Question 1 & 2: Develop the Model & Assess Predictor
Significance
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-squae 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
tire_df <- read_excel("Class Exercise 15_TireRatings.xlsx")
tire_df
## # A tibble: 68 × 5
## Tire Wet Noise Buy_Again Purchase
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 BFGoodrich g-Force Super Sport A/S 8 7.2 6.1 0
## 2 BFGoodrich g-Force Super Sport A/S H&V 8 7.2 6.6 1
## 3 BFGoodrich g-Force T/A KDWS 7.6 7.5 6.9 1
## 4 Bridgestone B381 6.6 5.4 6.6 0
## 5 Bridgestone Insignia SE200 5.8 6.3 4 0
## 6 Bridgestone Insignia SE200-02 6.3 5.7 4.5 0
## 7 Bridgestone Potenza G 019 Grid 7.7 5.2 5 0
## 8 Bridgestone Potenza RE92 5 6.2 2.5 0
## 9 Bridgestone Potenza RE92A 5.6 6.4 2.7 0
## 10 Bridgestone Potenza RE960AS Pole Position 8.8 8.5 8.1 1
## # ℹ 58 more rows
# Clean the data - drop irrelevant column
t_df <- subset(tire_df, select = c(Wet, Noise, Purchase))
t_df
## # A tibble: 68 × 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
## 7 7.7 5.2 0
## 8 5 6.2 0
## 9 5.6 6.4 0
## 10 8.8 8.5 1
## # ℹ 58 more rows
Step 3: Summarize the data
head(t_df)
## # 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 description of the features are presented in the table below.
Variable | Definition
--------------- | -------------
1. Wet | A tire's average wet traction performance rating
2. Noise | A tire's average noise level generated rating
3. Purchase | A respondent buying the tire again (1: yes and 0: no)
summary(t_df)
## 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
Step 4: Feature Selection (i.e., correlation analysis)
corr <- rcorr(as.matrix(t_df))
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
Interpretation: All the predictors are significant with the target variable. There's no multicollinearity in the data.
Step 5: Build the logistic regression model
model <- glm(Purchase ~ Wet + Noise, data = t_df, family = binomial)
summary(model)
##
## Call:
## glm(formula = Purchase ~ Wet + Noise, family = binomial, data = t_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: 8
Interpretation: All the independent variables were significant (p-value < 0.05)
Question 5: 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
Interpretation: A McFadden R-squared of 0.71 means 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 great fit.
Area Under the Curve (AUC)
The Area Under the Curve (AUC) score represents the ability of the model to correctly classify students who will return to Lakeland college and those who will not.
roc_curve <- roc(t_df$Purchase, fitted(model))
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
plot(roc_curve)
auc(roc_curve)
## Area under the curve: 0.9741
Interpretation: An AUC score of 0.97 indicates that the LR model has a high level of accuracy in predicting whether respondents would buy the tire again.