#1) Develop the logistic regression model
#### using x1 = Wet performance rating
#### and x2 = Noise performance rating to
#### y = Purchase. Write out the
#### estimated logistic regression equation.
#2)Are the independent variables significant
### based on the z-test? (Use alpha = 0.05)
#3) Assess the overall model significance
###using the: McFadden R-Squared
#4) Use the estimated logit to compute
### an estimate of 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.
#Install/ load packages
install.packages("Hmisc")
install.packages('pscl')
library(readxl)
## Warning: package 'readxl' was built under R version 4.3.3
library(Hmisc)
## Warning: package 'Hmisc' was built under R version 4.3.3
##
## Attaching package: 'Hmisc'
## The following objects are masked from 'package:base':
##
## format.pval, units
library(pscl)
## Warning: package 'pscl' was built under R version 4.3.3
## 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 4.3.3
## Type 'citation("pROC")' for a citation.
##
## Attaching package: 'pROC'
## The following objects are masked from 'package:stats':
##
## cov, smooth, var
##Load data
tired_af <- read_excel(file.choose())
tiredf = subset(tired_af, select = -c(Tire))
#Scrubbing
head(tired_af)
## # 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(tired_af)
## 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
head(tiredf)
## # 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 0
summary(tiredf)
## 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
#Correlation plot
corr <- rcorr(as.matrix(tiredf))
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 0
#Logistic model
model <- glm(Purchase ~ Wet + Noise , data = tiredf, family = binomial)
summary(model)
##
## Call:
## glm(formula = Purchase ~ Wet + Noise, family = binomial, data = tiredf)
##
## 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
print(model)
##
## Call: glm(formula = Purchase ~ Wet + Noise, family = binomial, data = tiredf)
##
## Coefficients:
## (Intercept) Wet Noise
## -39.498 3.374 1.816
##
## Degrees of Freedom: 67 Total (i.e. Null); 65 Residual
## Null Deviance: 93.32
## Residual Deviance: 27.53 AIC: 33.53
McFadden
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
#ROC(forfun)
roc_curve = roc(tiredf$Purchase, fitted(model))
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
plot(roc_curve)
auc(roc_curve)
## Area under the curve: 0.9741
#Predicttion with 8 rating on noise and wet
new_data1 <- data.frame(Wet = 8, Noise = 8, Buy_Again=1)
prob1<- predict(model, newdata= new_data1, type="response")
prob1
## 1
## 0.8836964
#prediction with 7 rating on noise and wet
new_data2 <- data.frame(Wet = 7, Noise = 7, Buy_Again=1)
prob2<- predict(model, newdata= new_data2, type="response") #Probability that customer will purchase the tire again
prob2
## 1
## 0.04058753