Daniel Mendoza
library(readxl)
library(Hmisc)
##
## Attaching package: 'Hmisc'
## The following objects are masked from 'package:base':
##
## format.pval, units
library(pscl)
## 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)
## Type 'citation("pROC")' for a citation.
##
## Attaching package: 'pROC'
## The following objects are masked from 'package:stats':
##
## cov, smooth, var
#data cleaning and summary statistics
data <- read_excel("/Users/danny/Downloads/ClassExcercise15 folder/Class Exercise 15_TireRatings.xlsx")
clean_data <- subset(data, select= -c(Tire))
head(clean_data)
## # 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(clean_data)
## 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
corr <- rcorr(as.matrix(clean_data))
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 repression
model <- glm(Purchase~Wet+Noise,data=clean_data,family=binomial)
summary(model)
##
## Call:
## glm(formula = Purchase ~ Wet + Noise, family = binomial, data = clean_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
null_model <- glm(Purchase~1,data=clean_data,family=binomial)
#likelihood test
anova(null_model,model,test="Chisq")
## Analysis of Deviance Table
##
## Model 1: Purchase ~ 1
## Model 2: Purchase ~ Wet + Noise
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 67 93.325
## 2 65 27.530 2 65.795 5.162e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#McFadden psuedo R squared model significance (abobve 0.2-0.4 is good)
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
#AUC
roc_curve <- roc(clean_data$Purchase,fitted(model))
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
plot(roc_curve)
auc(roc_curve)
## Area under the curve: 0.9741
#Predicting with new information
new_data1 <- data.frame(Wet=8,Noise=8, Purchase = 0) #prob didnt buy again
new_data2 <- data.frame(Wet=8,Noise=8, Purchase = 1) #bought again
#Predict probability question 4
prob1 <- predict(model,newdata = new_data1,type="response") #prob didnt buy
prob1*100
## 1
## 88.36964
prob2 <- predict(model,newdata = new_data2,type="response")
prob2*100
## 1
## 88.36964
#question5
new_data3 <- data.frame(Wet=7,Noise=7, Purchase = 0) #prob didnt buy again
new_data4 <- data.frame(Wet=7,Noise=7, Purchase = 1) #bought again
prob3 <- predict(model,newdata = new_data3,type="response") #prob didnt buy
prob3*100
## 1
## 4.058753
prob4 <- predict(model,newdata = new_data4,type="response")
prob4*100
## 1
## 4.058753
coefficients <- summary(model)$coefficients