# Load necessary libraries
library(readxl)
## Warning: package 'readxl' was built under R version 4.4.2
library(dplyr)
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
library(pscl)
## 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)
## 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, var
# Load the dataset
file_path <- file.choose()
data <- read_excel(file_path)
head(data)
## # A tibble: 6 × 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
summary(data)
## Tire Wet Noise Buy_Again
## Length:68 Min. :4.300 Min. :3.600 Min. :1.400
## Class :character 1st Qu.:6.450 1st Qu.:6.000 1st Qu.:3.850
## Mode :character Median :7.750 Median :7.100 Median :6.150
## Mean :7.315 Mean :6.903 Mean :5.657
## 3rd Qu.:8.225 3rd Qu.:7.925 3rd Qu.:7.400
## Max. :9.200 Max. :8.900 Max. :8.900
## Purchase
## Min. :0.0000
## 1st Qu.:0.0000
## Median :0.0000
## Mean :0.4412
## 3rd Qu.:1.0000
## Max. :1.0000
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
# Q3
mcfadden_r2 <- 1 - (model$deviance / model$null.deviance)
paste("McFadden R-Squared:", round(mcfadden_r2, 2))
## [1] "McFadden R-Squared: 0.71"
# Q4
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 %"
# Q5
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."
#ROC curve and calculate AUC for fun
roc_curve <- roc(data$Purchase, fitted(model))
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
plot(roc_curve, main = "ROC Curve")
auc_value <- auc(roc_curve)
paste("AUC:", round(auc_value, 2))
## [1] "AUC: 0.97"