Predicting Tire Rating at Tire Rack
Project Objective
To develop a logistic regression model to predict the likelihood of a customer purchasing a tire again based on its Wet and Noise performance ratingsQuestion 1 & 2: Develop the Model & Access Predictor Significance
Step 1: Install and load the libraries
#install.packages("readxl")
#install.packages("Hmisc")
#install.packages("pscl")
#if(!require(pROC)) install.packages("pROC")
library(readxl) #allows us to import excel files## Warning: package 'readxl' was built under R version 4.4.2library(Hmisc) #allows us to call the correlation function## Warning: package 'Hmisc' was built under R version 4.4.2##
## Attaching package: 'Hmisc'## The following objects are masked from 'package:base':
##
## format.pval, unitslibrary(pscl) #allows us to call the pseudo R-square package to evaluate our model## Warning: package 'pscl' was built under R version 4.4.2## 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 the curve (AUC) package to get the plot and AUC score## Warning: package 'pROC' was built under R version 4.4.2## Type 'citation("pROC")' for a citation.##
## Attaching package: 'pROC'## The following objects are masked from 'package:stats':
##
## cov, smooth, varStep 2: Import the data and clean the data
TireRatings_df <- read_excel(file.choose())
Tire_df <- subset(TireRatings_df, select = -c(Tire)) #drop irrelevant column##Step 3: Summarize the data
head(Tire_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 0Data Description: A description of some of the features are presented in the table below.
#Step 4: Summarize the data (i.e., descriptive statistics)
head(Tire_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(Tire_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. :1.0000Interpretation:#Step 5: Feature selection (i.e., correlation analysis)
corr <- rcorr(as.matrix(Tire_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 0Interpretation#Step 6: Build the logistic regression
model <- glm(Purchase ~ Wet + Noise, data = Tire_df, family = binomial)
summary(model)##
## Call:
## glm(formula = Purchase ~ Wet + Noise, family = binomial, data = Tire_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: 8Interpretation:Question 3: Overall Model Significance
Likelihood Ratio Test
# Fit a null model
null_model <- glm(Purchase ~ 1, data = Tire_df, family = binomial)
# Perform a likelihood ratio test
anova(null_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 ' ' 1InterpretationPsedudo-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 0.8305269Interpretation:Area Under the Curve (AUC)
roc_curve <- roc(Tire_df$Purchase, fitted(model))## Setting levels: control = 0, case = 1## Setting direction: controls < casesplot(roc_curve)
auc(roc_curve)## Area under the curve: 0.9741InterpretationQuestion 4 & 5: Predicting with New Information
# Given the following new tire information
new_data <- data.frame(Wet = 7, Noise = 7)
# Predict the probability
# probability that ...
prob <- predict(model, newdata = new_data, type = "response")
prob * 100## 1
## 4.058753Interpretation:# Coefficients from the model
intercept <- -39.4982
wet_coeff <- 3.3745
noise_coeff <- 1.8163
# Predictor values
wet_rating <- 8
noise_rating <- 8
# Compute the logit
logit <- intercept + (wet_coeff * wet_rating) + (noise_coeff * noise_rating)
# Compute the probability using the logistic function
probability <- exp(logit) / (1 + exp(logit))
# Print the result
probability## [1] 0.8837262