Question 1 & 2: Develop a Model & Assess Predictor
Significance
Step 1: Install and load required libraries
#install.packages("readxl")
#install.packages("Hmisc")
#install.packages("pscl")
#if(!require(pROC)) install.packages("pROC")
library(readxl)
## Warning: 套件 'readxl' 是用 R 版本 4.4.2 來建造的
library(Hmisc)
## Warning: 套件 'Hmisc' 是用 R 版本 4.4.2 來建造的
##
## 載入套件：'Hmisc'
## 下列物件被遮斷自 'package:base':
##
## format.pval, units
library(pscl)
## Warning: 套件 'pscl' 是用 R 版本 4.4.2 來建造的
## 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)
## Warning: 套件 'pROC' 是用 R 版本 4.4.2 來建造的
## Type 'citation("pROC")' for a citation.
##
## 載入套件：'pROC'
## 下列物件被遮斷自 'package:stats':
##
## cov, smooth, var
Step 2: Import &clean the data
data <- read_excel(file.choose())
data <- subset(data, select = -c(Tire))
Step 3: Summarize the data
head(data)
## # 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 0
Data Description: A description of the features are presented in the table below
Variable |Definition
-------------|--------
1. Wet |Refers to the tire's traction performance on wet roads, with scores ranging from 1 to 10, with higher scores indicating better performance;
2. Noise |Represents the level of noise when the tire is running, and the score range is also from 1 to 10. The higher the score, the less the noise.
3. Buy_Again |Reflects the consumer's willingness to buy the tire again, with a score from 1 to 10, where 10 means "definitely will buy it again" and the lower the score, the lower the willingness.
4. Purchase |Converts the consumer's willingness to buy again into a binary variable. If the Buy Again score is 7 or above, it is recorded as 1 (indicating that it may or will definitely be purchased), and if it is lower than 7, it is recorded as 0 (indicating that it may or will definitely not be purchased). Buy)
summary(data)
## 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. :1.0000
Interpretation : The median Wet is 7.75, with a median of noise is 7.1 meaning that most tires perform well in terms of wet performance and noise control
Step 4: Feature selection (i.e., correlation analysis)
corr <- rcorr(as.matrix(data))
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 0
Interpretation: All the predictors are significant with the target variable(i.e., Wet and Noise). There's no multicollinearity in the data.
Step 5: Build the logistic regression model
model <- glm(Purchase ~ Wet + Noise, data = data, family = binomial)
summary(model)
##
## Call:
## glm(formula = Purchase ~ Wet + Noise, family = binomial, data = data)
##
## 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
Likelihood Ratio Test
null_model <- glm(Purchase ~ 1, data = data, family = binomial)
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 ' ' 1
Interpretation: The deviance table shows that adding Wet and Noise to the model significantly improves fit (p-value = 5.162e-15), reducing residual deviance from 93.325 to 27.530. This indicates both variables are strong, significant predictors of purchase likelihood.
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 0.705 means that our LR model explains about the predictors Wet and Noise explain approximately 70.5% of the variation in the likelihood of a customer purchasing the tire again. This value is considered high for logistic regression models, further confirming the importance of these variables in predicting purchase decisions.