DB12Data605
Mathew Katz
2023-04-19
Using R, build a multiple regression model for data that interests you. Include in this model at least one quadratic term, one dichotomous term, and one dichotomous vs. quantitative interaction term. Interpret all coefficients. Conduct residual analysis. Was the linear model appropriate? Why or why not?
df = read.csv("/Users/mathew.katz/Desktop/CUNYSPS/mlb2022.txt")
df = df[-1,]
df## Rk Season Team Lg W GP W.1 L WL. ERA G CG SHO SV IP H R
## 2 1 2022 LAD NL 111 162 111 51 0.685 2.80 162 1 1 43 1451.1 1114 513
## 3 2 2022 HOU AL 106 162 106 56 0.654 2.90 162 3 1 53 1445.0 1121 518
## 4 3 2022 ATL NL 101 162 101 61 0.623 3.46 162 1 1 55 1448.0 1224 609
## 5 4 2022 NYM NL 101 162 101 61 0.623 3.58 162 0 0 41 1438.2 1274 606
## 6 5 2022 NYY AL 99 162 99 63 0.611 3.30 162 1 1 47 1451.2 1177 567
## 7 6 2022 STL NL 93 162 93 69 0.574 3.79 162 3 1 37 1436.0 1335 637
## 8 7 2022 TOR AL 92 162 92 70 0.568 3.89 162 0 0 46 1441.2 1356 679
## 9 8 2022 CLE AL 92 162 92 70 0.568 3.47 162 1 0 51 1456.0 1252 634
## 10 9 2022 SEA AL 90 162 90 72 0.556 3.59 162 0 0 40 1447.0 1277 623
## 11 10 2022 SDP NL 89 162 89 73 0.549 3.81 162 0 0 48 1443.1 1263 660
## 12 11 2022 PHI NL 87 162 87 75 0.537 3.98 162 3 1 42 1428.1 1330 685
## 13 12 2022 TBR AL 86 162 86 76 0.531 3.41 162 0 0 44 1435.2 1260 614
## 14 13 2022 MIL NL 86 162 86 76 0.531 3.83 162 0 0 52 1446.0 1238 688
## 15 14 2022 BAL AL 83 162 83 79 0.512 3.97 162 2 1 46 1433.2 1406 688
## 16 15 2022 CHW AL 81 162 81 81 0.500 3.94 162 2 1 48 1447.2 1330 717
## 17 16 2022 SFG NL 81 162 81 81 0.500 3.86 162 1 0 39 1433.0 1397 697
## 18 17 2022 BOS AL 78 162 78 84 0.481 4.54 162 5 2 39 1430.2 1411 787
## 19 18 2022 MIN AL 78 162 78 84 0.481 3.98 162 0 0 28 1437.1 1320 684
## 20 19 2022 ARI NL 74 162 74 88 0.457 4.26 162 0 0 33 1429.2 1345 740
## 21 20 2022 CHC NL 74 162 74 88 0.457 4.03 162 0 0 44 1444.0 1342 731
## 22 21 2022 LAA AL 73 162 73 89 0.451 3.79 162 2 2 38 1435.2 1241 668
## 23 22 2022 MIA NL 69 162 69 93 0.426 3.87 162 6 1 41 1437.2 1311 676
## 24 23 2022 COL NL 68 162 68 94 0.420 5.08 162 1 1 43 1425.1 1516 873
## 25 24 2022 TEX AL 68 162 68 94 0.420 4.22 162 1 1 37 1435.0 1345 743
## 26 25 2022 DET AL 66 162 66 96 0.407 4.04 162 0 0 38 1419.2 1336 713
## 27 26 2022 KCR AL 65 162 65 97 0.401 4.72 162 0 0 33 1416.0 1493 810
## 28 27 2022 PIT NL 62 162 62 100 0.383 4.66 162 0 0 33 1421.1 1432 817
## 29 28 2022 CIN NL 62 162 62 100 0.383 4.86 162 1 1 31 1423.2 1366 815
## 30 29 2022 OAK AL 60 162 60 102 0.370 4.54 162 0 0 34 1426.1 1394 770
## 31 30 2022 WSN NL 55 162 55 107 0.340 5.00 162 2 0 28 1411.2 1469 855
## ER HR BB IBB SO HBP BK WP BF ERA. FIP WHIP H9 HR9 BB9 SO9 SO.BB
## 2 451 152 407 13 1465 75 3 38 5865 149 3.45 1.048 6.9 0.9 2.5 9.1 3.60
## 3 465 134 458 6 1524 60 6 56 5856 134 3.28 1.093 7.0 0.8 2.9 9.5 3.33
## 4 556 148 500 21 1554 62 4 55 6031 121 3.46 1.191 7.6 0.9 3.1 9.7 3.11
## 5 573 169 428 13 1565 71 2 35 5950 108 3.50 1.183 8.0 1.1 2.7 9.8 3.66
## 6 533 157 444 10 1459 65 5 40 5938 119 3.56 1.117 7.3 1.0 2.8 9.0 3.29
## 7 605 146 489 11 1177 60 3 43 6014 101 3.94 1.270 8.4 0.9 3.1 7.4 2.41
## 8 623 180 424 15 1390 76 5 29 6053 100 3.85 1.235 8.5 1.1 2.6 8.7 3.28
## 9 562 172 435 14 1390 57 2 49 5989 110 3.75 1.159 7.7 1.1 2.7 8.6 3.20
## 10 577 186 447 24 1391 56 0 45 5986 105 3.90 1.191 7.9 1.2 2.8 8.7 3.11
## 11 611 173 468 6 1451 88 5 54 6047 100 3.82 1.199 7.9 1.1 2.9 9.0 3.10
## 12 631 150 463 16 1423 68 3 47 6006 102 3.60 1.255 8.4 0.9 2.9 9.0 3.07
## 13 544 172 384 15 1384 66 4 54 5930 108 3.68 1.145 7.9 1.1 2.4 8.7 3.60
## 14 615 190 521 12 1530 67 4 47 6057 104 3.92 1.216 7.7 1.2 3.2 9.5 2.94
## 15 633 171 443 8 1214 64 4 47 6058 102 4.03 1.290 8.8 1.1 2.8 7.6 2.74
## 16 633 166 533 15 1450 51 6 64 6145 102 3.81 1.287 8.3 1.0 3.3 9.0 2.72
## 17 615 132 441 16 1370 52 2 53 6070 106 3.43 1.283 8.8 0.8 2.8 8.6 3.11
## 18 721 185 526 17 1346 72 8 60 6167 93 4.17 1.354 8.9 1.2 3.3 8.5 2.56
## 19 636 184 468 19 1336 66 4 50 6042 98 4.03 1.244 8.3 1.2 2.9 8.4 2.85
## 20 676 191 504 18 1216 59 3 51 6065 96 4.33 1.293 8.5 1.2 3.2 7.7 2.41
## 21 646 207 540 19 1383 73 8 53 6162 102 4.33 1.303 8.4 1.3 3.4 8.6 2.56
## 22 604 168 540 23 1383 60 3 64 6038 108 3.96 1.241 7.8 1.1 3.4 8.7 2.56
## 23 618 173 511 19 1437 76 3 54 6056 105 3.90 1.267 8.2 1.1 3.2 9.0 2.81
## 24 804 184 539 12 1187 59 3 65 6240 92 4.38 1.442 9.6 1.2 3.4 7.5 2.20
## 25 673 169 581 16 1314 71 7 66 6167 94 4.17 1.342 8.4 1.1 3.6 8.2 2.26
## 26 637 167 511 9 1195 57 2 59 6047 94 4.16 1.301 8.5 1.1 3.2 7.6 2.34
## 27 742 173 589 15 1191 71 6 88 6249 86 4.42 1.470 9.5 1.1 3.7 7.6 2.02
## 28 736 164 586 23 1250 87 5 62 6263 88 4.27 1.420 9.1 1.0 3.7 7.9 2.13
## 29 769 213 612 21 1414 110 5 58 6220 93 4.59 1.389 8.6 1.3 3.9 8.9 2.31
## 30 719 195 503 37 1203 72 5 62 6121 83 4.41 1.330 8.8 1.2 3.2 7.6 2.39
## 31 785 244 558 12 1220 75 2 59 6220 78 4.98 1.436 9.4 1.6 3.6 7.8 2.19The data set here is pitching statistics for every team in MLB from last year, 2022. The columns are “Rk”, “Season”, “Team”, “Lg”, “W”, “GP”, “W.1”, “L”, “WL.”, “ERA”, “G”, “CG”, “SHO”, “SV”, “IP”, “H”, “R”, “ER”, “HR”, “BB”, “IBB”, “SO”, “HBP”, “BK”, “WP”, “BF”, “ERA.”, “FIP”, “WHIP”, “H9”, “HR9”, “BB9”, “SO9”, “SO.BB”, and “ERA_betterthan_average.”
Dichotomous term:
Is the team’s ERA better than league average?
df$ERA_betterthan_average[df$ERA > mean(df$ERA)] <- "No"
df$ERA_betterthan_average[df$ERA < mean(df$ERA)] <- "Yes"Quadratic term:
quad = I(df$FIP^2)Dichotomous vs. quantitative interaction term:
dvq = df$WHIP*df$HRmodel<-lm(df$W ~ df$ERA_betterthan_average + quad + dvq)
summary(model)##
## Call:
## lm(formula = df$W ~ df$ERA_betterthan_average + quad + dvq)
##
## Residuals:
## Min 1Q Median 3Q Max
## -17.071 -5.232 1.028 4.313 14.972
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 130.05980 12.24704 10.620 5.97e-11 ***
## df$ERA_betterthan_averageYes 5.35127 4.18021 1.280 0.2118
## quad -4.15387 1.64155 -2.530 0.0178 *
## dvq 0.06314 0.11198 0.564 0.5777
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.522 on 26 degrees of freedom
## Multiple R-squared: 0.7647, Adjusted R-squared: 0.7376
## F-statistic: 28.17 on 3 and 26 DF, p-value: 2.506e-08The only pvalue smaller than 0.05 (the test to see if the predictors are not meaningful) is the Quadratic term which was FIP squared. FIP takes into account only the things that a pitcher can control, such as strikeouts, walks, hit-by-pitches, and home runs allowed, and ignores the impact of defense behind them. By doing so, FIP aims to provide a more accurate picture of a pitcher’s performance and their ability to prevent runs from scoring. Its the new school Earned Run Average (ERA).
plot(model$fitted.values, model$residuals)
abline(0,0)
Residuals don’t look great but there is a definite linear relationship
between the independent variables and the dependent variable. There
would defnitely need to be more feature selection and more analysis but
this is a good start!