# 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
sacks = qb_stats_w_combine["sacked"]

# Generate clean data set
data.log.w_combine.for_sacks = data.frame(log(na.omit(cbind(sacks, college_stats)) + 
    0.1))

# Generate the linear model
lm.log.w_combine.sacks <- lm(formula = sacked ~ ., data = data.log.w_combine.for_sacks)

# Find optimum linear regression model for sacks
step_reg.log.w_combine.sacks <- stepAIC(lm.log.w_combine.sacks, direction = "both")
## Start:  AIC=-49.25
## sacked ~ 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     0.001 4.03 -51.2
## - age          1     0.002 4.03 -51.2
## - broad_jump   1     0.004 4.04 -51.2
## - height       1     0.004 4.04 -51.2
## - c_avg_inter  1     0.005 4.04 -51.2
## - X40          1     0.010 4.04 -51.2
## - weight       1     0.013 4.04 -51.1
## - wonderlic    1     0.076 4.11 -50.5
## - vert_leap    1     0.077 4.11 -50.5
## - c_numyrs     1     0.086 4.12 -50.4
## - shuttle      1     0.112 4.14 -50.2
## - c_avg_tds    1     0.154 4.19 -49.8
## <none>                     4.03 -49.3
## - c_rate       1     0.237 4.27 -49.1
## - c_avg_yds    1     0.342 4.37 -48.2
## - c_pct        1     0.501 4.53 -46.8
## - c_avg_cmpp   1     0.571 4.60 -46.2
## - c_avg_att    1     0.618 4.65 -45.8
## 
## Step:  AIC=-51.24
## sacked ~ 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
## - age          1     0.002 4.03 -53.2
## - broad_jump   1     0.003 4.04 -53.2
## - height       1     0.007 4.04 -53.2
## - c_avg_inter  1     0.007 4.04 -53.2
## - X40          1     0.009 4.04 -53.1
## - weight       1     0.017 4.05 -53.1
## - vert_leap    1     0.077 4.11 -52.5
## - wonderlic    1     0.082 4.12 -52.5
## - c_numyrs     1     0.085 4.12 -52.4
## - c_avg_tds    1     0.152 4.19 -51.8
## - shuttle      1     0.156 4.19 -51.8
## <none>                     4.03 -51.2
## - c_rate       1     0.238 4.27 -51.1
## - c_avg_yds    1     0.344 4.38 -50.1
## + cone         1     0.001 4.03 -49.3
## - c_pct        1     0.501 4.53 -48.8
## - c_avg_cmpp   1     0.570 4.60 -48.2
## - c_avg_att    1     0.617 4.65 -47.8
## 
## Step:  AIC=-53.22
## sacked ~ height + weight + 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
## - broad_jump   1     0.003 4.04 -55.2
## - c_avg_inter  1     0.007 4.04 -55.2
## - X40          1     0.009 4.04 -55.1
## - height       1     0.009 4.04 -55.1
## - weight       1     0.030 4.06 -54.9
## - c_numyrs     1     0.083 4.12 -54.4
## - vert_leap    1     0.084 4.12 -54.4
## - wonderlic    1     0.094 4.13 -54.3
## - c_avg_tds    1     0.150 4.19 -53.8
## - shuttle      1     0.168 4.20 -53.7
## <none>                     4.03 -53.2
## - c_rate       1     0.236 4.27 -53.1
## - c_avg_yds    1     0.342 4.38 -52.1
## + age          1     0.002 4.03 -51.2
## + cone         1     0.001 4.03 -51.2
## - c_pct        1     0.501 4.54 -50.8
## - c_avg_cmpp   1     0.572 4.61 -50.2
## - c_avg_att    1     0.621 4.66 -49.8
## 
## Step:  AIC=-55.2
## sacked ~ height + weight + 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
## 
##               Df Sum of Sq  RSS   AIC
## - X40          1     0.007 4.04 -57.1
## - c_avg_inter  1     0.012 4.05 -57.1
## - height       1     0.013 4.05 -57.1
## - weight       1     0.035 4.07 -56.9
## - c_numyrs     1     0.087 4.12 -56.4
## - wonderlic    1     0.095 4.13 -56.3
## - vert_leap    1     0.154 4.19 -55.8
## - c_avg_tds    1     0.179 4.22 -55.5
## - shuttle      1     0.198 4.24 -55.4
## <none>                     4.04 -55.2
## - c_rate       1     0.286 4.32 -54.6
## - c_avg_yds    1     0.411 4.45 -53.5
## + broad_jump   1     0.003 4.03 -53.2
## + age          1     0.002 4.04 -53.2
## + cone         1     0.001 4.04 -53.2
## - c_pct        1     0.499 4.54 -52.8
## - c_avg_cmpp   1     0.570 4.61 -52.2
## - c_avg_att    1     0.623 4.66 -51.7
## 
## Step:  AIC=-57.13
## sacked ~ height + weight + 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
## 
##               Df Sum of Sq  RSS   AIC
## - c_avg_inter  1     0.017 4.06 -59.0
## - height       1     0.021 4.07 -58.9
## - weight       1     0.051 4.09 -58.7
## - c_numyrs     1     0.081 4.13 -58.4
## - wonderlic    1     0.099 4.14 -58.2
## - vert_leap    1     0.158 4.20 -57.7
## - c_avg_tds    1     0.184 4.23 -57.4
## <none>                     4.04 -57.1
## - shuttle      1     0.289 4.33 -56.5
## - c_rate       1     0.294 4.34 -56.5
## - c_avg_yds    1     0.427 4.47 -55.3
## + X40          1     0.007 4.04 -55.2
## + age          1     0.002 4.04 -55.1
## + cone         1     0.001 4.04 -55.1
## + broad_jump   1     0.000 4.04 -55.1
## - c_pct        1     0.492 4.54 -54.8
## - c_avg_cmpp   1     0.563 4.61 -54.2
## - c_avg_att    1     0.616 4.66 -53.7
## 
## Step:  AIC=-58.97
## sacked ~ height + weight + c_avg_cmpp + c_rate + c_pct + c_avg_tds + 
##     c_avg_yds + c_numyrs + c_avg_att + wonderlic + shuttle + 
##     vert_leap
## 
##               Df Sum of Sq  RSS   AIC
## - height       1     0.024 4.09 -60.7
## - weight       1     0.048 4.11 -60.5
## - c_numyrs     1     0.083 4.14 -60.2
## - wonderlic    1     0.084 4.14 -60.2
## - vert_leap    1     0.155 4.22 -59.6
## - c_avg_tds    1     0.173 4.23 -59.4
## <none>                     4.06 -59.0
## - shuttle      1     0.282 4.34 -58.4
## - c_rate       1     0.328 4.39 -58.0
## + c_avg_inter  1     0.017 4.04 -57.1
## + X40          1     0.011 4.05 -57.1
## + cone         1     0.004 4.06 -57.0
## + broad_jump   1     0.000 4.06 -57.0
## + age          1     0.000 4.06 -57.0
## - c_avg_yds    1     0.479 4.54 -56.7
## - c_pct        1     0.594 4.65 -55.8
## - c_avg_cmpp   1     0.609 4.67 -55.7
## - c_avg_att    1     0.622 4.68 -55.6
## 
## Step:  AIC=-60.75
## sacked ~ weight + c_avg_cmpp + c_rate + c_pct + c_avg_tds + c_avg_yds + 
##     c_numyrs + c_avg_att + wonderlic + shuttle + vert_leap
## 
##               Df Sum of Sq  RSS   AIC
## - weight       1     0.024 4.11 -62.5
## - c_numyrs     1     0.099 4.18 -61.8
## - vert_leap    1     0.140 4.23 -61.5
## - wonderlic    1     0.144 4.23 -61.4
## <none>                     4.09 -60.7
## - c_avg_tds    1     0.230 4.32 -60.7
## - shuttle      1     0.281 4.37 -60.2
## - c_rate       1     0.395 4.48 -59.2
## + height       1     0.024 4.06 -59.0
## + X40          1     0.023 4.06 -59.0
## + c_avg_inter  1     0.020 4.07 -58.9
## + cone         1     0.011 4.07 -58.9
## + age          1     0.003 4.08 -58.8
## + broad_jump   1     0.001 4.08 -58.8
## - c_avg_yds    1     0.539 4.62 -58.0
## - c_pct        1     0.628 4.71 -57.3
## - c_avg_cmpp   1     0.659 4.74 -57.1
## - c_avg_att    1     0.683 4.77 -56.9
## 
## Step:  AIC=-62.53
## sacked ~ c_avg_cmpp + c_rate + c_pct + c_avg_tds + c_avg_yds + 
##     c_numyrs + c_avg_att + wonderlic + shuttle + vert_leap
## 
##               Df Sum of Sq  RSS   AIC
## - vert_leap    1     0.117 4.23 -63.5
## - c_numyrs     1     0.121 4.23 -63.4
## - wonderlic    1     0.141 4.25 -63.2
## <none>                     4.11 -62.5
## - c_avg_tds    1     0.278 4.39 -62.0
## - shuttle      1     0.281 4.39 -62.0
## - c_rate       1     0.417 4.53 -60.9
## + X40          1     0.028 4.08 -60.8
## + weight       1     0.024 4.09 -60.7
## + cone         1     0.015 4.09 -60.7
## + age          1     0.015 4.09 -60.7
## + c_avg_inter  1     0.014 4.09 -60.7
## + broad_jump   1     0.000 4.11 -60.5
## + height       1     0.000 4.11 -60.5
## - c_avg_yds    1     0.544 4.65 -59.8
## - c_pct        1     0.660 4.77 -58.9
## - c_avg_cmpp   1     0.701 4.81 -58.5
## - c_avg_att    1     0.723 4.83 -58.4
## 
## Step:  AIC=-63.46
## sacked ~ c_avg_cmpp + c_rate + c_pct + c_avg_tds + c_avg_yds + 
##     c_numyrs + c_avg_att + wonderlic + shuttle
## 
##               Df Sum of Sq  RSS   AIC
## - wonderlic    1     0.089 4.32 -64.7
## - c_numyrs     1     0.138 4.36 -64.2
## - shuttle      1     0.165 4.39 -64.0
## <none>                     4.23 -63.5
## - c_avg_tds    1     0.275 4.50 -63.1
## + vert_leap    1     0.117 4.11 -62.5
## - c_rate       1     0.368 4.59 -62.3
## + broad_jump   1     0.068 4.16 -62.1
## + c_avg_inter  1     0.016 4.21 -61.6
## + height       1     0.008 4.22 -61.5
## + age          1     0.005 4.22 -61.5
## - c_avg_yds    1     0.463 4.69 -61.5
## + X40          1     0.002 4.22 -61.5
## + weight       1     0.001 4.23 -61.5
## + cone         1     0.000 4.23 -61.5
## - c_pct        1     0.635 4.86 -60.1
## - c_avg_cmpp   1     0.671 4.90 -59.9
## - c_avg_att    1     0.681 4.91 -59.8
## 
## Step:  AIC=-64.66
## sacked ~ c_avg_cmpp + c_rate + c_pct + c_avg_tds + c_avg_yds + 
##     c_numyrs + c_avg_att + shuttle
## 
##               Df Sum of Sq  RSS   AIC
## - c_numyrs     1     0.114 4.43 -65.7
## - shuttle      1     0.124 4.44 -65.6
## <none>                     4.32 -64.7
## - c_avg_tds    1     0.280 4.60 -64.3
## - c_rate       1     0.372 4.69 -63.5
## + wonderlic    1     0.089 4.23 -63.5
## + vert_leap    1     0.066 4.25 -63.2
## + broad_jump   1     0.033 4.28 -63.0
## + height       1     0.028 4.29 -62.9
## + cone         1     0.008 4.31 -62.7
## + age          1     0.002 4.31 -62.7
## + c_avg_inter  1     0.002 4.31 -62.7
## + X40          1     0.001 4.31 -62.7
## + weight       1     0.000 4.32 -62.7
## - c_avg_yds    1     0.487 4.80 -62.6
## - c_pct        1     0.582 4.90 -61.9
## - c_avg_cmpp   1     0.617 4.93 -61.6
## - c_avg_att    1     0.636 4.95 -61.4
## 
## Step:  AIC=-65.67
## sacked ~ c_avg_cmpp + c_rate + c_pct + c_avg_tds + c_avg_yds + 
##     c_avg_att + shuttle
## 
##               Df Sum of Sq  RSS   AIC
## - shuttle      1     0.105 4.53 -66.8
## - c_avg_tds    1     0.199 4.63 -66.0
## <none>                     4.43 -65.7
## - c_rate       1     0.267 4.70 -65.4
## + c_numyrs     1     0.114 4.32 -64.7
## - c_avg_yds    1     0.374 4.80 -64.6
## + vert_leap    1     0.083 4.35 -64.4
## + wonderlic    1     0.066 4.36 -64.2
## + broad_jump   1     0.061 4.37 -64.2
## + height       1     0.024 4.41 -63.9
## - c_pct        1     0.474 4.90 -63.8
## + cone         1     0.011 4.42 -63.8
## + c_avg_inter  1     0.003 4.43 -63.7
## + age          1     0.002 4.43 -63.7
## + weight       1     0.002 4.43 -63.7
## + X40          1     0.000 4.43 -63.7
## - c_avg_cmpp   1     0.513 4.94 -63.5
## - c_avg_att    1     0.533 4.96 -63.4
## 
## Step:  AIC=-66.78
## sacked ~ c_avg_cmpp + c_rate + c_pct + c_avg_tds + c_avg_yds + 
##     c_avg_att
## 
##               Df Sum of Sq  RSS   AIC
## - c_avg_tds    1     0.220 4.76 -67.0
## <none>                     4.53 -66.8
## - c_rate       1     0.277 4.81 -66.5
## - c_avg_yds    1     0.379 4.91 -65.7
## + shuttle      1     0.105 4.43 -65.7
## + c_numyrs     1     0.096 4.44 -65.6
## + height       1     0.057 4.48 -65.3
## + X40          1     0.038 4.50 -65.1
## + wonderlic    1     0.035 4.50 -65.1
## - c_pct        1     0.469 5.00 -65.0
## + cone         1     0.016 4.52 -64.9
## + c_avg_inter  1     0.006 4.53 -64.8
## + broad_jump   1     0.005 4.53 -64.8
## + weight       1     0.005 4.53 -64.8
## + vert_leap    1     0.002 4.53 -64.8
## + age          1     0.000 4.53 -64.8
## - c_avg_cmpp   1     0.510 5.05 -64.7
## - c_avg_att    1     0.534 5.07 -64.6
## 
## Step:  AIC=-66.98
## sacked ~ c_avg_cmpp + c_rate + c_pct + c_avg_yds + c_avg_att
## 
##               Df Sum of Sq  RSS   AIC
## - c_rate       1    0.0568 4.81 -68.5
## - c_avg_yds    1    0.1604 4.92 -67.7
## <none>                     4.76 -67.0
## + c_avg_tds    1    0.2202 4.53 -66.8
## - c_pct        1    0.2855 5.04 -66.8
## - c_avg_cmpp   1    0.2994 5.05 -66.7
## - c_avg_att    1    0.3136 5.07 -66.6
## + shuttle      1    0.1267 4.63 -66.0
## + height       1    0.0803 4.67 -65.6
## + X40          1    0.0668 4.69 -65.5
## + wonderlic    1    0.0431 4.71 -65.3
## + c_avg_inter  1    0.0315 4.72 -65.2
## + c_numyrs     1    0.0208 4.73 -65.1
## + cone         1    0.0097 4.75 -65.1
## + broad_jump   1    0.0040 4.75 -65.0
## + vert_leap    1    0.0001 4.75 -65.0
## + age          1    0.0001 4.76 -65.0
## + weight       1    0.0000 4.76 -65.0
## 
## Step:  AIC=-68.53
## sacked ~ c_avg_cmpp + c_pct + c_avg_yds + c_avg_att
## 
##               Df Sum of Sq  RSS   AIC
## - c_pct        1    0.2306 5.04 -68.7
## - c_avg_cmpp   1    0.2536 5.07 -68.6
## <none>                     4.81 -68.5
## - c_avg_yds    1    0.2692 5.08 -68.5
## - c_avg_att    1    0.2896 5.10 -68.3
## + shuttle      1    0.1121 4.70 -67.4
## + height       1    0.0887 4.72 -67.2
## + X40          1    0.0738 4.74 -67.1
## + c_avg_inter  1    0.0704 4.74 -67.1
## + c_rate       1    0.0568 4.76 -67.0
## + wonderlic    1    0.0473 4.76 -66.9
## + cone         1    0.0081 4.80 -66.6
## + c_numyrs     1    0.0042 4.81 -66.6
## + vert_leap    1    0.0016 4.81 -66.5
## + weight       1    0.0009 4.81 -66.5
## + broad_jump   1    0.0005 4.81 -66.5
## + c_avg_tds    1    0.0004 4.81 -66.5
## + age          1    0.0004 4.81 -66.5
## 
## Step:  AIC=-68.75
## sacked ~ c_avg_cmpp + c_avg_yds + c_avg_att
## 
##               Df Sum of Sq  RSS   AIC
## - c_avg_cmpp   1     0.100 5.14 -70.0
## - c_avg_yds    1     0.165 5.21 -69.5
## <none>                     5.04 -68.7
## + c_pct        1     0.231 4.81 -68.5
## + shuttle      1     0.111 4.93 -67.6
## + X40          1     0.055 4.99 -67.2
## + height       1     0.055 4.99 -67.2
## + cone         1     0.049 4.99 -67.1
## + wonderlic    1     0.019 5.02 -66.9
## + c_avg_tds    1     0.016 5.03 -66.9
## + c_avg_inter  1     0.014 5.03 -66.9
## + c_numyrs     1     0.013 5.03 -66.8
## + c_rate       1     0.002 5.04 -66.8
## + broad_jump   1     0.001 5.04 -66.8
## + age          1     0.000 5.04 -66.8
## + weight       1     0.000 5.04 -66.7
## + vert_leap    1     0.000 5.04 -66.7
## - c_avg_att    1     0.951 5.99 -64.2
## 
## Step:  AIC=-70.01
## sacked ~ c_avg_yds + c_avg_att
## 
##               Df Sum of Sq  RSS   AIC
## <none>                     5.14 -70.0
## + shuttle      1     0.116 5.03 -68.9
## + c_avg_cmpp   1     0.100 5.04 -68.7
## + c_rate       1     0.080 5.06 -68.6
## + c_pct        1     0.077 5.07 -68.6
## + cone         1     0.075 5.07 -68.6
## + c_avg_inter  1     0.049 5.09 -68.4
## + height       1     0.042 5.10 -68.3
## + c_avg_tds    1     0.032 5.11 -68.2
## + X40          1     0.017 5.12 -68.1
## + vert_leap    1     0.009 5.13 -68.1
## + c_numyrs     1     0.009 5.13 -68.1
## + broad_jump   1     0.004 5.14 -68.0
## + weight       1     0.002 5.14 -68.0
## + age          1     0.001 5.14 -68.0
## + wonderlic    1     0.000 5.14 -68.0
## - c_avg_yds    1     0.953 6.09 -65.5
## - c_avg_att    1     0.992 6.13 -65.3
summary(step_reg.log.w_combine.sacks)
## 
## Call:
## lm(formula = sacked ~ c_avg_yds + c_avg_att, data = data.log.w_combine.for_sacks)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.1550 -0.2127  0.0025  0.2523  0.6274 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    2.459      0.564    4.36  0.00011 ***
## c_avg_yds      1.123      0.441    2.55  0.01544 *  
## c_avg_att     -1.393      0.536   -2.60  0.01362 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Residual standard error: 0.383 on 35 degrees of freedom
## Multiple R-squared: 0.162,   Adjusted R-squared: 0.115 
## F-statistic: 3.39 on 2 and 35 DF,  p-value: 0.0449
plot(step_reg.log.w_combine.sacks)

plot of chunk unnamed-chunk-1 plot of chunk unnamed-chunk-1 plot of chunk unnamed-chunk-1 plot of chunk unnamed-chunk-1

leaps.log.w_combine.sacks <- regsubsets(sacked ~ ., data = data.log.w_combine.for_sacks, 
    nbest = 10)
subsets(leaps.log.w_combine.sacks, statistic = "rsq")
## Error: invalid coordinate lengths

plot of chunk unnamed-chunk-1

cv.lm(df = data.log.w_combine.for_sacks, step_reg.log.w_combine.sacks, m = 5)  # 5 fold cross-validation
## Analysis of Variance Table
## 
## Response: sacked
##           Df Sum Sq Mean Sq F value Pr(>F)  
## c_avg_yds  1   0.01   0.006    0.04  0.846  
## c_avg_att  1   0.99   0.992    6.75  0.014 *
## Residuals 35   5.14   0.147                 
## ---
## 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

plot of chunk unnamed-chunk-1

## 
## fold 1 
## Observations in test set: 7 
##                   6    21    25    32    38     46     59
## Predicted    3.2022  3.23 3.268 3.056  3.25  3.437  3.122
## cvpred       3.2623  3.29 3.331 3.109  3.31  3.506  3.178
## sacked       3.1822  2.78 3.529 3.223  2.09  3.262  2.646
## CV residual -0.0801 -0.51 0.198 0.114 -1.22 -0.244 -0.532
## 
## Sum of squares = 2.14    Mean square = 0.31    n = 7 
## 
## fold 2 
## Observations in test set: 8 
##                 7     18    20    27    37     43     55   65
## Predicted    3.23 3.2952 3.091  3.10 3.196  2.932  3.202 3.34
## cvpred       3.20 3.2935 3.114  3.18 2.543  2.971  3.232 3.29
## sacked       2.95 3.3707 3.223  2.65 3.469  2.839  2.493 3.72
## CV residual -0.25 0.0773 0.109 -0.53 0.926 -0.132 -0.738 0.43
## 
## Sum of squares = 1.96    Mean square = 0.25    n = 8 
## 
## fold 3 
## Observations in test set: 8 
##                 5      12     13     16     39    40     50    56
## Predicted   3.321  3.3192  3.801  3.224 3.0378 3.021 3.2026 3.175
## cvpred      3.330  3.3293  3.977  3.199 2.9549 2.938 3.1743 3.136
## sacked      3.716  3.2995  3.558  3.096 3.0007 3.437 3.1822 3.500
## CV residual 0.386 -0.0297 -0.418 -0.104 0.0458 0.499 0.0079 0.363
## 
## Sum of squares = 0.72    Mean square = 0.09    n = 8 
## 
## fold 4 
## Observations in test set: 8 
##                  4    15    17    19   28     52    63     64
## Predicted    3.482 3.063 3.159 3.179 3.42  3.123 3.134 3.4748
## cvpred       3.433 2.994 3.090 3.122 3.37  3.065 3.053 3.4183
## sacked       3.371 3.262 3.786 3.405 3.81  2.950 3.614 3.4995
## CV residual -0.062 0.268 0.697 0.282 0.44 -0.115 0.561 0.0813
## 
## Sum of squares = 1.17    Mean square = 0.15    n = 8 
## 
## fold 5 
## Observations in test set: 7 
##                 1     3     24    30    42     49     61
## Predicted   3.302 3.399  3.032 3.021 3.219  3.135  3.175
## cvpred      3.282 3.350  3.052 3.045 3.200  3.147  3.253
## sacked      3.914 3.586  2.646 3.182 3.405  2.779  2.950
## CV residual 0.632 0.236 -0.406 0.137 0.204 -0.369 -0.303
## 
## Sum of squares = 0.91    Mean square = 0.13    n = 7 
## 
## Overall (Sum over all 7 folds) 
##    ms 
## 0.182