# 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
cpct = qb_stats["completion_percentage"]

# Generate clean data set
data.log.no_combine.for_cpct = data.frame(log(na.omit(cbind(cpct, college_stats)) + 
    0.1))

# Generate the linear model
lm.log.no_combine.cpct <- lm(formula = completion_percentage ~ ., data = data.log.no_combine.for_cpct)

# Find optimum linear regression model for cpct
step_reg.log.no_combine.cpct <- stepAIC(lm.log.no_combine.cpct, direction = "both")
## Start:  AIC=-393
## completion_percentage ~ 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_numyrs     1     0.000 40.3 -395
## - height       1     0.000 40.3 -395
## - c_rate       1     0.007 40.3 -395
## - c_avg_tds    1     0.011 40.3 -395
## - c_avg_inter  1     0.044 40.4 -395
## - c_avg_yds    1     0.061 40.4 -395
## - weight       1     0.177 40.5 -394
## - c_pct        1     0.267 40.6 -393
## - c_avg_cmpp   1     0.286 40.6 -393
## - c_avg_att    1     0.321 40.6 -393
## <none>                     40.3 -393
## - age          1     0.348 40.7 -393
## 
## Step:  AIC=-395
## completion_percentage ~ height + weight + age + c_avg_cmpp + 
##     c_rate + c_pct + c_avg_inter + c_avg_tds + c_avg_yds + c_avg_att
## 
##               Df Sum of Sq  RSS  AIC
## - height       1     0.000 40.3 -397
## - c_rate       1     0.008 40.3 -397
## - c_avg_tds    1     0.012 40.3 -397
## - c_avg_inter  1     0.046 40.4 -397
## - c_avg_yds    1     0.062 40.4 -397
## - weight       1     0.181 40.5 -396
## - c_pct        1     0.281 40.6 -395
## - c_avg_cmpp   1     0.299 40.6 -395
## - c_avg_att    1     0.333 40.7 -395
## <none>                     40.3 -395
## - age          1     0.348 40.7 -395
## + c_numyrs     1     0.000 40.3 -393
## 
## Step:  AIC=-397
## completion_percentage ~ weight + age + c_avg_cmpp + c_rate + 
##     c_pct + c_avg_inter + c_avg_tds + c_avg_yds + c_avg_att
## 
##               Df Sum of Sq  RSS  AIC
## - c_rate       1     0.008 40.3 -399
## - c_avg_tds    1     0.012 40.3 -399
## - c_avg_inter  1     0.046 40.4 -399
## - c_avg_yds    1     0.062 40.4 -399
## - weight       1     0.285 40.6 -397
## - c_pct        1     0.287 40.6 -397
## - c_avg_cmpp   1     0.306 40.6 -397
## - c_avg_att    1     0.341 40.7 -397
## <none>                     40.3 -397
## - age          1     0.352 40.7 -397
## + height       1     0.000 40.3 -395
## + c_numyrs     1     0.000 40.3 -395
## 
## Step:  AIC=-398.9
## completion_percentage ~ weight + age + c_avg_cmpp + c_pct + c_avg_inter + 
##     c_avg_tds + c_avg_yds + c_avg_att
## 
##               Df Sum of Sq  RSS  AIC
## - c_avg_tds    1     0.005 40.3 -401
## - c_avg_inter  1     0.243 40.6 -400
## - c_avg_yds    1     0.286 40.6 -399
## - c_pct        1     0.310 40.6 -399
## - weight       1     0.313 40.6 -399
## - c_avg_cmpp   1     0.317 40.6 -399
## - c_avg_att    1     0.339 40.7 -399
## <none>                     40.3 -399
## - age          1     0.355 40.7 -399
## + c_rate       1     0.008 40.3 -397
## + c_numyrs     1     0.000 40.3 -397
## + height       1     0.000 40.3 -397
## 
## Step:  AIC=-400.9
## completion_percentage ~ weight + age + c_avg_cmpp + c_pct + c_avg_inter + 
##     c_avg_yds + c_avg_att
## 
##               Df Sum of Sq  RSS  AIC
## - c_avg_inter  1     0.239 40.6 -402
## - weight       1     0.313 40.6 -401
## - c_pct        1     0.325 40.7 -401
## - c_avg_cmpp   1     0.330 40.7 -401
## <none>                     40.3 -401
## - age          1     0.351 40.7 -401
## - c_avg_att    1     0.354 40.7 -401
## - c_avg_yds    1     0.483 40.8 -400
## + c_avg_tds    1     0.005 40.3 -399
## + c_numyrs     1     0.001 40.3 -399
## + c_rate       1     0.000 40.3 -399
## + height       1     0.000 40.3 -399
## 
## Step:  AIC=-401.5
## completion_percentage ~ weight + age + c_avg_cmpp + c_pct + c_avg_yds + 
##     c_avg_att
## 
##               Df Sum of Sq  RSS  AIC
## - c_pct        1     0.159 40.7 -403
## - c_avg_cmpp   1     0.161 40.7 -403
## - c_avg_att    1     0.177 40.8 -402
## - weight       1     0.204 40.8 -402
## - age          1     0.332 40.9 -402
## <none>                     40.6 -402
## - c_avg_yds    1     0.405 41.0 -401
## + c_avg_inter  1     0.239 40.3 -401
## + c_rate       1     0.108 40.5 -400
## + c_numyrs     1     0.003 40.6 -400
## + c_avg_tds    1     0.001 40.6 -400
## + height       1     0.001 40.6 -400
## 
## Step:  AIC=-402.6
## completion_percentage ~ weight + age + c_avg_cmpp + c_avg_yds + 
##     c_avg_att
## 
##               Df Sum of Sq  RSS  AIC
## - c_avg_cmpp   1     0.005 40.7 -405
## - age          1     0.309 41.0 -403
## - weight       1     0.313 41.0 -403
## - c_avg_yds    1     0.321 41.1 -403
## - c_avg_att    1     0.334 41.1 -403
## <none>                     40.7 -403
## + c_pct        1     0.159 40.6 -402
## + c_avg_inter  1     0.074 40.7 -401
## + c_rate       1     0.033 40.7 -401
## + c_numyrs     1     0.012 40.7 -401
## + height       1     0.006 40.7 -401
## + c_avg_tds    1     0.003 40.7 -401
## 
## Step:  AIC=-404.6
## completion_percentage ~ weight + age + c_avg_yds + c_avg_att
## 
##               Df Sum of Sq  RSS  AIC
## - age          1     0.332 41.1 -405
## <none>                     40.7 -405
## - weight       1     0.350 41.1 -405
## - c_avg_yds    1     0.557 41.3 -403
## - c_avg_att    1     0.585 41.3 -403
## + c_avg_inter  1     0.062 40.7 -403
## + c_numyrs     1     0.010 40.7 -403
## + c_rate       1     0.009 40.7 -403
## + height       1     0.008 40.7 -403
## + c_avg_cmpp   1     0.005 40.7 -403
## + c_pct        1     0.003 40.7 -403
## + c_avg_tds    1     0.003 40.7 -403
## 
## Step:  AIC=-404.6
## completion_percentage ~ weight + c_avg_yds + c_avg_att
## 
##               Df Sum of Sq  RSS  AIC
## - weight       1     0.239 41.3 -405
## <none>                     41.1 -405
## + age          1     0.332 40.7 -405
## - c_avg_yds    1     0.561 41.6 -403
## - c_avg_att    1     0.606 41.7 -403
## + c_avg_inter  1     0.049 41.0 -403
## + c_avg_cmpp   1     0.027 41.0 -403
## + c_pct        1     0.022 41.0 -403
## + height       1     0.021 41.1 -403
## + c_numyrs     1     0.011 41.1 -403
## + c_rate       1     0.006 41.1 -403
## + c_avg_tds    1     0.002 41.1 -403
## 
## Step:  AIC=-405.3
## completion_percentage ~ c_avg_yds + c_avg_att
## 
##               Df Sum of Sq  RSS  AIC
## <none>                     41.3 -405
## + weight       1     0.239 41.1 -405
## + age          1     0.221 41.1 -405
## + height       1     0.181 41.1 -404
## - c_avg_yds    1     0.603 41.9 -404
## - c_avg_att    1     0.617 41.9 -404
## + c_avg_cmpp   1     0.068 41.2 -404
## + c_pct        1     0.058 41.3 -404
## + c_rate       1     0.004 41.3 -403
## + c_avg_inter  1     0.001 41.3 -403
## + c_avg_tds    1     0.000 41.3 -403
## + c_numyrs     1     0.000 41.3 -403
summary(step_reg.log.no_combine.cpct)
## 
## Call:
## lm(formula = completion_percentage ~ c_avg_yds + c_avg_att, data = data.log.no_combine.for_cpct)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -6.154 -0.035  0.027  0.104  0.326 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    3.484      0.355    9.82   <2e-16 ***
## c_avg_yds      0.347      0.188    1.84    0.066 .  
## c_avg_att     -0.389      0.208   -1.87    0.063 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Residual standard error: 0.421 on 233 degrees of freedom
## Multiple R-squared: 0.0147,  Adjusted R-squared: 0.00628 
## F-statistic: 1.74 on 2 and 233 DF,  p-value: 0.177
plot(step_reg.log.no_combine.cpct)

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.no_combine.cpct <- regsubsets(completion_percentage ~ ., data = data.log.no_combine.for_cpct, 
    nbest = 10)
subsets(leaps.log.no_combine.cpct, statistic = "rsq")
## Error: invalid coordinate lengths

plot of chunk unnamed-chunk-1

cv.lm(df = data.log.no_combine.for_cpct, step_reg.log.no_combine.cpct, m = 5)  # 5 fold cross-validation
## Analysis of Variance Table
## 
## Response: completion_percentage
##            Df Sum Sq Mean Sq F value Pr(>F)  
## c_avg_yds   1    0.0   0.001    0.00  0.951  
## c_avg_att   1    0.6   0.617    3.48  0.063 .
## Residuals 233   41.3   0.177                 
## ---
## 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: 47 
##                           3    15    18    24      26     35    37      39
## Predicted             3.985 3.953 3.912 3.909 3.98228 3.9118  3.85  3.9908
## cvpred                3.984 3.993 3.988 3.987 3.98275 3.9823  3.99  3.9803
## completion_percentage 4.052 4.109 4.109 4.114 3.98713 4.0271 -2.30  3.9435
## CV residual           0.068 0.116 0.122 0.127 0.00438 0.0448 -6.29 -0.0368
##                           41    45    52     56      62     71    72
## Predicted             3.9748 3.966 3.961 3.9782  3.8687 3.9676 3.966
## cvpred                3.9939 3.978 3.995 3.9847  3.9847 3.9781 3.970
## completion_percentage 4.0413 4.113 4.197 3.9982  3.9493 4.0254 4.159
## CV residual           0.0474 0.134 0.202 0.0135 -0.0354 0.0473 0.189
##                           76     79     81    85     88     89   103
## Predicted             3.9139 3.9293 3.9854 3.903 3.9628 3.9542 3.948
## cvpred                3.9702 3.9844 3.9863 3.977 3.9889 3.9804 3.962
## completion_percentage 4.0055 3.9982 4.0091 4.083 4.0395 4.0466 4.064
## CV residual           0.0353 0.0138 0.0229 0.106 0.0506 0.0662 0.101
##                           116     118   119   121     133    136    139
## Predicted              3.9329  3.9391 3.879 3.947 3.93409  3.964 3.9994
## cvpred                 3.9874  3.9853 3.975 3.969 3.96665  3.977 3.9350
## completion_percentage  3.8959  3.9396 4.098 4.142 3.97218  3.789 4.0236
## CV residual           -0.0915 -0.0457 0.123 0.173 0.00552 -0.188 0.0886
##                           149     152     159     165    166     170   173
## Predicted              3.9988  3.9565  3.8810 3.95566  3.940  3.9568 3.971
## cvpred                 3.9716  3.9906  3.9726 3.97838  3.986  3.9787 3.970
## completion_percentage  3.8939  3.9140  3.9220 3.98713  3.863  3.9180 4.086
## CV residual           -0.0778 -0.0766 -0.0506 0.00875 -0.123 -0.0607 0.115
##                          176    189    194    200     207    213     222
## Predicted             3.9504 3.9464 4.0479 3.9290  3.8852  3.980  3.6479
## cvpred                3.9576 3.9682 3.9011 3.9777  3.9789  3.961  3.9684
## completion_percentage 3.9871 4.0466 3.9815 4.0019  3.8857  3.686  3.9299
## CV residual           0.0295 0.0784 0.0804 0.0242 -0.0932 -0.275 -0.0385
##                           225     226    232     239
## Predicted              3.9631  3.9952 3.9423 3.89330
## cvpred                 3.9748  3.9652 3.9581 3.94526
## completion_percentage  3.8877  3.9040 4.0289 3.94739
## CV residual           -0.0871 -0.0612 0.0708 0.00213
## 
## Sum of squares = 40    Mean square = 0.85    n = 47 
## 
## fold 2 
## Observations in test set: 48 
##                           4     5       7     14     17    33      36
## Predicted             3.938 3.959  4.0871 4.0205 3.9527 3.836 3.94980
## cvpred                3.931 3.956  4.1105 4.0303 3.9483 3.807 3.94474
## completion_percentage 4.067 4.135  4.0960 4.0960 3.9778 4.066 3.95316
## CV residual           0.137 0.179 -0.0145 0.0657 0.0295 0.259 0.00842
##                          42     46     47    66   67     70    74     78
## Predicted             3.943 3.9188 3.9521  4.05 3.97 3.9104 3.932 4.0085
## cvpred                3.936 3.9073 3.9475  4.07 3.97 3.8972 3.923 4.0158
## completion_percentage 4.165 3.9455 4.0342  4.01 4.17 3.9299 4.062 4.0622
## CV residual           0.229 0.0382 0.0868 -0.06 0.20 0.0327 0.139 0.0464
##                            99     100    102   114    122     126     128
## Predicted              4.0298  3.9857 3.9472 3.897 3.9103  3.9789  4.0009
## cvpred                 4.0412  3.9882 3.9413 3.881 3.8969  3.9798  4.0065
## completion_percentage  3.9703  3.9570 4.0325 4.162 3.9665  3.9646  3.9703
## CV residual           -0.0709 -0.0312 0.0912 0.281 0.0696 -0.0152 -0.0362
##                         131    138    141   144   147    153    156
## Predicted             3.834 3.9503 3.9328 3.976 3.889 3.8803 3.9158
## cvpred                3.805 3.9454 3.9242 3.977 3.871 3.8607 3.9035
## completion_percentage 3.859 4.0073 3.9589 4.086 4.043 3.9455 3.9908
## CV residual           0.054 0.0619 0.0347 0.109 0.172 0.0847 0.0873
##                           158     161   163   164    171   172    174
## Predicted              4.0117  4.0062 3.924 3.932  3.968  4.06 4.0238
## cvpred                 4.0194  4.0127 3.914 3.923  3.967  4.07 4.0343
## completion_percentage  4.0091  3.9741 4.069 4.078  3.859  3.96 4.0893
## CV residual           -0.0102 -0.0387 0.155 0.155 -0.108 -0.11 0.0551
##                           177      179    184    185    188    192    201
## Predicted              3.9809  3.99062 3.9384  4.011  4.002  3.941  3.945
## cvpred                 3.9821  3.99396 3.9309  4.018  4.007  3.934  3.939
## completion_percentage  3.9759  3.99268 3.9532  3.630  3.775  3.811  3.857
## CV residual           -0.0062 -0.00128 0.0222 -0.389 -0.232 -0.123 -0.083
##                           203    206     209    215    216
## Predicted              3.9542  3.944  3.9403  3.882 3.8409
## cvpred                 3.9502  3.938  3.9330  3.862 3.8129
## completion_percentage  3.8774  3.831  3.8544  3.643 3.8816
## CV residual           -0.0727 -0.107 -0.0786 -0.219 0.0687
## 
## Sum of squares = 0.79    Mean square = 0.02    n = 48 
## 
## fold 3 
## Observations in test set: 47 
##                             2     6    25    29    34      43     44
## Predicted              3.9923 3.902 3.770 3.911 3.893  4.0011 3.9345
## cvpred                 4.0086 3.880 3.671 3.895 3.866  4.0184 3.9269
## completion_percentage  3.9927 4.034 4.096 4.029 4.029  3.9741 3.9778
## CV residual           -0.0159 0.154 0.425 0.134 0.163 -0.0443 0.0509
##                            48    50    51      55     59     60    65
## Predicted              3.9156 3.908 3.943  3.9326 3.9018 3.9392 3.906
## cvpred                 3.8983 3.889 3.939  3.9241 3.8806 3.9305 3.887
## completion_percentage  3.8177 4.114 4.111  3.8774 3.9741 3.9684 4.109
## CV residual           -0.0806 0.225 0.172 -0.0467 0.0934 0.0379 0.222
##                             77     80    86     87     90     94    101
## Predicted              3.94647 3.9740 3.940 3.9535 3.9539 3.9582 4.0232
## cvpred                 3.94270 3.9811 3.935 3.9490 3.9543 3.9591 4.0528
## completion_percentage  3.93574 4.0483 4.108 3.9815 4.0466 3.9722 4.0860
## CV residual           -0.00696 0.0672 0.173 0.0326 0.0923 0.0131 0.0332
##                           106     107    108   112   123     124   134
## Predicted              3.9995  3.9751  3.986 3.940 3.952 3.96546 3.923
## cvpred                 4.0176  3.9804  3.996 3.935 3.950 3.96842 3.908
## completion_percentage  3.9908  3.9338  3.816 4.047 3.995 3.97781 4.016
## CV residual           -0.0268 -0.0466 -0.181 0.111 0.045 0.00939 0.108
##                          137     148   157   178    180    181    182
## Predicted              3.946  3.9852 3.926 3.869 3.9550  4.016  4.030
## cvpred                 3.939  3.9977 3.902 3.833 3.9507  4.038  4.054
## completion_percentage  3.721  3.9853 4.004 4.022 4.0395  3.871  3.844
## CV residual           -0.218 -0.0124 0.102 0.188 0.0888 -0.166 -0.211
##                          186     193      195    199     202    210    217
## Predicted              4.058  3.8651  3.97566  3.946 3.89254 3.9330  3.969
## cvpred                 4.092  3.8256  3.98056  3.941 3.86803 3.9222  3.970
## completion_percentage  3.918  3.8089  3.97218  3.798 3.87743 3.9834  3.709
## CV residual           -0.174 -0.0167 -0.00838 -0.143 0.00941 0.0612 -0.261
##                           218    219    234    236    238
## Predicted              3.9469 3.8857 3.9486  4.063  4.063
## cvpred                 3.9377 3.8508 3.9376  4.099  4.100
## completion_percentage  3.8670 3.9279 4.0360  3.859  3.991
## CV residual           -0.0706 0.0771 0.0984 -0.241 -0.109
## 
## Sum of squares = 0.9    Mean square = 0.02    n = 47 
## 
## fold 4 
## Observations in test set: 47 
##                           9    10     11    13     16    22    27    28
## Predicted             3.948 3.933  4.025 3.893 3.9253 3.969 3.926 3.931
## cvpred                3.932 3.922  4.035 3.863 3.9049 3.961 3.916 3.913
## completion_percentage 4.104 3.996  3.842 3.996 3.9627 4.154 4.142 4.067
## CV residual           0.172 0.074 -0.193 0.133 0.0578 0.194 0.226 0.155
##                          31    32    38     49    53     58    64     68
## Predicted             3.916 3.923 3.944  4.017 3.880 3.9764 3.959  3.949
## cvpred                3.897 3.909 3.925  4.030 3.860 3.9722 3.949  3.944
## completion_percentage 4.154 4.197 4.124  3.932 4.047 4.0483 4.130  3.916
## CV residual           0.257 0.288 0.199 -0.098 0.187 0.0761 0.182 -0.028
##                            75    84      92      93     95     97    104
## Predicted              4.0038 3.912  3.9961  3.9927 3.9961 3.9056  3.992
## cvpred                 4.0064 3.888  4.0020  3.9995 4.0057 3.8931  4.003
## completion_percentage  3.9964 4.025  3.9318  3.9834 4.0091 3.9100  3.902
## CV residual           -0.0101 0.138 -0.0702 -0.0161 0.0035 0.0169 -0.101
##                          105     109     110    113     117     120    125
## Predicted             3.8991  3.9775  3.9394 3.9384  3.9144  3.9949 4.0242
## cvpred                3.8834  3.9776  3.9246 3.9241  3.8933  4.0206 4.0427
## completion_percentage 3.9200  3.9338  3.9120 4.0164  3.8816  3.9608 4.0570
## CV residual           0.0366 -0.0438 -0.0126 0.0923 -0.0117 -0.0598 0.0143
##                         127    130    143    145     146     162    183
## Predicted             3.968  4.029  4.093 3.9307  3.9232  3.9460 3.9332
## cvpred                3.974  4.046  4.142 3.9206  3.9072  3.9403 3.9202
## completion_percentage 4.076  3.865  3.934 3.9815  3.8918  3.9140 3.9778
## CV residual           0.102 -0.181 -0.208 0.0609 -0.0154 -0.0263 0.0576
##                          190    196    198    211    214    224    227
## Predicted             3.8739 3.8770 3.9332  3.975 3.9382  4.002  3.959
## cvpred                3.8443 3.8488 3.9359  3.986 3.9319  4.029  3.979
## completion_percentage 3.8586 3.8836 3.9474  3.829 3.9703  3.804  3.721
## CV residual           0.0143 0.0349 0.0115 -0.158 0.0384 -0.225 -0.258
##                          229     233    237
## Predicted              3.909  3.9206  4.050
## cvpred                 3.920  3.9111  4.086
## completion_percentage  3.638  3.8286  3.816
## CV residual           -0.282 -0.0824 -0.271
## 
## Sum of squares = 0.93    Mean square = 0.02    n = 47 
## 
## fold 5 
## Observations in test set: 47 
##                           1     8    12       19    20     21    23    30
## Predicted             3.949 3.953 3.965  3.99581 3.908 3.9220 4.001 3.928
## cvpred                3.936 3.941 3.952  3.98986 3.893 3.9074 4.012 3.914
## completion_percentage 4.162 4.064 4.057  3.98713 4.000 3.9741 4.151 4.036
## CV residual           0.226 0.123 0.105 -0.00273 0.107 0.0667 0.139 0.122
##                          40    54   57     61      69    73     82    83
## Predicted             3.958 3.950 3.94 3.9688  3.9871 3.925  4.007 3.977
## cvpred                3.949 3.935 3.92 3.9597  3.9793 3.915  3.999 3.966
## completion_percentage 4.108 4.111 4.08 4.0271  3.9627 4.057  3.791 4.140
## CV residual           0.158 0.175 0.16 0.0674 -0.0166 0.142 -0.208 0.174
##                           91     96    98    111     115    129    132
## Predicted              3.984 3.9554 3.984 4.0114  3.9715 3.9509 3.9033
## cvpred                 3.974 3.9460 3.983 4.0058  3.9632 3.9399 3.8903
## completion_percentage  3.816 3.9741 4.140 4.0342  3.9060 3.9684 3.9608
## CV residual           -0.158 0.0281 0.157 0.0284 -0.0572 0.0285 0.0705
##                           135    140    142  150    151    154   155   160
## Predicted              3.9699 4.0017 3.9683 3.94 3.8899  3.985 3.937 3.923
## cvpred                 3.9588 3.9942 3.9600 3.93 3.8729  3.993 3.922 3.913
## completion_percentage  3.9416 4.0236 3.9834 4.07 3.9040  3.906 4.098 4.055
## CV residual           -0.0172 0.0294 0.0234 0.14 0.0311 -0.087 0.175 0.142
##                           167    168    169    187   191    204   205
## Predicted              3.9972 4.0098 3.9156 3.8999 3.931 4.0182  3.93
## cvpred                 3.9953 4.0018 3.9046 3.8876 3.922 4.0125  3.92
## completion_percentage  3.9416 4.0466 3.9180 3.9140 3.995 4.0910  3.70
## CV residual           -0.0537 0.0447 0.0134 0.0264 0.073 0.0785 -0.22
##                           208      212   220     221     223   228   230
## Predicted              3.9491  3.90629 3.841 3.95065  3.9669 3.976 3.989
## cvpred                 3.9429  3.89532 3.829 3.94704  3.9609 3.974 3.986
## completion_percentage  3.9357  3.88773 3.944 3.94932  3.8774 4.057 4.121
## CV residual           -0.0072 -0.00759 0.115 0.00228 -0.0835 0.083 0.135
##                           235    240
## Predicted             3.91718  4.035
## cvpred                3.90514  4.041
## completion_percentage 3.91002  3.920
## CV residual           0.00489 -0.121
## 
## Sum of squares = 0.57    Mean square = 0.01    n = 47 
## 
## Overall (Sum over all 47 folds) 
##    ms 
## 0.183