Multi Logistic Regression
Sonia Mathew
July 27, 2017
Introduction
The Logistic Regression is a regression model in which the response variable (dependent variable) has categorical values such as True/False or 0/1. It actually measures the probability of a binary response as the value of response variable based on the mathematical equation relating it with the predictor variables.
Problem Definition
The objective is to predict based on diagnostic measurements whether a patient has diabetes or not.
Dataset
This dataset is originally from the National Institute of Diabetes and Digestive and Kidney Diseases. Several constraints were placed on the selection of these instances from a larger database. In particular, all patients here are females at least 21 years old of Pima Indian heritage.
Data Description Attributes: [, 1] Pregnancies: Number of times pregnant
[, 2] Glucose:Plasma glucose concentration a 2 hours in an oral glucose tolerance test
[, 3] BloodPressure:Diastolic blood pressure (mm Hg)
[, 4] SkinThickness:Triceps skin fold thickness (mm)
[, 5] Insulin:2-Hour serum insulin (mu U/ml)
[, 6] BMI: Body mass index (weight in kg/(height in m)^2)
[, 7] DiabetesPedigreeFunction: Diabetes pedigree function
[, 8] Age:Age (years)
[, 9] Outcome: Class variable (0 or 1), 0=Non diabetic and 1= Diabetic
Setup
library(tidyr)## Warning: package 'tidyr' was built under R version 3.3.3library(dplyr)## Warning: package 'dplyr' was built under R version 3.3.3##
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## intersect, setdiff, setequal, unionlibrary(ggplot2)## Warning: package 'ggplot2' was built under R version 3.3.3library(corrgram)## Warning: package 'corrgram' was built under R version 3.3.3library(gridExtra) ## Warning: package 'gridExtra' was built under R version 3.3.3##
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## combinelibrary(Deducer)## Warning: package 'Deducer' was built under R version 3.3.3## Loading required package: JGR## Warning: package 'JGR' was built under R version 3.3.3## Loading required package: rJava## Loading required package: JavaGD## Loading required package: iplots## Warning: package 'iplots' was built under R version 3.3.3##
## Please type JGR() to launch console. Platform specific launchers (.exe and .app) can also be obtained at http://www.rforge.net/JGR/files/.## Loading required package: car## Warning: package 'car' was built under R version 3.3.3##
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## select##
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## Note Non-JGR console detected:
## Deducer is best used from within JGR (http://jgr.markushelbig.org/).
## To Bring up GUI dialogs, type deducer().library(caret)## Warning: package 'caret' was built under R version 3.3.3## Loading required package: latticelibrary(pscl)## Warning: package 'pscl' was built under R version 3.3.3## Classes and Methods for R developed in the## Political Science Computational Laboratory## Department of Political Science## Stanford University## Simon Jackman## hurdle and zeroinfl functions by Achim ZeileisFunctions
Dataset
setwd("D:\\PGDM\\Trim 4\\MachineLearning")
dfrModel <- read.csv("./Data/niddkd-diabetes.csv", header=T, stringsAsFactors=F)
head(dfrModel)## Pregnancies Glucose BloodPressure SkinThickness Insulin BMI
## 1 6 148 72 35 0 33.6
## 2 1 85 66 29 0 26.6
## 3 8 183 64 0 0 23.3
## 4 1 89 66 23 94 28.1
## 5 0 137 40 35 168 43.1
## 6 5 116 74 0 0 25.6
## DiabetesPedigreeFunction Age Outcome
## 1 0.627 50 1
## 2 0.351 31 0
## 3 0.672 32 1
## 4 0.167 21 0
## 5 2.288 33 1
## 6 0.201 30 0Datatypes
str(dfrModel)## 'data.frame': 768 obs. of 9 variables:
## $ Pregnancies : int 6 1 8 1 0 5 3 10 2 8 ...
## $ Glucose : int 148 85 183 89 137 116 78 115 197 125 ...
## $ BloodPressure : int 72 66 64 66 40 74 50 0 70 96 ...
## $ SkinThickness : int 35 29 0 23 35 0 32 0 45 0 ...
## $ Insulin : int 0 0 0 94 168 0 88 0 543 0 ...
## $ BMI : num 33.6 26.6 23.3 28.1 43.1 25.6 31 35.3 30.5 0 ...
## $ DiabetesPedigreeFunction: num 0.627 0.351 0.672 0.167 2.288 ...
## $ Age : int 50 31 32 21 33 30 26 29 53 54 ...
## $ Outcome : int 1 0 1 0 1 0 1 0 1 1 ...Observation
Dataset is comprised of integer and numeric data
Check for Missing Data
lapply(dfrModel, FUN=detect_na)## $Pregnancies
## [1] 0
##
## $Glucose
## [1] 0
##
## $BloodPressure
## [1] 0
##
## $SkinThickness
## [1] 0
##
## $Insulin
## [1] 0
##
## $BMI
## [1] 0
##
## $DiabetesPedigreeFunction
## [1] 0
##
## $Age
## [1] 0
##
## $Outcome
## [1] 0Observation
Dataset has no missing data
Summarizing data
summarise(group_by(dfrModel, Pregnancies), n())## # A tibble: 17 × 2
## Pregnancies `n()`
## <int> <int>
## 1 0 111
## 2 1 135
## 3 2 103
## 4 3 75
## 5 4 68
## 6 5 57
## 7 6 50
## 8 7 45
## 9 8 38
## 10 9 28
## 11 10 24
## 12 11 11
## 13 12 9
## 14 13 10
## 15 14 2
## 16 15 1
## 17 17 1summarise(group_by(dfrModel, Glucose), n())## # A tibble: 136 × 2
## Glucose `n()`
## <int> <int>
## 1 0 5
## 2 44 1
## 3 56 1
## 4 57 2
## 5 61 1
## 6 62 1
## 7 65 1
## 8 67 1
## 9 68 3
## 10 71 4
## # ... with 126 more rowssummarise(group_by(dfrModel, BloodPressure), n())## # A tibble: 47 × 2
## BloodPressure `n()`
## <int> <int>
## 1 0 35
## 2 24 1
## 3 30 2
## 4 38 1
## 5 40 1
## 6 44 4
## 7 46 2
## 8 48 5
## 9 50 13
## 10 52 11
## # ... with 37 more rowssummarise(group_by(dfrModel, SkinThickness), n())## # A tibble: 51 × 2
## SkinThickness `n()`
## <int> <int>
## 1 0 227
## 2 7 2
## 3 8 2
## 4 10 5
## 5 11 6
## 6 12 7
## 7 13 11
## 8 14 6
## 9 15 14
## 10 16 6
## # ... with 41 more rowssummarise(group_by(dfrModel, Insulin), n())## # A tibble: 186 × 2
## Insulin `n()`
## <int> <int>
## 1 0 374
## 2 14 1
## 3 15 1
## 4 16 1
## 5 18 2
## 6 22 1
## 7 23 2
## 8 25 1
## 9 29 1
## 10 32 1
## # ... with 176 more rowssummarise(group_by(dfrModel, BMI), n())## # A tibble: 248 × 2
## BMI `n()`
## <dbl> <int>
## 1 0.0 11
## 2 18.2 3
## 3 18.4 1
## 4 19.1 1
## 5 19.3 1
## 6 19.4 1
## 7 19.5 2
## 8 19.6 3
## 9 19.9 1
## 10 20.0 1
## # ... with 238 more rowssummarise(group_by(dfrModel, DiabetesPedigreeFunction), n())## # A tibble: 517 × 2
## DiabetesPedigreeFunction `n()`
## <dbl> <int>
## 1 0.078 1
## 2 0.084 1
## 3 0.085 2
## 4 0.088 2
## 5 0.089 1
## 6 0.092 1
## 7 0.096 1
## 8 0.100 1
## 9 0.101 1
## 10 0.102 1
## # ... with 507 more rowssummarise(group_by(dfrModel, Age), n())## # A tibble: 52 × 2
## Age `n()`
## <int> <int>
## 1 21 63
## 2 22 72
## 3 23 38
## 4 24 46
## 5 25 48
## 6 26 33
## 7 27 32
## 8 28 35
## 9 29 29
## 10 30 21
## # ... with 42 more rowssummarise(group_by(dfrModel, Outcome), n())## # A tibble: 2 × 2
## Outcome `n()`
## <int> <int>
## 1 0 500
## 2 1 268Exploratory Analysis
lapply(dfrModel, FUN=summary)## $Pregnancies
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 1.000 3.000 3.845 6.000 17.000
##
## $Glucose
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 99.0 117.0 120.9 140.2 199.0
##
## $BloodPressure
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00 62.00 72.00 69.11 80.00 122.00
##
## $SkinThickness
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00 0.00 23.00 20.54 32.00 99.00
##
## $Insulin
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 0.0 30.5 79.8 127.2 846.0
##
## $BMI
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00 27.30 32.00 31.99 36.60 67.10
##
## $DiabetesPedigreeFunction
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0780 0.2438 0.3725 0.4719 0.6262 2.4200
##
## $Age
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 21.00 24.00 29.00 33.24 41.00 81.00
##
## $Outcome
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 0.000 0.000 0.349 1.000 1.000Histogram to check data distribution
hist(dfrModel$Pregnancies)
hist(dfrModel$Glucose)
hist(dfrModel$Age)
hist(dfrModel$BMI)
hist(dfrModel$Insulin)
Outliers Data
lapply(dfrModel, FUN=detect_outliers)## $Pregnancies
## integer(0)
##
## $Glucose
## integer(0)
##
## $BloodPressure
## [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
##
## $SkinThickness
## integer(0)
##
## $Insulin
## [1] 543 846 495 485 495 478 744 680 545 465 579 474 480 600 540 480 510
##
## $BMI
## [1] 0.0 0.0 0.0 0.0 0.0 67.1 0.0 0.0 0.0 0.0 0.0 0.0
##
## $DiabetesPedigreeFunction
## [1] 2.288 1.893 1.781 2.329 2.137 1.731 1.600 2.420 1.699 1.698
##
## $Age
## integer(0)
##
## $Outcome
## integer(0)Display Outliers
lapply(dfrModel[1:8],FUN=display_Outliers)## $Pregnancies
##
## $Glucose
##
## $BloodPressure
##
## $SkinThickness
##
## $Insulin
##
## $BMI
##
## $DiabetesPedigreeFunction
##
## $Age
Observation
Outliers are present in few features.
But Outlier count is low.
For this model we will work with the outliers.
Correlation
vctCorr = numeric(0)
for (i in names(dfrModel)){
cor.result <- cor(as.numeric(dfrModel$Outcome), as.numeric(dfrModel[,i]))
vctCorr <- c(vctCorr, cor.result)
}
dfrCorr <- vctCorr
names(dfrCorr) <- names(dfrModel)
dfrCorr## Pregnancies Glucose BloodPressure
## 0.22189815 0.46658140 0.06506836
## SkinThickness Insulin BMI
## 0.07475223 0.13054795 0.29269466
## DiabetesPedigreeFunction Age Outcome
## 0.17384407 0.23835598 1.00000000Data For Visualization
dfrGraph <- gather(dfrModel, variable, value, -Outcome)
head(dfrGraph)## Outcome variable value
## 1 1 Pregnancies 6
## 2 0 Pregnancies 1
## 3 1 Pregnancies 8
## 4 0 Pregnancies 1
## 5 1 Pregnancies 0
## 6 0 Pregnancies 5ggplot(dfrGraph) + #ggplot works better with factors
geom_jitter(aes(value,Outcome, colour=variable)) +
geom_smooth(aes(value,Outcome, colour=variable), method=lm, se=FALSE) +
facet_wrap(~variable, scales="free_x") +
labs(title="Relation Of diabetes With Other Features")
Split the Diabetes data into train and test
#splitdf <- function(dataframe , seed=NULL)
#{
#if(!is.null(seed)) set.seed(seed)
#index <- 1:nrow(dataframe)
#trainindex <- sample(index, trunc(length))
#trainset <- dataframe[trainindex,]
#testset <- dataframe[trainindex,]
#list(trainset=trainset,testset=testset)}dt=sort(sample(nrow(dfrModel), nrow(dfrModel)*.7))
train <- dfrModel[dt,]
test <- dfrModel[-dt,]observation The main dataset is split into test & train data.
Find Best Multi Logistic Model
Choose the best logistic model by using step().
stpModel=step(glm(data=train, formula=Outcome~., family=binomial), trace=0, steps=100)
summary(stpModel)##
## Call:
## glm(formula = Outcome ~ Pregnancies + Glucose + BMI + DiabetesPedigreeFunction,
## family = binomial, data = train)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.8755 -0.7029 -0.3522 0.6586 2.9611
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -9.893337 0.896413 -11.037 < 2e-16 ***
## Pregnancies 0.146557 0.034559 4.241 2.23e-05 ***
## Glucose 0.038241 0.004207 9.089 < 2e-16 ***
## BMI 0.101782 0.018132 5.613 1.98e-08 ***
## DiabetesPedigreeFunction 0.925853 0.378559 2.446 0.0145 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 687.70 on 536 degrees of freedom
## Residual deviance: 474.33 on 532 degrees of freedom
## AIC: 484.33
##
## Number of Fisher Scoring iterations: 5Observation
Best results given by Outcome ~ Pregnancies + Glucose + Insulin + BMI + DiabetesPedigreeFunction + Age.
p-values for the features are less than 0.05.
Difference between the null deviance and residual deviance is around 27%. Thus model is fit.
Make Final Multi Linear Model
# make model
mgmModel <- glm(data=train, formula=Outcome~Pregnancies+Glucose+BloodPressure+BMI, family=binomial(link="logit"))
# print summary
summary(mgmModel)##
## Call:
## glm(formula = Outcome ~ Pregnancies + Glucose + BloodPressure +
## BMI, family = binomial(link = "logit"), data = train)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.2561 -0.6866 -0.3590 0.6674 3.0408
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -9.385772 0.910175 -10.312 < 2e-16 ***
## Pregnancies 0.146631 0.034750 4.220 2.45e-05 ***
## Glucose 0.038714 0.004180 9.261 < 2e-16 ***
## BloodPressure -0.004507 0.006294 -0.716 0.474
## BMI 0.107668 0.018366 5.862 4.56e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 687.70 on 536 degrees of freedom
## Residual deviance: 479.96 on 532 degrees of freedom
## AIC: 489.96
##
## Number of Fisher Scoring iterations: 5Confusion Matrix
prdVal <- predict(mgmModel, type='response')
prdBln <- ifelse(prdVal > 0.5, 1, 0)
cnfmtrx <- table(prd=prdBln, act=train$Outcome)
confusionMatrix(cnfmtrx)## Confusion Matrix and Statistics
##
## act
## prd 0 1
## 0 314 72
## 1 41 110
##
## Accuracy : 0.7896
## 95% CI : (0.7526, 0.8233)
## No Information Rate : 0.6611
## P-Value [Acc > NIR] : 4.182e-11
##
## Kappa : 0.5101
## Mcnemar's Test P-Value : 0.00477
##
## Sensitivity : 0.8845
## Specificity : 0.6044
## Pos Pred Value : 0.8135
## Neg Pred Value : 0.7285
## Prevalence : 0.6611
## Detection Rate : 0.5847
## Detection Prevalence : 0.7188
## Balanced Accuracy : 0.7445
##
## 'Positive' Class : 0
## observation
Accuracy of the model is found to be 76% and sensitivity around 87%
Regression Data
dfrPlot <- mutate(train, PrdVal=prdVal, POutcome=prdBln)
head(dfrPlot)## Pregnancies Glucose BloodPressure SkinThickness Insulin BMI
## 1 6 148 72 35 0 33.6
## 2 1 85 66 29 0 26.6
## 3 8 183 64 0 0 23.3
## 4 1 89 66 23 94 28.1
## 5 10 115 0 0 0 35.3
## 6 2 197 70 45 543 30.5
## DiabetesPedigreeFunction Age Outcome PrdVal POutcome
## 1 0.627 50 1 0.62640709 1
## 2 0.351 31 0 0.03286456 0
## 3 0.672 32 1 0.74878970 1
## 4 0.167 21 0 0.04454935 0
## 5 0.134 29 0 0.58257083 1
## 6 0.158 53 1 0.81795331 1Regression Visulaization
#dfrPlot
ggplot(dfrPlot, aes(x=PrdVal, y=POutcome)) +
geom_point(shape=19, colour="blue", fill="blue") +
geom_smooth(method="gam", formula=y~s(log(x)), se=FALSE) +
labs(title="Binomial Regression Curve") +
labs(x="") +
labs(y="")
ROC Visulaization
rocplot(mgmModel)
Observation
Accuracy identified by the AUC model is around 83%.
Test Data
Predict using Test data
resVal <- predict(mgmModel, test, type="response")
prdOut <- ifelse(resVal > 0.5, 1, 0)
test <- mutate(test, Pvalue=resVal, POutcome=prdOut)
test ## Pregnancies Glucose BloodPressure SkinThickness Insulin BMI
## 1 0 137 40 35 168 43.1
## 2 5 116 74 0 0 25.6
## 3 3 78 50 32 88 31.0
## 4 1 103 30 38 83 43.3
## 5 1 115 70 30 96 34.6
## 6 9 119 80 35 0 29.0
## 7 10 125 70 26 115 31.1
## 8 7 147 76 0 0 39.4
## 9 1 97 66 15 140 23.2
## 10 5 117 92 0 0 34.1
## 11 2 90 68 42 0 38.2
## 12 3 180 64 25 70 34.0
## 13 7 187 68 39 304 37.7
## 14 0 100 88 60 110 46.8
## 15 0 105 64 41 142 41.5
## 16 2 141 58 34 128 25.4
## 17 7 114 66 0 0 32.8
## 18 5 99 74 27 0 29.0
## 19 2 100 66 20 90 32.9
## 20 5 139 64 35 140 28.6
## 21 4 129 86 20 270 35.1
## 22 3 113 44 13 0 22.4
## 23 2 110 74 29 125 32.4
## 24 15 136 70 32 110 37.1
## 25 7 81 78 40 48 46.7
## 26 1 71 48 18 76 20.4
## 27 1 163 72 0 0 39.0
## 28 1 126 56 29 152 28.7
## 29 3 83 58 31 18 34.3
## 30 8 155 62 26 495 34.0
## 31 4 76 62 0 0 34.0
## 32 4 99 76 15 51 23.2
## 33 6 111 64 39 0 34.2
## 34 3 120 70 30 135 42.9
## 35 3 170 64 37 225 34.5
## 36 0 100 70 26 50 30.8
## 37 0 129 80 0 0 31.2
## 38 5 106 82 30 0 39.5
## 39 2 108 52 26 63 32.5
## 40 0 102 75 23 0 0.0
## 41 4 114 65 0 0 21.9
## 42 9 156 86 28 155 34.3
## 43 17 163 72 41 114 40.9
## 44 2 100 64 23 0 29.7
## 45 0 131 88 0 0 31.6
## 46 3 111 90 12 78 28.4
## 47 1 79 60 42 48 43.5
## 48 5 143 78 0 0 45.0
## 49 5 130 82 0 0 39.1
## 50 0 119 64 18 92 34.9
## 51 7 194 68 28 0 35.9
## 52 1 128 98 41 58 32.0
## 53 3 111 62 0 0 22.6
## 54 8 85 55 20 0 24.4
## 55 5 158 84 41 210 39.4
## 56 4 148 60 27 318 30.9
## 57 1 138 82 0 0 40.1
## 58 8 196 76 29 280 37.5
## 59 1 96 64 27 87 33.2
## 60 7 184 84 33 0 35.5
## 61 2 81 60 22 0 27.7
## 62 0 140 65 26 130 42.6
## 63 12 151 70 40 271 41.8
## 64 5 112 66 0 0 37.8
## 65 0 177 60 29 478 34.6
## 66 2 158 90 0 0 31.6
## 67 7 119 0 0 0 25.2
## 68 1 100 66 15 56 23.6
## 69 0 101 76 0 0 35.7
## 70 3 162 52 38 0 37.2
## 71 0 117 80 31 53 45.2
## 72 9 164 84 21 0 30.8
## 73 6 119 50 22 176 27.1
## 74 10 122 68 0 0 31.2
## 75 0 165 90 33 680 52.3
## 76 1 111 86 19 0 30.1
## 77 12 92 62 7 258 27.6
## 78 1 193 50 16 375 25.9
## 79 3 191 68 15 130 30.9
## 80 4 95 70 32 0 32.1
## 81 3 142 80 15 0 32.4
## 82 2 146 0 0 0 27.5
## 83 2 108 62 32 56 25.2
## 84 3 122 78 0 0 23.0
## 85 7 106 60 24 0 26.5
## 86 5 155 84 44 545 38.7
## 87 0 107 62 30 74 36.6
## 88 0 126 84 29 215 30.7
## 89 14 100 78 25 184 36.6
## 90 8 112 72 0 0 23.6
## 91 2 144 58 33 135 31.6
## 92 0 137 68 14 148 24.8
## 93 2 124 68 28 205 32.9
## 94 6 80 66 30 0 26.2
## 95 2 155 74 17 96 26.6
## 96 3 99 80 11 64 19.3
## 97 3 115 66 39 140 38.1
## 98 4 129 60 12 231 27.5
## 99 3 112 74 30 0 31.6
## 100 0 124 70 20 0 27.4
## 101 2 112 75 32 0 35.7
## 102 1 122 64 32 156 35.1
## 103 10 179 70 0 0 35.1
## 104 8 118 72 19 0 23.1
## 105 2 87 58 16 52 32.7
## 106 1 180 0 0 0 43.3
## 107 9 152 78 34 171 34.2
## 108 1 130 70 13 105 25.9
## 109 3 99 62 19 74 21.8
## 110 5 0 80 32 0 41.0
## 111 4 92 80 0 0 42.2
## 112 1 90 62 12 43 27.2
## 113 4 147 74 25 293 34.9
## 114 6 124 72 0 0 27.6
## 115 2 105 58 40 94 34.9
## 116 12 140 82 43 325 39.2
## 117 1 87 60 37 75 37.2
## 118 1 109 60 8 182 25.4
## 119 5 116 74 29 0 32.3
## 120 3 100 68 23 81 31.6
## 121 1 100 66 29 196 32.0
## 122 5 166 76 0 0 45.7
## 123 0 131 66 40 0 34.3
## 124 3 82 70 0 0 21.1
## 125 4 95 64 0 0 32.0
## 126 9 72 78 25 0 31.6
## 127 4 115 72 0 0 28.9
## 128 1 172 68 49 579 42.4
## 129 6 102 90 39 0 35.7
## 130 1 97 68 21 0 27.2
## 131 3 129 64 29 115 26.4
## 132 1 119 88 41 170 45.3
## 133 2 94 68 18 76 26.0
## 134 0 141 0 0 0 42.4
## 135 12 140 85 33 0 37.4
## 136 1 82 64 13 95 21.2
## 137 10 148 84 48 237 37.6
## 138 1 71 62 0 0 21.8
## 139 8 74 70 40 49 35.3
## 140 8 120 0 0 0 30.0
## 141 6 154 78 41 140 46.1
## 142 7 136 90 0 0 29.9
## 143 4 114 64 0 0 28.9
## 144 8 126 74 38 75 25.9
## 145 4 132 86 31 0 28.0
## 146 0 123 88 37 0 35.2
## 147 8 194 80 0 0 26.1
## 148 2 83 65 28 66 36.8
## 149 4 99 68 38 0 32.8
## 150 3 80 0 0 0 0.0
## 151 2 117 90 19 71 25.2
## 152 7 94 64 25 79 33.3
## 153 8 120 78 0 0 25.0
## 154 0 139 62 17 210 22.1
## 155 9 91 68 0 0 24.2
## 156 13 76 60 0 0 32.8
## 157 6 129 90 7 326 19.6
## 158 3 87 60 18 0 21.8
## 159 1 77 56 30 56 33.3
## 160 4 132 0 0 0 32.9
## 161 0 105 90 0 0 29.6
## 162 0 57 60 0 0 21.7
## 163 0 127 80 37 210 36.3
## 164 3 128 72 25 190 32.4
## 165 1 84 64 23 115 36.9
## 166 1 97 70 40 0 38.1
## 167 8 110 76 0 0 27.8
## 168 11 103 68 40 0 46.2
## 169 6 99 60 19 54 26.9
## 170 0 91 80 0 0 32.4
## 171 2 95 54 14 88 26.1
## 172 4 154 72 29 126 31.3
## 173 0 121 66 30 165 34.3
## 174 2 130 96 0 0 22.6
## 175 6 108 44 20 130 24.0
## 176 0 151 90 46 0 42.1
## 177 8 100 76 0 0 38.7
## 178 8 143 66 0 0 34.9
## 179 7 150 78 29 126 35.2
## 180 1 92 62 25 41 19.5
## 181 1 111 62 13 182 24.0
## 182 7 168 88 42 321 38.2
## 183 6 117 96 0 0 28.7
## 184 9 112 82 24 0 28.2
## 185 0 119 0 0 0 32.4
## 186 2 92 76 20 0 24.2
## 187 6 183 94 0 0 40.8
## 188 2 108 64 0 0 30.8
## 189 0 132 78 0 0 32.4
## 190 4 94 65 22 0 24.7
## 191 2 111 60 0 0 26.2
## 192 1 128 82 17 183 27.5
## 193 13 104 72 0 0 31.2
## 194 7 97 76 32 91 40.9
## 195 6 147 80 0 0 29.5
## 196 1 106 70 28 135 34.2
## 197 2 101 58 35 90 21.8
## 198 11 127 106 0 0 39.0
## 199 3 80 82 31 70 34.2
## 200 1 199 76 43 0 42.9
## 201 10 111 70 27 0 27.5
## 202 3 123 100 35 240 57.3
## 203 9 156 86 0 0 24.8
## 204 3 121 52 0 0 36.0
## 205 2 101 58 17 265 24.2
## 206 2 56 56 28 45 24.2
## 207 2 129 74 26 205 33.2
## 208 1 107 50 19 0 28.3
## 209 2 121 70 32 95 39.1
## 210 7 142 90 24 480 30.4
## 211 3 169 74 19 125 29.9
## 212 6 80 80 36 0 39.8
## 213 10 115 0 0 0 0.0
## 214 2 127 46 21 335 34.4
## 215 9 164 78 0 0 32.8
## 216 10 94 72 18 0 23.1
## 217 1 108 60 46 178 35.5
## 218 5 97 76 27 0 35.6
## 219 1 149 68 29 127 29.3
## 220 2 92 52 0 0 30.1
## 221 2 174 88 37 120 44.5
## 222 2 106 56 27 165 29.0
## 223 4 95 60 32 0 35.4
## 224 1 102 74 0 0 39.5
## 225 11 120 80 37 150 42.3
## 226 1 147 94 41 0 49.3
## 227 1 81 74 41 57 46.3
## 228 1 121 78 39 74 39.0
## 229 2 88 58 26 16 28.4
## 230 2 122 70 27 0 36.8
## 231 1 126 60 0 0 30.1
## DiabetesPedigreeFunction Age Outcome Pvalue POutcome
## 1 2.288 33 1 0.593453069 1
## 2 0.201 30 0 0.149439373 0
## 3 0.248 26 1 0.056581468 0
## 4 0.183 33 0 0.326340182 0
## 5 0.529 32 1 0.201457990 0
## 6 0.263 29 1 0.332409252 0
## 7 0.205 41 1 0.488197241 0
## 8 0.257 43 1 0.774027865 1
## 9 0.487 22 0 0.036143512 0
## 10 0.337 38 0 0.296037049 0
## 11 0.503 27 1 0.141630959 0
## 12 0.271 26 0 0.801375488 1
## 13 0.254 41 1 0.932941722 1
## 14 0.962 31 0 0.294811501 0
## 15 0.173 22 0 0.242131456 0
## 16 0.699 24 0 0.238582209 0
## 17 0.258 42 1 0.329177853 0
## 18 0.203 32 0 0.115978769 0
## 19 0.867 28 1 0.121714489 0
## 20 0.411 26 0 0.382132350 0
## 21 0.231 23 0 0.398050760 0
## 22 0.140 22 0 0.086452816 0
## 23 0.698 27 0 0.157222245 0
## 24 0.153 43 1 0.852933818 1
## 25 0.261 42 0 0.366567022 0
## 26 0.323 22 0 0.010874995 0
## 27 1.222 33 1 0.720268476 1
## 28 0.801 21 0 0.178947688 0
## 29 0.336 25 0 0.091039300 0
## 30 0.543 46 1 0.763006291 1
## 31 0.391 25 0 0.077578914 0
## 32 0.223 21 0 0.056722336 0
## 33 0.260 24 0 0.306840804 0
## 34 0.452 30 0 0.500817330 1
## 35 0.356 30 1 0.742997422 1
## 36 0.597 21 0 0.074904217 0
## 37 0.703 29 0 0.198932173 0
## 38 0.286 38 0 0.339478343 0
## 39 0.318 22 0 0.161575811 0
## 40 0.572 21 0 0.003094709 0
## 41 0.432 37 0 0.089409029 0
## 42 1.189 42 1 0.782230098 1
## 43 0.817 47 1 0.970587052 1
## 44 0.368 21 0 0.090149037 0
## 45 0.743 32 1 0.212730819 0
## 46 0.495 29 0 0.119572897 0
## 47 0.678 23 0 0.145841011 0
## 48 0.190 47 0 0.798509146 1
## 49 0.956 37 1 0.554890687 1
## 50 0.725 23 0 0.212547204 0
## 51 0.745 41 1 0.937612819 1
## 52 1.321 33 1 0.217540595 0
## 53 0.142 21 0 0.076226528 0
## 54 0.136 42 0 0.072910662 0
## 55 0.395 29 1 0.790465230 1
## 56 0.150 29 1 0.496738065 0
## 57 0.236 28 0 0.512823644 1
## 58 0.605 57 1 0.955648734 1
## 59 0.289 21 0 0.096523193 0
## 60 0.355 41 1 0.900934993 1
## 61 0.290 25 0 0.037518103 0
## 62 0.431 24 1 0.581246247 1
## 63 0.742 38 1 0.917181564 1
## 64 0.261 41 1 0.367197611 0
## 65 1.072 21 1 0.715348770 1
## 66 0.805 66 1 0.505246469 1
## 67 0.209 37 0 0.261314649 0
## 68 0.666 26 0 0.042118557 0
## 69 0.198 26 0 0.121912465 0
## 70 0.652 24 1 0.749637729 1
## 71 0.089 24 0 0.413333505 0
## 72 0.831 32 1 0.772169020 1
## 73 1.318 33 1 0.230310135 0
## 74 0.258 41 0 0.464166230 0
## 75 0.427 23 0 0.902687196 1
## 76 0.143 23 0 0.110201892 0
## 77 0.926 44 1 0.202248049 0
## 78 0.655 24 0 0.689101682 1
## 79 0.299 34 0 0.812900805 1
## 80 0.612 24 0 0.121237471 0
## 81 0.200 63 0 0.420528852 0
## 82 0.240 28 1 0.382396672 0
## 83 0.128 21 0 0.077443868 0
## 84 0.254 40 0 0.109296455 0
## 85 0.296 29 1 0.158040118 0
## 86 0.619 34 0 0.756985367 1
## 87 0.757 25 1 0.170489920 0
## 88 0.520 24 0 0.170655891 0
## 89 0.412 46 1 0.531849446 1
## 90 0.840 58 0 0.159723291 0
## 91 0.422 25 1 0.406902376 0
## 92 0.143 21 0 0.152095614 0
## 93 0.875 30 1 0.258042125 0
## 94 0.313 41 0 0.052878843 0
## 95 0.433 27 1 0.363227723 0
## 96 0.284 30 0 0.032428345 0
## 97 0.150 28 0 0.334238122 0
## 98 0.527 31 0 0.246998292 0
## 99 0.197 25 1 0.176372884 0
## 100 0.254 36 1 0.124485828 0
## 101 0.148 21 0 0.222558561 0
## 102 0.692 30 1 0.263990087 0
## 103 0.200 37 0 0.922299770 1
## 104 1.476 46 0 0.185150001 0
## 105 0.166 25 0 0.078344614 0
## 106 0.282 41 1 0.916169973 1
## 107 0.893 33 1 0.759354350 1
## 108 0.472 22 0 0.150178066 0
## 109 0.279 26 0 0.045413856 0
## 110 0.346 37 1 0.009963658 0
## 111 0.237 29 0 0.258355901 0
## 112 0.580 24 0 0.042870929 0
## 113 0.385 30 0 0.578302965 1
## 114 0.368 29 1 0.257632337 0
## 115 0.225 25 0 0.177798963 0
## 116 0.528 58 1 0.838184198 1
## 117 0.509 22 0 0.105628346 0
## 118 0.947 21 0 0.072093666 0
## 119 0.660 35 1 0.265489161 0
## 120 0.949 28 0 0.121463422 0
## 121 0.444 42 0 0.097984168 0
## 122 0.340 27 1 0.913077827 1
## 123 0.196 22 1 0.285225910 0
## 124 0.389 25 0 0.021562024 0
## 125 0.161 31 1 0.122982150 0
## 126 0.280 38 0 0.097271109 0
## 127 0.376 46 1 0.173641952 0
## 128 0.702 28 1 0.842681824 1
## 129 0.674 28 0 0.246189686 0
## 130 1.095 22 0 0.054075177 0
## 131 0.219 28 1 0.198168593 0
## 132 0.507 26 0 0.462214303 0
## 133 0.561 21 0 0.049242592 0
## 134 0.205 29 1 0.654307719 1
## 135 0.244 41 0 0.808060407 1
## 136 0.415 23 0 0.016782762 0
## 137 1.001 51 1 0.814564493 1
## 138 0.416 26 0 0.011859238 0
## 139 0.705 39 0 0.134389059 0
## 140 0.183 38 1 0.416539399 0
## 141 0.571 27 0 0.887746193 1
## 142 0.210 50 0 0.430306402 0
## 143 0.126 24 0 0.173260903 0
## 144 0.162 39 0 0.293246318 0
## 145 0.419 63 0 0.256947939 0
## 146 0.197 29 0 0.226067456 0
## 147 0.551 67 0 0.851622050 1
## 148 0.629 24 0 0.098854134 0
## 149 0.145 33 0 0.149119253 0
## 150 0.174 22 0 0.002875209 0
## 151 0.313 21 0 0.094887712 0
## 152 0.738 41 0 0.194138564 0
## 153 0.409 64 0 0.226727453 0
## 154 0.207 21 0 0.129601003 0
## 155 0.200 58 0 0.095866194 0
## 156 0.180 41 0 0.218196025 0
## 157 0.582 60 0 0.140975727 0
## 158 0.444 21 0 0.029283347 0
## 159 1.251 24 0 0.050921234 0
## 160 0.302 23 1 0.463386619 0
## 161 0.197 46 0 0.073137870 0
## 162 0.735 67 0 0.005981411 0
## 163 0.804 23 0 0.284692239 0
## 164 0.549 27 1 0.304376361 0
## 165 0.471 28 0 0.090902458 0
## 166 0.218 30 0 0.154828302 0
## 167 0.237 58 0 0.213569854 0
## 168 0.126 42 0 0.707339887 1
## 169 0.497 32 0 0.114310660 0
## 170 0.601 27 0 0.060944230 0
## 171 0.748 22 0 0.054788896 0
## 172 0.338 37 0 0.551867589 1
## 173 0.203 33 1 0.213186164 0
## 174 0.268 21 0 0.113140108 0
## 175 0.813 35 0 0.125741950 0
## 176 0.371 21 1 0.642730901 1
## 177 0.190 42 0 0.373530149 0
## 178 0.129 41 1 0.686441815 1
## 179 0.692 54 1 0.708088762 1
## 180 0.482 25 0 0.020686751 0
## 181 0.138 23 0 0.066777005 0
## 182 0.787 40 1 0.865402556 1
## 183 0.157 30 0 0.210977424 0
## 184 1.282 50 1 0.256649690 0
## 185 0.141 24 1 0.215792040 0
## 186 1.698 28 0 0.036692991 0
## 187 1.461 45 0 0.927430981 1
## 188 0.158 21 0 0.131967981 0
## 189 0.393 21 0 0.242573080 0
## 190 0.148 21 0 0.057666432 0
## 191 0.343 23 0 0.095801487 0
## 192 0.115 22 0 0.155454021 0
## 193 0.465 38 1 0.396859345 0
## 194 0.871 32 1 0.367488463 0
## 195 0.178 50 1 0.500156374 1
## 196 0.142 22 0 0.145703995 0
## 197 0.155 22 0 0.043246238 0
## 198 0.190 51 0 0.703738097 1
## 199 1.292 27 1 0.073366665 0
## 200 1.394 22 1 0.939424513 1
## 201 0.141 40 1 0.273523007 0
## 202 0.880 22 0 0.822680821 1
## 203 0.230 53 1 0.563619779 1
## 204 0.127 25 1 0.349827431 0
## 205 0.614 23 0 0.055292759 0
## 206 0.332 22 0 0.010238053 0
## 207 0.591 25 0 0.297895184 0
## 208 0.181 29 0 0.093207460 0
## 209 0.886 23 0 0.374306500 0
## 210 0.128 43 1 0.501379314 1
## 211 0.268 31 1 0.618349905 1
## 212 0.177 28 0 0.184787820 0
## 213 0.261 30 1 0.030256018 0
## 214 0.176 22 0 0.336401685 0
## 215 0.148 45 1 0.811987602 1
## 216 0.595 56 0 0.107387105 0
## 217 0.415 24 0 0.181497579 0
## 218 0.378 52 1 0.196722084 0
## 219 0.349 42 1 0.349201049 0
## 220 0.141 22 0 0.074166777 0
## 221 0.646 24 1 0.884764186 1
## 222 0.426 22 0 0.107278802 0
## 223 0.284 28 0 0.170740321 0
## 224 0.293 42 1 0.202467082 0
## 225 0.785 48 1 0.743959351 1
## 226 0.358 27 1 0.791863010 1
## 227 1.096 32 0 0.189724594 0
## 228 0.261 28 0 0.330208958 0
## 229 0.766 22 0 0.052684467 0
## 230 0.340 27 0 0.326797056 0
## 231 0.349 47 1 0.199282224 0Observation
Predicted outcome is added as a column based on the resval.
summarise(group_by(test, Outcome), n())## # A tibble: 2 × 2
## Outcome `n()`
## <int> <int>
## 1 0 145
## 2 1 86Confusion Matrix of Test data
prdVal11 <- predict(mgmModel,test, type='response')
prdBln21 <- ifelse(prdVal11 > 0.5, 1, 0)
cnfmtrx <- table(prd=prdBln21, act=test$Outcome)
confusionMatrix(cnfmtrx)## Confusion Matrix and Statistics
##
## act
## prd 0 1
## 0 127 45
## 1 18 41
##
## Accuracy : 0.7273
## 95% CI : (0.665, 0.7836)
## No Information Rate : 0.6277
## P-Value [Acc > NIR] : 0.0008922
##
## Kappa : 0.3767
## Mcnemar's Test P-Value : 0.0010540
##
## Sensitivity : 0.8759
## Specificity : 0.4767
## Pos Pred Value : 0.7384
## Neg Pred Value : 0.6949
## Prevalence : 0.6277
## Detection Rate : 0.5498
## Detection Prevalence : 0.7446
## Balanced Accuracy : 0.6763
##
## 'Positive' Class : 0
## Observation
Accuracy between actual and predicted values of test data is around 75% and sensitivity is 83%.
test$POutcome <- as.factor(test$POutcome)
levels(test$POutcome) <- c("Non Diabetic", "Diabetic")
test## Pregnancies Glucose BloodPressure SkinThickness Insulin BMI
## 1 0 137 40 35 168 43.1
## 2 5 116 74 0 0 25.6
## 3 3 78 50 32 88 31.0
## 4 1 103 30 38 83 43.3
## 5 1 115 70 30 96 34.6
## 6 9 119 80 35 0 29.0
## 7 10 125 70 26 115 31.1
## 8 7 147 76 0 0 39.4
## 9 1 97 66 15 140 23.2
## 10 5 117 92 0 0 34.1
## 11 2 90 68 42 0 38.2
## 12 3 180 64 25 70 34.0
## 13 7 187 68 39 304 37.7
## 14 0 100 88 60 110 46.8
## 15 0 105 64 41 142 41.5
## 16 2 141 58 34 128 25.4
## 17 7 114 66 0 0 32.8
## 18 5 99 74 27 0 29.0
## 19 2 100 66 20 90 32.9
## 20 5 139 64 35 140 28.6
## 21 4 129 86 20 270 35.1
## 22 3 113 44 13 0 22.4
## 23 2 110 74 29 125 32.4
## 24 15 136 70 32 110 37.1
## 25 7 81 78 40 48 46.7
## 26 1 71 48 18 76 20.4
## 27 1 163 72 0 0 39.0
## 28 1 126 56 29 152 28.7
## 29 3 83 58 31 18 34.3
## 30 8 155 62 26 495 34.0
## 31 4 76 62 0 0 34.0
## 32 4 99 76 15 51 23.2
## 33 6 111 64 39 0 34.2
## 34 3 120 70 30 135 42.9
## 35 3 170 64 37 225 34.5
## 36 0 100 70 26 50 30.8
## 37 0 129 80 0 0 31.2
## 38 5 106 82 30 0 39.5
## 39 2 108 52 26 63 32.5
## 40 0 102 75 23 0 0.0
## 41 4 114 65 0 0 21.9
## 42 9 156 86 28 155 34.3
## 43 17 163 72 41 114 40.9
## 44 2 100 64 23 0 29.7
## 45 0 131 88 0 0 31.6
## 46 3 111 90 12 78 28.4
## 47 1 79 60 42 48 43.5
## 48 5 143 78 0 0 45.0
## 49 5 130 82 0 0 39.1
## 50 0 119 64 18 92 34.9
## 51 7 194 68 28 0 35.9
## 52 1 128 98 41 58 32.0
## 53 3 111 62 0 0 22.6
## 54 8 85 55 20 0 24.4
## 55 5 158 84 41 210 39.4
## 56 4 148 60 27 318 30.9
## 57 1 138 82 0 0 40.1
## 58 8 196 76 29 280 37.5
## 59 1 96 64 27 87 33.2
## 60 7 184 84 33 0 35.5
## 61 2 81 60 22 0 27.7
## 62 0 140 65 26 130 42.6
## 63 12 151 70 40 271 41.8
## 64 5 112 66 0 0 37.8
## 65 0 177 60 29 478 34.6
## 66 2 158 90 0 0 31.6
## 67 7 119 0 0 0 25.2
## 68 1 100 66 15 56 23.6
## 69 0 101 76 0 0 35.7
## 70 3 162 52 38 0 37.2
## 71 0 117 80 31 53 45.2
## 72 9 164 84 21 0 30.8
## 73 6 119 50 22 176 27.1
## 74 10 122 68 0 0 31.2
## 75 0 165 90 33 680 52.3
## 76 1 111 86 19 0 30.1
## 77 12 92 62 7 258 27.6
## 78 1 193 50 16 375 25.9
## 79 3 191 68 15 130 30.9
## 80 4 95 70 32 0 32.1
## 81 3 142 80 15 0 32.4
## 82 2 146 0 0 0 27.5
## 83 2 108 62 32 56 25.2
## 84 3 122 78 0 0 23.0
## 85 7 106 60 24 0 26.5
## 86 5 155 84 44 545 38.7
## 87 0 107 62 30 74 36.6
## 88 0 126 84 29 215 30.7
## 89 14 100 78 25 184 36.6
## 90 8 112 72 0 0 23.6
## 91 2 144 58 33 135 31.6
## 92 0 137 68 14 148 24.8
## 93 2 124 68 28 205 32.9
## 94 6 80 66 30 0 26.2
## 95 2 155 74 17 96 26.6
## 96 3 99 80 11 64 19.3
## 97 3 115 66 39 140 38.1
## 98 4 129 60 12 231 27.5
## 99 3 112 74 30 0 31.6
## 100 0 124 70 20 0 27.4
## 101 2 112 75 32 0 35.7
## 102 1 122 64 32 156 35.1
## 103 10 179 70 0 0 35.1
## 104 8 118 72 19 0 23.1
## 105 2 87 58 16 52 32.7
## 106 1 180 0 0 0 43.3
## 107 9 152 78 34 171 34.2
## 108 1 130 70 13 105 25.9
## 109 3 99 62 19 74 21.8
## 110 5 0 80 32 0 41.0
## 111 4 92 80 0 0 42.2
## 112 1 90 62 12 43 27.2
## 113 4 147 74 25 293 34.9
## 114 6 124 72 0 0 27.6
## 115 2 105 58 40 94 34.9
## 116 12 140 82 43 325 39.2
## 117 1 87 60 37 75 37.2
## 118 1 109 60 8 182 25.4
## 119 5 116 74 29 0 32.3
## 120 3 100 68 23 81 31.6
## 121 1 100 66 29 196 32.0
## 122 5 166 76 0 0 45.7
## 123 0 131 66 40 0 34.3
## 124 3 82 70 0 0 21.1
## 125 4 95 64 0 0 32.0
## 126 9 72 78 25 0 31.6
## 127 4 115 72 0 0 28.9
## 128 1 172 68 49 579 42.4
## 129 6 102 90 39 0 35.7
## 130 1 97 68 21 0 27.2
## 131 3 129 64 29 115 26.4
## 132 1 119 88 41 170 45.3
## 133 2 94 68 18 76 26.0
## 134 0 141 0 0 0 42.4
## 135 12 140 85 33 0 37.4
## 136 1 82 64 13 95 21.2
## 137 10 148 84 48 237 37.6
## 138 1 71 62 0 0 21.8
## 139 8 74 70 40 49 35.3
## 140 8 120 0 0 0 30.0
## 141 6 154 78 41 140 46.1
## 142 7 136 90 0 0 29.9
## 143 4 114 64 0 0 28.9
## 144 8 126 74 38 75 25.9
## 145 4 132 86 31 0 28.0
## 146 0 123 88 37 0 35.2
## 147 8 194 80 0 0 26.1
## 148 2 83 65 28 66 36.8
## 149 4 99 68 38 0 32.8
## 150 3 80 0 0 0 0.0
## 151 2 117 90 19 71 25.2
## 152 7 94 64 25 79 33.3
## 153 8 120 78 0 0 25.0
## 154 0 139 62 17 210 22.1
## 155 9 91 68 0 0 24.2
## 156 13 76 60 0 0 32.8
## 157 6 129 90 7 326 19.6
## 158 3 87 60 18 0 21.8
## 159 1 77 56 30 56 33.3
## 160 4 132 0 0 0 32.9
## 161 0 105 90 0 0 29.6
## 162 0 57 60 0 0 21.7
## 163 0 127 80 37 210 36.3
## 164 3 128 72 25 190 32.4
## 165 1 84 64 23 115 36.9
## 166 1 97 70 40 0 38.1
## 167 8 110 76 0 0 27.8
## 168 11 103 68 40 0 46.2
## 169 6 99 60 19 54 26.9
## 170 0 91 80 0 0 32.4
## 171 2 95 54 14 88 26.1
## 172 4 154 72 29 126 31.3
## 173 0 121 66 30 165 34.3
## 174 2 130 96 0 0 22.6
## 175 6 108 44 20 130 24.0
## 176 0 151 90 46 0 42.1
## 177 8 100 76 0 0 38.7
## 178 8 143 66 0 0 34.9
## 179 7 150 78 29 126 35.2
## 180 1 92 62 25 41 19.5
## 181 1 111 62 13 182 24.0
## 182 7 168 88 42 321 38.2
## 183 6 117 96 0 0 28.7
## 184 9 112 82 24 0 28.2
## 185 0 119 0 0 0 32.4
## 186 2 92 76 20 0 24.2
## 187 6 183 94 0 0 40.8
## 188 2 108 64 0 0 30.8
## 189 0 132 78 0 0 32.4
## 190 4 94 65 22 0 24.7
## 191 2 111 60 0 0 26.2
## 192 1 128 82 17 183 27.5
## 193 13 104 72 0 0 31.2
## 194 7 97 76 32 91 40.9
## 195 6 147 80 0 0 29.5
## 196 1 106 70 28 135 34.2
## 197 2 101 58 35 90 21.8
## 198 11 127 106 0 0 39.0
## 199 3 80 82 31 70 34.2
## 200 1 199 76 43 0 42.9
## 201 10 111 70 27 0 27.5
## 202 3 123 100 35 240 57.3
## 203 9 156 86 0 0 24.8
## 204 3 121 52 0 0 36.0
## 205 2 101 58 17 265 24.2
## 206 2 56 56 28 45 24.2
## 207 2 129 74 26 205 33.2
## 208 1 107 50 19 0 28.3
## 209 2 121 70 32 95 39.1
## 210 7 142 90 24 480 30.4
## 211 3 169 74 19 125 29.9
## 212 6 80 80 36 0 39.8
## 213 10 115 0 0 0 0.0
## 214 2 127 46 21 335 34.4
## 215 9 164 78 0 0 32.8
## 216 10 94 72 18 0 23.1
## 217 1 108 60 46 178 35.5
## 218 5 97 76 27 0 35.6
## 219 1 149 68 29 127 29.3
## 220 2 92 52 0 0 30.1
## 221 2 174 88 37 120 44.5
## 222 2 106 56 27 165 29.0
## 223 4 95 60 32 0 35.4
## 224 1 102 74 0 0 39.5
## 225 11 120 80 37 150 42.3
## 226 1 147 94 41 0 49.3
## 227 1 81 74 41 57 46.3
## 228 1 121 78 39 74 39.0
## 229 2 88 58 26 16 28.4
## 230 2 122 70 27 0 36.8
## 231 1 126 60 0 0 30.1
## DiabetesPedigreeFunction Age Outcome Pvalue POutcome
## 1 2.288 33 1 0.593453069 Diabetic
## 2 0.201 30 0 0.149439373 Non Diabetic
## 3 0.248 26 1 0.056581468 Non Diabetic
## 4 0.183 33 0 0.326340182 Non Diabetic
## 5 0.529 32 1 0.201457990 Non Diabetic
## 6 0.263 29 1 0.332409252 Non Diabetic
## 7 0.205 41 1 0.488197241 Non Diabetic
## 8 0.257 43 1 0.774027865 Diabetic
## 9 0.487 22 0 0.036143512 Non Diabetic
## 10 0.337 38 0 0.296037049 Non Diabetic
## 11 0.503 27 1 0.141630959 Non Diabetic
## 12 0.271 26 0 0.801375488 Diabetic
## 13 0.254 41 1 0.932941722 Diabetic
## 14 0.962 31 0 0.294811501 Non Diabetic
## 15 0.173 22 0 0.242131456 Non Diabetic
## 16 0.699 24 0 0.238582209 Non Diabetic
## 17 0.258 42 1 0.329177853 Non Diabetic
## 18 0.203 32 0 0.115978769 Non Diabetic
## 19 0.867 28 1 0.121714489 Non Diabetic
## 20 0.411 26 0 0.382132350 Non Diabetic
## 21 0.231 23 0 0.398050760 Non Diabetic
## 22 0.140 22 0 0.086452816 Non Diabetic
## 23 0.698 27 0 0.157222245 Non Diabetic
## 24 0.153 43 1 0.852933818 Diabetic
## 25 0.261 42 0 0.366567022 Non Diabetic
## 26 0.323 22 0 0.010874995 Non Diabetic
## 27 1.222 33 1 0.720268476 Diabetic
## 28 0.801 21 0 0.178947688 Non Diabetic
## 29 0.336 25 0 0.091039300 Non Diabetic
## 30 0.543 46 1 0.763006291 Diabetic
## 31 0.391 25 0 0.077578914 Non Diabetic
## 32 0.223 21 0 0.056722336 Non Diabetic
## 33 0.260 24 0 0.306840804 Non Diabetic
## 34 0.452 30 0 0.500817330 Diabetic
## 35 0.356 30 1 0.742997422 Diabetic
## 36 0.597 21 0 0.074904217 Non Diabetic
## 37 0.703 29 0 0.198932173 Non Diabetic
## 38 0.286 38 0 0.339478343 Non Diabetic
## 39 0.318 22 0 0.161575811 Non Diabetic
## 40 0.572 21 0 0.003094709 Non Diabetic
## 41 0.432 37 0 0.089409029 Non Diabetic
## 42 1.189 42 1 0.782230098 Diabetic
## 43 0.817 47 1 0.970587052 Diabetic
## 44 0.368 21 0 0.090149037 Non Diabetic
## 45 0.743 32 1 0.212730819 Non Diabetic
## 46 0.495 29 0 0.119572897 Non Diabetic
## 47 0.678 23 0 0.145841011 Non Diabetic
## 48 0.190 47 0 0.798509146 Diabetic
## 49 0.956 37 1 0.554890687 Diabetic
## 50 0.725 23 0 0.212547204 Non Diabetic
## 51 0.745 41 1 0.937612819 Diabetic
## 52 1.321 33 1 0.217540595 Non Diabetic
## 53 0.142 21 0 0.076226528 Non Diabetic
## 54 0.136 42 0 0.072910662 Non Diabetic
## 55 0.395 29 1 0.790465230 Diabetic
## 56 0.150 29 1 0.496738065 Non Diabetic
## 57 0.236 28 0 0.512823644 Diabetic
## 58 0.605 57 1 0.955648734 Diabetic
## 59 0.289 21 0 0.096523193 Non Diabetic
## 60 0.355 41 1 0.900934993 Diabetic
## 61 0.290 25 0 0.037518103 Non Diabetic
## 62 0.431 24 1 0.581246247 Diabetic
## 63 0.742 38 1 0.917181564 Diabetic
## 64 0.261 41 1 0.367197611 Non Diabetic
## 65 1.072 21 1 0.715348770 Diabetic
## 66 0.805 66 1 0.505246469 Diabetic
## 67 0.209 37 0 0.261314649 Non Diabetic
## 68 0.666 26 0 0.042118557 Non Diabetic
## 69 0.198 26 0 0.121912465 Non Diabetic
## 70 0.652 24 1 0.749637729 Diabetic
## 71 0.089 24 0 0.413333505 Non Diabetic
## 72 0.831 32 1 0.772169020 Diabetic
## 73 1.318 33 1 0.230310135 Non Diabetic
## 74 0.258 41 0 0.464166230 Non Diabetic
## 75 0.427 23 0 0.902687196 Diabetic
## 76 0.143 23 0 0.110201892 Non Diabetic
## 77 0.926 44 1 0.202248049 Non Diabetic
## 78 0.655 24 0 0.689101682 Diabetic
## 79 0.299 34 0 0.812900805 Diabetic
## 80 0.612 24 0 0.121237471 Non Diabetic
## 81 0.200 63 0 0.420528852 Non Diabetic
## 82 0.240 28 1 0.382396672 Non Diabetic
## 83 0.128 21 0 0.077443868 Non Diabetic
## 84 0.254 40 0 0.109296455 Non Diabetic
## 85 0.296 29 1 0.158040118 Non Diabetic
## 86 0.619 34 0 0.756985367 Diabetic
## 87 0.757 25 1 0.170489920 Non Diabetic
## 88 0.520 24 0 0.170655891 Non Diabetic
## 89 0.412 46 1 0.531849446 Diabetic
## 90 0.840 58 0 0.159723291 Non Diabetic
## 91 0.422 25 1 0.406902376 Non Diabetic
## 92 0.143 21 0 0.152095614 Non Diabetic
## 93 0.875 30 1 0.258042125 Non Diabetic
## 94 0.313 41 0 0.052878843 Non Diabetic
## 95 0.433 27 1 0.363227723 Non Diabetic
## 96 0.284 30 0 0.032428345 Non Diabetic
## 97 0.150 28 0 0.334238122 Non Diabetic
## 98 0.527 31 0 0.246998292 Non Diabetic
## 99 0.197 25 1 0.176372884 Non Diabetic
## 100 0.254 36 1 0.124485828 Non Diabetic
## 101 0.148 21 0 0.222558561 Non Diabetic
## 102 0.692 30 1 0.263990087 Non Diabetic
## 103 0.200 37 0 0.922299770 Diabetic
## 104 1.476 46 0 0.185150001 Non Diabetic
## 105 0.166 25 0 0.078344614 Non Diabetic
## 106 0.282 41 1 0.916169973 Diabetic
## 107 0.893 33 1 0.759354350 Diabetic
## 108 0.472 22 0 0.150178066 Non Diabetic
## 109 0.279 26 0 0.045413856 Non Diabetic
## 110 0.346 37 1 0.009963658 Non Diabetic
## 111 0.237 29 0 0.258355901 Non Diabetic
## 112 0.580 24 0 0.042870929 Non Diabetic
## 113 0.385 30 0 0.578302965 Diabetic
## 114 0.368 29 1 0.257632337 Non Diabetic
## 115 0.225 25 0 0.177798963 Non Diabetic
## 116 0.528 58 1 0.838184198 Diabetic
## 117 0.509 22 0 0.105628346 Non Diabetic
## 118 0.947 21 0 0.072093666 Non Diabetic
## 119 0.660 35 1 0.265489161 Non Diabetic
## 120 0.949 28 0 0.121463422 Non Diabetic
## 121 0.444 42 0 0.097984168 Non Diabetic
## 122 0.340 27 1 0.913077827 Diabetic
## 123 0.196 22 1 0.285225910 Non Diabetic
## 124 0.389 25 0 0.021562024 Non Diabetic
## 125 0.161 31 1 0.122982150 Non Diabetic
## 126 0.280 38 0 0.097271109 Non Diabetic
## 127 0.376 46 1 0.173641952 Non Diabetic
## 128 0.702 28 1 0.842681824 Diabetic
## 129 0.674 28 0 0.246189686 Non Diabetic
## 130 1.095 22 0 0.054075177 Non Diabetic
## 131 0.219 28 1 0.198168593 Non Diabetic
## 132 0.507 26 0 0.462214303 Non Diabetic
## 133 0.561 21 0 0.049242592 Non Diabetic
## 134 0.205 29 1 0.654307719 Diabetic
## 135 0.244 41 0 0.808060407 Diabetic
## 136 0.415 23 0 0.016782762 Non Diabetic
## 137 1.001 51 1 0.814564493 Diabetic
## 138 0.416 26 0 0.011859238 Non Diabetic
## 139 0.705 39 0 0.134389059 Non Diabetic
## 140 0.183 38 1 0.416539399 Non Diabetic
## 141 0.571 27 0 0.887746193 Diabetic
## 142 0.210 50 0 0.430306402 Non Diabetic
## 143 0.126 24 0 0.173260903 Non Diabetic
## 144 0.162 39 0 0.293246318 Non Diabetic
## 145 0.419 63 0 0.256947939 Non Diabetic
## 146 0.197 29 0 0.226067456 Non Diabetic
## 147 0.551 67 0 0.851622050 Diabetic
## 148 0.629 24 0 0.098854134 Non Diabetic
## 149 0.145 33 0 0.149119253 Non Diabetic
## 150 0.174 22 0 0.002875209 Non Diabetic
## 151 0.313 21 0 0.094887712 Non Diabetic
## 152 0.738 41 0 0.194138564 Non Diabetic
## 153 0.409 64 0 0.226727453 Non Diabetic
## 154 0.207 21 0 0.129601003 Non Diabetic
## 155 0.200 58 0 0.095866194 Non Diabetic
## 156 0.180 41 0 0.218196025 Non Diabetic
## 157 0.582 60 0 0.140975727 Non Diabetic
## 158 0.444 21 0 0.029283347 Non Diabetic
## 159 1.251 24 0 0.050921234 Non Diabetic
## 160 0.302 23 1 0.463386619 Non Diabetic
## 161 0.197 46 0 0.073137870 Non Diabetic
## 162 0.735 67 0 0.005981411 Non Diabetic
## 163 0.804 23 0 0.284692239 Non Diabetic
## 164 0.549 27 1 0.304376361 Non Diabetic
## 165 0.471 28 0 0.090902458 Non Diabetic
## 166 0.218 30 0 0.154828302 Non Diabetic
## 167 0.237 58 0 0.213569854 Non Diabetic
## 168 0.126 42 0 0.707339887 Diabetic
## 169 0.497 32 0 0.114310660 Non Diabetic
## 170 0.601 27 0 0.060944230 Non Diabetic
## 171 0.748 22 0 0.054788896 Non Diabetic
## 172 0.338 37 0 0.551867589 Diabetic
## 173 0.203 33 1 0.213186164 Non Diabetic
## 174 0.268 21 0 0.113140108 Non Diabetic
## 175 0.813 35 0 0.125741950 Non Diabetic
## 176 0.371 21 1 0.642730901 Diabetic
## 177 0.190 42 0 0.373530149 Non Diabetic
## 178 0.129 41 1 0.686441815 Diabetic
## 179 0.692 54 1 0.708088762 Diabetic
## 180 0.482 25 0 0.020686751 Non Diabetic
## 181 0.138 23 0 0.066777005 Non Diabetic
## 182 0.787 40 1 0.865402556 Diabetic
## 183 0.157 30 0 0.210977424 Non Diabetic
## 184 1.282 50 1 0.256649690 Non Diabetic
## 185 0.141 24 1 0.215792040 Non Diabetic
## 186 1.698 28 0 0.036692991 Non Diabetic
## 187 1.461 45 0 0.927430981 Diabetic
## 188 0.158 21 0 0.131967981 Non Diabetic
## 189 0.393 21 0 0.242573080 Non Diabetic
## 190 0.148 21 0 0.057666432 Non Diabetic
## 191 0.343 23 0 0.095801487 Non Diabetic
## 192 0.115 22 0 0.155454021 Non Diabetic
## 193 0.465 38 1 0.396859345 Non Diabetic
## 194 0.871 32 1 0.367488463 Non Diabetic
## 195 0.178 50 1 0.500156374 Diabetic
## 196 0.142 22 0 0.145703995 Non Diabetic
## 197 0.155 22 0 0.043246238 Non Diabetic
## 198 0.190 51 0 0.703738097 Diabetic
## 199 1.292 27 1 0.073366665 Non Diabetic
## 200 1.394 22 1 0.939424513 Diabetic
## 201 0.141 40 1 0.273523007 Non Diabetic
## 202 0.880 22 0 0.822680821 Diabetic
## 203 0.230 53 1 0.563619779 Diabetic
## 204 0.127 25 1 0.349827431 Non Diabetic
## 205 0.614 23 0 0.055292759 Non Diabetic
## 206 0.332 22 0 0.010238053 Non Diabetic
## 207 0.591 25 0 0.297895184 Non Diabetic
## 208 0.181 29 0 0.093207460 Non Diabetic
## 209 0.886 23 0 0.374306500 Non Diabetic
## 210 0.128 43 1 0.501379314 Diabetic
## 211 0.268 31 1 0.618349905 Diabetic
## 212 0.177 28 0 0.184787820 Non Diabetic
## 213 0.261 30 1 0.030256018 Non Diabetic
## 214 0.176 22 0 0.336401685 Non Diabetic
## 215 0.148 45 1 0.811987602 Diabetic
## 216 0.595 56 0 0.107387105 Non Diabetic
## 217 0.415 24 0 0.181497579 Non Diabetic
## 218 0.378 52 1 0.196722084 Non Diabetic
## 219 0.349 42 1 0.349201049 Non Diabetic
## 220 0.141 22 0 0.074166777 Non Diabetic
## 221 0.646 24 1 0.884764186 Diabetic
## 222 0.426 22 0 0.107278802 Non Diabetic
## 223 0.284 28 0 0.170740321 Non Diabetic
## 224 0.293 42 1 0.202467082 Non Diabetic
## 225 0.785 48 1 0.743959351 Diabetic
## 226 0.358 27 1 0.791863010 Diabetic
## 227 1.096 32 0 0.189724594 Non Diabetic
## 228 0.261 28 0 0.330208958 Non Diabetic
## 229 0.766 22 0 0.052684467 Non Diabetic
## 230 0.340 27 0 0.326797056 Non Diabetic
## 231 0.349 47 1 0.199282224 Non Diabetic