Predicting Customers Retention for Tire Rack
##Project Objective
To investigate Question 1 & 2: Develop the Model & Assesss Predictior Significance
Step 1: Install and load required libraries
#install.packages("Hmisc")
#install.packages('pscl')
if(!require(pROC)) install.packages('pROC')## Loading required package: pROC## 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, varlibrary(readxl)
library(Hmisc)## Warning: package 'Hmisc' was built under R version 4.3.3##
## Attaching package: 'Hmisc'## The following objects are masked from 'package:base':
##
## format.pval, unitslibrary(pscl)## 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.Step2: Import & clean Data
rating_df <- read_excel(file.choose())
r_df <- subset(rating_df, select = -c(Tire))Step 3: Data Summary
head(r_df)## # A tibble: 6 × 4
## Wet Noise Buy_Again Purchase
## <dbl> <dbl> <dbl> <dbl>
## 1 8 7.2 6.1 0
## 2 8 7.2 6.6 1
## 3 7.6 7.5 6.9 1
## 4 6.6 5.4 6.6 0
## 5 5.8 6.3 4 0
## 6 6.3 5.7 4.5 0summary(r_df)## Wet Noise Buy_Again Purchase
## Min. :4.300 Min. :3.600 Min. :1.400 Min. :0.0000
## 1st Qu.:6.450 1st Qu.:6.000 1st Qu.:3.850 1st Qu.:0.0000
## Median :7.750 Median :7.100 Median :6.150 Median :0.0000
## Mean :7.315 Mean :6.903 Mean :5.657 Mean :0.4412
## 3rd Qu.:8.225 3rd Qu.:7.925 3rd Qu.:7.400 3rd Qu.:1.0000
## Max. :9.200 Max. :8.900 Max. :8.900 Max. :1.0000Step 4: Feature selection (i.e., correlation analysis)
corr <- rcorr(as.matrix(r_df))
corr## Wet Noise Buy_Again Purchase
## Wet 1.00 0.76 0.91 0.74
## Noise 0.76 1.00 0.83 0.72
## Buy_Again 0.91 0.83 1.00 0.83
## Purchase 0.74 0.72 0.83 1.00
##
## n= 68
##
##
## P
## Wet Noise Buy_Again Purchase
## Wet 0 0 0
## Noise 0 0 0
## Buy_Again 0 0 0
## Purchase 0 0 0Step 5: Logistic Regression Model
model <- glm(Purchase ~ Wet + Noise, data = r_df, family = binomial)
summary(model)##
## Call:
## glm(formula = Purchase ~ Wet + Noise, family = binomial, data = r_df)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -39.4982 12.4779 -3.165 0.00155 **
## Wet 3.3745 1.2641 2.670 0.00760 **
## Noise 1.8163 0.8312 2.185 0.02887 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 93.325 on 67 degrees of freedom
## Residual deviance: 27.530 on 65 degrees of freedom
## AIC: 33.53
##
## Number of Fisher Scoring iterations: 8Intepretation: All the independent variables were significant (p-value < 0.05)Question 3: Overall Model Significance
Likely-hood Ratio Test
# Fit a null model
n_model <- glm(Purchase ~ 1, data = r_df, family = binomial)
#Ratio Test
anova(n_model, model, test = "Chisq")## Analysis of Deviance Table
##
## Model 1: Purchase ~ 1
## Model 2: Purchase ~ Wet + Noise
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 67 93.325
## 2 65 27.530 2 65.795 5.162e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Psuedo R-Squared
## Psuedo R-Squared
pR2(model)## fitting null model for pseudo-r2## llh llhNull G2 McFadden r2ML r2CU
## -13.7649516 -46.6623284 65.7947536 0.7050093 0.6199946 0.8305269Area Under the Curve (AUC)
roc_curve <- roc(r_df$Purchase, fitted(model))## Setting levels: control = 0, case = 1## Setting direction: controls < casesplot(roc_curve)
auc(roc_curve)## Area under the curve: 0.9741Question 4 & 5: Predicted Values
new_data1 <- data.frame(Wet = 7.0, Noise = 7.0, Purchase = 1)
new_data2 <- data.frame(Wet = 8.0, Noise = 8.0, Purchase = 1)
prob1 <- predict(model, newdata = new_data1, type = "response")
prob1*100 ## 1
## 4.058753prob2 <- predict(model, newdata = new_data2, type = "response")
prob2*100## 1
## 88.36964Question 6: Odds Ratio
coefficients <- summary(model)$coefficients
coefficients## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -39.498250 12.477885 -3.165460 0.001548378
## Wet 3.374494 1.264074 2.669538 0.007595577
## Noise 1.816276 0.831172 2.185199 0.028874250odds_ratio_Wet <- exp(coefficients["Wet", "Estimate"])
odds_ratio_Noise <- exp(coefficients["Noise", "Estimate"])
odds_ratio_Noise # 6.15%## [1] 6.148919odds_ratio_Wet # 29.21%## [1] 29.20949