Week 12 Discussion
Joey Bochnik
2024-04-10
library(Lahman)
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(ggplot2)# Load team data
teams_data <- Teams
# Select only the relevant columns we will select the year, team name, team ID, Wins (dependent variable), Strikeouts, Runs, Homeruns, Runs Allowed, Earned Run Average and, league ID (AL or NL)
teams_data <- teams_data %>%
select(yearID,name, teamID, W, SO, R, HR, RA, ERA,lgID)
# Focus on recent years for a more relevant analysis, e.g., last 10 years and remove 2020 beacuase it was a shorter season
recent_data <- teams_data %>%
filter(yearID >= 2013 & yearID != 2020)Inspect the head of the data to get some insight into the columns selected.
print(head(recent_data))## yearID name teamID W SO R HR RA ERA lgID
## 1 2013 Arizona Diamondbacks ARI 81 1142 685 130 695 3.92 NL
## 2 2013 Atlanta Braves ATL 96 1384 688 181 548 3.18 NL
## 3 2013 Baltimore Orioles BAL 85 1125 745 212 709 4.20 AL
## 4 2013 Boston Red Sox BOS 97 1308 853 178 656 3.79 AL
## 5 2013 Chicago White Sox CHA 63 1207 598 148 723 3.98 AL
## 6 2013 Chicago Cubs CHN 66 1230 602 172 689 4.00 NLInspect the tail to see we have data up to the 2022 season.
print(tail(recent_data))## yearID name teamID W SO R HR RA ERA lgID
## 265 2022 San Francisco Giants SFN 81 1462 716 183 697 3.85 NL
## 266 2022 St. Louis Cardinals SLN 93 1226 772 197 637 3.79 NL
## 267 2022 Tampa Bay Rays TBA 86 1395 666 139 614 3.41 AL
## 268 2022 Texas Rangers TEX 68 1446 707 198 743 4.22 AL
## 269 2022 Toronto Blue Jays TOR 92 1242 775 200 679 3.87 AL
## 270 2022 Washington Nationals WAS 55 1221 603 136 855 5.00 NLThe dimensions show that the data contains 270 rows and 10 columns
print(dim(recent_data))## [1] 270 10Check the league ID column to see if it can be used as the dichotomous term (binary). It should only have 2 values “AL” and “NL”. We can see from the code that this indeed is the case and this column only contains 2 values therefore it can be used as the dichotomous term.
# Check the unique values in the lgID column
league_id_vals <- unique(recent_data$lgID)
# Print the unique values
print(league_id_vals)## [1] NL AL
## Levels: AA AL FL NA NL PL UA# Count the number of unique values
num_unique_values <- length(league_id_vals)
print(num_unique_values)## [1] 2Create the quadratic term by squaring the HR column.
recent_data$HR_squared = recent_data$HR^2
print(recent_data)## yearID name teamID W SO R HR RA ERA lgID
## 1 2013 Arizona Diamondbacks ARI 81 1142 685 130 695 3.92 NL
## 2 2013 Atlanta Braves ATL 96 1384 688 181 548 3.18 NL
## 3 2013 Baltimore Orioles BAL 85 1125 745 212 709 4.20 AL
## 4 2013 Boston Red Sox BOS 97 1308 853 178 656 3.79 AL
## 5 2013 Chicago White Sox CHA 63 1207 598 148 723 3.98 AL
## 6 2013 Chicago Cubs CHN 66 1230 602 172 689 4.00 NL
## 7 2013 Cincinnati Reds CIN 90 1245 698 155 589 3.38 NL
## 8 2013 Cleveland Indians CLE 92 1283 745 171 662 3.82 AL
## 9 2013 Colorado Rockies COL 74 1204 706 159 760 4.44 NL
## 10 2013 Detroit Tigers DET 93 1073 796 176 624 3.61 AL
## 11 2013 Houston Astros HOU 51 1535 610 148 848 4.79 AL
## 12 2013 Kansas City Royals KCA 86 1048 648 112 601 3.45 AL
## 13 2013 Los Angeles Angels of Anaheim LAA 78 1221 733 164 737 4.23 AL
## 14 2013 Los Angeles Dodgers LAN 92 1146 649 138 582 3.25 NL
## 15 2013 Miami Marlins MIA 62 1232 513 95 646 3.71 NL
## 16 2013 Milwaukee Brewers MIL 74 1183 640 157 687 3.84 NL
## 17 2013 Minnesota Twins MIN 66 1430 614 151 788 4.55 AL
## 18 2013 New York Yankees NYA 85 1214 650 144 671 3.94 AL
## 19 2013 New York Mets NYN 74 1384 619 130 684 3.77 NL
## 20 2013 Oakland Athletics OAK 96 1178 767 186 625 3.56 AL
## 21 2013 Philadelphia Phillies PHI 73 1205 610 140 749 4.32 NL
## 22 2013 Pittsburgh Pirates PIT 94 1330 634 161 577 3.26 NL
## 23 2013 San Diego Padres SDN 76 1309 618 146 700 3.98 NL
## 24 2013 Seattle Mariners SEA 71 1353 624 188 754 4.31 AL
## 25 2013 San Francisco Giants SFN 76 1078 629 107 691 4.00 NL
## 26 2013 St. Louis Cardinals SLN 97 1110 783 125 596 3.42 NL
## 27 2013 Tampa Bay Rays TBA 92 1171 700 165 646 3.74 AL
## 28 2013 Texas Rangers TEX 91 1067 730 176 636 3.62 AL
## 29 2013 Toronto Blue Jays TOR 74 1123 712 185 756 4.25 AL
## 30 2013 Washington Nationals WAS 86 1192 656 161 626 3.59 NL
## 31 2014 Arizona Diamondbacks ARI 64 1165 615 118 742 4.26 NL
## 32 2014 Atlanta Braves ATL 79 1369 573 123 597 3.38 NL
## 33 2014 Baltimore Orioles BAL 96 1285 705 211 593 3.43 AL
## 34 2014 Boston Red Sox BOS 71 1337 634 123 715 4.01 AL
## 35 2014 Chicago White Sox CHA 73 1362 660 155 758 4.29 AL
## 36 2014 Chicago Cubs CHN 73 1477 614 157 707 3.91 NL
## 37 2014 Cincinnati Reds CIN 76 1252 595 131 612 3.59 NL
## 38 2014 Cleveland Indians CLE 85 1189 669 142 653 3.56 AL
## 39 2014 Colorado Rockies COL 66 1281 755 186 818 4.84 NL
## 40 2014 Detroit Tigers DET 90 1144 757 155 705 4.01 AL
## 41 2014 Houston Astros HOU 70 1442 629 163 723 4.11 AL
## 42 2014 Kansas City Royals KCA 89 985 651 95 624 3.51 AL
## 43 2014 Los Angeles Angels of Anaheim LAA 98 1266 773 155 630 3.58 AL
## 44 2014 Los Angeles Dodgers LAN 94 1246 718 134 617 3.40 NL
## 45 2014 Miami Marlins MIA 77 1419 645 122 674 3.78 NL
## 46 2014 Milwaukee Brewers MIL 82 1197 650 150 657 3.67 NL
## 47 2014 Minnesota Twins MIN 70 1329 715 128 777 4.57 AL
## 48 2014 New York Yankees NYA 84 1133 633 147 664 3.75 AL
## 49 2014 New York Mets NYN 79 1264 629 125 618 3.49 NL
## 50 2014 Oakland Athletics OAK 88 1104 729 146 572 3.22 AL
## 51 2014 Philadelphia Phillies PHI 73 1306 619 125 687 3.79 NL
## 52 2014 Pittsburgh Pirates PIT 88 1244 682 156 631 3.47 NL
## 53 2014 San Diego Padres SDN 77 1294 535 109 577 3.27 NL
## 54 2014 Seattle Mariners SEA 87 1232 634 136 554 3.17 AL
## 55 2014 San Francisco Giants SFN 88 1245 665 132 614 3.50 NL
## 56 2014 St. Louis Cardinals SLN 90 1133 619 105 603 3.50 NL
## 57 2014 Tampa Bay Rays TBA 77 1124 612 117 625 3.56 AL
## 58 2014 Texas Rangers TEX 67 1162 637 111 773 4.49 AL
## 59 2014 Toronto Blue Jays TOR 83 1151 723 177 686 4.00 AL
## 60 2014 Washington Nationals WAS 96 1304 686 152 555 3.03 NL
## 61 2015 Arizona Diamondbacks ARI 79 1312 720 154 713 4.04 NL
## 62 2015 Atlanta Braves ATL 67 1107 573 100 760 4.41 NL
## 63 2015 Baltimore Orioles BAL 81 1331 713 217 693 4.05 AL
## 64 2015 Boston Red Sox BOS 78 1148 748 161 753 4.31 AL
## 65 2015 Chicago White Sox CHA 76 1231 622 136 701 3.98 AL
## 66 2015 Chicago Cubs CHN 97 1518 689 171 608 3.36 NL
## 67 2015 Cincinnati Reds CIN 64 1255 640 167 754 4.33 NL
## 68 2015 Cleveland Indians CLE 81 1157 669 141 640 3.67 AL
## 69 2015 Colorado Rockies COL 68 1283 737 186 844 5.04 NL
## 70 2015 Detroit Tigers DET 74 1259 689 151 803 4.64 AL
## 71 2015 Houston Astros HOU 86 1392 729 230 618 3.57 AL
## 72 2015 Kansas City Royals KCA 95 973 724 139 641 3.73 AL
## 73 2015 Los Angeles Angels of Anaheim LAA 85 1150 661 176 675 3.94 AL
## 74 2015 Los Angeles Dodgers LAN 92 1258 667 187 595 3.44 NL
## 75 2015 Miami Marlins MIA 71 1150 613 120 678 4.02 NL
## 76 2015 Milwaukee Brewers MIL 68 1299 655 145 737 4.28 NL
## 77 2015 Minnesota Twins MIN 83 1264 696 156 700 4.07 AL
## 78 2015 New York Yankees NYA 87 1227 764 212 698 4.03 AL
## 79 2015 New York Mets NYN 90 1290 683 177 613 3.43 NL
## 80 2015 Oakland Athletics OAK 68 1119 694 146 729 4.14 AL
## 81 2015 Philadelphia Phillies PHI 63 1274 626 130 809 4.69 NL
## 82 2015 Pittsburgh Pirates PIT 98 1322 697 140 596 3.21 NL
## 83 2015 San Diego Padres SDN 74 1327 650 148 731 4.09 NL
## 84 2015 Seattle Mariners SEA 76 1336 656 198 726 4.16 AL
## 85 2015 San Francisco Giants SFN 84 1159 696 136 627 3.72 NL
## 86 2015 St. Louis Cardinals SLN 100 1267 647 137 525 2.94 NL
## 87 2015 Tampa Bay Rays TBA 80 1310 644 167 642 3.74 AL
## 88 2015 Texas Rangers TEX 88 1233 751 172 733 4.24 AL
## 89 2015 Toronto Blue Jays TOR 93 1151 891 232 670 3.80 AL
## 90 2015 Washington Nationals WAS 83 1344 703 177 635 3.62 NL
## 91 2016 Arizona Diamondbacks ARI 69 1427 752 190 890 5.09 NL
## 92 2016 Atlanta Braves ATL 68 1240 649 122 779 4.51 NL
## 93 2016 Baltimore Orioles BAL 89 1324 744 253 715 4.22 AL
## 94 2016 Boston Red Sox BOS 93 1160 878 208 694 4.00 AL
## 95 2016 Chicago White Sox CHA 78 1285 686 168 715 4.10 AL
## 96 2016 Chicago Cubs CHN 103 1339 808 199 556 3.15 NL
## 97 2016 Cincinnati Reds CIN 68 1284 716 164 854 4.91 NL
## 98 2016 Cleveland Indians CLE 94 1246 777 185 676 3.84 AL
## 99 2016 Colorado Rockies COL 75 1330 845 204 860 4.91 NL
## 100 2016 Detroit Tigers DET 86 1303 750 211 721 4.24 AL
## 101 2016 Houston Astros HOU 84 1452 724 198 701 4.06 AL
## 102 2016 Kansas City Royals KCA 81 1224 675 147 712 4.21 AL
## 103 2016 Los Angeles Angels of Anaheim LAA 74 991 717 156 727 4.28 AL
## 104 2016 Los Angeles Dodgers LAN 91 1321 725 189 638 3.70 NL
## 105 2016 Miami Marlins MIA 79 1213 655 128 682 4.05 NL
## 106 2016 Milwaukee Brewers MIL 73 1543 671 194 733 4.08 NL
## 107 2016 Minnesota Twins MIN 59 1426 722 200 889 5.08 AL
## 108 2016 New York Yankees NYA 84 1188 680 183 702 4.16 AL
## 109 2016 New York Mets NYN 87 1302 671 218 617 3.57 NL
## 110 2016 Oakland Athletics OAK 69 1145 653 169 761 4.51 AL
## 111 2016 Philadelphia Phillies PHI 71 1376 610 161 796 4.63 NL
## 112 2016 Pittsburgh Pirates PIT 78 1334 729 153 758 4.21 NL
## 113 2016 San Diego Padres SDN 68 1500 686 177 770 4.43 NL
## 114 2016 Seattle Mariners SEA 86 1288 768 223 707 4.00 AL
## 115 2016 San Francisco Giants SFN 87 1107 715 130 631 3.65 NL
## 116 2016 St. Louis Cardinals SLN 86 1318 779 225 712 4.08 NL
## 117 2016 Tampa Bay Rays TBA 68 1482 672 216 713 4.20 AL
## 118 2016 Texas Rangers TEX 95 1220 765 215 757 4.37 AL
## 119 2016 Toronto Blue Jays TOR 89 1362 759 221 666 3.78 AL
## 120 2016 Washington Nationals WAS 95 1252 763 203 612 3.51 NL
## 121 2017 Arizona Diamondbacks ARI 93 1456 812 220 659 3.66 NL
## 122 2017 Atlanta Braves ATL 72 1184 732 165 821 4.72 NL
## 123 2017 Baltimore Orioles BAL 75 1412 743 232 841 4.97 AL
## 124 2017 Boston Red Sox BOS 93 1224 785 168 668 3.70 AL
## 125 2017 Chicago White Sox CHA 67 1397 706 186 820 4.78 AL
## 126 2017 Chicago Cubs CHN 92 1401 822 223 695 3.95 NL
## 127 2017 Cincinnati Reds CIN 68 1329 753 219 869 5.17 NL
## 128 2017 Cleveland Indians CLE 102 1153 818 212 564 3.30 AL
## 129 2017 Colorado Rockies COL 87 1408 824 192 757 4.51 NL
## 130 2017 Detroit Tigers DET 64 1313 735 187 894 5.36 AL
## 131 2017 Houston Astros HOU 101 1087 896 238 700 4.12 AL
## 132 2017 Kansas City Royals KCA 80 1166 702 193 791 4.61 AL
## 133 2017 Los Angeles Angels of Anaheim LAA 80 1198 710 186 709 4.20 AL
## 134 2017 Los Angeles Dodgers LAN 104 1380 770 221 580 3.38 NL
## 135 2017 Miami Marlins MIA 77 1282 778 194 822 4.82 NL
## 136 2017 Milwaukee Brewers MIL 86 1571 732 224 697 4.00 NL
## 137 2017 Minnesota Twins MIN 85 1342 815 206 788 4.59 AL
## 138 2017 New York Yankees NYA 91 1386 858 241 660 3.72 AL
## 139 2017 New York Mets NYN 70 1291 735 224 863 5.01 NL
## 140 2017 Oakland Athletics OAK 75 1491 739 234 826 4.67 AL
## 141 2017 Philadelphia Phillies PHI 66 1417 690 174 782 4.55 NL
## 142 2017 Pittsburgh Pirates PIT 75 1213 668 151 731 4.22 NL
## 143 2017 San Diego Padres SDN 71 1499 604 189 816 4.67 NL
## 144 2017 Seattle Mariners SEA 78 1267 750 200 772 4.46 AL
## 145 2017 San Francisco Giants SFN 64 1204 639 128 776 4.50 NL
## 146 2017 St. Louis Cardinals SLN 83 1348 761 196 705 4.01 NL
## 147 2017 Tampa Bay Rays TBA 80 1538 694 228 704 3.97 AL
## 148 2017 Texas Rangers TEX 78 1493 799 237 816 4.66 AL
## 149 2017 Toronto Blue Jays TOR 76 1327 693 222 784 4.42 AL
## 150 2017 Washington Nationals WAS 97 1327 819 215 672 3.88 NL
## 151 2018 Arizona Diamondbacks ARI 82 1460 693 176 644 3.72 NL
## 152 2018 Atlanta Braves ATL 90 1290 759 175 657 3.75 NL
## 153 2018 Baltimore Orioles BAL 47 1412 622 188 892 5.18 AL
## 154 2018 Boston Red Sox BOS 108 1253 876 208 647 3.75 AL
## 155 2018 Chicago White Sox CHA 62 1594 656 182 848 4.83 AL
## 156 2018 Chicago Cubs CHN 95 1388 761 167 645 3.65 NL
## 157 2018 Cincinnati Reds CIN 67 1376 696 172 819 4.63 NL
## 158 2018 Cleveland Indians CLE 91 1189 818 216 648 3.77 AL
## 159 2018 Colorado Rockies COL 91 1397 780 210 745 4.33 NL
## 160 2018 Detroit Tigers DET 64 1341 630 135 796 4.58 AL
## 161 2018 Houston Astros HOU 103 1197 797 205 534 3.11 AL
## 162 2018 Kansas City Royals KCA 58 1310 638 155 833 4.94 AL
## 163 2018 Los Angeles Angels of Anaheim LAA 80 1300 721 214 722 4.15 AL
## 164 2018 Los Angeles Dodgers LAN 92 1436 804 235 610 3.38 NL
## 165 2018 Miami Marlins MIA 63 1384 589 128 809 4.76 NL
## 166 2018 Milwaukee Brewers MIL 96 1458 754 218 659 3.73 NL
## 167 2018 Minnesota Twins MIN 78 1328 738 166 775 4.50 AL
## 168 2018 New York Yankees NYA 100 1421 851 267 669 3.78 AL
## 169 2018 New York Mets NYN 77 1404 676 170 707 4.07 NL
## 170 2018 Oakland Athletics OAK 97 1381 813 227 674 3.81 AL
## 171 2018 Philadelphia Phillies PHI 80 1520 677 186 728 4.14 NL
## 172 2018 Pittsburgh Pirates PIT 82 1229 692 157 693 4.00 NL
## 173 2018 San Diego Padres SDN 66 1523 617 162 767 4.40 NL
## 174 2018 Seattle Mariners SEA 89 1221 677 176 711 4.13 AL
## 175 2018 San Francisco Giants SFN 73 1467 603 133 699 3.95 NL
## 176 2018 St. Louis Cardinals SLN 88 1380 759 205 691 3.85 NL
## 177 2018 Tampa Bay Rays TBA 90 1388 716 150 646 3.74 AL
## 178 2018 Texas Rangers TEX 67 1484 737 194 848 4.92 AL
## 179 2018 Toronto Blue Jays TOR 73 1387 709 217 832 4.85 AL
## 180 2018 Washington Nationals WAS 82 1289 771 191 682 4.04 NL
## 181 2019 Arizona Diamondbacks ARI 85 1360 813 220 743 4.25 NL
## 182 2019 Atlanta Braves ATL 97 1467 855 249 743 4.19 NL
## 183 2019 Baltimore Orioles BAL 54 1435 729 213 981 5.59 AL
## 184 2019 Boston Red Sox BOS 84 1382 901 245 828 4.70 AL
## 185 2019 Chicago White Sox CHA 72 1549 708 182 832 4.90 AL
## 186 2019 Chicago Cubs CHN 84 1460 814 256 717 4.10 NL
## 187 2019 Cincinnati Reds CIN 75 1436 701 227 711 4.18 NL
## 188 2019 Cleveland Indians CLE 93 1332 769 223 657 3.76 AL
## 189 2019 Colorado Rockies COL 71 1503 835 224 958 5.56 NL
## 190 2019 Detroit Tigers DET 47 1595 582 149 915 5.24 AL
## 191 2019 Houston Astros HOU 107 1166 920 288 640 3.66 AL
## 192 2019 Kansas City Royals KCA 59 1405 691 162 869 5.20 AL
## 193 2019 Los Angeles Angels of Anaheim LAA 72 1276 769 220 868 5.12 AL
## 194 2019 Los Angeles Dodgers LAN 106 1356 886 279 613 3.37 NL
## 195 2019 Miami Marlins MIA 57 1469 615 146 808 4.74 NL
## 196 2019 Milwaukee Brewers MIL 89 1563 769 250 766 4.40 NL
## 197 2019 Minnesota Twins MIN 101 1334 939 307 754 4.18 AL
## 198 2019 New York Yankees NYA 103 1437 943 306 739 4.31 AL
## 199 2019 New York Mets NYN 86 1384 791 242 737 4.24 NL
## 200 2019 Oakland Athletics OAK 97 1338 845 257 680 3.97 AL
## 201 2019 Philadelphia Phillies PHI 81 1453 774 215 794 4.53 NL
## 202 2019 Pittsburgh Pirates PIT 69 1213 758 163 911 5.18 NL
## 203 2019 San Diego Padres SDN 70 1581 682 219 789 4.60 NL
## 204 2019 Seattle Mariners SEA 68 1581 758 239 893 4.99 AL
## 205 2019 San Francisco Giants SFN 77 1435 678 167 773 4.38 NL
## 206 2019 St. Louis Cardinals SLN 91 1420 764 210 662 3.80 NL
## 207 2019 Tampa Bay Rays TBA 96 1493 769 217 656 3.65 AL
## 208 2019 Texas Rangers TEX 78 1578 810 223 878 5.06 AL
## 209 2019 Toronto Blue Jays TOR 67 1514 726 247 828 4.79 AL
## 210 2019 Washington Nationals WAS 93 1308 873 231 724 4.27 NL
## 211 2021 Arizona Diamondbacks ARI 52 1465 679 144 893 5.11 NL
## 212 2021 Atlanta Braves ATL 88 1453 790 239 656 3.88 NL
## 213 2021 Baltimore Orioles BAL 52 1454 659 195 956 5.84 AL
## 214 2021 Boston Red Sox BOS 92 1386 829 219 749 4.26 AL
## 215 2021 Chicago White Sox CHA 93 1389 796 190 636 3.73 AL
## 216 2021 Chicago Cubs CHN 71 1596 705 210 839 4.87 NL
## 217 2021 Cincinnati Reds CIN 83 1425 786 222 760 4.40 NL
## 218 2021 Cleveland Indians CLE 80 1387 717 203 727 4.34 AL
## 219 2021 Colorado Rockies COL 74 1356 739 182 796 4.82 NL
## 220 2021 Detroit Tigers DET 77 1514 697 179 756 4.32 AL
## 221 2021 Houston Astros HOU 95 1222 863 221 658 3.78 AL
## 222 2021 Kansas City Royals KCA 74 1258 686 163 788 4.64 AL
## 223 2021 Los Angeles Angels of Anaheim LAA 77 1394 723 190 804 4.69 AL
## 224 2021 Los Angeles Dodgers LAN 106 1408 830 237 561 3.01 NL
## 225 2021 Miami Marlins MIA 67 1553 623 158 701 3.96 NL
## 226 2021 Milwaukee Brewers MIL 95 1465 738 194 623 3.50 NL
## 227 2021 Minnesota Twins MIN 73 1405 729 228 834 4.83 AL
## 228 2021 New York Yankees NYA 92 1482 711 222 669 3.74 AL
## 229 2021 New York Mets NYN 77 1392 636 176 668 3.90 NL
## 230 2021 Oakland Athletics OAK 86 1349 743 199 687 4.02 AL
## 231 2021 Philadelphia Phillies PHI 82 1402 734 198 745 4.39 NL
## 232 2021 Pittsburgh Pirates PIT 61 1328 609 124 833 5.08 NL
## 233 2021 San Diego Padres SDN 79 1324 729 180 708 4.10 NL
## 234 2021 Seattle Mariners SEA 90 1492 697 199 748 4.30 AL
## 235 2021 San Francisco Giants SFN 107 1461 804 241 594 3.24 NL
## 236 2021 St. Louis Cardinals SLN 90 1341 706 198 672 3.98 NL
## 237 2021 Tampa Bay Rays TBA 100 1542 857 222 651 3.67 AL
## 238 2021 Texas Rangers TEX 60 1381 625 167 815 4.79 AL
## 239 2021 Toronto Blue Jays TOR 91 1218 846 262 663 3.91 AL
## 240 2021 Washington Nationals WAS 65 1303 724 182 820 4.80 NL
## 241 2022 Arizona Diamondbacks ARI 74 1341 702 173 740 4.25 NL
## 242 2022 Atlanta Braves ATL 101 1498 789 243 609 3.46 NL
## 243 2022 Baltimore Orioles BAL 83 1390 674 171 688 3.97 AL
## 244 2022 Boston Red Sox BOS 78 1373 735 155 787 4.53 AL
## 245 2022 Chicago White Sox CHA 81 1269 686 149 717 3.92 AL
## 246 2022 Chicago Cubs CHN 74 1448 657 159 731 4.00 NL
## 247 2022 Cincinnati Reds CIN 62 1430 648 156 815 4.86 NL
## 248 2022 Cleveland Guardians CLE 92 1122 698 127 634 3.46 AL
## 249 2022 Colorado Rockies COL 68 1330 698 149 873 5.06 NL
## 250 2022 Detroit Tigers DET 66 1413 557 110 713 4.04 AL
## 251 2022 Houston Astros HOU 106 1179 737 214 518 2.90 AL
## 252 2022 Kansas City Royals KCA 65 1287 640 138 810 4.70 AL
## 253 2022 Los Angeles Angels of Anaheim LAA 73 1539 623 190 668 3.77 AL
## 254 2022 Los Angeles Dodgers LAN 111 1374 847 212 513 2.80 NL
## 255 2022 Miami Marlins MIA 69 1429 586 144 676 3.86 NL
## 256 2022 Milwaukee Brewers MIL 86 1464 725 219 688 3.83 NL
## 257 2022 Minnesota Twins MIN 78 1353 696 178 684 3.98 AL
## 258 2022 New York Yankees NYA 99 1391 807 254 567 3.30 AL
## 259 2022 New York Mets NYN 101 1217 772 171 606 3.57 NL
## 260 2022 Oakland Athletics OAK 60 1389 568 137 770 4.52 AL
## 261 2022 Philadelphia Phillies PHI 87 1363 747 205 685 3.97 NL
## 262 2022 Pittsburgh Pirates PIT 62 1497 591 158 817 4.66 NL
## 263 2022 San Diego Padres SDN 89 1327 705 153 660 3.81 NL
## 264 2022 Seattle Mariners SEA 90 1397 690 197 623 3.59 AL
## 265 2022 San Francisco Giants SFN 81 1462 716 183 697 3.85 NL
## 266 2022 St. Louis Cardinals SLN 93 1226 772 197 637 3.79 NL
## 267 2022 Tampa Bay Rays TBA 86 1395 666 139 614 3.41 AL
## 268 2022 Texas Rangers TEX 68 1446 707 198 743 4.22 AL
## 269 2022 Toronto Blue Jays TOR 92 1242 775 200 679 3.87 AL
## 270 2022 Washington Nationals WAS 55 1221 603 136 855 5.00 NL
## HR_squared
## 1 16900
## 2 32761
## 3 44944
## 4 31684
## 5 21904
## 6 29584
## 7 24025
## 8 29241
## 9 25281
## 10 30976
## 11 21904
## 12 12544
## 13 26896
## 14 19044
## 15 9025
## 16 24649
## 17 22801
## 18 20736
## 19 16900
## 20 34596
## 21 19600
## 22 25921
## 23 21316
## 24 35344
## 25 11449
## 26 15625
## 27 27225
## 28 30976
## 29 34225
## 30 25921
## 31 13924
## 32 15129
## 33 44521
## 34 15129
## 35 24025
## 36 24649
## 37 17161
## 38 20164
## 39 34596
## 40 24025
## 41 26569
## 42 9025
## 43 24025
## 44 17956
## 45 14884
## 46 22500
## 47 16384
## 48 21609
## 49 15625
## 50 21316
## 51 15625
## 52 24336
## 53 11881
## 54 18496
## 55 17424
## 56 11025
## 57 13689
## 58 12321
## 59 31329
## 60 23104
## 61 23716
## 62 10000
## 63 47089
## 64 25921
## 65 18496
## 66 29241
## 67 27889
## 68 19881
## 69 34596
## 70 22801
## 71 52900
## 72 19321
## 73 30976
## 74 34969
## 75 14400
## 76 21025
## 77 24336
## 78 44944
## 79 31329
## 80 21316
## 81 16900
## 82 19600
## 83 21904
## 84 39204
## 85 18496
## 86 18769
## 87 27889
## 88 29584
## 89 53824
## 90 31329
## 91 36100
## 92 14884
## 93 64009
## 94 43264
## 95 28224
## 96 39601
## 97 26896
## 98 34225
## 99 41616
## 100 44521
## 101 39204
## 102 21609
## 103 24336
## 104 35721
## 105 16384
## 106 37636
## 107 40000
## 108 33489
## 109 47524
## 110 28561
## 111 25921
## 112 23409
## 113 31329
## 114 49729
## 115 16900
## 116 50625
## 117 46656
## 118 46225
## 119 48841
## 120 41209
## 121 48400
## 122 27225
## 123 53824
## 124 28224
## 125 34596
## 126 49729
## 127 47961
## 128 44944
## 129 36864
## 130 34969
## 131 56644
## 132 37249
## 133 34596
## 134 48841
## 135 37636
## 136 50176
## 137 42436
## 138 58081
## 139 50176
## 140 54756
## 141 30276
## 142 22801
## 143 35721
## 144 40000
## 145 16384
## 146 38416
## 147 51984
## 148 56169
## 149 49284
## 150 46225
## 151 30976
## 152 30625
## 153 35344
## 154 43264
## 155 33124
## 156 27889
## 157 29584
## 158 46656
## 159 44100
## 160 18225
## 161 42025
## 162 24025
## 163 45796
## 164 55225
## 165 16384
## 166 47524
## 167 27556
## 168 71289
## 169 28900
## 170 51529
## 171 34596
## 172 24649
## 173 26244
## 174 30976
## 175 17689
## 176 42025
## 177 22500
## 178 37636
## 179 47089
## 180 36481
## 181 48400
## 182 62001
## 183 45369
## 184 60025
## 185 33124
## 186 65536
## 187 51529
## 188 49729
## 189 50176
## 190 22201
## 191 82944
## 192 26244
## 193 48400
## 194 77841
## 195 21316
## 196 62500
## 197 94249
## 198 93636
## 199 58564
## 200 66049
## 201 46225
## 202 26569
## 203 47961
## 204 57121
## 205 27889
## 206 44100
## 207 47089
## 208 49729
## 209 61009
## 210 53361
## 211 20736
## 212 57121
## 213 38025
## 214 47961
## 215 36100
## 216 44100
## 217 49284
## 218 41209
## 219 33124
## 220 32041
## 221 48841
## 222 26569
## 223 36100
## 224 56169
## 225 24964
## 226 37636
## 227 51984
## 228 49284
## 229 30976
## 230 39601
## 231 39204
## 232 15376
## 233 32400
## 234 39601
## 235 58081
## 236 39204
## 237 49284
## 238 27889
## 239 68644
## 240 33124
## 241 29929
## 242 59049
## 243 29241
## 244 24025
## 245 22201
## 246 25281
## 247 24336
## 248 16129
## 249 22201
## 250 12100
## 251 45796
## 252 19044
## 253 36100
## 254 44944
## 255 20736
## 256 47961
## 257 31684
## 258 64516
## 259 29241
## 260 18769
## 261 42025
## 262 24964
## 263 23409
## 264 38809
## 265 33489
## 266 38809
## 267 19321
## 268 39204
## 269 40000
## 270 18496Multiple Regression Model
model.lm <- lm(W ~ HR * lgID + HR + HR_squared + SO + R + RA + ERA + lgID, data = recent_data)
print(summary(model.lm))##
## Call:
## lm(formula = W ~ HR * lgID + HR + HR_squared + SO + R + RA +
## ERA + lgID, data = recent_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.9593 -2.6031 -0.0307 2.5162 13.7163
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.847e+01 6.552e+00 13.502 < 2e-16 ***
## HR 2.381e-02 5.235e-02 0.455 0.649624
## lgIDNL -9.407e-01 2.472e+00 -0.381 0.703825
## HR_squared -3.189e-05 1.293e-04 -0.247 0.805426
## SO -1.307e-03 2.722e-03 -0.480 0.631427
## R 8.708e-02 5.696e-03 15.287 < 2e-16 ***
## RA -7.252e-02 1.968e-02 -3.684 0.000279 ***
## ERA -4.689e+00 3.155e+00 -1.486 0.138398
## HR:lgIDNL 4.047e-03 1.339e-02 0.302 0.762745
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.11 on 261 degrees of freedom
## Multiple R-squared: 0.8982, Adjusted R-squared: 0.895
## F-statistic: 287.7 on 8 and 261 DF, p-value: < 2.2e-16The summary for the model shows that we have a multiple R-squared value of 0.8982 which is pretty close to 1 which is very desirable. We see that we have significant P values for the “R” (runs) and “RA”. This makes sense that these two columns would have a high significance because you win games by scoring more runs than the opponent so we would expect for these columns to be important to the model. We can also see a overall significant p-value of < 2.2e-16. The low p-value and high R-squared values hint at this being a good model.
Residual Analysis
Assessing the models summary we can see that we have a median close to zero similar min and max values and also similar quartiles so this data does seem to be normally distributed with a median close to 0.
plot(fitted(model.lm), resid(model.lm))
The residual plot above shows that the residuals seem to be randomly scattered around 0 without any discernible pattern, suggesting that the linear model may be a reasonable fit for the data.
qqnorm(resid(model.lm))
qqline(resid(model.lm))
The Q-Q plot above shows that we have some divergence on either end of the line we see more extreme divergence at the end of the line but we follow the line very closely for the most part. This suggests that the data may not be perfectly normal but it is close to normal.
par(mfrow=c(2,2))
plot(model.lm)
Conclusion
In conclusion this model seems to be a good fit for the data based on the R-squared value of .89 and significant p-value. The residual analysis showed a residual plot with no pattern centered horizontally around 0 with what appears to be mostly constant variance. The QQ plot showed that the data is mostly normal with some divergence at either end. The analysis shows that this model fits well to the data and could be a useable model at predicting wins for MLB teams.