DATA-621 Project 5
Harpreet Shoker
19-Jul-2018
COVER PAGE
DATA621-Assignment-5
By - Harpreet Shoker
Date - 18-Jul-2018
University - City university of New York
Professor - Marcus Ellis
Abstract
In this homework assignment, we will explore, analyze and model a data set containing information on approximately 12795 commercially available wines using 16 variables. The variables are mostly related to the chemical properties of the wine being sold. The response variable is the number of sample cases of wine that were purchased by wine distribution companies after sampling a wine. These cases would be used to provide tasting samples to restaurants and wine stores around the United States. The more sample cases purchased, the more likely is a wine to be sold at a high end restaurant. A large wine manufacturer is studying the data in order to predict the number of wine cases ordered based upon the wine characteristics. If the wine manufacturer can predict the number of cases, then that manufacturer will be able to adjust their wine offering to maximize sales.
Our objective is to build a count regression model to predict the number of cases of wine that will be sold given certain properties of the wine. To attain our objective, we will be following the below best practice steps and guidelines:
1 -Data Exploration
2 -Data Preparation
3 -Build Models
4 -Select Models
DATA EXPLORATION
Reading the wine training data set from github
train <- read.csv('https://raw.githubusercontent.com/Harpreet1984/DATA621/master/HW5/wine-training-data.csv', na.string = c("", "NA"), stringsAsFactors = FALSE)
train$ï..INDEX = NULL
head(train)## TARGET FixedAcidity VolatileAcidity CitricAcid ResidualSugar Chlorides
## 1 3 3.2 1.160 -0.98 54.2 -0.567
## 2 3 4.5 0.160 -0.81 26.1 -0.425
## 3 5 7.1 2.640 -0.88 14.8 0.037
## 4 3 5.7 0.385 0.04 18.8 -0.425
## 5 4 8.0 0.330 -1.26 9.4 NA
## 6 0 11.3 0.320 0.59 2.2 0.556
## FreeSulfurDioxide TotalSulfurDioxide Density pH Sulphates Alcohol
## 1 NA 268 0.99280 3.33 -0.59 9.9
## 2 15 -327 1.02792 3.38 0.70 NA
## 3 214 142 0.99518 3.12 0.48 22.0
## 4 22 115 0.99640 2.24 1.83 6.2
## 5 -167 108 0.99457 3.12 1.77 13.7
## 6 -37 15 0.99940 3.20 1.29 15.4
## LabelAppeal AcidIndex STARS
## 1 0 8 2
## 2 -1 7 3
## 3 -1 8 3
## 4 -1 6 1
## 5 0 9 2
## 6 0 11 NAtest <- read.csv('https://raw.githubusercontent.com/Harpreet1984/DATA621/master/HW5/wine-evaluation-data.csv', na.string = c("", "NA"), stringsAsFactors = FALSE)Only data from the training_set may be used The training_set contains| 12795 raw observations The training_set contains| 16 features (including index and targets)
summary(train)## TARGET FixedAcidity VolatileAcidity CitricAcid
## Min. :0.000 Min. :-18.100 Min. :-2.7900 Min. :-3.2400
## 1st Qu.:2.000 1st Qu.: 5.200 1st Qu.: 0.1300 1st Qu.: 0.0300
## Median :3.000 Median : 6.900 Median : 0.2800 Median : 0.3100
## Mean :3.029 Mean : 7.076 Mean : 0.3241 Mean : 0.3084
## 3rd Qu.:4.000 3rd Qu.: 9.500 3rd Qu.: 0.6400 3rd Qu.: 0.5800
## Max. :8.000 Max. : 34.400 Max. : 3.6800 Max. : 3.8600
##
## ResidualSugar Chlorides FreeSulfurDioxide TotalSulfurDioxide
## Min. :-127.800 Min. :-1.1710 Min. :-555.00 Min. :-823.0
## 1st Qu.: -2.000 1st Qu.:-0.0310 1st Qu.: 0.00 1st Qu.: 27.0
## Median : 3.900 Median : 0.0460 Median : 30.00 Median : 123.0
## Mean : 5.419 Mean : 0.0548 Mean : 30.85 Mean : 120.7
## 3rd Qu.: 15.900 3rd Qu.: 0.1530 3rd Qu.: 70.00 3rd Qu.: 208.0
## Max. : 141.150 Max. : 1.3510 Max. : 623.00 Max. :1057.0
## NA's :616 NA's :638 NA's :647 NA's :682
## Density pH Sulphates Alcohol
## Min. :0.8881 Min. :0.480 Min. :-3.1300 Min. :-4.70
## 1st Qu.:0.9877 1st Qu.:2.960 1st Qu.: 0.2800 1st Qu.: 9.00
## Median :0.9945 Median :3.200 Median : 0.5000 Median :10.40
## Mean :0.9942 Mean :3.208 Mean : 0.5271 Mean :10.49
## 3rd Qu.:1.0005 3rd Qu.:3.470 3rd Qu.: 0.8600 3rd Qu.:12.40
## Max. :1.0992 Max. :6.130 Max. : 4.2400 Max. :26.50
## NA's :395 NA's :1210 NA's :653
## LabelAppeal AcidIndex STARS
## Min. :-2.000000 Min. : 4.000 Min. :1.000
## 1st Qu.:-1.000000 1st Qu.: 7.000 1st Qu.:1.000
## Median : 0.000000 Median : 8.000 Median :2.000
## Mean :-0.009066 Mean : 7.773 Mean :2.042
## 3rd Qu.: 1.000000 3rd Qu.: 8.000 3rd Qu.:3.000
## Max. : 2.000000 Max. :17.000 Max. :4.000
## NA's :3359our dataset has almost all the means/medians match up. Our observation is that all 15 features other than AcidIndex have virtualy no skew, kurtosis, or standard error.Here we are not transforming any data, but before we move on to making models we should see if we can impute some data using the means of otherwise normalized features. The last feature of this dataset is that we’re doing ‘count’ data, with a high zero count. (Meaning many people buy 0 crates of wine) This is problematic for both all three models we’ll be making. I’ll consider the use of zero-inflated models.
##
## Variables sorted by number of missings:
## Variable Count
## STARS 3359
## Sulphates 1210
## TotalSulfurDioxide 682
## Alcohol 653
## FreeSulfurDioxide 647
## Chlorides 638
## ResidualSugar 616
## pH 395
## TARGET 0
## FixedAcidity 0
## VolatileAcidity 0
## CitricAcid 0
## Density 0
## LabelAppeal 0
## AcidIndex 0We see here in the above figure some missing data with almost a fourth of STARS missing.
Since our data has already been normalized, during imputation we will be using means to impute objective features and predicting STARS (being subjective, but correlated to objective qualities) through OLS of the other features.
. 
Looking at correlation matrix to see what variables might make good predictive, parsimonious model.Wine sells if critics love it, the label is appealing, and its not too acidic.
DATA PREPARATION
Since our data has normalised values, we are not doing transformations since the distributions are more or less normally distributed. Transforming our features into buckets or some type of ordinal data seems like needless data loss.
The results of data imputation + throwing out observations with missing values, we lost 2 out of almost 13k observations. We’ll seperate some data before we train models, for cross validation later. Lets start making models
##
## iter imp variable
## 1 1 ResidualSugar Chlorides FreeSulfurDioxide TotalSulfurDioxide pH Sulphates Alcohol STARS
## 1 2 ResidualSugar Chlorides FreeSulfurDioxide TotalSulfurDioxide pH Sulphates Alcohol STARS
## 2 1 ResidualSugar Chlorides FreeSulfurDioxide TotalSulfurDioxide pH Sulphates Alcohol STARS
## 2 2 ResidualSugar Chlorides FreeSulfurDioxide TotalSulfurDioxide pH Sulphates Alcohol STARS
## 3 1 ResidualSugar Chlorides FreeSulfurDioxide TotalSulfurDioxide pH Sulphates Alcohol STARS
## 3 2 ResidualSugar Chlorides FreeSulfurDioxide TotalSulfurDioxide pH Sulphates Alcohol STARS
## 4 1 ResidualSugar Chlorides FreeSulfurDioxide TotalSulfurDioxide pH Sulphates Alcohol STARS
## 4 2 ResidualSugar Chlorides FreeSulfurDioxide TotalSulfurDioxide pH Sulphates Alcohol STARS
## 5 1 ResidualSugar Chlorides FreeSulfurDioxide TotalSulfurDioxide pH Sulphates Alcohol STARS
## 5 2 ResidualSugar Chlorides FreeSulfurDioxide TotalSulfurDioxide pH Sulphates Alcohol STARS##
## iter imp variable
## 1 1 ResidualSugar Chlorides FreeSulfurDioxide TotalSulfurDioxide pH Sulphates Alcohol STARS
## 1 2 ResidualSugar Chlorides FreeSulfurDioxide TotalSulfurDioxide pH Sulphates Alcohol STARS
## 2 1 ResidualSugar Chlorides FreeSulfurDioxide TotalSulfurDioxide pH Sulphates Alcohol STARS
## 2 2 ResidualSugar Chlorides FreeSulfurDioxide TotalSulfurDioxide pH Sulphates Alcohol STARS
## 3 1 ResidualSugar Chlorides FreeSulfurDioxide TotalSulfurDioxide pH Sulphates Alcohol STARS
## 3 2 ResidualSugar Chlorides FreeSulfurDioxide TotalSulfurDioxide pH Sulphates Alcohol STARS
## 4 1 ResidualSugar Chlorides FreeSulfurDioxide TotalSulfurDioxide pH Sulphates Alcohol STARS
## 4 2 ResidualSugar Chlorides FreeSulfurDioxide TotalSulfurDioxide pH Sulphates Alcohol STARS
## 5 1 ResidualSugar Chlorides FreeSulfurDioxide TotalSulfurDioxide pH Sulphates Alcohol STARS
## 5 2 ResidualSugar Chlorides FreeSulfurDioxide TotalSulfurDioxide pH Sulphates Alcohol STARS
##
## Variables sorted by number of missings:
## Variable Count
## TARGET 0
## FixedAcidity 0
## VolatileAcidity 0
## CitricAcid 0
## ResidualSugar 0
## Chlorides 0
## FreeSulfurDioxide 0
## TotalSulfurDioxide 0
## Density 0
## pH 0
## Sulphates 0
## Alcohol 0
## LabelAppeal 0
## AcidIndex 0
## STARS 0BUILD MODELS
Building these models here
Standara poisson Model
Zero - inflated poisson model - (target variable has a very high 0 occurence)
Zero - inflated negative Binomial
Linear Model
Let us first build a base line model with all variables to get better analyzing of the results
summary(pBase)##
## Call:
## glm(formula = TARGET ~ ., family = "poisson", data = train)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.3455 -0.7024 0.1221 0.6250 2.3598
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.505e+00 2.522e-01 5.968 2.40e-09 ***
## FixedAcidity -1.049e-03 1.056e-03 -0.994 0.32019
## VolatileAcidity -4.347e-02 8.441e-03 -5.150 2.61e-07 ***
## CitricAcid 9.852e-03 7.655e-03 1.287 0.19810
## ResidualSugar -1.178e-04 1.947e-04 -0.605 0.54513
## Chlorides -5.986e-02 2.037e-02 -2.939 0.00329 **
## FreeSulfurDioxide 9.571e-05 4.391e-05 2.180 0.02927 *
## TotalSulfurDioxide 9.032e-05 2.856e-05 3.162 0.00156 **
## Density -3.020e-01 2.474e-01 -1.221 0.22216
## pH -1.768e-02 9.658e-03 -1.830 0.06722 .
## Sulphates -1.930e-02 7.161e-03 -2.695 0.00703 **
## Alcohol 9.895e-04 1.771e-03 0.559 0.57628
## LabelAppeal 1.442e-01 7.816e-03 18.448 < 2e-16 ***
## AcidIndex -9.326e-02 5.777e-03 -16.142 < 2e-16 ***
## STARS 3.307e-01 6.941e-03 47.644 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 13689.4 on 7678 degrees of freedom
## Residual deviance: 9523.1 on 7664 degrees of freedom
## AIC: 28724
##
## Number of Fisher Scoring iterations: 5From the above results we see almost no correlation to our target variables in most variables
Model 1 - Standard poisson Model
parsimonious model of just STARS, LabelAppeal,and AcidIndex…Take out any variable deemed unfit and then run it through a zero-inflated poisson model for comparison.
summary(m1P)##
## Call:
## glm(formula = TARGET ~ STARS + LabelAppeal + AcidIndex, family = "poisson",
## data = train)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.3936 -0.7145 0.1540 0.6244 2.4888
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.155042 0.047838 24.14 <2e-16 ***
## STARS 0.333277 0.006909 48.24 <2e-16 ***
## LabelAppeal 0.144164 0.007811 18.46 <2e-16 ***
## AcidIndex -0.095581 0.005665 -16.87 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 13689.4 on 7678 degrees of freedom
## Residual deviance: 9589.1 on 7675 degrees of freedom
## AIC: 28768
##
## Number of Fisher Scoring iterations: 5Model - 2 Zero inflated Model
We’ll make two zero-inflated models, with and without our lowly correlated VolatileAcidity variable
With highly correlated variabls
summary(m1ZIP)##
## Call:
## zeroinfl(formula = TARGET ~ STARS + LabelAppeal + AcidIndex + VolatileAcidity,
## data = train, dist = "poisson")
##
## Pearson residuals:
## Min 1Q Median 3Q Max
## -2.30020 -0.41519 0.02999 0.44154 3.92847
##
## Count model coefficients (poisson with log link):
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.229570 0.051347 23.946 < 2e-16 ***
## STARS 0.111007 0.007898 14.055 < 2e-16 ***
## LabelAppeal 0.241204 0.008155 29.579 < 2e-16 ***
## AcidIndex -0.022299 0.006201 -3.596 0.000323 ***
## VolatileAcidity -0.015789 0.008800 -1.794 0.072788 .
##
## Zero-inflation model coefficients (binomial with logit link):
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.81415 0.25413 -7.139 9.43e-13 ***
## STARS -2.42199 0.08895 -27.227 < 2e-16 ***
## LabelAppeal 0.72321 0.05391 13.416 < 2e-16 ***
## AcidIndex 0.44698 0.03034 14.734 < 2e-16 ***
## VolatileAcidity 0.24800 0.05346 4.639 3.50e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Number of iterations in BFGS optimization: 17
## Log-likelihood: -1.265e+04 on 10 DfWithout highly correlated variables
summary(m2ZIP)##
## Call:
## zeroinfl(formula = TARGET ~ STARS + LabelAppeal + AcidIndex, data = train,
## dist = "poisson")
##
## Pearson residuals:
## Min 1Q Median 3Q Max
## -2.28811 -0.42556 0.02245 0.46292 4.21900
##
## Count model coefficients (poisson with log link):
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.226606 0.051292 23.914 < 2e-16 ***
## STARS 0.111199 0.007898 14.080 < 2e-16 ***
## LabelAppeal 0.241871 0.008154 29.664 < 2e-16 ***
## AcidIndex -0.022607 0.006203 -3.645 0.000268 ***
##
## Zero-inflation model coefficients (binomial with logit link):
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.72692 0.25328 -6.818 9.21e-12 ***
## STARS -2.42934 0.08922 -27.228 < 2e-16 ***
## LabelAppeal 0.72701 0.05402 13.458 < 2e-16 ***
## AcidIndex 0.44804 0.03038 14.748 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Number of iterations in BFGS optimization: 15
## Log-likelihood: -1.266e+04 on 8 DfFrom the coefficients we see its good to include VolatileAcidity in any Zero inflated model, as it definitely helps predict 0 counts. However the trade off is that it becomes a confounding variable while predicting the actual count above 0.
Lets build our negative binomial regression, then again with zero-inflation adjustment.
summary(nbBase)##
## Call:
## MASS::glm.nb(formula = TARGET ~ ., data = train, init.theta = 48469.64451,
## link = log)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.3454 -0.7024 0.1221 0.6250 2.3598
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.505e+00 2.522e-01 5.968 2.40e-09 ***
## FixedAcidity -1.049e-03 1.056e-03 -0.994 0.32020
## VolatileAcidity -4.347e-02 8.441e-03 -5.150 2.61e-07 ***
## CitricAcid 9.852e-03 7.655e-03 1.287 0.19811
## ResidualSugar -1.178e-04 1.947e-04 -0.605 0.54515
## Chlorides -5.986e-02 2.037e-02 -2.939 0.00329 **
## FreeSulfurDioxide 9.572e-05 4.391e-05 2.180 0.02928 *
## TotalSulfurDioxide 9.033e-05 2.856e-05 3.162 0.00156 **
## Density -3.020e-01 2.474e-01 -1.221 0.22217
## pH -1.768e-02 9.658e-03 -1.830 0.06722 .
## Sulphates -1.930e-02 7.162e-03 -2.695 0.00703 **
## Alcohol 9.896e-04 1.771e-03 0.559 0.57630
## LabelAppeal 1.442e-01 7.817e-03 18.447 < 2e-16 ***
## AcidIndex -9.326e-02 5.777e-03 -16.142 < 2e-16 ***
## STARS 3.307e-01 6.941e-03 47.643 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(48469.64) family taken to be 1)
##
## Null deviance: 13688.8 on 7678 degrees of freedom
## Residual deviance: 9522.7 on 7664 degrees of freedom
## AIC: 28726
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 48470
## Std. Err.: 72613
## Warning while fitting theta: iteration limit reached
##
## 2 x log-likelihood: -28694.12Same stats as the baseline poisson model, lets compare them using vuong test.
## Vuong Non-Nested Hypothesis Test-Statistic:
## (test-statistic is asymptotically distributed N(0,1) under the
## null that the models are indistinguishible)
## -------------------------------------------------------------
## Vuong z-statistic H_A p-value
## Raw 18.98088 model1 > model2 < 2.22e-16
## AIC-corrected 18.98088 model1 > model2 < 2.22e-16
## BIC-corrected 18.98088 model1 > model2 < 2.22e-16poisson model being better in this case; because I’m betting the data is overdispersed. Lets look.
## [1] 3.027347## [1] 3AER::dispersiontest(pBase,trafo =2)##
## Overdispersion test
##
## data: pBase
## z = -17.744, p-value = 1
## alternative hypothesis: true alpha is greater than 0
## sample estimates:
## alpha
## -0.07597519the change may be a result of imputation methods we used.
Model 3 Zero inflated negative Binomial
negative binomial, zero inflated model using everything statistically significant and one with our most salient variables.
Lastly, if I assume that wholesalers buy wine according to customer preference. I imagine most customers like fancy looking, sweet tasting wines. So I’ll make a minimal feature model including an interaction between alcohol (sweetness) and label appeal.
summary(m3ZInb)##
## Call:
## zeroinfl(formula = TARGET ~ STARS + LabelAppeal + Alcohol:LabelAppeal,
## data = train, dist = "negbin")
##
## Pearson residuals:
## Min 1Q Median 3Q Max
## -2.28333 -0.45537 0.00367 0.45516 5.91477
##
## Count model coefficients (negbin with log link):
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.051e+00 1.866e-02 56.331 <2e-16 ***
## STARS 1.125e-01 7.901e-03 14.244 <2e-16 ***
## LabelAppeal 2.372e-01 2.285e-02 10.384 <2e-16 ***
## LabelAppeal:Alcohol 4.724e-04 2.019e-03 0.234 0.815
## Log(theta) 1.550e+01 9.498e+00 1.632 0.103
##
## Zero-inflation model coefficients (binomial with logit link):
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.87990 0.10092 18.628 < 2e-16 ***
## STARS -2.44895 0.08693 -28.172 < 2e-16 ***
## LabelAppeal 0.63498 0.14240 4.459 8.23e-06 ***
## LabelAppeal:Alcohol 0.01337 0.01290 1.037 0.3
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Theta = 5407745.3594
## Number of iterations in BFGS optimization: 39
## Log-likelihood: -1.28e+04 on 9 Dfsummary(m1ZInb)##
## Call:
## zeroinfl(formula = TARGET ~ STARS + LabelAppeal + AcidIndex + VolatileAcidity +
## Alcohol, data = train, dist = "negbin")
##
## Pearson residuals:
## Min 1Q Median 3Q Max
## -2.29938 -0.40787 0.03028 0.43743 3.92667
##
## Count model coefficients (negbin with log link):
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.175102 0.055361 21.226 < 2e-16 ***
## STARS 0.109510 0.007916 13.834 < 2e-16 ***
## LabelAppeal 0.241448 0.008158 29.598 < 2e-16 ***
## AcidIndex -0.021411 0.006207 -3.450 0.000562 ***
## VolatileAcidity -0.016092 0.008799 -1.829 0.067422 .
## Alcohol 0.004824 0.001826 2.642 0.008243 **
## Log(theta) 17.738514 NA NA NA
##
## Zero-inflation model coefficients (binomial with logit link):
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.97405 0.28229 -6.993 2.69e-12 ***
## STARS -2.41664 0.08866 -27.256 < 2e-16 ***
## LabelAppeal 0.72362 0.05389 13.427 < 2e-16 ***
## AcidIndex 0.44751 0.03031 14.766 < 2e-16 ***
## VolatileAcidity 0.24637 0.05337 4.616 3.90e-06 ***
## Alcohol 0.01463 0.01119 1.308 0.191
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Theta = 50552037.539
## Number of iterations in BFGS optimization: 51
## Log-likelihood: -1.264e+04 on 13 Dfsummary(m2ZInb)##
## Call:
## zeroinfl(formula = TARGET ~ STARS + LabelAppeal + AcidIndex, data = train,
## dist = "negbin")
##
## Pearson residuals:
## Min 1Q Median 3Q Max
## -2.28811 -0.42556 0.02245 0.46292 4.21901
##
## Count model coefficients (negbin with log link):
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.226602 0.051292 23.914 < 2e-16 ***
## STARS 0.111199 0.007898 14.080 < 2e-16 ***
## LabelAppeal 0.241871 0.008154 29.664 < 2e-16 ***
## AcidIndex -0.022607 0.006203 -3.645 0.000268 ***
## Log(theta) 16.199059 NA NA NA
##
## Zero-inflation model coefficients (binomial with logit link):
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.72691 0.25328 -6.818 9.21e-12 ***
## STARS -2.42934 0.08922 -27.228 < 2e-16 ***
## LabelAppeal 0.72701 0.05402 13.458 < 2e-16 ***
## AcidIndex 0.44804 0.03038 14.748 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Theta = 10843314.0342
## Number of iterations in BFGS optimization: 39
## Log-likelihood: -1.266e+04 on 9 DfModel 4 Linear model
## Start: AIC=5425.05
## TARGET ~ FixedAcidity + VolatileAcidity + CitricAcid + ResidualSugar +
## Chlorides + FreeSulfurDioxide + TotalSulfurDioxide + Density +
## pH + Sulphates + Alcohol + LabelAppeal + AcidIndex + STARS
##
## Df Sum of Sq RSS AIC
## - ResidualSugar 1 1.1 15504 5423.6
## - FixedAcidity 1 2.0 15505 5424.0
## <none> 15503 5425.0
## - Density 1 4.1 15508 5425.1
## - CitricAcid 1 4.7 15508 5425.4
## - pH 1 5.6 15509 5425.8
## - Alcohol 1 8.1 15512 5427.1
## - FreeSulfurDioxide 1 11.3 15515 5428.6
## - Sulphates 1 17.9 15521 5431.9
## - TotalSulfurDioxide 1 21.4 15525 5433.6
## - Chlorides 1 25.3 15529 5435.5
## - VolatileAcidity 1 84.0 15588 5464.6
## - AcidIndex 1 678.6 16182 5752.0
## - LabelAppeal 1 1165.9 16669 5979.8
## - STARS 1 7309.8 22813 8389.3
##
## Step: AIC=5423.57
## TARGET ~ FixedAcidity + VolatileAcidity + CitricAcid + Chlorides +
## FreeSulfurDioxide + TotalSulfurDioxide + Density + pH + Sulphates +
## Alcohol + LabelAppeal + AcidIndex + STARS
##
## Df Sum of Sq RSS AIC
## - FixedAcidity 1 1.9 15506 5422.5
## <none> 15504 5423.6
## - Density 1 4.1 15509 5423.6
## - CitricAcid 1 4.7 15509 5423.9
## - pH 1 5.6 15510 5424.3
## - Alcohol 1 8.2 15513 5425.6
## - FreeSulfurDioxide 1 11.1 15516 5427.1
## - Sulphates 1 17.8 15522 5430.4
## - TotalSulfurDioxide 1 21.2 15526 5432.1
## - Chlorides 1 25.2 15530 5434.0
## - VolatileAcidity 1 84.0 15588 5463.1
## - AcidIndex 1 678.6 16183 5750.5
## - LabelAppeal 1 1166.1 16671 5978.4
## - STARS 1 7309.2 22814 8387.4
##
## Step: AIC=5422.52
## TARGET ~ VolatileAcidity + CitricAcid + Chlorides + FreeSulfurDioxide +
## TotalSulfurDioxide + Density + pH + Sulphates + Alcohol +
## LabelAppeal + AcidIndex + STARS
##
## Df Sum of Sq RSS AIC
## <none> 15506 5422.5
## - Density 1 4.1 15510 5422.5
## - CitricAcid 1 4.6 15511 5422.8
## - pH 1 5.6 15512 5423.3
## - Alcohol 1 8.3 15515 5424.6
## - FreeSulfurDioxide 1 11.0 15517 5426.0
## - Sulphates 1 18.1 15524 5429.5
## - TotalSulfurDioxide 1 21.4 15528 5431.1
## - Chlorides 1 25.0 15531 5432.9
## - VolatileAcidity 1 84.2 15591 5462.1
## - AcidIndex 1 713.7 16220 5766.0
## - LabelAppeal 1 1167.2 16674 5977.8
## - STARS 1 7309.0 22815 8386.0summary(Linear_model)##
## Call:
## lm(formula = TARGET ~ LabelAppeal + STARS, data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.0635 -0.8934 0.2322 0.9277 3.9042
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.97325 0.03669 26.52 <2e-16 ***
## LabelAppeal 0.42699 0.01945 21.96 <2e-16 ***
## STARS 1.12253 0.01783 62.97 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.464 on 7676 degrees of freedom
## Multiple R-squared: 0.4202, Adjusted R-squared: 0.4201
## F-statistic: 2782 on 2 and 7676 DF, p-value: < 2.2e-16summary(mLin1)##
## Call:
## lm(formula = TARGET ~ VolatileAcidity + CitricAcid + Chlorides +
## FreeSulfurDioxide + TotalSulfurDioxide + Density + pH + Sulphates +
## Alcohol + LabelAppeal + AcidIndex + STARS, data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.1659 -0.8790 0.1836 1.0060 4.1041
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.841e+00 6.197e-01 6.198 6.00e-10 ***
## VolatileAcidity -1.342e-01 2.081e-02 -6.451 1.18e-10 ***
## CitricAcid 2.867e-02 1.895e-02 1.513 0.130275
## Chlorides -1.777e-01 5.052e-02 -3.518 0.000437 ***
## FreeSulfurDioxide 2.539e-04 1.089e-04 2.332 0.019735 *
## TotalSulfurDioxide 2.284e-04 7.016e-05 3.255 0.001138 **
## Density -8.661e-01 6.090e-01 -1.422 0.155010
## pH -3.952e-02 2.378e-02 -1.662 0.096617 .
## Sulphates -5.241e-02 1.754e-02 -2.988 0.002819 **
## Alcohol 8.849e-03 4.374e-03 2.023 0.043086 *
## LabelAppeal 4.553e-01 1.895e-02 24.022 < 2e-16 ***
## AcidIndex -2.336e-01 1.244e-02 -18.783 < 2e-16 ***
## STARS 1.057e+00 1.759e-02 60.112 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.422 on 7666 degrees of freedom
## Multiple R-squared: 0.4537, Adjusted R-squared: 0.4528
## F-statistic: 530.5 on 12 and 7666 DF, p-value: < 2.2e-16Only using STARS and LabelAppeal can compete with a stepwise backward regression of every variable within .3 adjusted R2. While the stepwise regression has a better F-statistic in this case,.
SELECT MODELS
Linear model with two variables LabelAppeal and STARS got a R2 of .42 However we would like a model that can delineate between will and won’t sell. ZIP and ZINB were able to ascertain that we can best provide that information using acid index as well.
Testing the RMSE of our best ZIP model against the RMSE (while only using real predictions numbers (no decimals)) or our best (simplest) linear model we see that the simple linear model has a high RMSE at 1.44 to the ZIPS 1.35. I see no reason not to use AcidIndex, for a three variable ZIP model. Lets send in our predictions.
## [1] 1.441672 1.355328results = predict(m2ZIP,test)
hist(results)
write.csv(results,'WinePredictions.csv')