Master Analyst 2
Stenroos
December 13, 2017
Chopped Master Analysis
We were given a data set consisting of roughly 4000 entries with 25 variables about resturaunt ratings. Our goal was to figure out what made a person rate a resturaunt a certain way.
We discussed what we wanted to do with our data and after going through our different types of analysis that we have learned this semester, we decided we wanted to run a linear regression, a logistical regression, and then focus on CART analysis with decision trees. We also concluded that we wanted to use rating as our dependent variable to try and predict that variable.
We started by bringing in our original data set and then 3 of the edited data set we used.
We also created a table and barchart to show the distribution of our dependent variable, rating.
RRD <- read.csv("~/Business Analytics/RestaurantRatersComplete.csv")
RRDE <- read.csv("~/Business Analytics/RRD Edited2.csv")
RRDE2 <- read.csv("~/Business Analytics/RRD Edited2.csv")
RRDE3 <- read.csv("~/Business Analytics/RRD Edited2.csv")
library(lattice)
head(RRDE)## smoker drink_level dress_preference ambience transport marital_status
## 1 TRUE social drinker informal family public single
## 2 TRUE social drinker informal family public single
## 3 TRUE social drinker informal family public single
## 4 TRUE social drinker informal family public single
## 5 FALSE abstemious no preference family car owner single
## 6 FALSE abstemious no preference family car owner single
## hijos birth_year religion activity budget rating food_rating
## 1 independent 1989 Catholic student high 0 0
## 2 independent 1989 Catholic student high 0 0
## 3 independent 1989 Catholic student high 0 1
## 4 independent 1989 Catholic student high 0 1
## 5 independent 1943 Christian student high 1 2
## 6 independent 1943 Christian student high 1 2
## service_rating
## 1 0
## 2 0
## 3 1
## 4 1
## 5 1
## 6 0table(RRDE$rating)##
## 0 1 2
## 1773 968 1202barchart(table(RRDE$rating),ylab="Rating",col="red")
Data Cleanup
At first glance we saw that there was some missing data. We had roughly 200 cells of question marks so we chose to remove these as that was a very small amount compared to 4000 rows. We did the removal in excel just by sorting the columns to find the missing data and deleting them.
Then in order for us to run our logisitic regression and CART analysis we needed to change our categorical variables to numeric. Most of the variables were categorical so we had to do quite a bit of recoding to make dummy variables for these. We had to make many assumptions as there wasn’t much information given about the variables. For example we are assuming that for the rating variable that 0 is a bad rating, 1 is an average rating, and 2 is a perfect rating. We also assumed we could scale all of these variables on an increasing scale. A good example of our thought process would be the transport variable where we decided car owner was the best, on foot was the worst, and that public was between the two. The only variable we didn’t scale was religion, where we clumped all the religions together so a person was either religious or not. Below you can see our recode.
library(car)## Warning: package 'car' was built under R version 3.4.2RRDE3$smoker=recode(RRDE3$smoker,"'FALSE'=0; 'TRUE'=1")
RRDE3$drink_level=recode(RRDE3$drink_level,"'abstemious'=0; 'casual drinker'=1; 'social drinker'=2")
RRDE3$dress_preference=recode(RRDE3$dress_preference,"'no preference'=0; 'informal'=1; 'formal'=2; 'elegant'=3")
RRDE3$ambience=recode(RRDE3$ambience,"'solitary'=0; 'friends'=1; 'family'=2")
RRDE3$transport=recode(RRDE3$transport,"'on foot'=0; 'public'=1; 'car owner'=2")
RRDE3$marital_status=recode(RRDE3$marital_status,"'single'=0; 'widowed'=1; 'married'=2")
RRDE3$hijos=recode(RRDE3$hijos,"'dependent'=0; 'independent'=1; 'kids'=2")
RRDE3$activity=recode(RRDE3$activity,"'unemployed'=0; 'student'=1; 'working-class'=2; 'professional'=3")
RRDE3$budget=recode(RRDE3$budget,"'low'=0; 'medium'=1; 'high'=2")
RRDE3$religion=recode(RRDE3$religion,"'none'=0; 'Catholic'=1; 'Christian'=1; 'Jewish'=1; 'Mormon'=1")
RRDE3$rating=recode(RRDE3$rating,"'0'=0; '1'=0; '2'=1")This was our first recode for the RRDE3 which we will use for our logistic regression because we recoded rating to be binary, either 0 for a non-perfect rating or 1 for a perfect rating. There will be another recode for RRDE2 which we will use for our CART analysis because we left our rating as a 0, 1, or 2. This recode is the same besides the rating variable. This recode is below.
RRDE2$smoker=recode(RRDE2$smoker,"'FALSE'=0; 'TRUE'=1")
RRDE2$drink_level=recode(RRDE2$drink_level,"'abstemious'=0; 'casual drinker'=1; 'social drinker'=2")
RRDE2$dress_preference=recode(RRDE2$dress_preference,"'no preference'=0; 'informal'=1; 'formal'=2; 'elegant'=3")
RRDE2$ambience=recode(RRDE2$ambience,"'solitary'=0; 'friends'=1; 'family'=2")
RRDE2$transport=recode(RRDE2$transport,"'on foot'=0; 'public'=1; 'car owner'=2")
RRDE2$marital_status=recode(RRDE2$marital_status,"'single'=0; 'widowed'=1; 'married'=2")
RRDE2$hijos=recode(RRDE2$hijos,"'dependent'=0; 'independent'=1; 'kids'=2")
RRDE2$activity=recode(RRDE2$activity,"'unemployed'=0; 'student'=1; 'working-class'=2; 'professional'=3")
RRDE2$budget=recode(RRDE2$budget,"'low'=0; 'medium'=1; 'high'=2")
RRDE2$religion=recode(RRDE2$religion,"'none'=0; 'Catholic'=1; 'Christian'=1; 'Jewish'=1; 'Mormon'=1")Linear Regression
We wanted to start with a linear regression as it is one of the easier things to try right away and see how it works. Also it can give a pretty good idea of what may or may not be significant as far as variables are concerned.
m1=lm(rating~.,data=RRDE)
summary(m1)##
## Call:
## lm(formula = rating ~ ., data = RRDE)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.91982 -0.07269 -0.01253 0.06254 1.90696
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.8934985 1.6133807 3.653 0.000263 ***
## smokerTRUE -0.0343015 0.0259226 -1.323 0.185837
## drink_levelcasual drinker -0.0680991 0.0254250 -2.678 0.007428 **
## drink_levelsocial drinker -0.1078001 0.0253675 -4.250 2.19e-05 ***
## dress_preferenceformal -0.0806879 0.0672568 -1.200 0.230329
## dress_preferenceinformal -0.2004827 0.0695671 -2.882 0.003975 **
## dress_preferenceno preference -0.2006370 0.0712205 -2.817 0.004870 **
## ambiencefriends 0.0512738 0.0222279 2.307 0.021122 *
## ambiencesolitary -0.0339017 0.0267831 -1.266 0.205665
## transporton foot -0.0810585 0.0323891 -2.503 0.012367 *
## transportpublic -0.1638244 0.0256980 -6.375 2.04e-10 ***
## marital_statussingle 0.1276733 0.0509882 2.504 0.012321 *
## marital_statuswidow 0.5316636 0.1003315 5.299 1.23e-07 ***
## hijosindependent -0.0918057 0.0833669 -1.101 0.270866
## hijoskids -0.3145672 0.0840026 -3.745 0.000183 ***
## birth_year -0.0027530 0.0008356 -3.295 0.000994 ***
## religionChristian -0.1012856 0.0531072 -1.907 0.056569 .
## religionJewish -0.4772020 0.0978924 -4.875 1.13e-06 ***
## religionMormon -0.3960469 0.1122700 -3.528 0.000424 ***
## religionnone -0.1064383 0.0285816 -3.724 0.000199 ***
## activitystudent 0.0260464 0.0314700 0.828 0.407915
## activityunemployed -0.4237667 0.1426878 -2.970 0.002997 **
## activityworking-class 0.2436041 0.1380733 1.764 0.077758 .
## budgetlow 0.1024578 0.0643328 1.593 0.111326
## budgetmedium 0.1296879 0.0622091 2.085 0.037160 *
## food_rating 0.4019010 0.0128045 31.387 < 2e-16 ***
## service_rating 0.4430751 0.0120789 36.682 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3553 on 3916 degrees of freedom
## Multiple R-squared: 0.8291, Adjusted R-squared: 0.828
## F-statistic: 730.7 on 26 and 3916 DF, p-value: < 2.2e-16As you can see from our output, our adujusted R^2 was .828 which is very good. The thing we didn’t like was that we included food rating and service rating in this as we thought of those as very linear predictors of overall rating. We decided to run another linear regression while excluding those variables.
m2=lm(rating~.-food_rating-service_rating,data=RRDE)
summary(m2)##
## Call:
## lm(formula = rating ~ . - food_rating - service_rating, data = RRDE)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.12437 -0.21372 -0.04191 0.34246 1.80844
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 11.562597 2.453929 4.712 2.54e-06 ***
## smokerTRUE -0.069991 0.039413 -1.776 0.075837 .
## drink_levelcasual drinker -0.278258 0.038389 -7.248 5.06e-13 ***
## drink_levelsocial drinker -0.099708 0.038635 -2.581 0.009895 **
## dress_preferenceformal -0.309930 0.102320 -3.029 0.002469 **
## dress_preferenceinformal -0.586003 0.105637 -5.547 3.09e-08 ***
## dress_preferenceno preference -0.691712 0.107970 -6.407 1.66e-10 ***
## ambiencefriends 0.019435 0.033847 0.574 0.565874
## ambiencesolitary 0.011622 0.040729 0.285 0.775386
## transporton foot 0.150827 0.049035 3.076 0.002113 **
## transportpublic -0.317942 0.039001 -8.152 4.76e-16 ***
## marital_statussingle -0.710426 0.075553 -9.403 < 2e-16 ***
## marital_statuswidow -0.598117 0.150746 -3.968 7.39e-05 ***
## hijosindependent -0.010283 0.126920 -0.081 0.935427
## hijoskids -1.188992 0.126387 -9.408 < 2e-16 ***
## birth_year -0.004371 0.001272 -3.437 0.000595 ***
## religionChristian -0.304440 0.080768 -3.769 0.000166 ***
## religionJewish -0.580632 0.149064 -3.895 9.98e-05 ***
## religionMormon -0.622124 0.170925 -3.640 0.000276 ***
## religionnone 0.033246 0.043426 0.766 0.443977
## activitystudent -0.058774 0.047897 -1.227 0.219861
## activityunemployed -0.706535 0.216765 -3.259 0.001126 **
## activityworking-class -0.423875 0.209736 -2.021 0.043348 *
## budgetlow -0.160007 0.097790 -1.636 0.101872
## budgetmedium 0.165608 0.094744 1.748 0.080552 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5411 on 3918 degrees of freedom
## Multiple R-squared: 0.6034, Adjusted R-squared: 0.6009
## F-statistic: 248.3 on 24 and 3918 DF, p-value: < 2.2e-16Now looking at this output you can see that our R^2 dropped drastically. Although .60 isn’t terrible, you can tell that food and service ratings are what is dominating our regressions.
The next step I wanted to do was run a training and test set on our data set.
set.seed(1)
n=length(RRDE$rating)
n1=2700
n2=n-n1
train=sample(1:n,n1)
m7=lm(rating~.,data=RRDE[train,])
summary(m7)##
## Call:
## lm(formula = rating ~ ., data = RRDE[train, ])
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.60386 -0.07570 -0.01157 0.04994 1.90309
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.874168 1.948945 5.066 4.33e-07 ***
## smokerTRUE -0.018268 0.030692 -0.595 0.551759
## drink_levelcasual drinker -0.061937 0.030474 -2.032 0.042209 *
## drink_levelsocial drinker -0.101196 0.031172 -3.246 0.001183 **
## dress_preferenceformal -0.006525 0.075507 -0.086 0.931148
## dress_preferenceinformal -0.155562 0.078722 -1.976 0.048248 *
## dress_preferenceno preference -0.119038 0.080834 -1.473 0.140973
## ambiencefriends 0.046512 0.026661 1.745 0.081175 .
## ambiencesolitary -0.021905 0.032399 -0.676 0.499027
## transporton foot -0.085072 0.039499 -2.154 0.031346 *
## transportpublic -0.181663 0.031173 -5.828 6.30e-09 ***
## marital_statussingle 0.155445 0.060826 2.556 0.010656 *
## marital_statuswidow 0.643030 0.111410 5.772 8.75e-09 ***
## hijosindependent -0.114208 0.104428 -1.094 0.274203
## hijoskids -0.324818 0.106349 -3.054 0.002278 **
## birth_year -0.004795 0.001009 -4.752 2.12e-06 ***
## religionChristian -0.156663 0.059628 -2.627 0.008654 **
## religionJewish -0.390398 0.116970 -3.338 0.000857 ***
## religionMormon -0.294024 0.135112 -2.176 0.029631 *
## religionnone -0.117977 0.034017 -3.468 0.000532 ***
## activitystudent 0.079406 0.038903 2.041 0.041336 *
## activityunemployed -0.478342 0.161422 -2.963 0.003070 **
## activityworking-class 0.323035 0.158886 2.033 0.042139 *
## budgetlow 0.062614 0.082684 0.757 0.448955
## budgetmedium 0.118878 0.080315 1.480 0.138951
## food_rating 0.381054 0.015334 24.850 < 2e-16 ***
## service_rating 0.455689 0.014570 31.275 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3506 on 2673 degrees of freedom
## Multiple R-squared: 0.8339, Adjusted R-squared: 0.8323
## F-statistic: 516.1 on 26 and 2673 DF, p-value: < 2.2e-16pred=predict(m7,newdat=RRDE[-train,])
obs=RRDE$rating[-train]
diff=obs-pred
percdiff=abs(diff)/obs
me=mean(diff)
rmse=sqrt(sum(diff**2)/n2)
mape=100*(mean(percdiff))
me # mean error## [1] -0.01413392rmse # root mean square error## [1] 0.3678476mape # mean absolute percent error ## [1] InfHere we see that our training and test sets did okay so our data set would be good at predicting but we would still like to dive further into other analysis.
Logistic Regression
As mentioned before, we have recode one of the data sets to be used in a logistic regression analysis by making our dependent variable binary.
m2=glm(rating~., family=binomial,data=RRDE3)
m2##
## Call: glm(formula = rating ~ ., family = binomial, data = RRDE3)
##
## Coefficients:
## (Intercept) smoker drink_level1
## 69.87837 -0.58323 0.22203
## drink_level2 dress_preference1 dress_preference2
## 0.01060 0.17308 0.25062
## dress_preference3 ambience1 ambience2
## 0.51823 0.91948 0.83211
## transport1 transport2 marital_status2
## -1.25954 -0.28712 0.04129
## marital_statuswidow hijos1 hijos2
## 2.75872 -0.95435 -2.33720
## birth_year religion1 activity1
## -0.04271 0.87638 10.14821
## activity2 activity3 budget1
## 12.13832 9.37795 0.19138
## budget2 food_rating service_rating
## -2.09213 1.51763 2.14975
##
## Degrees of Freedom: 3942 Total (i.e. Null); 3919 Residual
## Null Deviance: 4849
## Residual Deviance: 2025 AIC: 2073summary(m2)##
## Call:
## glm(formula = rating ~ ., family = binomial, data = RRDE3)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.1271 -0.2062 -0.1098 0.3141 3.4999
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 69.87837 266.57180 0.262 0.793216
## smoker -0.58323 0.21708 -2.687 0.007216 **
## drink_level1 0.22203 0.21634 1.026 0.304752
## drink_level2 0.01060 0.22241 0.048 0.962004
## dress_preference1 0.17308 0.23504 0.736 0.461516
## dress_preference2 0.25062 0.21875 1.146 0.251937
## dress_preference3 0.51823 0.45785 1.132 0.257691
## ambience1 0.91948 0.27926 3.293 0.000993 ***
## ambience2 0.83211 0.21899 3.800 0.000145 ***
## transport1 -1.25954 0.28488 -4.421 9.81e-06 ***
## transport2 -0.28712 0.30154 -0.952 0.341002
## marital_status2 0.04129 0.45160 0.091 0.927156
## marital_statuswidow 2.75872 0.68822 4.008 6.11e-05 ***
## hijos1 -0.95435 1.07941 -0.884 0.376620
## hijos2 -2.33719 1.11829 -2.090 0.036620 *
## birth_year -0.04271 0.00749 -5.702 1.18e-08 ***
## religion1 0.87638 0.24572 3.567 0.000362 ***
## activity1 10.14821 266.15825 0.038 0.969585
## activity2 12.13832 266.17031 0.046 0.963626
## activity3 9.37795 266.15823 0.035 0.971893
## budget1 0.19138 0.17623 1.086 0.277480
## budget2 -2.09213 0.48374 -4.325 1.53e-05 ***
## food_rating 1.51763 0.10348 14.666 < 2e-16 ***
## service_rating 2.14975 0.10568 20.342 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 4849.2 on 3942 degrees of freedom
## Residual deviance: 2024.7 on 3919 degrees of freedom
## AIC: 2072.7
##
## Number of Fisher Scoring iterations: 13Here we get our regression output but I think a training and test data set and calculating error give us a better idea about how well our data set is a predicting.
n=dim(RRDE3)[1]
n## [1] 3943n1=floor(n*(0.6))
n1## [1] 2365n2=n-n1
n2## [1] 1578train=sample(1:n,n1)
response=RRDE3$rating
XRRDE3 <- model.matrix(rating~.,data=RRDE3)[,-1]
xtrain <- XRRDE3[train,]
xnew <- XRRDE3[-train,]
ytrain <- response[train]
ynew <- response[-train]
## model fitted on the training data set
m9=glm(response~.,family=binomial,data=data.frame(response=ytrain,xtrain))
summary(m9)##
## Call:
## glm(formula = response ~ ., family = binomial, data = data.frame(response = ytrain,
## xtrain))
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.1472 -0.1891 -0.1009 0.2764 3.5448
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 95.54370 515.00490 0.186 0.852821
## smoker -0.28006 0.28844 -0.971 0.331578
## drink_level1 -0.06522 0.28915 -0.226 0.821554
## drink_level2 -0.07640 0.30562 -0.250 0.802589
## dress_preference1 0.25544 0.32042 0.797 0.425342
## dress_preference2 0.19136 0.29757 0.643 0.520171
## dress_preference3 1.43589 0.64527 2.225 0.026064 *
## ambience1 1.43661 0.38306 3.750 0.000177 ***
## ambience2 0.92837 0.30189 3.075 0.002104 **
## transport1 -1.50333 0.38934 -3.861 0.000113 ***
## transport2 -0.71146 0.41025 -1.734 0.082879 .
## marital_status2 -0.34982 0.60913 -0.574 0.565763
## marital_statuswidow 2.89613 0.89743 3.227 0.001250 **
## hijos1 -1.16799 1.11035 -1.052 0.292840
## hijos2 -2.40295 1.18518 -2.027 0.042611 *
## birth_year -0.05598 0.01079 -5.190 2.11e-07 ***
## religion1 1.21311 0.34362 3.530 0.000415 ***
## activity1 10.53501 514.56171 0.020 0.983665
## activity2 13.11259 514.57691 0.025 0.979670
## activity3 9.49395 514.56172 0.018 0.985279
## budget1 0.19441 0.23367 0.832 0.405403
## budget2 -2.52656 0.72788 -3.471 0.000518 ***
## food_rating 1.58027 0.13792 11.458 < 2e-16 ***
## service_rating 2.31552 0.14443 16.032 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 2915.2 on 2364 degrees of freedom
## Residual deviance: 1162.3 on 2341 degrees of freedom
## AIC: 1210.3
##
## Number of Fisher Scoring iterations: 14## create predictions for the test (evaluation) data set
ptest=predict(m9,newdata=data.frame(xnew),type="response")
## predicted probabilities
hist(ptest)
plot(ynew~ptest)
## coding as 1 if probability 0.5 or larger
gg1=floor(ptest+0.5)
ttt=table(ynew,gg1)
ttt## gg1
## ynew 0 1
## 0 1028 73
## 1 112 365error=(ttt[1,2]+ttt[2,1])/n2
error## [1] 0.117237bb=cbind(ptest,ynew)
bb## ptest ynew
## 2 2.203520e-04 0
## 5 6.280620e-01 0
## 7 1.072628e-02 0
## 8 1.072628e-02 0
## 12 1.069184e-03 0
## 14 1.069184e-03 0
## 16 1.072628e-02 0
## 20 6.280620e-01 1
## 22 3.478541e-01 1
## 24 3.478541e-01 1
## 25 3.478541e-01 1
## 26 3.478541e-01 1
## 31 8.446742e-02 0
## 34 5.077236e-03 0
## 37 5.077236e-03 0
## 40 5.077236e-03 0
## 41 5.077236e-03 0
## 42 5.077236e-03 0
## 43 5.077236e-03 0
## 50 5.077236e-03 0
## 52 5.077236e-03 0
## 53 5.077236e-03 0
## 54 5.077236e-03 0
## 62 5.077236e-03 0
## 64 5.077236e-03 0
## 70 5.077236e-03 0
## 72 5.077236e-03 0
## 86 5.077236e-03 0
## 88 5.077236e-03 0
## 89 5.077236e-03 0
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## 96 5.077236e-03 0
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## 105 5.077236e-03 0
## 106 5.077236e-03 0
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## 111 5.077236e-03 0
## 116 5.077236e-03 0
## 118 5.077236e-03 0
## 119 5.077236e-03 0
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## 130 5.077236e-03 0
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## 176 5.077236e-03 0
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## 186 5.077236e-03 0
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## 195 5.077236e-03 0
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## 2851 8.577979e-04 0
## 2 2.203520e-04 0
## 3358 1.736770e-07 0
## 3365 1.736770e-07 0
## 3366 1.736770e-07 0xbar=mean(ynew)
xbar## [1] 0.3022814axis=dim(n2)
ax=dim(n2)
ay=dim(n2)
axis[1]=1
ax[1]=xbar
ay[1]=bb1[1,2]
for (i in 2:n2) {
axis[i]=i
ax[i]=xbar*i
ay[i]=ay[i-1]+bb1[i,2]
}
aaa=cbind(bb1[,1],bb1[,2],ay,ax)
aaa[1:20,]## ay ax
## 2085 0.9992379 1 1 0.3022814
## 2086 0.9992379 1 2 0.6045627
## 2087 0.9992379 1 3 0.9068441
## 2092 0.9992379 1 4 1.2091255
## 2947 0.9973893 1 5 1.5114068
## 2957 0.9973893 1 6 1.8136882
## 1602 0.9929340 1 7 2.1159696
## 2628 0.9922509 0 7 2.4182510
## 1972 0.9921059 1 8 2.7205323
## 1975 0.9921059 1 9 3.0228137
## 1976 0.9921059 1 10 3.3250951
## 3021 0.9891040 1 11 3.6273764
## 2393 0.9885339 1 12 3.9296578
## 2395 0.9885339 1 13 4.2319392
## 2396 0.9885339 1 14 4.5342205
## 1991 0.9873438 1 15 4.8365019
## 1994 0.9873438 1 16 5.1387833
## 2860 0.9863914 0 16 5.4410646
## 2861 0.9863914 0 16 5.7433460
## 2862 0.9863914 0 16 6.0456274plot(axis,ay,xlab="number of cases",ylab="number of successes",main="Lift: Cum successes sorted by pred val/success prob")
points(axis,ax,type="l")
As we can see our error is right around 10% which I think tells us that our logistic model is also a good predictor. The problem is that both regressions we have run are still fairly simple.
CART Decision Trees
We decided that we wanted to focus in on a CART analysis to go above and beyond our regression analysis. We did similar things in this analysis such as using rating as our dependent variable and using our 14 variable data set again. He is our first tree:
library(tree)## Warning: package 'tree' was built under R version 3.4.2length(RRDE2$rating)## [1] 3943## Construct the tree
fullrtree <- tree(rating ~., data=RRDE2, mindev=0.1, mincut=1)
fullrtree <- tree(rating ~., data=RRDE2, mincut=1)
fullrtree## node), split, n, deviance, yval
## * denotes terminal node
##
## 1) root 3943 2892.00 0.85520
## 2) food_rating < 0.5 1797 155.00 0.06233
## 4) service_rating < 0.5 1713 27.72 0.01284 *
## 5) service_rating > 0.5 84 37.57 1.07100 *
## 3) food_rating > 0.5 2146 661.70 1.51900
## 6) service_rating < 1.5 1196 329.10 1.23800
## 12) food_rating < 1.5 653 137.30 1.09300 *
## 13) food_rating > 1.5 543 161.60 1.41300 *
## 7) service_rating > 1.5 950 119.60 1.87300 *plot(fullrtree, col=8)
text(fullrtree, pretty=1)
As you can see from this tree, the main two predictors of overall rating are food rating and service rating which makes a lot of sense. The sub-ratings are going to be a very good predictor of how well a resturaunt is rated overall. After seeing this we wanted to run decision trees showing how the food rating and service rating were predicted so that they could supplement the overall rating. For these two trees we held rating and the opposite sub-rating out to get a better tree. Here are those two trees with the first one predicting food rating and the second, service rating.
frtree <- tree(food_rating ~.-rating-service_rating, data=RRDE2, mindev=0.1, mincut=1)
frtree <- tree(food_rating ~.-rating-service_rating, data=RRDE2, mincut=1)
frtree## node), split, n, deviance, yval
## * denotes terminal node
##
## 1) root 3943 3085.0 0.8844
## 2) budget: 0 1980 708.3 0.2768
## 4) hijos: 1 538 301.8 1.0190
## 8) birth_year < 1988.5 226 129.4 0.6770 *
## 9) birth_year > 1988.5 312 126.9 1.2660 *
## 5) hijos: 2 1442 0.0 0.0000 *
## 3) budget: 1,2 1963 908.7 1.4970 *plot(frtree, col=8)
text(frtree, pretty=1)
srtree <- tree(service_rating ~.-rating-food_rating, data=RRDE2, mindev=0.1, mincut=1)
srtree <- tree(service_rating ~.-rating-food_rating, data=RRDE2, mincut=1)
srtree## node), split, n, deviance, yval
## * denotes terminal node
##
## 1) root 3943 2678.00 0.7616
## 2) hijos: 2 1633 398.80 0.1488
## 4) budget: 0 1442 0.00 0.0000 *
## 5) budget: 1 191 125.80 1.2720 *
## 3) hijos: 0,1 2310 1232.00 1.1950
## 6) birth_year < 1965.5 232 91.52 1.6030 *
## 7) birth_year > 1965.5 2078 1098.00 1.1490
## 14) transport: 1,2 1815 896.90 1.1000 *
## 15) transport: 0 263 165.70 1.4900 *plot(srtree, col=8)
text(srtree, pretty=1)
These 3 trees together could be helpful to predict overall rating but after doing this we got the idea of running a tree with the rating as our dependent and removing the sub-ratings to get a better prediction. This tree is below:
rtree <- tree(rating ~.-food_rating-service_rating, data=RRDE2, mindev=0.1, mincut=1)
rtree <- tree(rating ~.-food_rating-service_rating, data=RRDE2, mincut=1)
rtree## node), split, n, deviance, yval
## * denotes terminal node
##
## 1) root 3943 2892.00 0.8552
## 2) hijos: 2 1633 400.90 0.1506
## 4) budget: 0 1442 0.00 0.0000 *
## 5) budget: 1 191 121.20 1.2880 *
## 3) hijos: 0,1 2310 1108.00 1.3530
## 6) transport: 1,2 2037 971.30 1.3040
## 12) birth_year < 1965.5 222 71.32 1.7340 *
## 13) birth_year > 1965.5 1815 853.90 1.2520 *
## 7) transport: 0 273 95.28 1.7180 *plot(rtree, col=8)
text(rtree, pretty=1)
As you can see this tree used a couple more and obviously different variables than our first tree. From this tree one could conclude that someone with kids (hijos=2), uses public transportation or owns a car (transport= 1, 2), and was born before 1966 will give the highest rating. These conclusions sound similar to what other groups had been seeing as well.
To finish of my analysis I wanted to focus on the largest type of cuisine there was, Mexican. I wanted to run more decision trees and see how they compared to the ones we ran before.
First I condensed the data set down to 900 entries, the ones that were Mexican cuisine. Then I did the same recode as before and ran the first tree using rating as a dependent variable and removing the sub-ratings again.
MFD <- read.csv("~/Business Analytics/Mexican Food Data.csv")
MFD$smoker=recode(MFD$smoker,"'FALSE'=0; 'TRUE'=1")
MFD$drink_level=recode(MFD$drink_level,"'abstemious'=0; 'casual drinker'=1; 'social drinker'=2")
MFD$dress_preference=recode(MFD$dress_preference,"'no preference'=0; 'informal'=1; 'formal'=2; 'elegant'=3")
MFD$ambience=recode(MFD$ambience,"'solitary'=0; 'friends'=1; 'family'=2")
MFD$transport=recode(MFD$transport,"'on foot'=0; 'public'=1; 'car owner'=2")
MFD$marital_status=recode(MFD$marital_status,"'single'=0; 'widowed'=1; 'married'=2")
MFD$hijos=recode(MFD$hijos,"'dependent'=0; 'independent'=1; 'kids'=2")
MFD$activity=recode(MFD$activity,"'unemployed'=0; 'student'=1; 'working-class'=2; 'professional'=3")
MFD$budget=recode(MFD$budget,"'low'=0; 'medium'=1; 'high'=2")
MFD$religion=recode(MFD$religion,"'none'=0; 'Catholic'=1; 'Christian'=1; 'Jewish'=1; 'Mormon'=1")
length(MFD$rating)## [1] 900## Construct the tree
rtree <- tree(rating ~.-food_rating-service_rating, data=MFD, mindev=0.1, mincut=1)
rtree <- tree(rating ~.-food_rating-service_rating, data=MFD, mincut=1)
rtree## node), split, n, deviance, yval
## * denotes terminal node
##
## 1) root 900 551.900 1.1890
## 2) drink_level: 1 306 185.600 0.9314
## 4) birth_year < 1988.5 86 41.450 0.4767
## 8) dress_preference: 1 44 7.886 0.1591 *
## 9) dress_preference: 0,2 42 24.480 0.8095
## 18) birth_year < 1987 27 10.740 0.5185 *
## 19) birth_year > 1987 15 7.333 1.3330 *
## 5) birth_year > 1988.5 220 119.400 1.1090 *
## 3) drink_level: 0,2 594 335.600 1.3220
## 6) dress_preference: 0 186 116.200 1.1240
## 12) ambience: 2 103 68.190 0.8350
## 24) activity: 3 18 1.778 0.1111 *
## 25) activity: 1,2 85 54.990 0.9882
## 50) transport: 0 11 1.636 0.1818 *
## 51) transport: 1,2 74 45.140 1.1080 *
## 13) ambience: 0,1 83 28.720 1.4820 *
## 7) dress_preference: 1,2,3 408 208.800 1.4120 *plot(rtree, col=8)
text(rtree, pretty=1)
As you can see this tree is a bit more complicated. There are more branches and it can get confusing. This is a good time to prune the tree. First I want to look at the plot to figure out which alpha value to use.
rcut <- prune.tree(rtree)
rcut## $size
## [1] 9 8 7 6 5 3 2 1
##
## $dev
## [1] 431.4380 437.8401 446.0568 455.1477 466.5759 496.4195 521.1430 551.8889
##
## $k
## [1] -Inf 6.402116 8.216737 9.090934 11.428162 14.921790 24.723517
## [8] 30.745890
##
## $method
## [1] "deviance"
##
## attr(,"class")
## [1] "prune" "tree.sequence"plot(rcut)
Looking at the plot above I chose k=5 because that comes after the largest drop off but it gradually goes down from there. Then I made the tree using this alpha.
rcut <- prune.tree(rtree,k=5)
plot(rcut)
text(rcut, pretty=1)
rcut## node), split, n, deviance, yval
## * denotes terminal node
##
## 1) root 900 551.900 1.1890
## 2) drink_level: 1 306 185.600 0.9314
## 4) birth_year < 1988.5 86 41.450 0.4767
## 8) dress_preference: 1 44 7.886 0.1591 *
## 9) dress_preference: 0,2 42 24.480 0.8095
## 18) birth_year < 1987 27 10.740 0.5185 *
## 19) birth_year > 1987 15 7.333 1.3330 *
## 5) birth_year > 1988.5 220 119.400 1.1090 *
## 3) drink_level: 0,2 594 335.600 1.3220
## 6) dress_preference: 0 186 116.200 1.1240
## 12) ambience: 2 103 68.190 0.8350
## 24) activity: 3 18 1.778 0.1111 *
## 25) activity: 1,2 85 54.990 0.9882
## 50) transport: 0 11 1.636 0.1818 *
## 51) transport: 1,2 74 45.140 1.1080 *
## 13) ambience: 0,1 83 28.720 1.4820 *
## 7) dress_preference: 1,2,3 408 208.800 1.4120 *As you can see the tree didn’t actually change but this would still be a good tree to minimize error. For the fun of it to show how the pruning works I will use an alpha of 10.
rcut <- prune.tree(rtree,k=10)
plot(rcut)
text(rcut, pretty=1)
rcut## node), split, n, deviance, yval
## * denotes terminal node
##
## 1) root 900 551.900 1.1890
## 2) drink_level: 1 306 185.600 0.9314
## 4) birth_year < 1988.5 86 41.450 0.4767 *
## 5) birth_year > 1988.5 220 119.400 1.1090 *
## 3) drink_level: 0,2 594 335.600 1.3220
## 6) dress_preference: 0 186 116.200 1.1240
## 12) ambience: 2 103 68.190 0.8350
## 24) activity: 3 18 1.778 0.1111 *
## 25) activity: 1,2 85 54.990 0.9882 *
## 13) ambience: 0,1 83 28.720 1.4820 *
## 7) dress_preference: 1,2,3 408 208.800 1.4120 *These decision trees for the mexican food used many different variables to predict rating so it is tough to tell if our initial assessment of the overall data set was good or not. Age popped up in both trees but drink level effected Mexican resturaunts the most while it didn’t seem to effect the overall data set at all.
To conclude, we had 3 different types of analysis that concluded similar things and I tried to include different ways to double check these as well. I think this data set was a good way to let us showcase and practice the tools we learned this semester.