#Tire Rating at the Super Cool Tire Store
##Project Objective
Using Regression Models to figure out tire ratingsQuestion 1 and 2: Develop the logistic regression model
Step 1:Install and Load Libraries
#install.packages("readxl")
#install.packages("Hmisc")
#install.packages("pscl")
#if(!require(pROC)) install.packages("pROC")
library(readxl)
library(Hmisc)##
## Attaching package: 'Hmisc'## The following objects are masked from 'package:base':
##
## format.pval, unitslibrary(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, varStep 2: Important and Clean up the data
tire_rating <- read_excel("Class Exercise 15_TireRatings.xlsx")
tire_df <- subset(tire_rating, select = -c(Tire))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 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. :1.0000#Interpt: Average wet 7.3, average noise 6.9, average buy again 5.6Step 4: Correlation
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 0Wet 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 1.00Step 5: Build 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: 8All of them SignificantQuestion 3: Overall Model Significance
Likelihood Ratio Test
null_model <- glm(Purchase ~ 1, data = tire_df, 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 ' ' 1Psuedo 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 0.8305269A value of 0.70 suggests that the model explains 70% of the variability in the dependent variable
(whether a respondent would purchase the tire again or not) based on the independent variables (Wet, Noise, and Buy Again).
This is considered very high for a logistic regression model, as McFadden R-squared values
between 0.2 and 0.4 are typically regarded as an excellent fit in most practical scenarios.Area Under the Curve
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: 0.9741Interp: A AUC score of 0.97 showcases that the LR model has a high level of accuracy.Question 4 & 5: New Information
predict_data_8 <- data.frame(Wet = 8, Noise = 8)
probability_8 <- predict(model, newdata = predict_data_8, type = "response")
paste("Probability Wet = 8, Noise = 8:", round(probability_8 * 100, 2), "%")## [1] "Probability Wet = 8, Noise = 8: 88.37 %"#Predict
predict_data_7 <- data.frame(Wet = 7, Noise = 7)
probability_7 <- predict(model, newdata = predict_data_7, type = "response")
paste("Probability of Wet = 7, Noise = 7:", round(probability_7 * 100, 2), "%, indicating very low likelihood of repurchase with these average ratings.")## [1] "Probability of Wet = 7, Noise = 7: 4.06 %, indicating very low likelihood of repurchase with these average ratings."Probability Wet = 8, Noise = 8: 88.37 %
Probability of Wet = 7, Noise = 7: 4.06