Class Exercise 5 - Tire Rack

Project Objective

The Tire Rack maintains an independent consumer survey to help drivers help each other by sharing their long-term tire experiences.

Question 1 & 2

Step 1: Install and load libraries

library(readxl)
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.

Step 2: Import data

data <- read_excel("Class Exercise 15_TireRatings.xlsx")

Step 3: 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

The estimated logistic regression equation has the following variables: b0 = -39.50; b1 = 3.37; b2 = 1.82. The variables are significant based on the z-test with alpha = 0.05.

Question 3

Step 4: Overall Model Significance (McFadden 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

The McFadden R-Squared is equal to 0.71.

Question 4

Step 5: Probability for Wet = 8, Noise = 8

coefficients <- coef(model)
intercept <- coefficients[1]
b1 <- coefficients[2]
b2 <- coefficients[3]
wet <- 8
noise <- 8

logit <- intercept + b1 * wet + b2 * noise
probability <- exp(logit) / (1 + exp(logit))
probability

## (Intercept) 
##   0.8836964

The probability that a customer will probably or definitely purchase a particular tire again with a Wet performance rating of 8 and a Noise performance rating of 8 is equal to 88.37%

Question 5

Step 6: Probability for Wet = 7, Noise = 7

wet <- 7
noise <- 7

logit <- intercept + b1 * wet + b2 * noise
probability <- exp(logit) / (1 + exp(logit))
probability

## (Intercept) 
##  0.04058753

The probability that a customer will probably or definitely purchase a particular tire again with a Wet performance rating of 7 and a Noise performance rating of 7 is equal to 4.06%