Importing the Dataset
df = read.csv('dataset.csv', header = TRUE)
attach(df)
names(df)## [1] "Charges" "Age" "Gender" "BMI" "children" "Smoking"
## [7] "Region"head(df)## Charges Age Gender BMI children Smoking Region
## 1 16885 19 female 27.900 0 yes southwest
## 2 1726 18 male 33.770 1 no southeast
## 3 4449 28 male 33.000 3 no southeast
## 4 21984 33 male 22.705 0 no northwest
## 5 3867 32 male 28.880 0 no northwest
## 6 3757 31 female 25.740 0 no southeastsummary(df)## Charges Age Gender BMI
## Min. : 1122 Min. :18.00 female:662 Min. :15.96
## 1st Qu.: 4740 1st Qu.:27.00 male :676 1st Qu.:26.30
## Median : 9382 Median :39.00 Median :30.40
## Mean :13270 Mean :39.21 Mean :30.66
## 3rd Qu.:16640 3rd Qu.:51.00 3rd Qu.:34.69
## Max. :63770 Max. :64.00 Max. :53.13
## children Smoking Region
## Min. :0.000 no :1064 northeast:324
## 1st Qu.:0.000 yes: 274 northwest:325
## Median :1.000 southeast:364
## Mean :1.095 southwest:325
## 3rd Qu.:2.000
## Max. :5.000hist(Charges, ylab = "Frequency", col = "blue",breaks = 30)
library(tidyverse)## ── Attaching packages ── tidyverse 1.2.1 ──## ✔ ggplot2 3.1.0 ✔ purrr 0.3.0
## ✔ tibble 2.0.1 ✔ dplyr 0.8.0.1
## ✔ tidyr 0.8.2 ✔ stringr 1.3.1
## ✔ readr 1.3.1 ✔ forcats 0.3.0## ── Conflicts ───── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()ggplot(df,aes(x = Charges, color = Smoking))+
geom_histogram(fill = "white", position = "dodge")+
theme(legend.position = "top")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
ggplot(df)+
geom_violin(mapping = aes(x = Smoking, y = Charges, fill = Gender), draw_quantiles = (c(0.25,0.5,0.75)))
ggplot(df)+
geom_point(mapping = aes(x = Age, y = Charges, colour = Smoking))
ggplot(df,aes(x = BMI))+
geom_histogram(fill = "blue", position = "dodge")+
theme(legend.position = "top")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
ggplot(df)+
geom_point(mapping = aes(x = BMI, y = Charges))
bg<-ggplot(df, aes(children))
bg+geom_bar(fill = "blue")
p<-ggplot(df, aes(children,y = Charges, group = children))
p+geom_boxplot(fill = "white", color = "blue")
df$Gender = as.numeric(df$Gender)
df$Smoking = as.numeric(df$Smoking)
df$Region = as.numeric(df$Region)library(corrplot)## corrplot 0.84 loadedcostCorr<-cor(df)corrplot(costCorr, method = "pie")
Before we perform independent two-sample T-test to check the mean difference in charges for smokers and non-smokers, we will look at the boxplot of those variables. The boxplot shows that smokers and non-smokers have unequal variances, so in the t-test we will set the parameter as unequal variances.
boxplot(Charges ~ Smoking)
Let’s perform the t-test. 1. Our Null Hypothesis is that Charges of smokers and non-smokers have equal means. 2. Alternative Hypothesis is Charges for smokers and non-smokers’ means are not equal. 3. We perform 2 sided test, because we have equal sign. 4. We take confidence interval of 95%.
?t.testt.test(Charges~Smoking, mu = 0, alt = "two.sided",conf.level = 0.95, var.equql = FALSE)##
## Welch Two Sample t-test
##
## data: Charges by Smoking
## t = -32.752, df = 311.85, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -25034.72 -22197.22
## sample estimates:
## mean in group no mean in group yes
## 8434.266 32050.234boxplot(Charges~Gender)
t.test(Charges~Gender, mu = 0, alt = "two.sided",conf.level = 0.95, var.equql = FALSE)##
## Welch Two Sample t-test
##
## data: Charges by Gender
## t = -2.1009, df = 1313.4, p-value = 0.03584
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -2682.46911 -91.83495
## sample estimates:
## mean in group female mean in group male
## 12569.59 13956.74One-way ANOVA, Region independent variable.
df$Region = as.factor(df$Region)
levels(Region)## [1] "northeast" "northwest" "southeast" "southwest"df = read.csv('dataset.csv', header = TRUE)
reg<-ggplot(df,aes(x = Region, y = Charges, fill = Region))
reg + geom_boxplot()
One-Way anova for Region Variable
oneWay<-aov(Charges~Region)
summary(oneWay)## Df Sum Sq Mean Sq F value Pr(>F)
## Region 3 1.301e+09 433589497 2.97 0.0309 *
## Residuals 1334 1.948e+11 146007098
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Multiple Linear Regression First Model. In the first model, we take three independent variables, Age, BMI and Smoking.
fit<-lm(Charges~Age + BMI + Smoking)
summary(fit)##
## Call:
## lm(formula = Charges ~ Age + BMI + Smoking)
##
## Residuals:
## Min 1Q Median 3Q Max
## -12415.1 -2971.2 -980.1 1480.3 28971.9
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -11676.84 937.57 -12.45 <2e-16 ***
## Age 259.55 11.93 21.75 <2e-16 ***
## BMI 322.61 27.49 11.74 <2e-16 ***
## Smokingyes 23823.69 412.87 57.70 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6092 on 1334 degrees of freedom
## Multiple R-squared: 0.7475, Adjusted R-squared: 0.7469
## F-statistic: 1316 on 3 and 1334 DF, p-value: < 2.2e-16plot(fit)
car::vif(fit)## Age BMI Smoking
## 1.012747 1.012128 1.000669car::vif(fit)## Age BMI Smoking
## 1.012747 1.012128 1.000669library(MASS)##
## Attaching package: 'MASS'## The following object is masked from 'package:dplyr':
##
## selectsresid<-studres(fit)
hist(sresid, main = "Distribution of Studentized Residuals",breaks = 40, xlab = "Studentized Residuals")
fit<-lm(Charges~Age + BMI + Smoking)
fit2<-lm(Charges~Age+BMI+Smoking+children)
anova(fit,fit2)## Analysis of Variance Table
##
## Model 1: Charges ~ Age + BMI + Smoking
## Model 2: Charges ~ Age + BMI + Smoking + children
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 1334 4.9513e+10
## 2 1333 4.9078e+10 1 434747446 11.808 0.0006079 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1fit2<-lm(Charges~Age+BMI+Smoking+children)
summary(fit2)##
## Call:
## lm(formula = Charges ~ Age + BMI + Smoking + children)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11897.7 -2920.9 -986.4 1392.1 29509.7
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -12102.76 941.98 -12.848 < 2e-16 ***
## Age 257.85 11.90 21.675 < 2e-16 ***
## BMI 321.85 27.38 11.756 < 2e-16 ***
## Smokingyes 23811.40 411.22 57.904 < 2e-16 ***
## children 473.49 137.79 3.436 0.000608 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6068 on 1333 degrees of freedom
## Multiple R-squared: 0.7497, Adjusted R-squared: 0.7489
## F-statistic: 998.1 on 4 and 1333 DF, p-value: < 2.2e-16