187 0.36556
## + `openings10_Scandinavian Defense` 0.7749 0.37872
## + titleW_N 0.5478 0.45921
## + `openings10_Sicilian Defense: Bowdler Attack` 0.4398 0.50722
## + `openings10_Sicilian Defense` 0.1632 0.68621
## + `openings10_Scotch Game` 0.0800 0.77731
## + `openings10_Van't Kruijs Opening` 0.0244 0.87582
## + `openings10_Queen's Pawn Game: Mason Attack` 0.0182 0.89258
## - turns 601.5666 < 2.2e-16
##
## + duration ***
## + rated_True ***
## + increment_1 ***
## + titleW_PRO ***
## + titleB_GM ***
## + titleW_GM *
## + titleB_PRO *
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` .
## + ratingDifference .
## + `openings10_Horwitz Defense`
## <none>
## + openings10_Others
## + titleB_N
## + `openings10_Queen's Pawn Game: Chigorin Variation`
## + `openings10_Scandinavian Defense`
## + titleW_N
## + `openings10_Sicilian Defense: Bowdler Attack`
## + `openings10_Sicilian Defense`
## + `openings10_Scotch Game`
## + `openings10_Van't Kruijs Opening`
## + `openings10_Queen's Pawn Game: Mason Attack`
## - turns ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=-62784.19
## result_y ~ turns + duration
##
## Df Sum of Sq
## + rated_True 1 1.3296
## + increment_1 1 0.9527
## + titleW_PRO 1 0.8744
## + titleB_GM 1 0.7089
## + titleW_GM 1 0.2674
## + titleB_PRO 1 0.2044
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 1 0.1670
## + ratingDifference 1 0.1236
## + openings10_Others 1 0.1086
## <none>
## + `openings10_Horwitz Defense` 1 0.0837
## + `openings10_Queen's Pawn Game: Chigorin Variation` 1 0.0325
## + `openings10_Scandinavian Defense` 1 0.0217
## + `openings10_Sicilian Defense: Bowdler Attack` 1 0.0206
## + `openings10_Van't Kruijs Opening` 1 0.0146
## + titleB_N 1 0.0105
## + `openings10_Sicilian Defense` 1 0.0089
## + `openings10_Scotch Game` 1 0.0037
## + titleW_N 1 0.0036
## + `openings10_Queen's Pawn Game: Mason Attack` 1 0.0019
## - duration 1 2.1376
## - turns 1 27.1580
## RSS AIC
## + rated_True 875.18 -62813
## + increment_1 875.56 -62804
## + titleW_PRO 875.64 -62802
## + titleB_GM 875.80 -62798
## + titleW_GM 876.25 -62788
## + titleB_PRO 876.31 -62787
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 876.35 -62786
## + ratingDifference 876.39 -62785
## + openings10_Others 876.40 -62785
## <none> 876.51 -62784
## + `openings10_Horwitz Defense` 876.43 -62784
## + `openings10_Queen's Pawn Game: Chigorin Variation` 876.48 -62783
## + `openings10_Scandinavian Defense` 876.49 -62783
## + `openings10_Sicilian Defense: Bowdler Attack` 876.49 -62783
## + `openings10_Van't Kruijs Opening` 876.50 -62783
## + titleB_N 876.50 -62782
## + `openings10_Sicilian Defense` 876.50 -62782
## + `openings10_Scotch Game` 876.51 -62782
## + titleW_N 876.51 -62782
## + `openings10_Queen's Pawn Game: Mason Attack` 876.51 -62782
## - duration 878.65 -62737
## - turns 903.67 -62174
## F value Pr(>F)
## + rated_True 30.4654 3.441e-08
## + increment_1 21.8214 3.012e-06
## + titleW_PRO 20.0262 7.681e-06
## + titleB_GM 16.2326 5.623e-05
## + titleW_GM 6.1204 0.01337
## + titleB_PRO 4.6772 0.03058
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 3.8212 0.05062
## + ratingDifference 2.8279 0.09265
## + openings10_Others 2.4840 0.11502
## <none>
## + `openings10_Horwitz Defense` 1.9156 0.16636
## + `openings10_Queen's Pawn Game: Chigorin Variation` 0.7439 0.38841
## + `openings10_Scandinavian Defense` 0.4973 0.48071
## + `openings10_Sicilian Defense: Bowdler Attack` 0.4709 0.49256
## + `openings10_Van't Kruijs Opening` 0.3329 0.56394
## + titleB_N 0.2400 0.62422
## + `openings10_Sicilian Defense` 0.2033 0.65210
## + `openings10_Scotch Game` 0.0844 0.77147
## + titleW_N 0.0819 0.77472
## + `openings10_Queen's Pawn Game: Mason Attack` 0.0435 0.83487
## - duration 48.9087 2.766e-12
## - turns 621.3863 < 2.2e-16
##
## + rated_True ***
## + increment_1 ***
## + titleW_PRO ***
## + titleB_GM ***
## + titleW_GM *
## + titleB_PRO *
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` .
## + ratingDifference .
## + openings10_Others
## <none>
## + `openings10_Horwitz Defense`
## + `openings10_Queen's Pawn Game: Chigorin Variation`
## + `openings10_Scandinavian Defense`
## + `openings10_Sicilian Defense: Bowdler Attack`
## + `openings10_Van't Kruijs Opening`
## + titleB_N
## + `openings10_Sicilian Defense`
## + `openings10_Scotch Game`
## + titleW_N
## + `openings10_Queen's Pawn Game: Mason Attack`
## - duration ***
## - turns ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=-62812.64
## result_y ~ turns + duration + rated_True
##
## Df Sum of Sq
## + titleW_PRO 1 0.8340
## + increment_1 1 0.7753
## + titleB_GM 1 0.6217
## + titleB_PRO 1 0.2155
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 1 0.1690
## + titleW_GM 1 0.1586
## + ratingDifference 1 0.1000
## + openings10_Others 1 0.0928
## <none>
## + `openings10_Horwitz Defense` 1 0.0719
## + `openings10_Queen's Pawn Game: Chigorin Variation` 1 0.0350
## + `openings10_Scandinavian Defense` 1 0.0269
## + `openings10_Sicilian Defense: Bowdler Attack` 1 0.0177
## + titleB_N 1 0.0120
## + `openings10_Sicilian Defense` 1 0.0098
## + `openings10_Van't Kruijs Opening` 1 0.0087
## + `openings10_Scotch Game` 1 0.0034
## + `openings10_Queen's Pawn Game: Mason Attack` 1 0.0016
## + titleW_N 1 0.0015
## - rated_True 1 1.3296
## - duration 1 1.7928
## - turns 1 27.9898
## RSS AIC
## + titleW_PRO 874.35 -62830
## + increment_1 874.41 -62828
## + titleB_GM 874.56 -62825
## + titleB_PRO 874.97 -62816
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 875.01 -62815
## + titleW_GM 875.03 -62814
## + ratingDifference 875.08 -62813
## + openings10_Others 875.09 -62813
## <none> 875.18 -62813
## + `openings10_Horwitz Defense` 875.11 -62812
## + `openings10_Queen's Pawn Game: Chigorin Variation` 875.15 -62811
## + `openings10_Scandinavian Defense` 875.16 -62811
## + `openings10_Sicilian Defense: Bowdler Attack` 875.17 -62811
## + titleB_N 875.17 -62811
## + `openings10_Sicilian Defense` 875.17 -62811
## + `openings10_Van't Kruijs Opening` 875.18 -62811
## + `openings10_Scotch Game` 875.18 -62811
## + `openings10_Queen's Pawn Game: Mason Attack` 875.18 -62811
## + titleW_N 875.18 -62811
## - rated_True 876.51 -62784
## - duration 876.98 -62774
## - turns 903.17 -62183
## F value Pr(>F)
## + titleW_PRO 19.1273 1.229e-05
## + increment_1 17.7809 2.489e-05
## + titleB_GM 14.2554 0.0001601
## + titleB_PRO 4.9400 0.0262529
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 3.8734 0.0490710
## + titleW_GM 3.6352 0.0565845
## + ratingDifference 2.2912 0.1301222
## + openings10_Others 2.1266 0.1447779
## <none>
## + `openings10_Horwitz Defense` 1.6472 0.1993544
## + `openings10_Queen's Pawn Game: Chigorin Variation` 0.8027 0.3702836
## + `openings10_Scandinavian Defense` 0.6154 0.4327537
## + `openings10_Sicilian Defense: Bowdler Attack` 0.4057 0.5241615
## + titleB_N 0.2755 0.5996863
## + `openings10_Sicilian Defense` 0.2245 0.6356155
## + `openings10_Van't Kruijs Opening` 0.2002 0.6545949
## + `openings10_Scotch Game` 0.0786 0.7791619
## + `openings10_Queen's Pawn Game: Mason Attack` 0.0374 0.8466192
## + titleW_N 0.0343 0.8530707
## - rated_True 30.4654 3.441e-08
## - duration 41.0807 1.493e-10
## - turns 641.3603 < 2.2e-16
##
## + titleW_PRO ***
## + increment_1 ***
## + titleB_GM ***
## + titleB_PRO *
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` *
## + titleW_GM .
## + ratingDifference
## + openings10_Others
## <none>
## + `openings10_Horwitz Defense`
## + `openings10_Queen's Pawn Game: Chigorin Variation`
## + `openings10_Scandinavian Defense`
## + `openings10_Sicilian Defense: Bowdler Attack`
## + titleB_N
## + `openings10_Sicilian Defense`
## + `openings10_Van't Kruijs Opening`
## + `openings10_Scotch Game`
## + `openings10_Queen's Pawn Game: Mason Attack`
## + titleW_N
## - rated_True ***
## - duration ***
## - turns ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=-62829.76
## result_y ~ turns + duration + rated_True + titleW_PRO
##
## Df Sum of Sq
## + increment_1 1 0.7831
## + titleB_GM 1 0.5470
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 1 0.1582
## + titleW_N 1 0.1561
## + titleW_GM 1 0.0893
## <none>
## + `openings10_Horwitz Defense` 1 0.0736
## + openings10_Others 1 0.0664
## + ratingDifference 1 0.0456
## + `openings10_Queen's Pawn Game: Chigorin Variation` 1 0.0331
## + `openings10_Scandinavian Defense` 1 0.0258
## + `openings10_Sicilian Defense: Bowdler Attack` 1 0.0102
## + titleB_PRO 1 0.0081
## + `openings10_Van't Kruijs Opening` 1 0.0073
## + `openings10_Sicilian Defense` 1 0.0063
## + titleB_N 1 0.0028
## + `openings10_Queen's Pawn Game: Mason Attack` 1 0.0019
## + `openings10_Scotch Game` 1 0.0011
## - titleW_PRO 1 0.8340
## - rated_True 1 1.2891
## - duration 1 1.7671
## - turns 1 27.6239
## RSS AIC
## + increment_1 873.57 -62846
## + titleB_GM 873.80 -62840
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 874.19 -62831
## + titleW_N 874.19 -62831
## + titleW_GM 874.26 -62830
## <none> 874.35 -62830
## + `openings10_Horwitz Defense` 874.28 -62829
## + openings10_Others 874.28 -62829
## + ratingDifference 874.30 -62829
## + `openings10_Queen's Pawn Game: Chigorin Variation` 874.32 -62829
## + `openings10_Scandinavian Defense` 874.32 -62828
## + `openings10_Sicilian Defense: Bowdler Attack` 874.34 -62828
## + titleB_PRO 874.34 -62828
## + `openings10_Van't Kruijs Opening` 874.34 -62828
## + `openings10_Sicilian Defense` 874.34 -62828
## + titleB_N 874.35 -62828
## + `openings10_Queen's Pawn Game: Mason Attack` 874.35 -62828
## + `openings10_Scotch Game` 874.35 -62828
## - titleW_PRO 875.18 -62813
## - rated_True 875.64 -62802
## - duration 876.12 -62791
## - turns 901.97 -62208
## F value Pr(>F)
## + increment_1 17.9752 2.248e-05
## + titleB_GM 12.5530 0.0003965
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 3.6282 0.0568238
## + titleW_N 3.5800 0.0584937
## + titleW_GM 2.0471 0.1525116
## <none>
## + `openings10_Horwitz Defense` 1.6889 0.1937588
## + openings10_Others 1.5236 0.2170834
## + ratingDifference 1.0455 0.3065623
## + `openings10_Queen's Pawn Game: Chigorin Variation` 0.7585 0.3838052
## + `openings10_Scandinavian Defense` 0.5917 0.4417851
## + `openings10_Sicilian Defense: Bowdler Attack` 0.2339 0.6286829
## + titleB_PRO 0.1859 0.6663234
## + `openings10_Van't Kruijs Opening` 0.1681 0.6817882
## + `openings10_Sicilian Defense` 0.1453 0.7030444
## + titleB_N 0.0641 0.8001844
## + `openings10_Queen's Pawn Game: Mason Attack` 0.0432 0.8352709
## + `openings10_Scotch Game` 0.0242 0.8763239
## - titleW_PRO 19.1273 1.229e-05
## - rated_True 29.5655 5.469e-08
## - duration 40.5281 1.980e-10
## - turns 633.5483 < 2.2e-16
##
## + increment_1 ***
## + titleB_GM ***
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` .
## + titleW_N .
## + titleW_GM
## <none>
## + `openings10_Horwitz Defense`
## + openings10_Others
## + ratingDifference
## + `openings10_Queen's Pawn Game: Chigorin Variation`
## + `openings10_Scandinavian Defense`
## + `openings10_Sicilian Defense: Bowdler Attack`
## + titleB_PRO
## + `openings10_Van't Kruijs Opening`
## + `openings10_Sicilian Defense`
## + titleB_N
## + `openings10_Queen's Pawn Game: Mason Attack`
## + `openings10_Scotch Game`
## - titleW_PRO ***
## - rated_True ***
## - duration ***
## - turns ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=-62845.74
## result_y ~ turns + duration + rated_True + titleW_PRO + increment_1
##
## Df Sum of Sq
## + titleB_GM 1 0.5162
## + titleW_N 1 0.1784
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 1 0.1539
## <none>
## + `openings10_Horwitz Defense` 1 0.0723
## + titleW_GM 1 0.0665
## + openings10_Others 1 0.0651
## + ratingDifference 1 0.0386
## + `openings10_Queen's Pawn Game: Chigorin Variation` 1 0.0331
## + `openings10_Scandinavian Defense` 1 0.0246
## + `openings10_Van't Kruijs Opening` 1 0.0094
## + `openings10_Sicilian Defense: Bowdler Attack` 1 0.0094
## + titleB_PRO 1 0.0085
## + `openings10_Sicilian Defense` 1 0.0057
## + `openings10_Queen's Pawn Game: Mason Attack` 1 0.0016
## + `openings10_Scotch Game` 1 0.0009
## + titleB_N 1 0.0007
## - increment_1 1 0.7831
## - titleW_PRO 1 0.8417
## - rated_True 1 1.1137
## - duration 1 1.7594
## - turns 1 27.9287
## RSS AIC
## + titleB_GM 873.05 -62856
## + titleW_N 873.39 -62848
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 873.41 -62847
## <none> 873.57 -62846
## + `openings10_Horwitz Defense` 873.49 -62845
## + titleW_GM 873.50 -62845
## + openings10_Others 873.50 -62845
## + ratingDifference 873.53 -62845
## + `openings10_Queen's Pawn Game: Chigorin Variation` 873.53 -62844
## + `openings10_Scandinavian Defense` 873.54 -62844
## + `openings10_Van't Kruijs Opening` 873.56 -62844
## + `openings10_Sicilian Defense: Bowdler Attack` 873.56 -62844
## + titleB_PRO 873.56 -62844
## + `openings10_Sicilian Defense` 873.56 -62844
## + `openings10_Queen's Pawn Game: Mason Attack` 873.57 -62844
## + `openings10_Scotch Game` 873.57 -62844
## + titleB_N 873.57 -62844
## - increment_1 874.35 -62830
## - titleW_PRO 874.41 -62828
## - rated_True 874.68 -62822
## - duration 875.33 -62807
## - turns 901.50 -62217
## F value Pr(>F)
## + titleB_GM 11.8546 0.0005764
## + titleW_N 4.0950 0.0430245
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 3.5338 0.0601437
## <none>
## + `openings10_Horwitz Defense` 1.6600 0.1976249
## + titleW_GM 1.5257 0.2167795
## + openings10_Others 1.4953 0.2214145
## + ratingDifference 0.8857 0.3466503
## + `openings10_Queen's Pawn Game: Chigorin Variation` 0.7607 0.3831285
## + `openings10_Scandinavian Defense` 0.5653 0.4521524
## + `openings10_Van't Kruijs Opening` 0.2169 0.6414231
## + `openings10_Sicilian Defense: Bowdler Attack` 0.2149 0.6429750
## + titleB_PRO 0.1947 0.6590526
## + `openings10_Sicilian Defense` 0.1314 0.7169790
## + `openings10_Queen's Pawn Game: Mason Attack` 0.0366 0.8483456
## + `openings10_Scotch Game` 0.0214 0.8838056
## + titleB_N 0.0158 0.8998632
## - increment_1 17.9752 2.248e-05
## - titleW_PRO 19.3216 1.110e-05
## - rated_True 25.5645 4.316e-07
## - duration 40.3851 2.130e-10
## - turns 641.0810 < 2.2e-16
##
## + titleB_GM ***
## + titleW_N *
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` .
## <none>
## + `openings10_Horwitz Defense`
## + titleW_GM
## + openings10_Others
## + ratingDifference
## + `openings10_Queen's Pawn Game: Chigorin Variation`
## + `openings10_Scandinavian Defense`
## + `openings10_Van't Kruijs Opening`
## + `openings10_Sicilian Defense: Bowdler Attack`
## + titleB_PRO
## + `openings10_Sicilian Defense`
## + `openings10_Queen's Pawn Game: Mason Attack`
## + `openings10_Scotch Game`
## + titleB_N
## - increment_1 ***
## - titleW_PRO ***
## - rated_True ***
## - duration ***
## - turns ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=-62855.59
## result_y ~ turns + duration + rated_True + titleW_PRO + increment_1 +
## titleB_GM
##
## Df Sum of Sq
## + titleW_N 1 0.1551
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 1 0.1505
## + ratingDifference 1 0.0919
## <none>
## + `openings10_Horwitz Defense` 1 0.0702
## + titleW_GM 1 0.0606
## + openings10_Others 1 0.0598
## + `openings10_Queen's Pawn Game: Chigorin Variation` 1 0.0315
## + `openings10_Scandinavian Defense` 1 0.0259
## + `openings10_Sicilian Defense: Bowdler Attack` 1 0.0087
## + `openings10_Van't Kruijs Opening` 1 0.0086
## + `openings10_Sicilian Defense` 1 0.0056
## + titleB_N 1 0.0017
## + titleB_PRO 1 0.0016
## + `openings10_Queen's Pawn Game: Mason Attack` 1 0.0015
## + `openings10_Scotch Game` 1 0.0007
## - titleB_GM 1 0.5162
## - increment_1 1 0.7522
## - titleW_PRO 1 0.7685
## - rated_True 1 1.0460
## - duration 1 1.7753
## - turns 1 27.8343
## RSS AIC
## + titleW_N 872.90 -62857
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 872.90 -62857
## + ratingDifference 872.96 -62856
## <none> 873.05 -62856
## + `openings10_Horwitz Defense` 872.98 -62855
## + titleW_GM 872.99 -62855
## + openings10_Others 872.99 -62855
## + `openings10_Queen's Pawn Game: Chigorin Variation` 873.02 -62854
## + `openings10_Scandinavian Defense` 873.02 -62854
## + `openings10_Sicilian Defense: Bowdler Attack` 873.04 -62854
## + `openings10_Van't Kruijs Opening` 873.04 -62854
## + `openings10_Sicilian Defense` 873.04 -62854
## + titleB_N 873.05 -62854
## + titleB_PRO 873.05 -62854
## + `openings10_Queen's Pawn Game: Mason Attack` 873.05 -62854
## + `openings10_Scotch Game` 873.05 -62854
## - titleB_GM 873.57 -62846
## - increment_1 873.80 -62840
## - titleW_PRO 873.82 -62840
## - rated_True 874.10 -62834
## - duration 874.83 -62817
## - turns 900.88 -62228
## F value Pr(>F)
## + titleW_N 3.5636 0.0590727
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 3.4571 0.0629942
## + ratingDifference 2.1105 0.1463027
## <none>
## + `openings10_Horwitz Defense` 1.6126 0.2041371
## + titleW_GM 1.3918 0.2381236
## + openings10_Others 1.3727 0.2413555
## + `openings10_Queen's Pawn Game: Chigorin Variation` 0.7226 0.3953141
## + `openings10_Scandinavian Defense` 0.5949 0.4405394
## + `openings10_Sicilian Defense: Bowdler Attack` 0.1991 0.6554690
## + `openings10_Van't Kruijs Opening` 0.1965 0.6575730
## + `openings10_Sicilian Defense` 0.1296 0.7188776
## + titleB_N 0.0398 0.8418636
## + titleB_PRO 0.0374 0.8467404
## + `openings10_Queen's Pawn Game: Mason Attack` 0.0354 0.8508579
## + `openings10_Scotch Game` 0.0164 0.8981674
## - titleB_GM 11.8546 0.0005764
## - increment_1 17.2764 3.245e-05
## - titleW_PRO 17.6507 2.666e-05
## - rated_True 24.0232 9.593e-07
## - duration 40.7720 1.748e-10
## - turns 639.2592 < 2.2e-16
##
## + titleW_N .
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` .
## + ratingDifference
## <none>
## + `openings10_Horwitz Defense`
## + titleW_GM
## + openings10_Others
## + `openings10_Queen's Pawn Game: Chigorin Variation`
## + `openings10_Scandinavian Defense`
## + `openings10_Sicilian Defense: Bowdler Attack`
## + `openings10_Van't Kruijs Opening`
## + `openings10_Sicilian Defense`
## + titleB_N
## + titleB_PRO
## + `openings10_Queen's Pawn Game: Mason Attack`
## + `openings10_Scotch Game`
## - titleB_GM ***
## - increment_1 ***
## - titleW_PRO ***
## - rated_True ***
## - duration ***
## - turns ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=-62857.16
## result_y ~ turns + duration + rated_True + titleW_PRO + increment_1 +
## titleB_GM + titleW_N
##
## Df Sum of Sq
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 1 0.1487
## <none>
## + `openings10_Horwitz Defense` 1 0.0690
## + openings10_Others 1 0.0464
## + titleW_GM 1 0.0455
## + `openings10_Scandinavian Defense` 1 0.0359
## + titleB_N 1 0.0321
## + ratingDifference 1 0.0310
## + `openings10_Queen's Pawn Game: Chigorin Variation` 1 0.0275
## - titleW_N 1 0.1551
## + `openings10_Sicilian Defense: Bowdler Attack` 1 0.0083
## + `openings10_Sicilian Defense` 1 0.0051
## + `openings10_Van't Kruijs Opening` 1 0.0030
## + `openings10_Queen's Pawn Game: Mason Attack` 1 0.0012
## + `openings10_Scotch Game` 1 0.0007
## + titleB_PRO 1 0.0001
## - titleB_GM 1 0.4929
## - increment_1 1 0.7732
## - titleW_PRO 1 0.9230
## - rated_True 1 1.0542
## - duration 1 1.8361
## - turns 1 27.1076
## RSS AIC
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 872.75 -62859
## <none> 872.90 -62857
## + `openings10_Horwitz Defense` 872.83 -62857
## + openings10_Others 872.85 -62856
## + titleW_GM 872.85 -62856
## + `openings10_Scandinavian Defense` 872.86 -62856
## + titleB_N 872.86 -62856
## + ratingDifference 872.86 -62856
## + `openings10_Queen's Pawn Game: Chigorin Variation` 872.87 -62856
## - titleW_N 873.05 -62856
## + `openings10_Sicilian Defense: Bowdler Attack` 872.89 -62855
## + `openings10_Sicilian Defense` 872.89 -62855
## + `openings10_Van't Kruijs Opening` 872.89 -62855
## + `openings10_Queen's Pawn Game: Mason Attack` 872.89 -62855
## + `openings10_Scotch Game` 872.89 -62855
## + titleB_PRO 872.90 -62855
## - titleB_GM 873.39 -62848
## - increment_1 873.67 -62841
## - titleW_PRO 873.82 -62838
## - rated_True 873.95 -62835
## - duration 874.73 -62817
## - turns 900.00 -62246
## F value Pr(>F)
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 3.4157 0.0645945
## <none>
## + `openings10_Horwitz Defense` 1.5850 0.2080527
## + openings10_Others 1.0649 0.3021041
## + titleW_GM 1.0453 0.3066040
## + `openings10_Scandinavian Defense` 0.8237 0.3641035
## + titleB_N 0.7364 0.3908109
## + ratingDifference 0.7123 0.3987078
## + `openings10_Queen's Pawn Game: Chigorin Variation` 0.6323 0.4265401
## - titleW_N 3.5636 0.0590727
## + `openings10_Sicilian Defense: Bowdler Attack` 0.1905 0.6625443
## + `openings10_Sicilian Defense` 0.1165 0.7329066
## + `openings10_Van't Kruijs Opening` 0.0686 0.7933724
## + `openings10_Queen's Pawn Game: Mason Attack` 0.0284 0.8662086
## + `openings10_Scotch Game` 0.0161 0.8991513
## + titleB_PRO 0.0030 0.9564627
## - titleB_GM 11.3227 0.0007671
## - increment_1 17.7603 2.516e-05
## - titleW_PRO 21.2015 4.160e-06
## - rated_True 24.2142 8.688e-07
## - duration 42.1736 8.548e-11
## - turns 622.6499 < 2.2e-16
##
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` .
## <none>
## + `openings10_Horwitz Defense`
## + openings10_Others
## + titleW_GM
## + `openings10_Scandinavian Defense`
## + titleB_N
## + ratingDifference
## + `openings10_Queen's Pawn Game: Chigorin Variation`
## - titleW_N .
## + `openings10_Sicilian Defense: Bowdler Attack`
## + `openings10_Sicilian Defense`
## + `openings10_Van't Kruijs Opening`
## + `openings10_Queen's Pawn Game: Mason Attack`
## + `openings10_Scotch Game`
## + titleB_PRO
## - titleB_GM ***
## - increment_1 ***
## - titleW_PRO ***
## - rated_True ***
## - duration ***
## - turns ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=-62858.57
## result_y ~ turns + duration + rated_True + titleW_PRO + increment_1 +
## titleB_GM + titleW_N + `openings10_Scandinavian Defense: Mieses-Kotroc Variation`
##
## Df Sum of Sq
## <none>
## + `openings10_Horwitz Defense` 1 0.0714
## + titleW_GM 1 0.0484
## + ratingDifference 1 0.0366
## + titleB_N 1 0.0341
## + `openings10_Scandinavian Defense` 1 0.0341
## + `openings10_Queen's Pawn Game: Chigorin Variation` 1 0.0292
## - `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 1 0.1487
## - titleW_N 1 0.1533
## + openings10_Others 1 0.0117
## + `openings10_Sicilian Defense: Bowdler Attack` 1 0.0094
## + `openings10_Sicilian Defense` 1 0.0060
## + `openings10_Van't Kruijs Opening` 1 0.0037
## + `openings10_Scotch Game` 1 0.0010
## + `openings10_Queen's Pawn Game: Mason Attack` 1 0.0009
## + titleB_PRO 1 0.0003
## - titleB_GM 1 0.4898
## - increment_1 1 0.7690
## - titleW_PRO 1 0.9113
## - rated_True 1 1.0567
## - duration 1 1.8352
## - turns 1 27.1250
## RSS AIC
## <none> 872.75 -62859
## + `openings10_Horwitz Defense` 872.68 -62858
## + titleW_GM 872.70 -62858
## + ratingDifference 872.71 -62857
## + titleB_N 872.71 -62857
## + `openings10_Scandinavian Defense` 872.71 -62857
## + `openings10_Queen's Pawn Game: Chigorin Variation` 872.72 -62857
## - `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 872.90 -62857
## - titleW_N 872.90 -62857
## + openings10_Others 872.73 -62857
## + `openings10_Sicilian Defense: Bowdler Attack` 872.74 -62857
## + `openings10_Sicilian Defense` 872.74 -62857
## + `openings10_Van't Kruijs Opening` 872.74 -62857
## + `openings10_Scotch Game` 872.75 -62857
## + `openings10_Queen's Pawn Game: Mason Attack` 872.75 -62857
## + titleB_PRO 872.75 -62857
## - titleB_GM 873.24 -62849
## - increment_1 873.52 -62843
## - titleW_PRO 873.66 -62840
## - rated_True 873.80 -62836
## - duration 874.58 -62818
## - turns 899.87 -62247
## F value Pr(>F)
## <none>
## + `openings10_Horwitz Defense` 1.6405 0.2002743
## + titleW_GM 1.1108 0.2919195
## + ratingDifference 0.8415 0.3589844
## + titleB_N 0.7837 0.3760177
## + `openings10_Scandinavian Defense` 0.7830 0.3762496
## + `openings10_Queen's Pawn Game: Chigorin Variation` 0.6701 0.4130413
## - `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 3.4157 0.0645945
## - titleW_N 3.5222 0.0605672
## + openings10_Others 0.2697 0.6035434
## + `openings10_Sicilian Defense: Bowdler Attack` 0.2149 0.6429636
## + `openings10_Sicilian Defense` 0.1373 0.7109562
## + `openings10_Van't Kruijs Opening` 0.0854 0.7701759
## + `openings10_Scotch Game` 0.0232 0.8789448
## + `openings10_Queen's Pawn Game: Mason Attack` 0.0212 0.8842716
## + titleB_PRO 0.0062 0.9370965
## - titleB_GM 11.2508 0.0007974
## - increment_1 17.6667 2.643e-05
## - titleW_PRO 20.9346 4.781e-06
## - rated_True 24.2741 8.422e-07
## - duration 42.1581 8.616e-11
## - turns 623.1237 < 2.2e-16
##
## <none>
## + `openings10_Horwitz Defense`
## + titleW_GM
## + ratingDifference
## + titleB_N
## + `openings10_Scandinavian Defense`
## + `openings10_Queen's Pawn Game: Chigorin Variation`
## - `openings10_Scandinavian Defense: Mieses-Kotroc Variation` .
## - titleW_N .
## + openings10_Others
## + `openings10_Sicilian Defense: Bowdler Attack`
## + `openings10_Sicilian Defense`
## + `openings10_Van't Kruijs Opening`
## + `openings10_Scotch Game`
## + `openings10_Queen's Pawn Game: Mason Attack`
## + titleB_PRO
## - titleB_GM ***
## - increment_1 ***
## - titleW_PRO ***
## - rated_True ***
## - duration ***
## - turns ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1x <- step(reg_2_i,scope=list(lower=reg_2_i,upper=reg_2_f),direction = "forward",test="F",trace=TRUE)## Start: AIC=-62146.56
## result_y ~ 1
##
## Df Sum of Sq
## + turns 1 26.3546
## + duration 1 1.3342
## + titleW_PRO 1 1.2516
## + titleB_GM 1 0.7822
## + rated_True 1 0.6773
## + increment_1 1 0.5802
## + titleB_PRO 1 0.4740
## + titleW_GM 1 0.1659
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 1 0.1536
## + openings10_Others 1 0.1179
## + `openings10_Horwitz Defense` 1 0.1160
## <none>
## + titleB_N 1 0.0879
## + titleW_N 1 0.0822
## + `openings10_Queen's Pawn Game: Chigorin Variation` 1 0.0358
## + ratingDifference 1 0.0311
## + `openings10_Queen's Pawn Game: Mason Attack` 1 0.0177
## + `openings10_Scotch Game` 1 0.0126
## + `openings10_Sicilian Defense` 1 0.0109
## + `openings10_Van't Kruijs Opening` 1 0.0057
## + `openings10_Sicilian Defense: Bowdler Attack` 1 0.0036
## + `openings10_Scandinavian Defense` 1 0.0014
## RSS AIC
## + turns 878.65 -62737
## + duration 903.67 -62174
## + titleW_PRO 903.75 -62172
## + titleB_GM 904.22 -62162
## + rated_True 904.33 -62160
## + increment_1 904.43 -62157
## + titleB_PRO 904.53 -62155
## + titleW_GM 904.84 -62148
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 904.85 -62148
## + openings10_Others 904.89 -62147
## + `openings10_Horwitz Defense` 904.89 -62147
## <none> 905.01 -62147
## + titleB_N 904.92 -62147
## + titleW_N 904.92 -62146
## + `openings10_Queen's Pawn Game: Chigorin Variation` 904.97 -62145
## + ratingDifference 904.97 -62145
## + `openings10_Queen's Pawn Game: Mason Attack` 904.99 -62145
## + `openings10_Scotch Game` 904.99 -62145
## + `openings10_Sicilian Defense` 904.99 -62145
## + `openings10_Van't Kruijs Opening` 905.00 -62145
## + `openings10_Sicilian Defense: Bowdler Attack` 905.00 -62145
## + `openings10_Scandinavian Defense` 905.00 -62145
## F value Pr(>F)
## + turns 601.5666 < 2.2e-16
## + duration 29.6100 5.345e-08
## + titleW_PRO 27.7764 1.376e-07
## + titleB_GM 17.3485 3.124e-05
## + rated_True 15.0218 0.0001066
## + increment_1 12.8657 0.0003355
## + titleB_PRO 10.5106 0.0011888
## + titleW_GM 3.6768 0.0551894
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 3.4050 0.0650128
## + openings10_Others 2.6125 0.1060404
## + `openings10_Horwitz Defense` 2.5718 0.1088027
## <none>
## + titleB_N 1.9478 0.1628436
## + titleW_N 1.8218 0.1771103
## + `openings10_Queen's Pawn Game: Chigorin Variation` 0.7929 0.3732204
## + ratingDifference 0.6895 0.4063349
## + `openings10_Queen's Pawn Game: Mason Attack` 0.3912 0.5316929
## + `openings10_Scotch Game` 0.2792 0.5972210
## + `openings10_Sicilian Defense` 0.2411 0.6234178
## + `openings10_Van't Kruijs Opening` 0.1254 0.7233047
## + `openings10_Sicilian Defense: Bowdler Attack` 0.0790 0.7787161
## + `openings10_Scandinavian Defense` 0.0317 0.8586319
##
## + turns ***
## + duration ***
## + titleW_PRO ***
## + titleB_GM ***
## + rated_True ***
## + increment_1 ***
## + titleB_PRO **
## + titleW_GM .
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` .
## + openings10_Others
## + `openings10_Horwitz Defense`
## <none>
## + titleB_N
## + titleW_N
## + `openings10_Queen's Pawn Game: Chigorin Variation`
## + ratingDifference
## + `openings10_Queen's Pawn Game: Mason Attack`
## + `openings10_Scotch Game`
## + `openings10_Sicilian Defense`
## + `openings10_Van't Kruijs Opening`
## + `openings10_Sicilian Defense: Bowdler Attack`
## + `openings10_Scandinavian Defense`
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=-62737.34
## result_y ~ turns
##
## Df Sum of Sq
## + duration 1 2.13758
## + rated_True 1 1.67431
## + increment_1 1 0.98678
## + titleW_PRO 1 0.90866
## + titleB_GM 1 0.70155
## + titleW_GM 1 0.28171
## + titleB_PRO 1 0.21644
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 1 0.16744
## + ratingDifference 1 0.12982
## + `openings10_Horwitz Defense` 1 0.09814
## <none>
## + openings10_Others 1 0.07264
## + titleB_N 1 0.04424
## + `openings10_Queen's Pawn Game: Chigorin Variation` 1 0.03587
## + `openings10_Scandinavian Defense` 1 0.03395
## + titleW_N 1 0.02400
## + `openings10_Sicilian Defense: Bowdler Attack` 1 0.01927
## + `openings10_Sicilian Defense` 1 0.00715
## + `openings10_Scotch Game` 1 0.00350
## + `openings10_Van't Kruijs Opening` 1 0.00107
## + `openings10_Queen's Pawn Game: Mason Attack` 1 0.00080
## RSS AIC
## + duration 876.51 -62784
## + rated_True 876.98 -62774
## + increment_1 877.66 -62758
## + titleW_PRO 877.74 -62756
## + titleB_GM 877.95 -62751
## + titleW_GM 878.37 -62742
## + titleB_PRO 878.43 -62740
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 878.48 -62739
## + ratingDifference 878.52 -62738
## + `openings10_Horwitz Defense` 878.55 -62738
## <none> 878.65 -62737
## + openings10_Others 878.58 -62737
## + titleB_N 878.61 -62736
## + `openings10_Queen's Pawn Game: Chigorin Variation` 878.62 -62736
## + `openings10_Scandinavian Defense` 878.62 -62736
## + titleW_N 878.63 -62736
## + `openings10_Sicilian Defense: Bowdler Attack` 878.63 -62736
## + `openings10_Sicilian Defense` 878.64 -62736
## + `openings10_Scotch Game` 878.65 -62735
## + `openings10_Van't Kruijs Opening` 878.65 -62735
## + `openings10_Queen's Pawn Game: Mason Attack` 878.65 -62735
## F value Pr(>F)
## + duration 48.9087 2.766e-12
## + rated_True 38.2887 6.220e-10
## + increment_1 22.5483 2.063e-06
## + titleW_PRO 20.7615 5.233e-06
## + titleB_GM 16.0256 6.272e-05
## + titleW_GM 6.4319 0.01122
## + titleB_PRO 4.9415 0.02623
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 3.8224 0.05058
## + ratingDifference 2.9636 0.08517
## + `openings10_Horwitz Defense` 2.2404 0.13446
## <none>
## + openings10_Others 1.6581 0.19788
## + titleB_N 1.0097 0.31498
## + `openings10_Queen's Pawn Game: Chigorin Variation` 0.8187 0.36556
## + `openings10_Scandinavian Defense` 0.7749 0.37872
## + titleW_N 0.5478 0.45921
## + `openings10_Sicilian Defense: Bowdler Attack` 0.4398 0.50722
## + `openings10_Sicilian Defense` 0.1632 0.68621
## + `openings10_Scotch Game` 0.0800 0.77731
## + `openings10_Van't Kruijs Opening` 0.0244 0.87582
## + `openings10_Queen's Pawn Game: Mason Attack` 0.0182 0.89258
##
## + duration ***
## + rated_True ***
## + increment_1 ***
## + titleW_PRO ***
## + titleB_GM ***
## + titleW_GM *
## + titleB_PRO *
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` .
## + ratingDifference .
## + `openings10_Horwitz Defense`
## <none>
## + openings10_Others
## + titleB_N
## + `openings10_Queen's Pawn Game: Chigorin Variation`
## + `openings10_Scandinavian Defense`
## + titleW_N
## + `openings10_Sicilian Defense: Bowdler Attack`
## + `openings10_Sicilian Defense`
## + `openings10_Scotch Game`
## + `openings10_Van't Kruijs Opening`
## + `openings10_Queen's Pawn Game: Mason Attack`
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=-62784.19
## result_y ~ turns + duration
##
## Df Sum of Sq
## + rated_True 1 1.32955
## + increment_1 1 0.95273
## + titleW_PRO 1 0.87443
## + titleB_GM 1 0.70891
## + titleW_GM 1 0.26742
## + titleB_PRO 1 0.20438
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 1 0.16698
## + ratingDifference 1 0.12358
## + openings10_Others 1 0.10856
## <none>
## + `openings10_Horwitz Defense` 1 0.08372
## + `openings10_Queen's Pawn Game: Chigorin Variation` 1 0.03251
## + `openings10_Scandinavian Defense` 1 0.02173
## + `openings10_Sicilian Defense: Bowdler Attack` 1 0.02058
## + `openings10_Van't Kruijs Opening` 1 0.01455
## + titleB_N 1 0.01049
## + `openings10_Sicilian Defense` 1 0.00888
## + `openings10_Scotch Game` 1 0.00369
## + titleW_N 1 0.00358
## + `openings10_Queen's Pawn Game: Mason Attack` 1 0.00190
## RSS AIC
## + rated_True 875.18 -62813
## + increment_1 875.56 -62804
## + titleW_PRO 875.64 -62802
## + titleB_GM 875.80 -62798
## + titleW_GM 876.25 -62788
## + titleB_PRO 876.31 -62787
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 876.35 -62786
## + ratingDifference 876.39 -62785
## + openings10_Others 876.40 -62785
## <none> 876.51 -62784
## + `openings10_Horwitz Defense` 876.43 -62784
## + `openings10_Queen's Pawn Game: Chigorin Variation` 876.48 -62783
## + `openings10_Scandinavian Defense` 876.49 -62783
## + `openings10_Sicilian Defense: Bowdler Attack` 876.49 -62783
## + `openings10_Van't Kruijs Opening` 876.50 -62783
## + titleB_N 876.50 -62782
## + `openings10_Sicilian Defense` 876.50 -62782
## + `openings10_Scotch Game` 876.51 -62782
## + titleW_N 876.51 -62782
## + `openings10_Queen's Pawn Game: Mason Attack` 876.51 -62782
## F value Pr(>F)
## + rated_True 30.4654 3.441e-08
## + increment_1 21.8214 3.012e-06
## + titleW_PRO 20.0262 7.681e-06
## + titleB_GM 16.2326 5.623e-05
## + titleW_GM 6.1204 0.01337
## + titleB_PRO 4.6772 0.03058
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 3.8212 0.05062
## + ratingDifference 2.8279 0.09265
## + openings10_Others 2.4840 0.11502
## <none>
## + `openings10_Horwitz Defense` 1.9156 0.16636
## + `openings10_Queen's Pawn Game: Chigorin Variation` 0.7439 0.38841
## + `openings10_Scandinavian Defense` 0.4973 0.48071
## + `openings10_Sicilian Defense: Bowdler Attack` 0.4709 0.49256
## + `openings10_Van't Kruijs Opening` 0.3329 0.56394
## + titleB_N 0.2400 0.62422
## + `openings10_Sicilian Defense` 0.2033 0.65210
## + `openings10_Scotch Game` 0.0844 0.77147
## + titleW_N 0.0819 0.77472
## + `openings10_Queen's Pawn Game: Mason Attack` 0.0435 0.83487
##
## + rated_True ***
## + increment_1 ***
## + titleW_PRO ***
## + titleB_GM ***
## + titleW_GM *
## + titleB_PRO *
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` .
## + ratingDifference .
## + openings10_Others
## <none>
## + `openings10_Horwitz Defense`
## + `openings10_Queen's Pawn Game: Chigorin Variation`
## + `openings10_Scandinavian Defense`
## + `openings10_Sicilian Defense: Bowdler Attack`
## + `openings10_Van't Kruijs Opening`
## + titleB_N
## + `openings10_Sicilian Defense`
## + `openings10_Scotch Game`
## + titleW_N
## + `openings10_Queen's Pawn Game: Mason Attack`
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=-62812.64
## result_y ~ turns + duration + rated_True
##
## Df Sum of Sq
## + titleW_PRO 1 0.83399
## + increment_1 1 0.77533
## + titleB_GM 1 0.62172
## + titleB_PRO 1 0.21555
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 1 0.16902
## + titleW_GM 1 0.15862
## + ratingDifference 1 0.09999
## + openings10_Others 1 0.09280
## <none>
## + `openings10_Horwitz Defense` 1 0.07188
## + `openings10_Queen's Pawn Game: Chigorin Variation` 1 0.03503
## + `openings10_Scandinavian Defense` 1 0.02686
## + `openings10_Sicilian Defense: Bowdler Attack` 1 0.01771
## + titleB_N 1 0.01202
## + `openings10_Sicilian Defense` 1 0.00980
## + `openings10_Van't Kruijs Opening` 1 0.00874
## + `openings10_Scotch Game` 1 0.00343
## + `openings10_Queen's Pawn Game: Mason Attack` 1 0.00163
## + titleW_N 1 0.00150
## RSS AIC
## + titleW_PRO 874.35 -62830
## + increment_1 874.41 -62828
## + titleB_GM 874.56 -62825
## + titleB_PRO 874.97 -62816
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 875.01 -62815
## + titleW_GM 875.03 -62814
## + ratingDifference 875.08 -62813
## + openings10_Others 875.09 -62813
## <none> 875.18 -62813
## + `openings10_Horwitz Defense` 875.11 -62812
## + `openings10_Queen's Pawn Game: Chigorin Variation` 875.15 -62811
## + `openings10_Scandinavian Defense` 875.16 -62811
## + `openings10_Sicilian Defense: Bowdler Attack` 875.17 -62811
## + titleB_N 875.17 -62811
## + `openings10_Sicilian Defense` 875.17 -62811
## + `openings10_Van't Kruijs Opening` 875.18 -62811
## + `openings10_Scotch Game` 875.18 -62811
## + `openings10_Queen's Pawn Game: Mason Attack` 875.18 -62811
## + titleW_N 875.18 -62811
## F value Pr(>F)
## + titleW_PRO 19.1273 1.229e-05
## + increment_1 17.7809 2.489e-05
## + titleB_GM 14.2554 0.0001601
## + titleB_PRO 4.9400 0.0262529
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 3.8734 0.0490710
## + titleW_GM 3.6352 0.0565845
## + ratingDifference 2.2912 0.1301222
## + openings10_Others 2.1266 0.1447779
## <none>
## + `openings10_Horwitz Defense` 1.6472 0.1993544
## + `openings10_Queen's Pawn Game: Chigorin Variation` 0.8027 0.3702836
## + `openings10_Scandinavian Defense` 0.6154 0.4327537
## + `openings10_Sicilian Defense: Bowdler Attack` 0.4057 0.5241615
## + titleB_N 0.2755 0.5996863
## + `openings10_Sicilian Defense` 0.2245 0.6356155
## + `openings10_Van't Kruijs Opening` 0.2002 0.6545949
## + `openings10_Scotch Game` 0.0786 0.7791619
## + `openings10_Queen's Pawn Game: Mason Attack` 0.0374 0.8466192
## + titleW_N 0.0343 0.8530707
##
## + titleW_PRO ***
## + increment_1 ***
## + titleB_GM ***
## + titleB_PRO *
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` *
## + titleW_GM .
## + ratingDifference
## + openings10_Others
## <none>
## + `openings10_Horwitz Defense`
## + `openings10_Queen's Pawn Game: Chigorin Variation`
## + `openings10_Scandinavian Defense`
## + `openings10_Sicilian Defense: Bowdler Attack`
## + titleB_N
## + `openings10_Sicilian Defense`
## + `openings10_Van't Kruijs Opening`
## + `openings10_Scotch Game`
## + `openings10_Queen's Pawn Game: Mason Attack`
## + titleW_N
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=-62829.76
## result_y ~ turns + duration + rated_True + titleW_PRO
##
## Df Sum of Sq
## + increment_1 1 0.78309
## + titleB_GM 1 0.54702
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 1 0.15817
## + titleW_N 1 0.15607
## + titleW_GM 1 0.08925
## <none>
## + `openings10_Horwitz Defense` 1 0.07364
## + openings10_Others 1 0.06643
## + ratingDifference 1 0.04558
## + `openings10_Queen's Pawn Game: Chigorin Variation` 1 0.03307
## + `openings10_Scandinavian Defense` 1 0.02580
## + `openings10_Sicilian Defense: Bowdler Attack` 1 0.01020
## + titleB_PRO 1 0.00811
## + `openings10_Van't Kruijs Opening` 1 0.00733
## + `openings10_Sicilian Defense` 1 0.00634
## + titleB_N 1 0.00279
## + `openings10_Queen's Pawn Game: Mason Attack` 1 0.00189
## + `openings10_Scotch Game` 1 0.00106
## RSS AIC
## + increment_1 873.57 -62846
## + titleB_GM 873.80 -62840
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 874.19 -62831
## + titleW_N 874.19 -62831
## + titleW_GM 874.26 -62830
## <none> 874.35 -62830
## + `openings10_Horwitz Defense` 874.28 -62829
## + openings10_Others 874.28 -62829
## + ratingDifference 874.30 -62829
## + `openings10_Queen's Pawn Game: Chigorin Variation` 874.32 -62829
## + `openings10_Scandinavian Defense` 874.32 -62828
## + `openings10_Sicilian Defense: Bowdler Attack` 874.34 -62828
## + titleB_PRO 874.34 -62828
## + `openings10_Van't Kruijs Opening` 874.34 -62828
## + `openings10_Sicilian Defense` 874.34 -62828
## + titleB_N 874.35 -62828
## + `openings10_Queen's Pawn Game: Mason Attack` 874.35 -62828
## + `openings10_Scotch Game` 874.35 -62828
## F value Pr(>F)
## + increment_1 17.9752 2.248e-05
## + titleB_GM 12.5530 0.0003965
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 3.6282 0.0568238
## + titleW_N 3.5800 0.0584937
## + titleW_GM 2.0471 0.1525116
## <none>
## + `openings10_Horwitz Defense` 1.6889 0.1937588
## + openings10_Others 1.5236 0.2170834
## + ratingDifference 1.0455 0.3065623
## + `openings10_Queen's Pawn Game: Chigorin Variation` 0.7585 0.3838052
## + `openings10_Scandinavian Defense` 0.5917 0.4417851
## + `openings10_Sicilian Defense: Bowdler Attack` 0.2339 0.6286829
## + titleB_PRO 0.1859 0.6663234
## + `openings10_Van't Kruijs Opening` 0.1681 0.6817882
## + `openings10_Sicilian Defense` 0.1453 0.7030444
## + titleB_N 0.0641 0.8001844
## + `openings10_Queen's Pawn Game: Mason Attack` 0.0432 0.8352709
## + `openings10_Scotch Game` 0.0242 0.8763239
##
## + increment_1 ***
## + titleB_GM ***
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` .
## + titleW_N .
## + titleW_GM
## <none>
## + `openings10_Horwitz Defense`
## + openings10_Others
## + ratingDifference
## + `openings10_Queen's Pawn Game: Chigorin Variation`
## + `openings10_Scandinavian Defense`
## + `openings10_Sicilian Defense: Bowdler Attack`
## + titleB_PRO
## + `openings10_Van't Kruijs Opening`
## + `openings10_Sicilian Defense`
## + titleB_N
## + `openings10_Queen's Pawn Game: Mason Attack`
## + `openings10_Scotch Game`
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=-62845.74
## result_y ~ turns + duration + rated_True + titleW_PRO + increment_1
##
## Df Sum of Sq
## + titleB_GM 1 0.51617
## + titleW_N 1 0.17837
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 1 0.15393
## <none>
## + `openings10_Horwitz Defense` 1 0.07231
## + titleW_GM 1 0.06646
## + openings10_Others 1 0.06514
## + ratingDifference 1 0.03859
## + `openings10_Queen's Pawn Game: Chigorin Variation` 1 0.03314
## + `openings10_Scandinavian Defense` 1 0.02463
## + `openings10_Van't Kruijs Opening` 1 0.00945
## + `openings10_Sicilian Defense: Bowdler Attack` 1 0.00936
## + titleB_PRO 1 0.00848
## + `openings10_Sicilian Defense` 1 0.00573
## + `openings10_Queen's Pawn Game: Mason Attack` 1 0.00159
## + `openings10_Scotch Game` 1 0.00093
## + titleB_N 1 0.00069
## RSS AIC
## + titleB_GM 873.05 -62856
## + titleW_N 873.39 -62848
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 873.41 -62847
## <none> 873.57 -62846
## + `openings10_Horwitz Defense` 873.49 -62845
## + titleW_GM 873.50 -62845
## + openings10_Others 873.50 -62845
## + ratingDifference 873.53 -62845
## + `openings10_Queen's Pawn Game: Chigorin Variation` 873.53 -62844
## + `openings10_Scandinavian Defense` 873.54 -62844
## + `openings10_Van't Kruijs Opening` 873.56 -62844
## + `openings10_Sicilian Defense: Bowdler Attack` 873.56 -62844
## + titleB_PRO 873.56 -62844
## + `openings10_Sicilian Defense` 873.56 -62844
## + `openings10_Queen's Pawn Game: Mason Attack` 873.57 -62844
## + `openings10_Scotch Game` 873.57 -62844
## + titleB_N 873.57 -62844
## F value Pr(>F)
## + titleB_GM 11.8546 0.0005764
## + titleW_N 4.0950 0.0430245
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 3.5338 0.0601437
## <none>
## + `openings10_Horwitz Defense` 1.6600 0.1976249
## + titleW_GM 1.5257 0.2167795
## + openings10_Others 1.4953 0.2214145
## + ratingDifference 0.8857 0.3466503
## + `openings10_Queen's Pawn Game: Chigorin Variation` 0.7607 0.3831285
## + `openings10_Scandinavian Defense` 0.5653 0.4521524
## + `openings10_Van't Kruijs Opening` 0.2169 0.6414231
## + `openings10_Sicilian Defense: Bowdler Attack` 0.2149 0.6429750
## + titleB_PRO 0.1947 0.6590526
## + `openings10_Sicilian Defense` 0.1314 0.7169790
## + `openings10_Queen's Pawn Game: Mason Attack` 0.0366 0.8483456
## + `openings10_Scotch Game` 0.0214 0.8838056
## + titleB_N 0.0158 0.8998632
##
## + titleB_GM ***
## + titleW_N *
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` .
## <none>
## + `openings10_Horwitz Defense`
## + titleW_GM
## + openings10_Others
## + ratingDifference
## + `openings10_Queen's Pawn Game: Chigorin Variation`
## + `openings10_Scandinavian Defense`
## + `openings10_Van't Kruijs Opening`
## + `openings10_Sicilian Defense: Bowdler Attack`
## + titleB_PRO
## + `openings10_Sicilian Defense`
## + `openings10_Queen's Pawn Game: Mason Attack`
## + `openings10_Scotch Game`
## + titleB_N
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=-62855.59
## result_y ~ turns + duration + rated_True + titleW_PRO + increment_1 +
## titleB_GM
##
## Df Sum of Sq
## + titleW_N 1 0.155146
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 1 0.150510
## + ratingDifference 1 0.091891
## <none>
## + `openings10_Horwitz Defense` 1 0.070214
## + titleW_GM 1 0.060598
## + openings10_Others 1 0.059770
## + `openings10_Queen's Pawn Game: Chigorin Variation` 1 0.031462
## + `openings10_Scandinavian Defense` 1 0.025903
## + `openings10_Sicilian Defense: Bowdler Attack` 1 0.008669
## + `openings10_Van't Kruijs Opening` 1 0.008556
## + `openings10_Sicilian Defense` 1 0.005642
## + titleB_N 1 0.001733
## + titleB_PRO 1 0.001627
## + `openings10_Queen's Pawn Game: Mason Attack` 1 0.001539
## + `openings10_Scotch Game` 1 0.000713
## RSS AIC
## + titleW_N 872.90 -62857
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 872.90 -62857
## + ratingDifference 872.96 -62856
## <none> 873.05 -62856
## + `openings10_Horwitz Defense` 872.98 -62855
## + titleW_GM 872.99 -62855
## + openings10_Others 872.99 -62855
## + `openings10_Queen's Pawn Game: Chigorin Variation` 873.02 -62854
## + `openings10_Scandinavian Defense` 873.02 -62854
## + `openings10_Sicilian Defense: Bowdler Attack` 873.04 -62854
## + `openings10_Van't Kruijs Opening` 873.04 -62854
## + `openings10_Sicilian Defense` 873.04 -62854
## + titleB_N 873.05 -62854
## + titleB_PRO 873.05 -62854
## + `openings10_Queen's Pawn Game: Mason Attack` 873.05 -62854
## + `openings10_Scotch Game` 873.05 -62854
## F value Pr(>F)
## + titleW_N 3.5636 0.05907 .
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 3.4571 0.06299 .
## + ratingDifference 2.1105 0.14630
## <none>
## + `openings10_Horwitz Defense` 1.6126 0.20414
## + titleW_GM 1.3918 0.23812
## + openings10_Others 1.3727 0.24136
## + `openings10_Queen's Pawn Game: Chigorin Variation` 0.7226 0.39531
## + `openings10_Scandinavian Defense` 0.5949 0.44054
## + `openings10_Sicilian Defense: Bowdler Attack` 0.1991 0.65547
## + `openings10_Van't Kruijs Opening` 0.1965 0.65757
## + `openings10_Sicilian Defense` 0.1296 0.71888
## + titleB_N 0.0398 0.84186
## + titleB_PRO 0.0374 0.84674
## + `openings10_Queen's Pawn Game: Mason Attack` 0.0354 0.85086
## + `openings10_Scotch Game` 0.0164 0.89817
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=-62857.16
## result_y ~ turns + duration + rated_True + titleW_PRO + increment_1 +
## titleB_GM + titleW_N
##
## Df Sum of Sq
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 1 0.148687
## <none>
## + `openings10_Horwitz Defense` 1 0.069004
## + openings10_Others 1 0.046363
## + titleW_GM 1 0.045508
## + `openings10_Scandinavian Defense` 1 0.035862
## + titleB_N 1 0.032062
## + ratingDifference 1 0.031009
## + `openings10_Queen's Pawn Game: Chigorin Variation` 1 0.027526
## + `openings10_Sicilian Defense: Bowdler Attack` 1 0.008292
## + `openings10_Sicilian Defense` 1 0.005071
## + `openings10_Van't Kruijs Opening` 1 0.002987
## + `openings10_Queen's Pawn Game: Mason Attack` 1 0.001236
## + `openings10_Scotch Game` 1 0.000699
## + titleB_PRO 1 0.000130
## RSS AIC
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 872.75 -62859
## <none> 872.90 -62857
## + `openings10_Horwitz Defense` 872.83 -62857
## + openings10_Others 872.85 -62856
## + titleW_GM 872.85 -62856
## + `openings10_Scandinavian Defense` 872.86 -62856
## + titleB_N 872.86 -62856
## + ratingDifference 872.86 -62856
## + `openings10_Queen's Pawn Game: Chigorin Variation` 872.87 -62856
## + `openings10_Sicilian Defense: Bowdler Attack` 872.89 -62855
## + `openings10_Sicilian Defense` 872.89 -62855
## + `openings10_Van't Kruijs Opening` 872.89 -62855
## + `openings10_Queen's Pawn Game: Mason Attack` 872.89 -62855
## + `openings10_Scotch Game` 872.89 -62855
## + titleB_PRO 872.90 -62855
## F value Pr(>F)
## + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 3.4157 0.06459 .
## <none>
## + `openings10_Horwitz Defense` 1.5850 0.20805
## + openings10_Others 1.0649 0.30210
## + titleW_GM 1.0453 0.30660
## + `openings10_Scandinavian Defense` 0.8237 0.36410
## + titleB_N 0.7364 0.39081
## + ratingDifference 0.7123 0.39871
## + `openings10_Queen's Pawn Game: Chigorin Variation` 0.6323 0.42654
## + `openings10_Sicilian Defense: Bowdler Attack` 0.1905 0.66254
## + `openings10_Sicilian Defense` 0.1165 0.73291
## + `openings10_Van't Kruijs Opening` 0.0686 0.79337
## + `openings10_Queen's Pawn Game: Mason Attack` 0.0284 0.86621
## + `openings10_Scotch Game` 0.0161 0.89915
## + titleB_PRO 0.0030 0.95646
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: AIC=-62858.57
## result_y ~ turns + duration + rated_True + titleW_PRO + increment_1 +
## titleB_GM + titleW_N + `openings10_Scandinavian Defense: Mieses-Kotroc Variation`
##
## Df Sum of Sq RSS AIC
## <none> 872.75 -62859
## + `openings10_Horwitz Defense` 1 0.071409 872.68 -62858
## + titleW_GM 1 0.048354 872.70 -62858
## + ratingDifference 1 0.036631 872.71 -62857
## + titleB_N 1 0.034116 872.71 -62857
## + `openings10_Scandinavian Defense` 1 0.034083 872.71 -62857
## + `openings10_Queen's Pawn Game: Chigorin Variation` 1 0.029169 872.72 -62857
## + openings10_Others 1 0.011740 872.73 -62857
## + `openings10_Sicilian Defense: Bowdler Attack` 1 0.009355 872.74 -62857
## + `openings10_Sicilian Defense` 1 0.005978 872.74 -62857
## + `openings10_Van't Kruijs Opening` 1 0.003716 872.74 -62857
## + `openings10_Scotch Game` 1 0.001010 872.75 -62857
## + `openings10_Queen's Pawn Game: Mason Attack` 1 0.000922 872.75 -62857
## + titleB_PRO 1 0.000271 872.75 -62857
## F value Pr(>F)
## <none>
## + `openings10_Horwitz Defense` 1.6405 0.2003
## + titleW_GM 1.1108 0.2919
## + ratingDifference 0.8415 0.3590
## + titleB_N 0.7837 0.3760
## + `openings10_Scandinavian Defense` 0.7830 0.3762
## + `openings10_Queen's Pawn Game: Chigorin Variation` 0.6701 0.4130
## + openings10_Others 0.2697 0.6035
## + `openings10_Sicilian Defense: Bowdler Attack` 0.2149 0.6430
## + `openings10_Sicilian Defense` 0.1373 0.7110
## + `openings10_Van't Kruijs Opening` 0.0854 0.7702
## + `openings10_Scotch Game` 0.0232 0.8789
## + `openings10_Queen's Pawn Game: Mason Attack` 0.0212 0.8843
## + titleB_PRO 0.0062 0.9371After running step function we have concluded that model with variables ‘turns’, ‘rated_True’, ‘duration’, ‘increment_1’, ‘titleW_PRO’ , ‘titleB_GM’, ‘openings10_Scandinavian Defense: Mieses-Kotroc Variation’ and’titleW_N’ are significantly contributing to the model.
#Estiimating Regression Model Now before doing further analysis let us first split database in training and testing datasets in ratio of 4:1
reg_2<- lm(result_y ~ turns + rated_True + duration + increment_1 + titleW_PRO +
titleB_GM + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` +
titleW_N,chessData_2)
summary(reg_2)##
## Call:
## lm(formula = result_y ~ turns + rated_True + duration + increment_1 +
## titleW_PRO + titleB_GM + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` +
## titleW_N, data = chessData_2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.03308 0.01515 0.03842 0.06534 0.36774
##
## Coefficients:
## Estimate
## (Intercept) 1.006e+00
## turns -1.109e-03
## rated_True 1.859e-02
## duration -5.625e-04
## increment_1 -1.252e-02
## titleW_PRO 1.605e-02
## titleB_GM -8.237e-02
## `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 2.412e-02
## titleW_N 1.138e-02
## Std. Error t value
## (Intercept) 5.491e-03 183.265
## turns 4.442e-05 -24.962
## rated_True 3.774e-03 4.927
## duration 8.663e-05 -6.493
## increment_1 2.980e-03 -4.203
## titleW_PRO 3.508e-03 4.575
## titleB_GM 2.456e-02 -3.354
## `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 1.305e-02 1.848
## titleW_N 6.066e-03 1.877
## Pr(>|t|)
## (Intercept) < 2e-16 ***
## turns < 2e-16 ***
## rated_True 8.42e-07 ***
## duration 8.62e-11 ***
## increment_1 2.64e-05 ***
## titleW_PRO 4.78e-06 ***
## titleB_GM 0.000797 ***
## `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 0.064594 .
## titleW_N 0.060567 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2086 on 20049 degrees of freedom
## Multiple R-squared: 0.03564, Adjusted R-squared: 0.03526
## F-statistic: 92.63 on 8 and 20049 DF, p-value: < 2.2e-16# Partition the data set
set.seed(1610)
# Split the dataset
split <- sample.split(chessData_2[,5],SplitRatio=0.8)
training <- subset(chessData_2,split=="TRUE")
testing <- subset(chessData_2,split=="FALSE")
str(training);str(testing)## 'data.frame': 16046 obs. of 22 variables:
## $ turns : int 13 16 61 5 9 66 119 39 38 31 ...
## $ duration : num 15 5 20 10 15 15 10 20 20 8 ...
## $ ratingDifference : int 309 61 -15 248 -695 47 172 109 -486 -226 ...
## $ rated_True : int 0 1 1 0 0 1 1 0 0 0 ...
## $ result_y : int 1 1 1 0 1 1 1 1 1 1 ...
## $ openings10_Horwitz Defense : int 0 0 0 0 0 0 0 0 0 0 ...
## $ openings10_Others : int 1 1 1 1 1 1 0 0 1 1 ...
## $ openings10_Queen's Pawn Game: Chigorin Variation : int 0 0 0 0 0 0 0 0 0 0 ...
## $ openings10_Queen's Pawn Game: Mason Attack : int 0 0 0 0 0 0 0 0 0 0 ...
## $ openings10_Scandinavian Defense : int 0 0 0 0 0 0 0 0 0 0 ...
## $ openings10_Scandinavian Defense: Mieses-Kotroc Variation: int 0 0 0 0 0 0 1 0 0 0 ...
## $ openings10_Scotch Game : int 0 0 0 0 0 0 0 0 0 0 ...
## $ openings10_Sicilian Defense : int 0 0 0 0 0 0 0 0 0 0 ...
## $ openings10_Sicilian Defense: Bowdler Attack : int 0 0 0 0 0 0 0 0 0 0 ...
## $ openings10_Van't Kruijs Opening : int 0 0 0 0 0 0 0 1 0 0 ...
## $ titleW_GM : int 0 0 0 0 0 0 0 0 0 0 ...
## $ titleW_N : int 0 0 0 0 0 0 0 0 0 0 ...
## $ titleW_PRO : int 1 1 1 1 1 1 1 1 1 1 ...
## $ titleB_GM : int 0 0 0 0 0 0 0 0 0 0 ...
## $ titleB_N : int 1 0 0 1 0 0 0 0 0 0 ...
## $ titleB_PRO : int 0 1 1 0 0 1 1 1 0 1 ...
## $ increment_1 : int 1 1 0 0 1 0 0 1 1 0 ...## 'data.frame': 4012 obs. of 22 variables:
## $ turns : int 61 95 33 60 43 36 13 43 64 22 ...
## $ duration : num 5 30 10 5 15 10 10 10 10 15 ...
## $ ratingDifference : int -4 54 97 -555 47 201 -310 746 198 -522 ...
## $ rated_True : int 1 1 1 0 0 1 1 1 1 0 ...
## $ result_y : int 1 1 1 1 1 1 1 1 1 1 ...
## $ openings10_Horwitz Defense : int 0 0 0 0 0 0 0 0 0 0 ...
## $ openings10_Others : int 1 1 1 0 1 1 1 1 1 1 ...
## $ openings10_Queen's Pawn Game: Chigorin Variation : int 0 0 0 0 0 0 0 0 0 0 ...
## $ openings10_Queen's Pawn Game: Mason Attack : int 0 0 0 0 0 0 0 0 0 0 ...
## $ openings10_Scandinavian Defense : int 0 0 0 0 0 0 0 0 0 0 ...
## $ openings10_Scandinavian Defense: Mieses-Kotroc Variation: int 0 0 0 0 0 0 0 0 0 0 ...
## $ openings10_Scotch Game : int 0 0 0 0 0 0 0 0 0 0 ...
## $ openings10_Sicilian Defense : int 0 0 0 0 0 0 0 0 0 0 ...
## $ openings10_Sicilian Defense: Bowdler Attack : int 0 0 0 0 0 0 0 0 0 0 ...
## $ openings10_Van't Kruijs Opening : int 0 0 0 0 0 0 0 0 0 0 ...
## $ titleW_GM : int 0 0 0 0 0 0 0 0 0 0 ...
## $ titleW_N : int 0 0 0 0 1 0 1 0 1 1 ...
## $ titleW_PRO : int 1 1 1 1 0 1 0 0 0 0 ...
## $ titleB_GM : int 0 0 0 0 0 0 0 0 0 0 ...
## $ titleB_N : int 0 0 0 0 1 1 0 1 1 0 ...
## $ titleB_PRO : int 1 1 1 0 0 0 1 0 0 1 ...
## $ increment_1 : int 1 1 0 1 1 0 0 1 1 0 ...prop.table(table(chessData_2$result_y))##
## 0 1
## 0.04736265 0.95263735prop.table(table(training$result_y))##
## 0 1
## 0.04736383 0.95263617prop.table(table(testing$result_y))##
## 0 1
## 0.04735793 0.95264207model <- glm(result_y ~ turns + rated_True + duration + increment_1 + titleW_PRO +
titleB_GM + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` +
titleW_N,training,family=binomial)
summary(model)##
## Call:
## glm(formula = result_y ~ turns + rated_True + duration + increment_1 +
## titleW_PRO + titleB_GM + `openings10_Scandinavian Defense: Mieses-Kotroc Variation` +
## titleW_N, family = binomial, data = training)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.0915 0.2027 0.2522 0.3231 2.2997
##
## Coefficients:
## Estimate
## (Intercept) 4.0899940
## turns -0.0201797
## rated_True 0.4648474
## duration -0.0082701
## increment_1 -0.2742533
## titleW_PRO 0.3586824
## titleB_GM -1.0775934
## `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 0.7041227
## titleW_N 0.2322901
## Std. Error z value
## (Intercept) 0.1357621 30.126
## turns 0.0009675 -20.858
## rated_True 0.0901829 5.154
## duration 0.0015747 -5.252
## increment_1 0.0767014 -3.576
## titleW_PRO 0.0835296 4.294
## titleB_GM 0.3644022 -2.957
## `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 0.4592343 1.533
## titleW_N 0.1592176 1.459
## Pr(>|z|)
## (Intercept) < 2e-16 ***
## turns < 2e-16 ***
## rated_True 2.54e-07 ***
## duration 1.50e-07 ***
## increment_1 0.000349 ***
## titleW_PRO 1.75e-05 ***
## titleB_GM 0.003105 **
## `openings10_Scandinavian Defense: Mieses-Kotroc Variation` 0.125213
## titleW_N 0.144579
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 6119.3 on 16045 degrees of freedom
## Residual deviance: 5615.0 on 16037 degrees of freedom
## AIC: 5633
##
## Number of Fisher Scoring iterations: 6vif(model)## turns
## 1.035163
## rated_True
## 1.053800
## duration
## 1.034476
## increment_1
## 1.015655
## titleW_PRO
## 1.151950
## titleB_GM
## 1.017931
## `openings10_Scandinavian Defense: Mieses-Kotroc Variation`
## 1.000514
## titleW_N
## 1.158684We have ran logistictic regression on the training dataset and the logit of model is as follows: =b04.0899940+ turns -0.0201797+ rated_True0.4648474+ duration -0.0082701+ increment_1* -0.2742533+ titleW_PRO* 0.3586824+ titleB_GM -1.0775934+ openings10_Scandinavian Defense: Mieses-Kotroc Variation0.7041227+ titleW_N*0.2322901
We also tested multi collinearity and found there is no severe multicollinearity in the model
#Testing Assumptions for the model
#Checking linearity assumptions
# predict
res_train <- predict(model,training,type="response")
length(res_train)## [1] 16046logit_train <- log(res_train/(1-res_train))
plot(logit_train,training$age)
# Check for influential points
plot(model,5)
# Model Significance
with(model,null.deviance-deviance)## [1] 504.2511with(model,df.null-df.residual)## [1] 8#p-value of the test
with(model,pchisq(null.deviance-deviance,df.null-df.residual,lower.tail=FALSE))## [1] 8.612628e-104We tested for the linearity and did not observed any linearity. There were no influential points as well. To check the overall significance of model we ran chi-square test and found that is significant. We also observed that the individual predictors are also significant at 95% confidence interval.
Validating the Model
# predicting probabilities on test data from logistic model
res_test <- predict(model,testing,type="response")
length(res_test)## [1] 4012# Performance on test data
# Confusion matrix with threshold 0.5
Predicted_type <- ifelse(res_test>0.5, "Positive","Negative")
p <- table(ActualValue = testing$result_y, PredictedValue = Predicted_type)
accuracy <- (p[1,1]+p[2,2])/sum(p)
# Confusion matrix with threshold 0.3
Predicted_type <- res_test>0.3
p <- table(ActualValue = testing$result_y, PredictedValue = Predicted_type)
p## PredictedValue
## ActualValue FALSE TRUE
## 0 1 189
## 1 1 3821accuracy <- (p[1,1]+p[2,2])/sum(p)
# ROC curve and AUC
plotROC(actuals =testing$result_y , predictedScores = res_test)
# Binary Classification
# cut off value while minimizing mis-classification error
# cut off value while minimizing mis-classifying ones
optimalCutoff(actuals =testing$result_y , predictedScores = res_test,optimiseFor = "misclasserror")## [1] 0.3342428# Confusion matrix with threshold 0.3342
Predicted_type <- ifelse(res_test>0.3342, "Positive","Negative")
p <- table(ActualValue = testing$result_y, PredictedValue = Predicted_type)
accuracy <- (p[1,1]+p[2,2])/sum(p)After verification of assumption we validated the model using test dataset. The optimal cut-off value came 0.3342 The model accuracy is 95.28%. The area under the ROC curve came out to be 0.6937
Results
Model - 1 Logit =b00.2177480 + ratingDifference0.0038254+ titleW_GM-0.7581523+ turns-0.0022050+ openings10_Van't Kruijs Opening-0.5280239+ openings10_Scandinavian Defense-0.4583319+openings10_Scandinavian Defense: Mieses-Kotroc Variation0.4719704+openings10_Sicilian Defense: Bowdler Attack-0.1827203+titleW_PRO0.1181613+titleB_PRO-0.1003448+openings10_Sicilian Defense-0.1791304+titleB_GM 0.3152878 Optimal Cutoff:0.5462 Accuracy: 65.54 AUROC: 0.7261
Model - 2 Logit = =b04.0899940+ turns -0.0201797+ rated_True0.4648474+ duration -0.0082701+ increment_1* -0.2742533+ titleW_PRO* 0.3586824+ titleB_GM -1.0775934+ openings10_Scandinavian Defense: Mieses-Kotroc Variation0.7041227+ titleW_N*0.2322901
Optimal Cutoff: 0.3342 Accuracy:95.28% AUROC: 0.6937
Conclusion
Model 1 1. With increase in Rating Difference the probability of white winning increases. Playing ‘Scandinavian Defense:Mieses-Kotroc Variation’ over ‘French Defense: Knight Variation’ increases likelihood of winning for player with white pieces. 2. With decrease in number of turns the probability of white winning increases. Playing “Van’t Kruijs Opening” , “Scandinavian Defense`”, & Sicilian Defense: Bowdler over ‘French Defense: Knight Variation’ decreases likelihood of winning for player with white pieces.
Model 2 1.With increase in Rating Difference the probability of getting an outcome increases. 2.Playing ’Sicilian Defense: Bowdler Attack and Sicilian Defense result more in draw games. 3.The probability of getting an outcome is high for a player with rating greater than 2400 compared to one with rating less than 1200 rating
##Appe….