Project Objectives
To investigate the relationship between wet traction performance, noise level, and customer purchasing likelihood.
Question 1 & 2: Develop the logistic regression model
Step 1: Install and load required libraries
#install.packages("readxl")
#install.packages("Hmisc")
#install.packages("pscl")
library(readxl)
library(Hmisc)
##
## Attaching package: 'Hmisc'
## The following objects are masked from 'package:base':
##
## format.pval, units
library(pscl)
## 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)
## 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
Class_Exercise_15_TireRatings <- read_excel("/Users/amritahimmatraopet/Desktop/R Markdown/Class Exercise 15_TireRatings.xlsx")
Class_Exercise_15_TireRatings <- subset(Class_Exercise_15_TireRatings, select = -c(Tire, Buy_Again))
Step 3: Summarize the data
head(Class_Exercise_15_TireRatings)
## # A tibble: 6 × 3
## Wet Noise Purchase
## <dbl> <dbl> <dbl>
## 1 8 7.2 0
## 2 8 7.2 1
## 3 7.6 7.5 1
## 4 6.6 5.4 0
## 5 5.8 6.3 0
## 6 6.3 5.7 0
Data Description: A dexcription of some of the features presented in the table below.
Variable | Definition
1. Wet | Tire's wet traction performance
2. Noise | Tire's noise level
3. Buy Again | Whether customer wants to buy again
4. Purchase | Likeliness for customer to purchase (1: yes and 0: no)
summary(Class_Exercise_15_TireRatings)
## Wet Noise Purchase
## Min. :4.300 Min. :3.600 Min. :0.0000
## 1st Qu.:6.450 1st Qu.:6.000 1st Qu.:0.0000
## Median :7.750 Median :7.100 Median :0.0000
## Mean :7.315 Mean :6.903 Mean :0.4412
## 3rd Qu.:8.225 3rd Qu.:7.925 3rd Qu.:1.0000
## Max. :9.200 Max. :8.900 Max. :1.0000
Interpretation: The median Wet Traction is 7.75 and the median Noise Level is 7.10
Step 4: Feature selection (i.e., correlation analysis)
corr <- rcorr(as.matrix(Class_Exercise_15_TireRatings))
corr
## Wet Noise Purchase
## Wet 1.00 0.76 0.74
## Noise 0.76 1.00 0.72
## Purchase 0.74 0.72 1.00
##
## n= 68
##
##
## P
## Wet Noise Purchase
## Wet 0 0
## Noise 0 0
## Purchase 0 0
Step 5: Build the logistic regression model
model <- glm(Purchase ~ Wet + Noise, data = Class_Exercise_15_TireRatings, family = binomial)
summary(model)
##
## Call:
## glm(formula = Purchase ~ Wet + Noise, family = binomial, data = Class_Exercise_15_TireRatings)
##
## 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: 8
Interpretation: All the independent variables were significant (p value < 0.05).
Question 3: Overall Model Significance
Pseudo-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 0.8305269
The McFadden R-Squared value is 0.705, meaning that our LR model explains about 70.5% of the variability in the outcome relative to a model with no predictors. This is considered a strong fit.