# 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)
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
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
##
## 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