Introduction
In this homework, I will explore, analyze and model a data set containing approximately 12,000 commercially available wines.The variable 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 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.
My 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.
Read the data set
train_data <- read.csv("https://raw.githubusercontent.com/miachen410/DATA621/master/HW%235/wine-training-data.csv", header = TRUE)
eval_data <- read.csv("https://raw.githubusercontent.com/miachen410/DATA621/master/HW%235/wine-evaluation-data.csv", header = TRUE)
Data Exploration and Cleaning
head(train_data)
## INDEX TARGET FixedAcidity VolatileAcidity CitricAcid ResidualSugar Chlorides
## 1 1 3 3.2 1.160 -0.98 54.2 -0.567
## 2 2 3 4.5 0.160 -0.81 26.1 -0.425
## 3 4 5 7.1 2.640 -0.88 14.8 0.037
## 4 5 3 5.7 0.385 0.04 18.8 -0.425
## 5 6 4 8.0 0.330 -1.26 9.4 NA
## 6 7 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 NA
summary(train_data)
## INDEX TARGET FixedAcidity VolatileAcidity
## Min. : 1 Min. :0.000 Min. :-18.100 Min. :-2.7900
## 1st Qu.: 4038 1st Qu.:2.000 1st Qu.: 5.200 1st Qu.: 0.1300
## Median : 8110 Median :3.000 Median : 6.900 Median : 0.2800
## Mean : 8070 Mean :3.029 Mean : 7.076 Mean : 0.3241
## 3rd Qu.:12106 3rd Qu.:4.000 3rd Qu.: 9.500 3rd Qu.: 0.6400
## Max. :16129 Max. :8.000 Max. : 34.400 Max. : 3.6800
##
## CitricAcid ResidualSugar Chlorides FreeSulfurDioxide
## Min. :-3.2400 Min. :-127.800 Min. :-1.1710 Min. :-555.00
## 1st Qu.: 0.0300 1st Qu.: -2.000 1st Qu.:-0.0310 1st Qu.: 0.00
## Median : 0.3100 Median : 3.900 Median : 0.0460 Median : 30.00
## Mean : 0.3084 Mean : 5.419 Mean : 0.0548 Mean : 30.85
## 3rd Qu.: 0.5800 3rd Qu.: 15.900 3rd Qu.: 0.1530 3rd Qu.: 70.00
## Max. : 3.8600 Max. : 141.150 Max. : 1.3510 Max. : 623.00
## NA's :616 NA's :638 NA's :647
## TotalSulfurDioxide Density pH Sulphates
## Min. :-823.0 Min. :0.8881 Min. :0.480 Min. :-3.1300
## 1st Qu.: 27.0 1st Qu.:0.9877 1st Qu.:2.960 1st Qu.: 0.2800
## Median : 123.0 Median :0.9945 Median :3.200 Median : 0.5000
## Mean : 120.7 Mean :0.9942 Mean :3.208 Mean : 0.5271
## 3rd Qu.: 208.0 3rd Qu.:1.0005 3rd Qu.:3.470 3rd Qu.: 0.8600
## Max. :1057.0 Max. :1.0992 Max. :6.130 Max. : 4.2400
## NA's :682 NA's :395 NA's :1210
## Alcohol LabelAppeal AcidIndex STARS
## Min. :-4.70 Min. :-2.000000 Min. : 4.000 Min. :1.000
## 1st Qu.: 9.00 1st Qu.:-1.000000 1st Qu.: 7.000 1st Qu.:1.000
## Median :10.40 Median : 0.000000 Median : 8.000 Median :2.000
## Mean :10.49 Mean :-0.009066 Mean : 7.773 Mean :2.042
## 3rd Qu.:12.40 3rd Qu.: 1.000000 3rd Qu.: 8.000 3rd Qu.:3.000
## Max. :26.50 Max. : 2.000000 Max. :17.000 Max. :4.000
## NA's :653 NA's :3359
nrow(train_data)
## [1] 12795
train_data <- train_data[, -1]
eval_data <- eval_data[, -1]
summary(eval_data)
## TARGET FixedAcidity VolatileAcidity CitricAcid
## Mode:logical Min. :-18.200 Min. :-2.8300 Min. :-3.1200
## NA's:3335 1st Qu.: 5.200 1st Qu.: 0.0800 1st Qu.: 0.0000
## Median : 6.900 Median : 0.2800 Median : 0.3100
## Mean : 6.864 Mean : 0.3103 Mean : 0.3124
## 3rd Qu.: 9.000 3rd Qu.: 0.6300 3rd Qu.: 0.6050
## Max. : 33.500 Max. : 3.6100 Max. : 3.7600
##
## ResidualSugar Chlorides FreeSulfurDioxide TotalSulfurDioxide
## Min. :-128.300 Min. :-1.15000 Min. :-563.00 Min. :-769.00
## 1st Qu.: -2.600 1st Qu.: 0.01600 1st Qu.: 3.00 1st Qu.: 27.25
## Median : 3.600 Median : 0.04700 Median : 30.00 Median : 124.00
## Mean : 5.319 Mean : 0.06143 Mean : 34.95 Mean : 123.41
## 3rd Qu.: 17.200 3rd Qu.: 0.17100 3rd Qu.: 79.25 3rd Qu.: 210.00
## Max. : 145.400 Max. : 1.26300 Max. : 617.00 Max. :1004.00
## NA's :168 NA's :138 NA's :152 NA's :157
## Density pH Sulphates Alcohol
## Min. :0.8898 Min. :0.600 Min. :-3.0700 Min. :-4.20
## 1st Qu.:0.9883 1st Qu.:2.980 1st Qu.: 0.3300 1st Qu.: 9.00
## Median :0.9946 Median :3.210 Median : 0.5000 Median :10.40
## Mean :0.9947 Mean :3.237 Mean : 0.5346 Mean :10.58
## 3rd Qu.:1.0005 3rd Qu.:3.490 3rd Qu.: 0.8200 3rd Qu.:12.50
## Max. :1.0998 Max. :6.210 Max. : 4.1800 Max. :25.60
## NA's :104 NA's :310 NA's :185
## LabelAppeal AcidIndex STARS
## Min. :-2.00000 Min. : 5.000 Min. :1.00
## 1st Qu.:-1.00000 1st Qu.: 7.000 1st Qu.:1.00
## Median : 0.00000 Median : 8.000 Median :2.00
## Mean : 0.01349 Mean : 7.748 Mean :2.04
## 3rd Qu.: 1.00000 3rd Qu.: 8.000 3rd Qu.:3.00
## Max. : 2.00000 Max. :17.000 Max. :4.00
## NA's :841
Histograms
hist(train_data$TARGET, col = "orange", xlab = " Target ", main = "Wine Counts")
Boxplot
ggplot(melt(train_data), aes(x=factor(variable), y=value)) + facet_wrap(~variable, scale="free") + geom_boxplot()
## No id variables; using all as measure variables
## Warning: Removed 8200 rows containing non-finite values (stat_boxplot).
Correlation
corrplot(as.matrix(cor(train_data, use = "pairwise.complete")),method = "circle")
Data Preparation
# Replacing N/A with mean for calculation
train_data$ResidualSugar[is.na(train_data$ResidualSugar)] <- mean(train_data$ResidualSugar, na.rm=TRUE)
train_data$Chlorides[is.na(train_data$Chlorides)] <- mean(train_data$Chlorides, na.rm=TRUE)
train_data$FreeSulfurDioxide[is.na(train_data$FreeSulfurDioxide)] <- mean(train_data$FreeSulfurDioxide, na.rm=TRUE)
train_data$TotalSulfurDioxide[is.na(train_data$TotalSulfurDioxide)] <- mean(train_data$TotalSulfurDioxide, na.rm=TRUE)
train_data$pH[is.na(train_data$pH)] <- mean(train_data$pH, na.rm=TRUE)
train_data$Sulphates[is.na(train_data$Sulphates)] <- mean(train_data$Sulphates, na.rm=TRUE)
train_data$Sulphates[is.na(train_data$Sulphates)] <- mean(train_data$Sulphates, na.rm=TRUE)
train_data$Alcohol[is.na(train_data$Alcohol)] <- mean(train_data$Alcohol, na.rm=TRUE)
train_data$STARS[is.na(train_data$STARS)] <- mean(train_data$STARS, na.rm=TRUE)
eval_data$ResidualSugar[is.na(eval_data$ResidualSugar)] <- mean(eval_data$ResidualSugar, na.rm=TRUE)
eval_data$Chlorides[is.na(eval_data$Chlorides)] <- mean(eval_data$Chlorides, na.rm=TRUE)
eval_data$FreeSulfurDioxide[is.na(eval_data$FreeSulfurDioxide)] <- mean(eval_data$FreeSulfurDioxide, na.rm=TRUE)
eval_data$TotalSulfurDioxide[is.na(eval_data$TotalSulfurDioxide)] <- mean(eval_data$TotalSulfurDioxide, na.rm=TRUE)
eval_data$pH[is.na(eval_data$pH)] <- mean(eval_data$pH, na.rm=TRUE)
eval_data$Sulphates[is.na(eval_data$Sulphates)] <- mean(eval_data$Sulphates, na.rm=TRUE)
eval_data$Alcohol[is.na(eval_data$Alcohol)] <- mean(eval_data$Alcohol, na.rm=TRUE)
eval_data$STARS[is.na(eval_data$STARS)] <- mean(eval_data$STARS, na.rm=TRUE)
Build Model
# Possion Distribution
model1 = glm(TARGET ~., data = train_data, family = poisson)
summary(model1)
##
## Call:
## glm(formula = TARGET ~ ., family = poisson, data = train_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.5118 -0.5144 0.2080 0.6344 2.5664
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.045e+00 1.957e-01 10.448 < 2e-16 ***
## FixedAcidity -4.444e-04 8.194e-04 -0.542 0.587585
## VolatileAcidity -5.097e-02 6.492e-03 -7.851 4.12e-15 ***
## CitricAcid 1.343e-02 5.892e-03 2.280 0.022631 *
## ResidualSugar 1.489e-04 1.545e-04 0.964 0.335073
## Chlorides -6.058e-02 1.645e-02 -3.683 0.000231 ***
## FreeSulfurDioxide 1.420e-04 3.513e-05 4.041 5.31e-05 ***
## TotalSulfurDioxide 1.072e-04 2.268e-05 4.727 2.28e-06 ***
## Density -4.364e-01 1.921e-01 -2.272 0.023074 *
## pH -2.411e-02 7.639e-03 -3.156 0.001599 **
## Sulphates -1.901e-02 5.738e-03 -3.313 0.000924 ***
## Alcohol 5.528e-03 1.410e-03 3.920 8.85e-05 ***
## LabelAppeal 1.996e-01 6.014e-03 33.180 < 2e-16 ***
## AcidIndex -1.232e-01 4.461e-03 -27.616 < 2e-16 ***
## STARS 2.113e-01 6.491e-03 32.543 < 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: 22861 on 12794 degrees of freedom
## Residual deviance: 18511 on 12780 degrees of freedom
## AIC: 50483
##
## Number of Fisher Scoring iterations: 5
# Exclude the predictor that are not significant
model2 = glm(TARGET ~ VolatileAcidity + CitricAcid + Chlorides + FreeSulfurDioxide
+ TotalSulfurDioxide + Density + pH + Sulphates + Alcohol + LabelAppeal
+ AcidIndex + STARS, data = train_data,
family = poisson)
summary(model2)
##
## Call:
## glm(formula = TARGET ~ VolatileAcidity + CitricAcid + Chlorides +
## FreeSulfurDioxide + TotalSulfurDioxide + Density + pH + Sulphates +
## Alcohol + LabelAppeal + AcidIndex + STARS, family = poisson,
## data = train_data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.5135 -0.5169 0.2084 0.6350 2.5697
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.045e+00 1.957e-01 10.451 < 2e-16 ***
## VolatileAcidity -5.106e-02 6.491e-03 -7.866 3.68e-15 ***
## CitricAcid 1.336e-02 5.892e-03 2.267 0.023405 *
## Chlorides -6.056e-02 1.645e-02 -3.681 0.000232 ***
## FreeSulfurDioxide 1.422e-04 3.513e-05 4.047 5.19e-05 ***
## TotalSulfurDioxide 1.078e-04 2.268e-05 4.753 2.00e-06 ***
## Density -4.366e-01 1.921e-01 -2.273 0.023025 *
## pH -2.401e-02 7.637e-03 -3.143 0.001671 **
## Sulphates -1.910e-02 5.737e-03 -3.328 0.000873 ***
## Alcohol 5.503e-03 1.410e-03 3.904 9.47e-05 ***
## LabelAppeal 1.996e-01 6.014e-03 33.190 < 2e-16 ***
## AcidIndex -1.236e-01 4.409e-03 -28.031 < 2e-16 ***
## STARS 2.113e-01 6.491e-03 32.554 < 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: 22861 on 12794 degrees of freedom
## Residual deviance: 18513 on 12782 degrees of freedom
## AIC: 50481
##
## Number of Fisher Scoring iterations: 5
# Linera Model
model3 = lm(TARGET ~., data = train_data)
summary(model3)
##
## Call:
## lm(formula = TARGET ~ ., data = train_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.2735 -0.7440 0.3694 1.1250 4.3210
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.451e+00 5.543e-01 9.833 < 2e-16 ***
## FixedAcidity -1.152e-03 2.326e-03 -0.495 0.620510
## VolatileAcidity -1.564e-01 1.847e-02 -8.470 < 2e-16 ***
## CitricAcid 4.009e-02 1.681e-02 2.385 0.017085 *
## ResidualSugar 4.892e-04 4.392e-04 1.114 0.265349
## Chlorides -1.946e-01 4.660e-02 -4.175 2.99e-05 ***
## FreeSulfurDioxide 4.284e-04 9.988e-05 4.289 1.81e-05 ***
## TotalSulfurDioxide 3.122e-04 6.417e-05 4.865 1.16e-06 ***
## Density -1.289e+00 5.453e-01 -2.364 0.018098 *
## pH -6.458e-02 2.164e-02 -2.984 0.002850 **
## Sulphates -5.560e-02 1.631e-02 -3.409 0.000654 ***
## Alcohol 1.929e-02 3.991e-03 4.832 1.37e-06 ***
## LabelAppeal 6.042e-01 1.693e-02 35.684 < 2e-16 ***
## AcidIndex -3.290e-01 1.122e-02 -29.313 < 2e-16 ***
## STARS 7.153e-01 1.953e-02 36.617 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.634 on 12780 degrees of freedom
## Multiple R-squared: 0.2811, Adjusted R-squared: 0.2803
## F-statistic: 356.9 on 14 and 12780 DF, p-value: < 2.2e-16
Model Selection
predict1 <- predict(model2, newdata=eval_data, type="response")
summary(predict1)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.8397 2.3207 2.8487 3.0524 3.5567 9.5182
predict2 <- predict(model3, newdata=eval_data, type="response")
summary(predict2)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -0.3319 2.3733 2.9959 3.0525 3.6876 6.6712