To investigate the relationship between the ratings for tire’s wet traction performance and the ratings for the noise level on likelihood of repurchasing.#install.packages('Hmisc')
#install.packages('pscl')
#install.packages('pROC')
library(readxl) #allows us to import excel files
library(Hmisc) #allows us to call the correlation function##
## Attaching package: 'Hmisc'## The following objects are masked from 'package:base':
##
## format.pval, unitslibrary(pscl) #allows us to call the pseudo R-square package to evaluate our model## 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 the curve (AUC) package to get the plot and AUC score## Type 'citation("pROC")' for a citation.##
## Attaching package: 'pROC'## The following objects are masked from 'package:stats':
##
## cov, smooth, vardata <- read_excel("Class Exercise 15_TireRatings.xlsx")
data1 <- subset(data, select = -c(Tire))head(data1)## # 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(data1)## 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. :1.0000corr <- rcorr(as.matrix(data1))
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 the predictors are significant with the target variabe (i.e., Purchace). There is no multicollinearity in the data.model <- glm(Purchase ~ Wet + Noise, data = data1, family = binomial)
summary(model)##
## Call:
## glm(formula = Purchase ~ Wet + Noise, family = binomial, data = data1)
##
## 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)
The estimated logistic regression equation is y_hat = e-39.50+3.37x1+1.82x2 / 1+e-39.50+3.37x1+1.82x2.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: A McFadden R-squared of 0.705 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 an excellent fit since the value is above 0.7.##Quetion 4 and 5: Predicting with New Information
# Given the following new customer information
# Suppose that the Wet and Noise performance ratings were 8
data3 <- data.frame(Wet = 8, Noise = 8)
# Predicting the probability
prob <- predict(model, newdata = data3, type = "response")
prob * 100## 1
## 88.36964# Suppose that the Wet and Noise performance ratings were 7
data4 <- data.frame(Wet = 7, Noise = 7)
# Predicting the probability
prob1 <- predict(model, newdata = data4, type = "response")
prob1 * 100## 1
## 4.058753Interpretation
(1) There is a 88.37% chance that the customer will buy the tire again if the both ratings were 8
(2) There is only a 4.06% chance that the customer will buy the tire again if the both ratings were 7.