# Fetch Data
qb_stats_w_combine <- read.csv("../data/qb_stats_w_combine.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", "X40",
"wonderlic", "cone", "shuttle", "vert_leap", "broad_jump")
college_stats = qb_stats_w_combine[, predictors]
# Set the resopnse variables
wins = qb_stats_w_combine["wins"]
# Generate clean data set
data.log.w_combine.for_wins = data.frame(log(na.omit(cbind(wins, college_stats)) +
0.1))
# Generate the linear model
lm.log.w_combine.wins <- lm(formula = wins ~ ., data = data.log.w_combine.for_wins)
# Find optimum linear regression model for wins
step_reg.log.w_combine.wins <- stepAIC(lm.log.w_combine.wins, direction = "both")
## Start: AIC=16.59
## wins ~ height + weight + age + c_avg_cmpp + c_rate + c_pct +
## c_avg_inter + c_avg_tds + c_avg_yds + c_numyrs + c_avg_att +
## X40 + wonderlic + cone + shuttle + vert_leap + broad_jump
##
## Df Sum of Sq RSS AIC
## - cone 1 0.042 23.8 14.7
## - height 1 0.064 23.8 14.7
## - X40 1 0.097 23.8 14.8
## - shuttle 1 0.102 23.8 14.8
## - weight 1 0.103 23.8 14.8
## - c_pct 1 0.120 23.8 14.8
## - vert_leap 1 0.156 23.9 14.8
## - c_avg_cmpp 1 0.243 24.0 15.0
## - c_avg_att 1 0.360 24.1 15.2
## - c_avg_inter 1 0.416 24.1 15.3
## - age 1 0.528 24.2 15.4
## - c_avg_yds 1 0.529 24.2 15.4
## - broad_jump 1 0.554 24.3 15.5
## - c_avg_tds 1 0.616 24.3 15.6
## - c_rate 1 0.640 24.4 15.6
## <none> 23.7 16.6
## - wonderlic 1 1.348 25.1 16.8
## - c_numyrs 1 1.872 25.6 17.6
##
## Step: AIC=14.66
## wins ~ height + weight + age + c_avg_cmpp + c_rate + c_pct +
## c_avg_inter + c_avg_tds + c_avg_yds + c_numyrs + c_avg_att +
## X40 + wonderlic + shuttle + vert_leap + broad_jump
##
## Df Sum of Sq RSS AIC
## - X40 1 0.101 23.9 12.8
## - height 1 0.102 23.9 12.8
## - c_pct 1 0.123 23.9 12.9
## - vert_leap 1 0.142 23.9 12.9
## - weight 1 0.145 23.9 12.9
## - shuttle 1 0.196 23.9 13.0
## - c_avg_cmpp 1 0.246 24.0 13.1
## - c_avg_att 1 0.361 24.1 13.2
## - c_avg_yds 1 0.530 24.3 13.5
## - c_avg_inter 1 0.533 24.3 13.5
## - age 1 0.544 24.3 13.6
## - broad_jump 1 0.599 24.4 13.6
## - c_avg_tds 1 0.600 24.4 13.6
## - c_rate 1 0.636 24.4 13.7
## <none> 23.8 14.7
## - wonderlic 1 1.367 25.1 14.8
## - c_numyrs 1 1.835 25.6 15.6
## + cone 1 0.042 23.7 16.6
##
## Step: AIC=12.83
## wins ~ height + weight + age + c_avg_cmpp + c_rate + c_pct +
## c_avg_inter + c_avg_tds + c_avg_yds + c_numyrs + c_avg_att +
## wonderlic + shuttle + vert_leap + broad_jump
##
## Df Sum of Sq RSS AIC
## - height 1 0.058 23.9 10.9
## - weight 1 0.111 24.0 11.0
## - shuttle 1 0.118 24.0 11.0
## - c_pct 1 0.156 24.0 11.1
## - vert_leap 1 0.189 24.0 11.1
## - c_avg_cmpp 1 0.277 24.1 11.3
## - c_avg_att 1 0.369 24.2 11.4
## - c_avg_inter 1 0.438 24.3 11.5
## - c_avg_yds 1 0.450 24.3 11.6
## - broad_jump 1 0.504 24.4 11.6
## - age 1 0.505 24.4 11.7
## - c_avg_tds 1 0.518 24.4 11.7
## - c_rate 1 0.552 24.4 11.7
## <none> 23.9 12.8
## - wonderlic 1 1.292 25.1 12.9
## - c_numyrs 1 1.833 25.7 13.7
## + X40 1 0.101 23.8 14.7
## + cone 1 0.046 23.8 14.8
##
## Step: AIC=10.92
## wins ~ weight + age + c_avg_cmpp + c_rate + c_pct + c_avg_inter +
## c_avg_tds + c_avg_yds + c_numyrs + c_avg_att + wonderlic +
## shuttle + vert_leap + broad_jump
##
## Df Sum of Sq RSS AIC
## - weight 1 0.054 24.0 9.01
## - shuttle 1 0.125 24.0 9.13
## - c_pct 1 0.174 24.1 9.21
## - vert_leap 1 0.184 24.1 9.22
## - c_avg_cmpp 1 0.319 24.2 9.44
## - c_avg_att 1 0.434 24.4 9.62
## - c_avg_inter 1 0.480 24.4 9.70
## - broad_jump 1 0.528 24.4 9.78
## - c_avg_yds 1 0.552 24.5 9.81
## - age 1 0.579 24.5 9.86
## - c_avg_tds 1 0.671 24.6 10.00
## - c_rate 1 0.693 24.6 10.04
## <none> 23.9 10.92
## - wonderlic 1 1.836 25.8 11.81
## - c_numyrs 1 1.940 25.9 11.97
## + cone 1 0.073 23.8 12.80
## + height 1 0.058 23.9 12.83
## + X40 1 0.057 23.9 12.83
##
## Step: AIC=9.01
## wins ~ age + c_avg_cmpp + c_rate + c_pct + c_avg_inter + c_avg_tds +
## c_avg_yds + c_numyrs + c_avg_att + wonderlic + shuttle +
## vert_leap + broad_jump
##
## Df Sum of Sq RSS AIC
## - shuttle 1 0.076 24.0 7.13
## - vert_leap 1 0.153 24.1 7.26
## - c_pct 1 0.208 24.2 7.35
## - c_avg_cmpp 1 0.373 24.3 7.61
## - c_avg_inter 1 0.471 24.4 7.77
## - c_avg_att 1 0.494 24.5 7.81
## - c_avg_yds 1 0.562 24.5 7.92
## - broad_jump 1 0.595 24.6 7.97
## - c_rate 1 0.726 24.7 8.18
## - c_avg_tds 1 0.754 24.7 8.22
## - age 1 0.875 24.8 8.41
## <none> 24.0 9.01
## - wonderlic 1 1.946 25.9 10.06
## - c_numyrs 1 2.114 26.1 10.31
## + cone 1 0.083 23.9 10.88
## + X40 1 0.059 23.9 10.91
## + weight 1 0.054 23.9 10.92
## + height 1 0.001 24.0 11.01
##
## Step: AIC=7.13
## wins ~ age + c_avg_cmpp + c_rate + c_pct + c_avg_inter + c_avg_tds +
## c_avg_yds + c_numyrs + c_avg_att + wonderlic + vert_leap +
## broad_jump
##
## Df Sum of Sq RSS AIC
## - vert_leap 1 0.094 24.1 5.29
## - c_pct 1 0.186 24.2 5.43
## - c_avg_cmpp 1 0.344 24.4 5.69
## - c_avg_att 1 0.460 24.5 5.87
## - c_avg_inter 1 0.473 24.5 5.89
## - c_avg_yds 1 0.526 24.6 5.98
## - broad_jump 1 0.617 24.7 6.12
## - c_rate 1 0.702 24.7 6.26
## - c_avg_tds 1 0.771 24.8 6.37
## - age 1 0.830 24.9 6.46
## <none> 24.0 7.13
## - wonderlic 1 1.902 25.9 8.10
## - c_numyrs 1 2.078 26.1 8.37
## + cone 1 0.145 23.9 8.90
## + shuttle 1 0.076 24.0 9.01
## + height 1 0.018 24.0 9.10
## + X40 1 0.008 24.0 9.12
## + weight 1 0.004 24.0 9.13
##
## Step: AIC=5.29
## wins ~ age + c_avg_cmpp + c_rate + c_pct + c_avg_inter + c_avg_tds +
## c_avg_yds + c_numyrs + c_avg_att + wonderlic + broad_jump
##
## Df Sum of Sq RSS AIC
## - c_pct 1 0.188 24.3 3.59
## - c_avg_cmpp 1 0.334 24.5 3.82
## - c_avg_inter 1 0.417 24.6 3.95
## - c_avg_att 1 0.431 24.6 3.98
## - c_avg_yds 1 0.448 24.6 4.00
## - c_rate 1 0.622 24.8 4.28
## - c_avg_tds 1 0.697 24.8 4.40
## - broad_jump 1 0.759 24.9 4.49
## - age 1 0.818 24.9 4.59
## <none> 24.1 5.29
## - wonderlic 1 1.855 26.0 6.17
## - c_numyrs 1 2.002 26.1 6.39
## + vert_leap 1 0.094 24.0 7.13
## + cone 1 0.075 24.1 7.16
## + X40 1 0.035 24.1 7.23
## + shuttle 1 0.017 24.1 7.26
## + height 1 0.014 24.1 7.26
## + weight 1 0.005 24.1 7.28
##
## Step: AIC=3.59
## wins ~ age + c_avg_cmpp + c_rate + c_avg_inter + c_avg_tds +
## c_avg_yds + c_numyrs + c_avg_att + wonderlic + broad_jump
##
## Df Sum of Sq RSS AIC
## - c_avg_yds 1 0.288 24.6 2.05
## - c_rate 1 0.462 24.8 2.32
## - c_avg_att 1 0.505 24.8 2.39
## - c_avg_tds 1 0.551 24.9 2.46
## - c_avg_inter 1 0.629 24.9 2.58
## - c_avg_cmpp 1 0.667 25.0 2.64
## - broad_jump 1 0.760 25.1 2.79
## - age 1 0.810 25.1 2.87
## <none> 24.3 3.59
## - wonderlic 1 1.814 26.1 4.39
## - c_numyrs 1 1.926 26.2 4.56
## + c_pct 1 0.188 24.1 5.29
## + vert_leap 1 0.096 24.2 5.43
## + cone 1 0.077 24.2 5.47
## + X40 1 0.059 24.3 5.49
## + weight 1 0.022 24.3 5.55
## + height 1 0.008 24.3 5.58
## + shuttle 1 0.008 24.3 5.58
##
## Step: AIC=2.05
## wins ~ age + c_avg_cmpp + c_rate + c_avg_inter + c_avg_tds +
## c_numyrs + c_avg_att + wonderlic + broad_jump
##
## Df Sum of Sq RSS AIC
## - c_avg_tds 1 0.299 24.9 0.52
## - c_avg_inter 1 0.351 25.0 0.60
## - c_rate 1 0.497 25.1 0.83
## - c_avg_cmpp 1 0.630 25.2 1.03
## - c_avg_att 1 0.667 25.3 1.09
## - broad_jump 1 0.730 25.3 1.19
## - age 1 0.742 25.4 1.21
## <none> 24.6 2.05
## - wonderlic 1 1.670 26.3 2.61
## - c_numyrs 1 1.731 26.3 2.70
## + c_avg_yds 1 0.288 24.3 3.59
## + cone 1 0.106 24.5 3.88
## + height 1 0.031 24.6 4.00
## + c_pct 1 0.028 24.6 4.00
## + weight 1 0.022 24.6 4.01
## + vert_leap 1 0.021 24.6 4.01
## + shuttle 1 0.013 24.6 4.03
## + X40 1 0.001 24.6 4.05
##
## Step: AIC=0.52
## wins ~ age + c_avg_cmpp + c_rate + c_avg_inter + c_numyrs + c_avg_att +
## wonderlic + broad_jump
##
## Df Sum of Sq RSS AIC
## - c_rate 1 0.200 25.1 -1.169
## - c_avg_cmpp 1 0.356 25.3 -0.927
## - c_avg_att 1 0.369 25.3 -0.907
## - c_avg_inter 1 0.395 25.3 -0.866
## - broad_jump 1 0.592 25.5 -0.565
## - age 1 0.861 25.8 -0.156
## <none> 24.9 0.519
## - wonderlic 1 1.656 26.6 1.029
## - c_numyrs 1 1.679 26.6 1.063
## + c_avg_tds 1 0.299 24.6 2.048
## + cone 1 0.119 24.8 2.332
## + c_pct 1 0.068 24.8 2.413
## + weight 1 0.052 24.9 2.438
## + shuttle 1 0.046 24.9 2.447
## + height 1 0.038 24.9 2.460
## + c_avg_yds 1 0.037 24.9 2.462
## + vert_leap 1 0.036 24.9 2.463
## + X40 1 0.002 24.9 2.517
##
## Step: AIC=-1.17
## wins ~ age + c_avg_cmpp + c_avg_inter + c_numyrs + c_avg_att +
## wonderlic + broad_jump
##
## Df Sum of Sq RSS AIC
## - c_avg_cmpp 1 0.167 25.3 -2.911
## - c_avg_att 1 0.170 25.3 -2.906
## - c_avg_inter 1 0.236 25.4 -2.805
## - broad_jump 1 0.497 25.6 -2.405
## - age 1 0.727 25.8 -2.056
## <none> 25.1 -1.169
## - wonderlic 1 1.457 26.6 -0.970
## - c_numyrs 1 1.588 26.7 -0.778
## + c_avg_yds 1 0.236 24.9 0.463
## + c_rate 1 0.200 24.9 0.519
## + c_pct 1 0.146 25.0 0.604
## + cone 1 0.127 25.0 0.632
## + weight 1 0.062 25.1 0.735
## + vert_leap 1 0.054 25.1 0.747
## + height 1 0.040 25.1 0.769
## + shuttle 1 0.040 25.1 0.769
## + c_avg_tds 1 0.002 25.1 0.827
## + X40 1 0.000 25.1 0.830
##
## Step: AIC=-2.91
## wins ~ age + c_avg_inter + c_numyrs + c_avg_att + wonderlic +
## broad_jump
##
## Df Sum of Sq RSS AIC
## - c_avg_att 1 0.004 25.3 -4.90
## - broad_jump 1 0.622 25.9 -3.96
## - c_avg_inter 1 0.670 25.9 -3.89
## - age 1 0.890 26.2 -3.56
## <none> 25.3 -2.91
## - wonderlic 1 1.459 26.7 -2.72
## - c_numyrs 1 1.768 27.1 -2.27
## + c_avg_cmpp 1 0.167 25.1 -1.17
## + c_pct 1 0.153 25.1 -1.15
## + weight 1 0.103 25.2 -1.07
## + cone 1 0.103 25.2 -1.07
## + vert_leap 1 0.086 25.2 -1.04
## + height 1 0.044 25.2 -0.98
## + c_avg_tds 1 0.031 25.2 -0.96
## + shuttle 1 0.029 25.2 -0.96
## + X40 1 0.017 25.3 -0.94
## + c_rate 1 0.010 25.3 -0.93
## + c_avg_yds 1 0.006 25.3 -0.92
##
## Step: AIC=-4.9
## wins ~ age + c_avg_inter + c_numyrs + wonderlic + broad_jump
##
## Df Sum of Sq RSS AIC
## - broad_jump 1 0.62 25.9 -5.96
## - age 1 0.91 26.2 -5.52
## <none> 25.3 -4.90
## - wonderlic 1 1.69 27.0 -4.38
## - c_numyrs 1 1.91 27.2 -4.07
## + weight 1 0.10 25.2 -3.06
## + vert_leap 1 0.08 25.2 -3.03
## + cone 1 0.08 25.2 -3.02
## + c_pct 1 0.05 25.2 -2.99
## + height 1 0.04 25.2 -2.97
## + shuttle 1 0.03 25.2 -2.95
## + X40 1 0.02 25.3 -2.93
## + c_avg_yds 1 0.01 25.3 -2.92
## + c_avg_att 1 0.00 25.3 -2.91
## + c_avg_cmpp 1 0.00 25.3 -2.91
## + c_avg_tds 1 0.00 25.3 -2.90
## + c_rate 1 0.00 25.3 -2.90
## - c_avg_inter 1 3.90 29.2 -1.30
##
## Step: AIC=-5.96
## wins ~ age + c_avg_inter + c_numyrs + wonderlic
##
## Df Sum of Sq RSS AIC
## - age 1 1.25 27.1 -6.13
## <none> 25.9 -5.96
## - c_numyrs 1 1.55 27.4 -5.70
## + broad_jump 1 0.62 25.3 -4.90
## - wonderlic 1 2.16 28.1 -4.84
## + cone 1 0.40 25.5 -4.58
## + shuttle 1 0.27 25.6 -4.38
## + X40 1 0.23 25.7 -4.31
## + weight 1 0.18 25.7 -4.24
## + vert_leap 1 0.18 25.7 -4.23
## + c_pct 1 0.14 25.8 -4.17
## + height 1 0.05 25.9 -4.04
## + c_rate 1 0.03 25.9 -4.01
## + c_avg_cmpp 1 0.02 25.9 -3.99
## + c_avg_tds 1 0.01 25.9 -3.98
## + c_avg_yds 1 0.00 25.9 -3.97
## + c_avg_att 1 0.00 25.9 -3.96
## - c_avg_inter 1 3.45 29.4 -3.09
##
## Step: AIC=-6.13
## wins ~ c_avg_inter + c_numyrs + wonderlic
##
## Df Sum of Sq RSS AIC
## - wonderlic 1 1.31 28.4 -6.30
## <none> 27.1 -6.13
## + age 1 1.25 25.9 -5.96
## - c_numyrs 1 1.61 28.8 -5.89
## + broad_jump 1 0.95 26.2 -5.52
## + weight 1 0.78 26.4 -5.27
## + cone 1 0.57 26.6 -4.95
## + X40 1 0.42 26.7 -4.74
## + vert_leap 1 0.32 26.8 -4.60
## + shuttle 1 0.29 26.9 -4.56
## + c_pct 1 0.23 26.9 -4.46
## + c_rate 1 0.11 27.0 -4.29
## + c_avg_tds 1 0.03 27.1 -4.18
## + c_avg_att 1 0.01 27.1 -4.15
## + c_avg_cmpp 1 0.01 27.1 -4.14
## + c_avg_yds 1 0.00 27.1 -4.13
## + height 1 0.00 27.1 -4.13
## - c_avg_inter 1 4.40 31.6 -2.27
##
## Step: AIC=-6.3
## wins ~ c_avg_inter + c_numyrs
##
## Df Sum of Sq RSS AIC
## - c_numyrs 1 1.22 29.7 -6.67
## <none> 28.5 -6.30
## + wonderlic 1 1.31 27.1 -6.13
## + broad_jump 1 1.24 27.2 -6.03
## + weight 1 0.98 27.5 -5.67
## + X40 1 0.70 27.8 -5.27
## + vert_leap 1 0.57 27.9 -5.09
## + age 1 0.39 28.1 -4.84
## + c_avg_att 1 0.20 28.3 -4.57
## + shuttle 1 0.09 28.4 -4.43
## + c_avg_cmpp 1 0.07 28.4 -4.40
## + height 1 0.05 28.4 -4.37
## + c_avg_yds 1 0.05 28.4 -4.37
## + cone 1 0.04 28.4 -4.35
## + c_pct 1 0.03 28.4 -4.35
## + c_rate 1 0.03 28.4 -4.34
## + c_avg_tds 1 0.00 28.4 -4.30
## - c_avg_inter 1 3.86 32.3 -3.34
##
## Step: AIC=-6.67
## wins ~ c_avg_inter
##
## Df Sum of Sq RSS AIC
## <none> 29.7 -6.67
## + c_numyrs 1 1.215 28.5 -6.30
## + weight 1 1.186 28.5 -6.26
## + wonderlic 1 0.912 28.8 -5.89
## + broad_jump 1 0.702 29.0 -5.60
## + age 1 0.506 29.2 -5.34
## - c_avg_inter 1 2.664 32.3 -5.31
## + X40 1 0.425 29.2 -5.23
## + vert_leap 1 0.339 29.3 -5.12
## + c_pct 1 0.295 29.4 -5.06
## + c_rate 1 0.282 29.4 -5.04
## + c_avg_tds 1 0.114 29.6 -4.82
## + shuttle 1 0.069 29.6 -4.76
## + cone 1 0.040 29.6 -4.72
## + height 1 0.031 29.6 -4.71
## + c_avg_yds 1 0.030 29.6 -4.71
## + c_avg_cmpp 1 0.020 29.6 -4.69
## + c_avg_att 1 0.002 29.7 -4.67
summary(step_reg.log.w_combine.wins)
##
## Call:
## lm(formula = wins ~ c_avg_inter, data = data.log.w_combine.for_wins)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.536 -0.380 0.046 0.593 1.104
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.051 0.360 5.70 1.6e-06 ***
## c_avg_inter -0.315 0.173 -1.82 0.076 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.895 on 37 degrees of freedom
## Multiple R-squared: 0.0824, Adjusted R-squared: 0.0576
## F-statistic: 3.32 on 1 and 37 DF, p-value: 0.0764
plot(step_reg.log.w_combine.wins)
leaps.log.w_combine.wins <- regsubsets(wins ~ ., data = data.log.w_combine.for_wins,
nbest = 10)
subsets(leaps.log.w_combine.wins, statistic = "rsq")
## Error: invalid coordinate lengths
cv.lm(df = data.log.w_combine.for_wins, step_reg.log.w_combine.wins, m = 5) # 5 fold cross-validation
## Analysis of Variance Table
##
## Response: wins
## Df Sum Sq Mean Sq F value Pr(>F)
## c_avg_inter 1 2.66 2.664 3.32 0.076 .
## Residuals 37 29.67 0.802
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## fold 1
## Observations in test set: 7
## 3 21 24 40 42 52 61
## c_avg_inter 2.028 1.8083 2.60 2.436 2.061 2.573 0.470
## cvpred 1.558 1.5997 1.45 1.481 1.552 1.455 1.853
## wins 0.742 1.6292 -2.30 1.808 1.131 0.742 2.092
## CV residual -0.816 0.0295 -3.75 0.327 -0.421 -0.713 0.239
##
## Sum of squares = 15.6 Mean square = 2.23 n = 7
##
## fold 2
## Observations in test set: 8
## 6 18 25 37 43 50 55 63
## c_avg_inter 2.028 2.061 2.38 -2.30 2.493 2.407 2.132 2.4656
## cvpred 1.391 1.375 1.22 3.54 1.160 1.203 1.339 1.1736
## wins 2.208 1.808 2.41 2.41 1.629 0.742 1.131 0.0953
## CV residual 0.818 0.434 1.19 -1.13 0.469 -0.461 -0.208 -1.0783
##
## Sum of squares = 5.2 Mean square = 0.65 n = 8
##
## fold 3
## Observations in test set: 8
## 5 7 16 20 28 32 49 64
## c_avg_inter 2.01 1.723 2.31 2.1223 1.92 2.180 1.8871 1.411
## cvpred 1.36 1.447 1.26 1.3218 1.38 1.304 1.3956 1.545
## wins 2.41 1.629 2.09 0.0953 2.41 1.411 1.4110 1.960
## CV residual 1.05 0.182 0.83 -1.2265 1.02 0.107 0.0154 0.415
##
## Sum of squares = 4.56 Mean square = 0.57 n = 8
##
## fold 4
## Observations in test set: 8
## 12 13 26 30 38 39 59 65
## c_avg_inter 2.3125 0.8879 1.629 2.429 1.677 2.436 2.61 1.579
## cvpred 1.3399 1.7637 1.543 1.305 1.529 1.303 1.25 1.558
## wins 0.0953 1.8083 1.411 2.092 1.131 1.131 1.13 2.407
## CV residual -1.2446 0.0446 -0.132 0.787 -0.398 -0.172 -0.12 0.849
##
## Sum of squares = 3.11 Mean square = 0.39 n = 8
##
## fold 5
## Observations in test set: 8
## 1 4 15 17 19 27 46 56
## c_avg_inter 2.050 1.019 2.235 2.092 2.028 2.66 1.692 2.03
## cvpred 1.323 1.726 1.251 1.307 1.332 1.08 1.463 1.33
## wins 1.960 0.742 1.960 1.411 0.742 2.31 2.092 2.41
## CV residual 0.637 -0.985 0.709 0.104 -0.590 1.23 0.629 1.08
##
## Sum of squares = 5.3 Mean square = 0.66 n = 8
##
## Overall (Sum over all 8 folds)
## ms
## 0.866