train = read.csv('reg_train_in.csv')
names(train)
##  [1] "Point_ID" "Input_1"  "Input_2"  "Input_3"  "Input_4"  "Input_5" 
##  [7] "Input_6"  "Input_7"  "Input_8"  "Input_9"  "Input_10" "Input_11"
## [13] "Input_12" "Input_13" "Input_14"

Plots of label vs feature

library(plyr)
library(ggplot2)
plotlist = llply(names(train)[names(train) != "Point_ID"], function(featureName) {
  p = ggplot(train, aes_string(x=featureName, y="Point_ID")) +
    geom_point(alpha=.3)
  return(p)
})
source('multiplot.R')
multiplot(plotlist=plotlist, cols=4)

Baseline OLS model

linModel = lm(Point_ID ~ ., train)
summary(linModel)
## 
## Call:
## lm(formula = Point_ID ~ ., data = train)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -548.81 -123.87  -10.65  122.04  481.26 
## 
## Coefficients:
##               Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)  3.725e+02  1.911e+00  194.899  < 2e-16 ***
## Input_1      4.256e+00  4.324e-04 9843.434  < 2e-16 ***
## Input_2      1.743e+02  1.050e+01   16.600  < 2e-16 ***
## Input_3     -2.309e+01  5.657e+00   -4.082 4.48e-05 ***
## Input_4      3.603e+02  1.887e+01   19.097  < 2e-16 ***
## Input_5     -5.930e+01  8.036e+00   -7.379 1.63e-13 ***
## Input_6     -5.672e+02  1.596e+01  -35.539  < 2e-16 ***
## Input_7     -7.801e-01  9.202e-01   -0.848    0.397    
## Input_8      1.173e+02  8.881e+00   13.203  < 2e-16 ***
## Input_9     -6.706e+01  9.759e+00   -6.872 6.45e-12 ***
## Input_10     2.105e+02  8.587e+00   24.520  < 2e-16 ***
## Input_11    -2.833e-01  9.146e-01   -0.310    0.757    
## Input_12    -1.402e+02  7.821e+00  -17.932  < 2e-16 ***
## Input_13    -1.355e+02  1.061e+01  -12.772  < 2e-16 ***
## Input_14     1.306e+02  9.845e+00   13.271  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 168.5 on 33735 degrees of freedom
## Multiple R-squared:  0.9997, Adjusted R-squared:  0.9997 
## F-statistic: 8.061e+06 on 14 and 33735 DF,  p-value: < 2.2e-16

It looks like Point_ID is the only linearly correlated feature, with features [2,3,4,5,6,8,9,10,12,13,14] providing some quantization information

linModel = lm(Point_ID ~ Input_1, train)
summary(linModel)
## 
## Call:
## lm(formula = Point_ID ~ Input_1, data = train)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -389.41 -125.77  -15.76  122.98  417.38 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 3.904e+02  1.864e+00   209.5   <2e-16 ***
## Input_1     4.251e+00  4.138e-04 10274.4   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 174.2 on 33748 degrees of freedom
## Multiple R-squared:  0.9997, Adjusted R-squared:  0.9997 
## F-statistic: 1.056e+08 on 1 and 33748 DF,  p-value: < 2.2e-16