# Fetch Data
qb_stats <- read.csv("../data/qb_stats.csv")
# Grab the college predictors
predictors <- c("height", "weight", "age", "c_avg_cmpp", "c_rate", "c_pct",
"c_avg_inter", "c_avg_tds", "c_avg_yds", "c_numyrs", "c_avg_att")
college_stats = qb_stats[, predictors]
# Set the resopnse variables
games_started = qb_stats["games_started"]
# Generate clean data set
data.scaled.no_combine.for_games_started = data.frame(scale(na.omit(cbind(games_started,
college_stats))))
# Generate the linear model
lm.scaled.no_combine.games_started <- lm(formula = games_started ~ ., data = data.scaled.no_combine.for_games_started)
# Find optimum linear regression model for games_started
step_reg.scaled.no_combine.games_started <- stepAIC(lm.scaled.no_combine.games_started,
direction = "both")
## Start: AIC=-2.33
## games_started ~ height + weight + age + c_avg_cmpp + c_rate +
## c_pct + c_avg_inter + c_avg_tds + c_avg_yds + c_numyrs +
## c_avg_att
##
## Df Sum of Sq RSS AIC
## - c_avg_cmpp 1 0.03 215 -4.30
## - c_numyrs 1 0.04 215 -4.29
## - c_avg_inter 1 0.27 215 -4.03
## - c_rate 1 0.41 216 -3.87
## - c_avg_tds 1 0.42 216 -3.86
## - c_pct 1 0.44 216 -3.84
## - height 1 1.01 216 -3.20
## - c_avg_att 1 1.28 216 -2.91
## - age 1 1.32 216 -2.87
## <none> 215 -2.33
## - c_avg_yds 1 3.53 219 -0.42
## - weight 1 8.15 223 4.60
##
## Step: AIC=-4.3
## games_started ~ height + weight + age + c_rate + c_pct + c_avg_inter +
## c_avg_tds + c_avg_yds + c_numyrs + c_avg_att
##
## Df Sum of Sq RSS AIC
## - c_numyrs 1 0.03 215 -6.27
## - c_avg_inter 1 0.25 215 -6.01
## - c_rate 1 0.40 216 -5.85
## - c_avg_tds 1 0.49 216 -5.75
## - c_pct 1 0.60 216 -5.62
## - height 1 1.02 216 -5.15
## - age 1 1.29 216 -4.85
## <none> 215 -4.30
## + c_avg_cmpp 1 0.03 215 -2.33
## - c_avg_att 1 3.76 219 -2.14
## - c_avg_yds 1 4.03 219 -1.84
## - weight 1 8.21 223 2.70
##
## Step: AIC=-6.27
## games_started ~ height + weight + age + c_rate + c_pct + c_avg_inter +
## c_avg_tds + c_avg_yds + c_avg_att
##
## Df Sum of Sq RSS AIC
## - c_avg_inter 1 0.23 215 -8.01
## - c_rate 1 0.41 216 -7.81
## - c_avg_tds 1 0.48 216 -7.73
## - c_pct 1 0.59 216 -7.61
## - height 1 1.00 216 -7.15
## - age 1 1.29 216 -6.84
## <none> 215 -6.27
## + c_numyrs 1 0.03 215 -4.30
## + c_avg_cmpp 1 0.02 215 -4.29
## - c_avg_att 1 3.94 219 -3.92
## - c_avg_yds 1 4.12 219 -3.72
## - weight 1 8.32 223 0.84
##
## Step: AIC=-8.01
## games_started ~ height + weight + age + c_rate + c_pct + c_avg_tds +
## c_avg_yds + c_avg_att
##
## Df Sum of Sq RSS AIC
## - c_rate 1 0.33 216 -9.64
## - c_avg_tds 1 0.41 216 -9.55
## - c_pct 1 0.66 216 -9.28
## - height 1 1.07 216 -8.82
## - age 1 1.26 217 -8.61
## <none> 215 -8.01
## + c_avg_inter 1 0.23 215 -6.27
## + c_avg_cmpp 1 0.01 215 -6.02
## + c_numyrs 1 0.01 215 -6.01
## - c_avg_yds 1 3.98 219 -5.62
## - c_avg_att 1 4.43 220 -5.12
## - weight 1 9.58 225 0.43
##
## Step: AIC=-9.64
## games_started ~ height + weight + age + c_pct + c_avg_tds + c_avg_yds +
## c_avg_att
##
## Df Sum of Sq RSS AIC
## - c_pct 1 0.33 216 -11.27
## - c_avg_tds 1 0.83 216 -10.71
## - height 1 1.03 217 -10.50
## - age 1 1.12 217 -10.39
## <none> 216 -9.64
## + c_rate 1 0.33 215 -8.01
## + c_avg_inter 1 0.15 216 -7.81
## + c_avg_cmpp 1 0.10 216 -7.75
## + c_numyrs 1 0.02 216 -7.66
## - c_avg_yds 1 3.81 220 -7.43
## - c_avg_att 1 5.17 221 -5.95
## - weight 1 9.47 225 -1.33
##
## Step: AIC=-11.27
## games_started ~ height + weight + age + c_avg_tds + c_avg_yds +
## c_avg_att
##
## Df Sum of Sq RSS AIC
## - c_avg_tds 1 0.83 217 -12.36
## - height 1 0.94 217 -12.23
## - age 1 0.99 217 -12.18
## <none> 216 -11.27
## + c_avg_cmpp 1 0.38 216 -9.70
## + c_pct 1 0.33 216 -9.64
## + c_avg_inter 1 0.29 216 -9.59
## + c_rate 1 0.00 216 -9.28
## + c_numyrs 1 0.00 216 -9.27
## - c_avg_yds 1 5.01 221 -7.78
## - c_avg_att 1 6.43 222 -6.23
## - weight 1 9.92 226 -2.50
##
## Step: AIC=-12.36
## games_started ~ height + weight + age + c_avg_yds + c_avg_att
##
## Df Sum of Sq RSS AIC
## - age 1 0.73 218 -13.55
## - height 1 0.82 218 -13.45
## <none> 217 -12.36
## + c_avg_tds 1 0.83 216 -11.27
## + c_pct 1 0.32 216 -10.71
## + c_avg_cmpp 1 0.31 216 -10.70
## + c_avg_inter 1 0.14 217 -10.51
## + c_rate 1 0.03 217 -10.39
## + c_numyrs 1 0.00 217 -10.36
## - c_avg_yds 1 5.35 222 -8.51
## - c_avg_att 1 5.62 222 -8.22
## - weight 1 9.68 226 -3.87
##
## Step: AIC=-13.55
## games_started ~ height + weight + c_avg_yds + c_avg_att
##
## Df Sum of Sq RSS AIC
## - height 1 1.00 219 -14.5
## <none> 218 -13.6
## + age 1 0.73 217 -12.4
## + c_avg_tds 1 0.57 217 -12.2
## + c_avg_cmpp 1 0.24 217 -11.8
## + c_pct 1 0.20 217 -11.8
## + c_avg_inter 1 0.13 217 -11.7
## + c_rate 1 0.02 218 -11.6
## + c_numyrs 1 0.00 218 -11.6
## - c_avg_yds 1 5.27 223 -9.8
## - c_avg_att 1 5.47 223 -9.6
## - weight 1 11.30 229 -3.4
##
## Step: AIC=-14.46
## games_started ~ weight + c_avg_yds + c_avg_att
##
## Df Sum of Sq RSS AIC
## <none> 219 -14.46
## + height 1 1.00 218 -13.55
## + age 1 0.90 218 -13.45
## + c_avg_tds 1 0.43 218 -12.93
## + c_avg_cmpp 1 0.17 218 -12.65
## + c_avg_inter 1 0.16 218 -12.64
## + c_pct 1 0.13 218 -12.60
## + c_rate 1 0.03 218 -12.49
## + c_numyrs 1 0.00 219 -12.46
## - c_avg_yds 1 5.33 224 -10.68
## - c_avg_att 1 5.50 224 -10.50
## - weight 1 12.36 231 -3.26
summary(step_reg.scaled.no_combine.games_started)
##
## Call:
## lm(formula = games_started ~ weight + c_avg_yds + c_avg_att,
## data = data.scaled.no_combine.for_games_started)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.757 -0.774 -0.083 0.789 2.218
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.48e-16 6.21e-02 0.00 1.00000
## weight 2.38e-01 6.51e-02 3.65 0.00032 ***
## c_avg_yds 6.09e-01 2.54e-01 2.40 0.01722 *
## c_avg_att -6.15e-01 2.52e-01 -2.44 0.01558 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.962 on 236 degrees of freedom
## Multiple R-squared: 0.0855, Adjusted R-squared: 0.0739
## F-statistic: 7.36 on 3 and 236 DF, p-value: 9.83e-05
plot(step_reg.scaled.no_combine.games_started)
leaps.scaled.no_combine.games_started <- regsubsets(games_started ~ ., data = data.scaled.no_combine.for_games_started,
nbest = 10)
subsets(leaps.scaled.no_combine.games_started, statistic = "rsq")
## Error: invalid coordinate lengths
cv.lm(df = data.scaled.no_combine.for_games_started, step_reg.scaled.no_combine.games_started,
m = 5) # 5 fold cross-validation
## Analysis of Variance Table
##
## Response: games_started
## Df Sum Sq Mean Sq F value Pr(>F)
## weight 1 14.9 14.92 16.11 8e-05 ***
## c_avg_yds 1 0.0 0.03 0.03 0.864
## c_avg_att 1 5.5 5.50 5.94 0.016 *
## Residuals 236 218.6 0.93
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Warning:
##
## As there is >1 explanatory variable, cross-validation predicted values for
## a fold are not a linear function of corresponding overall predicted
## values. Lines that are shown for the different folds are approximate
##
## fold 1
## Observations in test set: 48
## 3 15 25 27 29 34 38 45
## Predicted 0.263 -0.0153 0.379 -0.171 0.0693 0.0893 0.252 0.136
## cvpred 0.225 -0.1028 0.485 -0.134 0.1005 0.2014 0.212 0.149
## games_started 1.338 -1.0082 1.673 -1.008 -1.3433 -0.6731 1.673 -0.338
## CV residual 1.113 -0.9054 1.188 -0.875 -1.4438 -0.8744 1.461 -0.487
## 46 47 48 50 61 63 65 67
## Predicted 0.0536 -0.173 -0.1271 -0.198 0.23 0.4205 -0.317 0.0781
## cvpred 0.1039 -0.157 -0.0731 -0.154 0.25 0.2991 -0.308 0.0624
## games_started 1.3377 -0.673 -1.3433 -1.008 -1.01 0.3323 1.673 -1.3433
## CV residual 1.2338 -0.516 -1.2702 -0.855 -1.26 0.0332 1.981 -1.4057
## 71 75 78 94 96 97 98 101
## Predicted 0.140 0.545 0.658 -0.0102 0.0603 -0.0486 0.243 0.14910
## cvpred 0.153 0.498 0.646 -0.0275 0.0881 0.0343 0.327 -0.13172
## games_started 1.673 1.338 1.673 -0.6731 -0.3379 -1.3433 -1.008 -0.00279
## CV residual 1.520 0.840 1.027 -0.6455 -0.4260 -1.3776 -1.335 0.12892
## 110 113 114 135 138 139 150 158
## Predicted 0.3570 -0.124 -0.0470 -0.4622 -0.0154 0.0731 0.104 -0.389
## cvpred 0.3947 -0.134 0.0366 -0.5886 -0.0591 0.1389 0.136 -0.427
## games_started 0.3323 0.667 0.6675 -0.6731 0.3323 0.3323 1.003 1.673
## CV residual -0.0623 0.802 0.6308 -0.0845 0.3915 0.1934 0.867 2.100
## 171 172 174 176 177 183 184
## Predicted -0.0497 0.160 -0.108 -0.07853 0.0517 0.0178 0.04375
## cvpred -0.1242 0.146 -0.211 -0.02429 0.1015 0.0502 0.10210
## games_started -0.6731 -1.008 1.673 -0.00279 -0.3379 -1.3433 -0.00279
## CV residual -0.5488 -1.155 1.884 0.02150 -0.4394 -1.3935 -0.10489
## 190 193 200 211 214 215 217 219
## Predicted -0.3563 -0.559 -0.264 0.213 -0.553 -0.264 -0.220 -0.398
## cvpred -0.2693 -0.492 -0.242 0.276 -0.570 -0.199 -0.197 -0.347
## games_started -0.3379 -1.008 -0.673 -1.343 -1.343 -1.343 -0.673 -0.673
## CV residual -0.0687 -0.516 -0.431 -1.619 -0.774 -1.144 -0.476 -0.326
## 231
## Predicted -0.460
## cvpred -0.441
## games_started 1.003
## CV residual 1.443
##
## Sum of squares = 50.6 Mean square = 1.05 n = 48
##
## fold 2
## Observations in test set: 48
## 11 12 18 22 26 33 36 42
## Predicted 0.67684 0.202 0.0483 0.265 0.988 0.223 0.150 0.0296
## cvpred 0.67585 0.245 0.0694 0.292 0.958 0.189 0.159 0.0663
## games_started -0.00279 -0.673 0.6675 1.673 1.338 0.332 -1.008 0.6675
## CV residual -0.67865 -0.918 0.5981 1.381 0.380 0.144 -1.167 0.6011
## 43 44 49 57 58 70 80 90
## Predicted 0.306 0.201 0.159 -0.0560 0.6409 0.200 -0.08437 -0.0998
## cvpred 0.311 0.223 0.173 -0.0265 0.6360 0.207 -0.05099 -0.0534
## games_started -1.343 -1.008 -1.343 1.3377 0.6675 -0.673 -0.00279 -1.3433
## CV residual -1.655 -1.231 -1.516 1.3642 0.0315 -0.880 0.04820 -1.2899
## 100 103 105 106 108 116 123 125
## Predicted 0.396 0.029 0.20906 0.420 0.105 -0.0636 -0.0772 0.180
## cvpred 0.399 0.022 0.19614 0.437 0.108 -0.0294 -0.0509 0.183
## games_started 0.667 -0.338 -0.00279 1.673 -1.008 -1.3433 1.6729 1.003
## CV residual 0.268 -0.360 -0.19894 1.236 -1.116 -1.3139 1.7237 0.820
## 128 137 143 144 146 147 149
## Predicted 0.19978 -0.183 0.187 0.0931 0.09376 -0.269 -0.0982
## cvpred 0.20108 -0.174 0.174 0.0950 0.10556 -0.257 -0.0798
## games_started -0.00279 -0.673 1.673 1.6729 -0.00279 -0.673 -1.3433
## CV residual -0.20387 -0.499 1.499 1.5778 -0.10836 -0.416 -1.2635
## 152 160 161 167 175 179 188
## Predicted -0.00172 -0.0223 -0.0646 -0.0985 -0.162 -0.206 -0.01181
## cvpred 0.04560 -0.0234 -0.0583 -0.1007 -0.142 -0.190 -0.00554
## games_started -0.33792 1.6729 -0.3379 -1.3433 -1.343 0.332 1.00260
## CV residual -0.38352 1.6962 -0.2796 -1.2427 -1.202 0.522 1.00814
## 191 197 201 202 210 218 224 225
## Predicted -0.291 0.04324 -0.139 -0.364 -0.0791 0.00463 -0.261 -0.223
## cvpred -0.274 0.03444 -0.114 -0.319 -0.0668 -0.00558 -0.252 -0.198
## games_started -1.008 -0.00279 0.667 -1.343 0.6675 -0.00279 0.332 -0.338
## CV residual -0.734 -0.03724 0.782 -1.024 0.7343 0.00279 0.585 -0.140
## 226 240
## Predicted 0.00309 -0.6695
## cvpred 0.00575 -0.6434
## games_started -0.67306 -0.6731
## CV residual -0.67881 -0.0297
##
## Sum of squares = 42.4 Mean square = 0.88 n = 48
##
## fold 3
## Observations in test set: 48
## 6 8 16 21 28 31 32
## Predicted 0.07507 0.0373 -0.0675 0.170 -0.393 0.0262 0.23314
## cvpred 0.02037 0.0356 -0.0984 0.101 -0.376 -0.0145 0.18580
## games_started -0.00279 1.6729 -0.3379 -0.673 -1.008 1.6729 -0.00279
## CV residual -0.02316 1.6373 -0.2395 -0.774 -0.632 1.6874 -0.18859
## 35 39 52 54 60 68 73 79
## Predicted -0.155 0.410 0.585 -0.115 -0.1090 0.0720 0.1094 -0.0838
## cvpred -0.172 0.411 0.531 -0.110 -0.0883 0.0759 0.0986 -0.0954
## games_started -1.343 0.667 0.667 -0.673 -1.3433 0.3323 0.6675 1.6729
## CV residual -1.172 0.257 0.137 -0.563 -1.2550 0.2565 0.5689 1.7683
## 81 83 84 89 91 92 107 109
## Predicted 0.0754 1.038 -0.0918 0.0987 0.682 0.255 0.191 -0.00326
## cvpred 0.1120 0.955 -0.1428 0.0992 0.645 0.278 0.206 0.03241
## games_started -0.6731 1.673 1.0026 0.3323 -0.673 -1.343 -0.673 1.33773
## CV residual -0.7851 0.718 1.1454 0.2331 -1.318 -1.621 -0.879 1.30532
## 115 117 119 120 122 126 142 148
## Predicted 0.227 -0.242 -0.205 0.23691 -0.115 0.0585 -0.00567 0.191
## cvpred 0.232 -0.260 -0.221 0.26720 -0.129 0.0935 0.02516 0.214
## games_started 0.667 -1.343 0.667 -0.00279 1.003 -1.3433 -0.00279 1.003
## CV residual 0.435 -1.083 0.888 -0.27000 1.132 -1.4368 -0.02796 0.788
## 154 166 169 170 180 187 189
## Predicted -0.08134 -0.0322 -0.259 -0.3024 -0.33219 -0.4130 -0.575
## cvpred 0.00297 -0.0394 -0.236 -0.2510 -0.26109 -0.3882 -0.486
## games_started -1.34332 -0.3379 -0.673 -0.3379 -0.00279 -0.3379 -1.343
## CV residual -1.34628 -0.2986 -0.437 -0.0869 0.25830 0.0503 -0.858
## 198 206 212 213 221 227 232
## Predicted -0.0811 -0.197 -0.35583 -0.372 0.0229 0.0152 -0.42990
## cvpred -0.0467 -0.167 -0.32156 -0.282 0.0681 0.0641 -0.34608
## games_started -1.0082 -0.338 -0.00279 -1.343 1.0026 -0.3379 -0.33792
## CV residual -0.9615 -0.171 0.31877 -1.061 0.9345 -0.4020 0.00815
## 234 237 239
## Predicted -0.191 0.09536 -0.327
## cvpred -0.117 0.15967 -0.252
## games_started 1.003 -0.00279 -1.343
## CV residual 1.120 -0.16247 -1.092
##
## Sum of squares = 37.6 Mean square = 0.78 n = 48
##
## fold 4
## Observations in test set: 48
## 2 4 9 19 20 23 41 51
## Predicted 0.615 0.05802 -0.362 0.278 0.225 0.347 0.41345 0.236
## cvpred 0.613 -0.00943 -0.353 0.214 0.179 0.236 0.43030 0.195
## games_started 1.338 1.67286 0.332 1.338 -0.673 1.338 -0.00279 0.667
## CV residual 0.724 1.68230 0.685 1.124 -0.852 1.102 -0.43309 0.473
## 53 59 69 72 74 76 77 85
## Predicted -0.272 -0.04870 0.1174 0.200 0.02195 0.0366 -0.0427 -0.176
## cvpred -0.342 -0.09726 0.0752 0.130 0.00244 -0.0428 -0.0759 -0.239
## games_started 0.667 -0.00279 1.6729 1.003 -1.00819 0.3323 -1.0082 -0.673
## CV residual 1.009 0.09447 1.5976 0.873 -1.01063 0.3751 -0.9323 -0.434
## 111 121 124 127 129 130 131 132
## Predicted 0.0803 -0.0156 -0.08541 0.304 0.260 0.549 -0.238 -0.224
## cvpred 0.0370 -0.0850 -0.12259 0.226 0.211 0.488 -0.329 -0.281
## games_started 1.6729 0.3323 -0.00279 1.003 -1.008 1.338 0.667 0.667
## CV residual 1.6359 0.4174 0.11980 0.777 -1.219 0.849 0.996 0.949
## 133 134 136 140 156 157 163
## Predicted -0.345 0.06037 0.1233 0.223 0.0423 -0.02855 0.046632
## cvpred -0.405 -0.00899 0.0698 0.191 -0.0371 -0.12260 -0.000403
## games_started -0.673 0.66747 -1.0082 0.332 -0.6731 -0.00279 -0.673055
## CV residual -0.268 0.67646 -1.0780 0.142 -0.6360 0.11980 -0.672652
## 164 168 173 178 181 182 194
## Predicted -0.0396 -0.0666 -0.00537 -0.545 -0.217 -0.19839 0.0127
## cvpred -0.0858 -0.0630 -0.06419 -0.602 -0.246 -0.25681 -0.0815
## games_started 0.6675 -1.3433 1.33773 1.673 1.003 -0.00279 -0.6731
## CV residual 0.7532 -1.2803 1.40192 2.274 1.249 0.25401 -0.5916
## 196 203 204 208 209 222 223 228
## Predicted -0.50267 0.131 -0.0963 -0.168 -0.270 -0.882 -0.225 -0.223
## cvpred -0.54924 0.110 -0.1202 -0.240 -0.338 -0.990 -0.287 -0.297
## games_started -0.00279 1.003 -0.3379 -0.673 -0.673 -1.008 -0.673 -1.343
## CV residual 0.54645 0.892 -0.2177 -0.433 -0.335 -0.018 -0.386 -1.047
## 230 236
## Predicted -0.125 -0.0236
## cvpred -0.198 -0.0994
## games_started -0.338 -0.3379
## CV residual -0.140 -0.2385
##
## Sum of squares = 38.2 Mean square = 0.8 n = 48
##
## fold 5
## Observations in test set: 48
## 1 5 7 10 13 14 17 24
## Predicted -0.147 0.370 0.793 0.170 -0.0383 0.736 0.292 -0.0318
## cvpred -0.167 0.418 0.879 0.198 -0.0162 0.810 0.331 -0.0196
## games_started 1.673 -1.343 1.673 -0.338 -1.0082 1.673 -0.338 1.6729
## CV residual 1.840 -1.762 0.794 -0.536 -0.9920 0.863 -0.669 1.6924
## 30 37 40 55 56 62 64 66
## Predicted 0.154 -0.5614 0.0143 -0.01374 0.193 -0.271 0.16220 0.290
## cvpred 0.185 -0.5990 0.0127 -0.00809 0.209 -0.279 0.18114 0.305
## games_started 1.338 -0.6731 -1.0082 -1.34332 -1.343 -0.673 -0.00279 1.338
## CV residual 1.153 -0.0741 -1.0209 -1.33522 -1.552 -0.394 -0.18394 1.033
## 82 86 87 88 93 95 99 102
## Predicted 0.37323 -0.329 0.255 0.357 0.176 0.290 0.02157 5.44e-03
## cvpred 0.40354 -0.370 0.286 0.401 0.188 0.318 0.00976 -4.24e-05
## games_started -0.00279 -1.343 -1.343 1.673 1.673 0.667 -1.34332 1.67e+00
## CV residual -0.40634 -0.973 -1.630 1.272 1.485 0.349 -1.35308 1.67e+00
## 104 112 118 141 145 151 153 155
## Predicted 0.6590 0.414 -0.292 -0.390 -0.326 -0.481 -0.44158 -0.0686
## cvpred 0.7392 0.476 -0.328 -0.439 -0.367 -0.516 -0.47729 -0.0711
## games_started 0.6675 -1.343 -1.008 -0.673 1.673 -0.338 -0.00279 0.6675
## CV residual -0.0717 -1.820 -0.681 -0.235 2.040 0.178 0.47450 0.7386
## 159 162 165 185 186 192 195 199
## Predicted -0.434 0.148 -0.409 0.496 -0.00327 -0.01854 -0.0338 -0.359
## cvpred -0.481 0.169 -0.468 0.536 -0.02075 -0.02038 -0.0463 -0.409
## games_started 0.667 -1.008 0.332 -0.338 -0.00279 -0.00279 -1.0082 1.003
## CV residual 1.149 -1.177 0.800 -0.874 0.01796 0.01759 -0.9619 1.412
## 205 207 216 220 229 233 235 238
## Predicted -0.215 -0.2855 -0.239 -0.508 -0.188 -0.0946 -0.408 -0.0155
## cvpred -0.245 -0.3075 -0.257 -0.571 -0.221 -0.1026 -0.456 -0.0360
## games_started -1.343 -0.3379 1.003 -0.338 -1.343 1.0026 -1.008 0.3323
## CV residual -1.098 -0.0304 1.259 0.233 -1.122 1.1052 -0.552 0.3683
##
## Sum of squares = 54.2 Mean square = 1.13 n = 48
##
## Overall (Sum over all 48 folds)
## ms
## 0.929