Predicting Whether a Customer Who Receives the Catalog Will Use the Coupon

Project Objective

To investigate the relationship between customers who receive a catalog and customers who use a coupon at Simmons's apparel stores

Step 1: Install and load required libraries

library(readxl)
library(Hmisc) #allows us to call the correlation function

## Warning: package 'Hmisc' was built under R version 4.3.3

## 
## Attaching package: 'Hmisc'

## The following objects are masked from 'package:base':
## 
##     format.pval, units

library(pscl) #allows us to call the pseudo R-square package to evaluate our model

## Warning: package 'pscl' was built under R version 4.3.3

## Classes and Methods for R originally developed in the
## Political Science Computational Laboratory
## Department of Political Science
## Stanford University (2002-2015),
## by and under the direction of Simon Jackman.
## hurdle and zeroinfl functions by Achim Zeileis.

library(pROC) #allows us to run the Area Under Curve (AUC) package to get the plot and AUC score

## Warning: package 'pROC' was built under R version 4.3.3

## Type 'citation("pROC")' for a citation.

## 
## Attaching package: 'pROC'

## The following objects are masked from 'package:stats':
## 
##     cov, smooth, var

Step 2: Import & clean the data

# Import the Data
Sim_df <- read_excel("Chap 15.9 Simmons.xlsx")

Step 3: Summarize the data

summary(Sim_df)

##     Customer         Spending          Card         Coupon   
##  Min.   :  1.00   Min.   :1.058   Min.   :0.0   Min.   :0.0  
##  1st Qu.: 25.75   1st Qu.:2.059   1st Qu.:0.0   1st Qu.:0.0  
##  Median : 50.50   Median :2.805   Median :0.5   Median :0.0  
##  Mean   : 50.50   Mean   :3.334   Mean   :0.5   Mean   :0.4  
##  3rd Qu.: 75.25   3rd Qu.:4.468   3rd Qu.:1.0   3rd Qu.:1.0  
##  Max.   :100.00   Max.   :7.076   Max.   :1.0   Max.   :1.0

This gives the descriptive statistics of the data

sapply(Sim_df, sd)

##   Customer   Spending       Card     Coupon 
## 29.0114920  1.7412979  0.5025189  0.4923660

This gives us the standard deviation using the "sd" function

xtabs(~Coupon + Card, data = Sim_df)

##       Card
## Coupon  0  1
##      0 36 24
##      1 14 26

Step 4: Building the model

The "glm" function enables us to call the logistic regression model. The family is binomial as we are dealing with binary outcome variables

Sim_logit <- glm(Coupon ~ Spending + Card, data = Sim_df, family = "binomial")
summary(Sim_logit)

## 
## Call:
## glm(formula = Coupon ~ Spending + Card, family = "binomial", 
##     data = Sim_df)
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  -2.1464     0.5772  -3.718 0.000201 ***
## Spending      0.3416     0.1287   2.655 0.007928 ** 
## Card          1.0987     0.4447   2.471 0.013483 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 134.60  on 99  degrees of freedom
## Residual deviance: 120.97  on 97  degrees of freedom
## AIC: 126.97
## 
## Number of Fisher Scoring iterations: 4

Interpretation: They are all significant at alpha = 0.05

Step 5: Interpreting the Logistic Regression Equation using odds ratios only

exp(coef(Sim_logit))

## (Intercept)    Spending        Card 
##   0.1169074   1.4072585   3.0003587

Interpretation: For every customer that has a "Simmons Credit Card" the odds of the outcome are multipied by about 3.00. Therefore, having a card increases the odds of the outcome by 200% (three times).

For every one unit increase in "Spending", the odds of the outcome occurring are multipllied by approximately 1.4073. For each additional dollar spent, the odds of the outcome increase by 40.73%.

Odds ratios and 95% CI

exp(cbind(OR = coef(Sim_logit), confint(Sim_logit)))

## Waiting for profiling to be done...

##                    OR      2.5 %    97.5 %
## (Intercept) 0.1169074 0.03492214 0.3420819
## Spending    1.4072585 1.10120789 1.8311893
## Card        3.0003587 1.27732463 7.3760631

Interpretation: The CI for "Spending" does not contain the value of 1, we can conlude that x1 has a significant relationship with the estimated odds ratio. The CI for "Card" does not contain the value of 1, we can conclude that x2 has a significant relationship with the estimated odds ratio.