README.md

Bank Marketing Regression with R

This project was created for an upper-division statistics course at UT. We used data from UCI's dataset on their Machine Learning Repository. We are trying to predict whether customers that are called to promote creating a new bank account would follow through based on many attributes.

The script in this repo is replicated below in a more readable form:

1. Download csv and view

   marketing <- read.csv("https://raw.githubusercontent.com/MichaelZetune/Bank-Regression-with-R/master/Bank_Data.csv")
   View(marketing)

2. Analyze and clean variables:

We can keep the following variables as is for now:

• age: (numeric)
• job : type of job (categorical: 'admin.','blue-collar','entrepreneur','housemaid','management','retired','self-employed','services','student','technician','unemployed','unknown')
• marital : marital status (categorical: 'divorced','married','single','unknown'; note: 'divorced' means divorced or widowed)
• education: (categorical: 'basic.4y','basic.6y','basic.9y','high.school','illiterate','professional.course','university.degree','unknown')
• default: has credit in default? (categorical: 'no','yes','unknown')
• housing: has housing loan? (categorical: 'no','yes','unknown')
• loan: has personal loan? (categorical: 'no','yes','unknown') related with the last contact of the current campaign:
• contact: contact communication type (categorical: 'cellular','telephone')
• month: last contact month of year (categorical: 'jan', 'feb', 'mar', ..., 'nov', 'dec')
• day_of_week: last contact day of the week (categorical: 'mon','tue','wed','thu','fri')

Other attributes:

• campaign: number of contacts performed during this campaign and for this client (numeric, includes last contact)
• previous: number of contacts performed before this campaign and for this client (numeric)
• poutcome: outcome of the previous marketing campaign (categorical: 'failure','nonexistent','success') social and economic context attributes
• emp.var.rate: employment variation rate - quarterly indicator (numeric)
• cons.price.idx: consumer price index - monthly indicator (numeric)
• cons.conf.idx: consumer confidence index - monthly indicator (numeric)
• euribor3m: euribor 3 month rate - daily indicator (numeric)
• nr.employed: number of employees - quarterly indicator (numeric)

We need to do some cleaning for duration, pdays, and make.account:

duration: last contact duration, in seconds (numeric). Important note: this attribute highly affects the output target (e.g., if duration=0 then y='no'). Yet, the duration is not known before a call is performed. Also, after the end of the call y is obviously known. Thus, this input should only be included for benchmark purposes and should be discarded if the intention is to have a realistic predictive model.

Thus, we should discard duration:

marketing$duration <- NULL

pdays: number of days that passed by after the client was last contacted from a previous campaign (numeric; 999 means client was not previously contacted)

Since 999 is an arbitrary dummy varaible, we should make it NA:

marketing$pdays[marketing$pdays == 999] <- NA

Since the vast majority of the data points are NA now, we will discard this column:

marketing$pdays <- NULL

make.account - has the client subscribed a term deposit? (binary: 'yes','no')

Let's make this a clearer dummy variable to suit it for logistic regression. We'll change the name of the column slightly and delete the original column to make this happen:

marketing$made.account[marketing$make.account == 'yes'] <- 1
marketing$made.account[marketing$make.account == 'no'] <- 0
marketing$make.account <- NULL

Now we will create the initial model, using all of the variables:

model1 <- glm(made.account ~ ., data=marketing, family='binomial')
summary(model1)

3. Check Assumptions:

Assumption 1: The dependent variable should be binary

• This is true because made.account is now 0 or 1

Assumption 2: Observations should be independent of each other

• Since customers are unrelated individuals in our data, this is true

Assumption 3: No multicollinearity among independent variables

library(car)
vif(model1) # returns error, fix is below

VIF returns an error with aliased coefficients, so we need to find where the perfect multicollinearity is:

alias(model1)

We find that loan is "unknown" if and only if housing is "unknown". So we should eliminate rows from the dataset where housing is unknown

marketing <- subset(marketing, marketing$housing != 'unknown')
model1 <- glm(made.account ~ ., data=marketing, family='binomial')
alias(model1)

Now use a correlation matrix to verify minimal multicollinearity in general:

marketing.numeric.bool <- unlist(lapply(marketing, is.numeric))
marketing.numeric <- marketing[ , marketing.numeric.bool]
cor(marketing.numeric)

Assumption 4: Large data set

• The marketing data set has over 4000 rows, which is a very large data set for this problem

4. Create a backward, forward, and 'both' model and hold on to them to assess performance later

null <- glm(made.account ~ 1, data=marketing, family='binomial')
full <- glm(made.account ~ ., data=marketing, family='binomial')

backward.model <- step(full, scope=list(lower=null, upper=full), direction='backward')
summary(backward.model)
AIC(backward.model)

forward.model <- step(null, scope = list(lower=null, upper=full), direction = 'forward')
summary(forward.model)
AIC(forward.model)

both.model <- step(null, scope=list(lower=null, upper=full), direction='both')
summary(both.model)
AIC(both.model)

5. Exhaustive Search for Best Attributes

Now we will try an exhaustive search of all variables in the dataset. A warning was returned in regards to linear dependencies, so we had to exclude the housing and loan columns from the analysis

install.packages("leaps")
library(leaps)

This next command will take some time to run, but it's retreiving the best subset while considering up to 20 variables in the dataset.

regsubsets.output <- regsubsets(made.account ~ age + job + marital + education + default + month + day_of_week + campaign + previous + poutcome + emp.var.rate + cons.price.idx + euribor3m + nr.employed, data=marketing, nvmax=20)

Use outmat variable to see the best subset of variables for 1,2 ... 8 variables

best.subset.summary <- summary(regsubsets.output)
best.subset.summary$outmat

Use Adjusted R^2 to find the best model from regsubsets

best.subset.overall <- which.max(best.subset.summary$adjr2)
best.subset.overall

The regsubsets function suggests using 19 of the variables. These variables create the logistic regression. Many of these variables are dummy variables, so the final model is actually looks smaller:

subset.model <- glm(made.account ~ age + job + month + campaign + previous + poutcome + emp.var.rate + euribor3m + nr.employed, data=marketing, family='binomial')
summary(subset.model)

6. Analyze Models

We now have four models to consider: forward.model, backward.model, both.model, and subset.model. Compare AIC and R^2:

# AIC Comparison
AIC(forward.model) # 2230.536
AIC(backward.model) # 2224.604
AIC(both.model) #2230.536
AIC(subset.model) #2256.057

# Pseudo R^2 Comparison
# forward.model
1-(2196.5/2783.7) # = .2109
# backward.model
1-(2188.6/2783.7) # = .2138
# both.model
1-(2196.5/2783.7) # = .2109
# subset.model
1-(2198.1/2783.7) # = .2104

Additionally, predictive accuracy is listed below. They are approximately the same across models.

# Naive model
sum(marketing$made.account == 0)/nrow(marketing) #0.8899

# forward.model
predicted.frwd <- (predict(forward.model, type = 'response') >= 0.5)
actual.frwd <- (marketing$made.account == 1)
sum(predicted.frwd == actual.frwd) / nrow(marketing) #0.9041

# backward.model
predicted.bwrd <- (predict(backward.model, type = 'response') >= 0.5)
actual.bwrd <- (marketing$made.account == 1)
sum(predicted.bwrd == actual.bwrd) / nrow(marketing) #0.9033

# both.model
predicted.both <- (predict(both.model, type = 'response') >= 0.5)
actual.both <- (marketing$made.account == 1)
sum(predicted.both == actual.both) / nrow(marketing) #0.9041

# subset.model
predicted.sub <- (predict(subset.model, type = 'response') >= 0.5)
actual.sub <- (marketing$made.account == 1)
sum(predicted.sub == actual.sub) / nrow(marketing) #0.9021

7. Conclusion

Since the pseudo R^2s and predictive accuracy are about the same, we use AIC to judge. The backward.model clearly has is the best at modeling our bank marketing information. Cheers!

summary(backward.model)