Class Exercise 15
Project Objective
To investigate the relationship between respondents buying a tire again and the tire's wet and noise ratings at The Tire Rack.Question 1 & 2: Develop the model
Step 1: Install and load required libraries
#install.packages("readxl")
#install.packages("Hmisc")
#install.packages("pscl")
#if(!require(pROC)) install.packages("pROC")
library(readxl) # import excel files
library(Hmisc) # call 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, unitslibrary(pscl) # call the pseudo R-squared package to evaluate the 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) # run the area under the curve(AUC) package to plot and get the 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, varStep 2: Import and clean the data
TireRatings_df <- read_excel("Class Exercise 15_TireRatings.xlsx")
tire_df <- subset(TireRatings_df, select = -(Tire)) # remove irrelevant columnStep 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 the features are presented in the table below.
Variable | Definition
------------ | ------------
1. Wet | The average of the ratings for each tire’s wet traction performance
2. Noise | The average of the ratings for the noise level generated by each tire
3. Buy_Again | The average of the buy-again responses
4. Purchase | The respondent buying the tire again (1: yes and 0: no)summary(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: The average wet rating is 7.31 and the average noise rating is 6.9. Step 4: Feature seleciton, 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: All predictors are significant with the target variable but there is multicollinearity between the independent variablesStep 5: Build the logistic regression model
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: 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 0.8305269Interpretation: The McFadden R-squared is 0.7050, so 70.5% of the variablility in the outcome relative a the model with no predictors. This is not considered a good fit because it is not between 0.2 and 0.4.Area under the curve
# Compute ROC curve and AUC score
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: 0.9741Interpretation: The AUC score is 0.97, which means it has a very high level of accuracy in predicting tire purchases.Question 4 & 5:Predicting with new data
# Given the following data
new_data1 <- data.frame(Wet = 7, Noise = 7) # Question 4
new_data2 <- data.frame(Wet = 8, Noise = 8) # Question 5
# Predict the probablility
prob1 <- predict(model, newdata = new_data1, type = "response") # Question 4
prob1*100 ## 1
## 4.058753prob2 <- predict(model, newdata = new_data2, type = "response") # Question 5
prob2*100## 1
## 88.36964Interpretation:
4) There's a 4.06% probability that customer will purchase a tire again with wet and noise ratings of 7.
5) There's a 88.37% probability that customer will purchase a tire again with wet and noise ratings of 8.