Question 1 and 2: Logistic Regression Model
Step 1: Load required packages
library(readxl) # Allows import of excel files
library(Hmisc) # Allows us to call correlation function
##
## Attaching package: 'Hmisc'
## The following objects are masked from 'package:base':
##
## format.pval, units
library(pscl) # Allows us to find the pseudo r squared
## 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 plot the area under the curve and to get the AUC value
## Type 'citation("pROC")' for a citation.
##
## Attaching package: 'pROC'
## The following objects are masked from 'package:stats':
##
## cov, smooth, var
Step 2: Import the data
tires_df <- read_excel("Class Exercise15_TireRatings.xlsx") # Load tire data
Step 3: Summarize the data for descriptive statistics
head(tires_df) # View a snapshot of the 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(tires_df) # Get insights from the 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
Interpretation: Tire Rack's survey indicates that consumers on average rated rated 7.32 for wet and 6.90 for noise.
Step 4: Set up the logistic model
model <- glm(Purchase ~ Wet + Noise, data = tires_df, family = binomial)
Step 5: Test independent variables for significance
summary(model) # View the p values and obtain b0, b1, and b2
##
## Call:
## glm(formula = Purchase ~ Wet + Noise, family = binomial, data = tires_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: 8
Interpretation: 0.01 for wet < 0.05. 0.03 for noise < 0.05. All independent variables are significant.
Question 3: Test overall model significance
pR2(model) # Pseudo R squared
## 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: Model is not very significant because 0.71 is not between
# 0.2 and 0.4
Question 4: Estimate probability that customer will purchase a tier
again with a rating of 8 in both independent variables.
newdata1 <- data.frame(Wet = 8, Noise = 8) # Set up input to the model
prob1 <- predict(model, newdata = newdata1, type = "response") # Plug in numbers
prob1 # 0.88
## 1
## 0.8836964
prob1*100 # 88.37% will purchase a tier again
## 1
## 88.36964
Interpretation: These customers were happy with their tire quality, so they
bought again.
Question 5: Estimate the probability that customer will purchase a
tier again with a rating of 7 in both independent variables.
newdata2 <- data.frame(Wet = 7, Noise = 7) # Set up input to the model
prob2 <- predict(model, newdata = newdata2, type = "response") # Plug in numbers
prob2 # 0.04
## 1
## 0.04058753
prob2*100 # 4.06% will purchase tier again
## 1
## 4.058753
Interpretation: Because most of these customers were not happy with their tier quality,
most didn't buy the specific tire again.