getwd()
## [1] "F:/Seminar"
df <- read.csv(file = "Insurance.csv")
str(df)
## 'data.frame': 1338 obs. of 7 variables:
## $ age : int 19 18 28 33 32 31 46 37 37 60 ...
## $ Gender : Factor w/ 2 levels "female","male": 1 2 2 2 2 1 1 1 2 1 ...
## $ bmi : num 27.9 33.8 33 22.7 28.9 ...
## $ children: int 0 1 3 0 0 0 1 3 2 0 ...
## $ smoker : Factor w/ 2 levels "no","yes": 2 1 1 1 1 1 1 1 1 1 ...
## $ region : Factor w/ 4 levels "northeast","northwest",..: 4 3 3 2 2 3 3 2 1 2 ...
## $ Expences: num 16885 1726 4449 21984 3867 ...
# age = An integer indicating the age of the primary beneficiary
# Gender = The policy holder's gender
# bmi = The body mass index
# children = An integer indicating the num of children
# smoker = Whether the insured smokes or not
# region = Place of residence
colnames(df)[7] <- "Expences"
str(df)
## 'data.frame': 1338 obs. of 7 variables:
## $ age : int 19 18 28 33 32 31 46 37 37 60 ...
## $ Gender : Factor w/ 2 levels "female","male": 1 2 2 2 2 1 1 1 2 1 ...
## $ bmi : num 27.9 33.8 33 22.7 28.9 ...
## $ children: int 0 1 3 0 0 0 1 3 2 0 ...
## $ smoker : Factor w/ 2 levels "no","yes": 2 1 1 1 1 1 1 1 1 1 ...
## $ region : Factor w/ 4 levels "northeast","northwest",..: 4 3 3 2 2 3 3 2 1 2 ...
## $ Expences: num 16885 1726 4449 21984 3867 ...
table(df$region)
##
## northeast northwest southeast southwest
## 324 325 364 325
hist(df$Expences)
summary(df$Expences)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1122 4740 9382 13270 16640 63770
cor(df[-c(2,5,6)])
## age bmi children Expences
## age 1.0000000 0.1092719 0.04246900 0.29900819
## bmi 0.1092719 1.0000000 0.01275890 0.19834097
## children 0.0424690 0.0127589 1.00000000 0.06799823
## Expences 0.2990082 0.1983410 0.06799823 1.00000000
library(psych)
## Warning: package 'psych' was built under R version 3.5.3
pairs.panels(df[-c(2,5,6)])
attach(df)
model <- lm(Expences ~ age + children + bmi + Gender + smoker + region, data = df)
model
##
## Call:
## lm(formula = Expences ~ age + children + bmi + Gender + smoker +
## region, data = df)
##
## Coefficients:
## (Intercept) age children bmi
## -11938.5 256.9 475.5 339.2
## Gendermale smokeryes regionnorthwest regionsoutheast
## -131.3 23848.5 -353.0 -1035.0
## regionsouthwest
## -960.1
summary(model)
##
## Call:
## lm(formula = Expences ~ age + children + bmi + Gender + smoker +
## region, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11304.9 -2848.1 -982.1 1393.9 29992.8
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -11938.5 987.8 -12.086 < 2e-16 ***
## age 256.9 11.9 21.587 < 2e-16 ***
## children 475.5 137.8 3.451 0.000577 ***
## bmi 339.2 28.6 11.860 < 2e-16 ***
## Gendermale -131.3 332.9 -0.394 0.693348
## smokeryes 23848.5 413.1 57.723 < 2e-16 ***
## regionnorthwest -353.0 476.3 -0.741 0.458769
## regionsoutheast -1035.0 478.7 -2.162 0.030782 *
## regionsouthwest -960.0 477.9 -2.009 0.044765 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6062 on 1329 degrees of freedom
## Multiple R-squared: 0.7509, Adjusted R-squared: 0.7494
## F-statistic: 500.8 on 8 and 1329 DF, p-value: < 2.2e-16
df$age2 <- df$age^2
df$bmi30 <- ifelse(test = df$bmi >= 30, yes = 1,no = 0)
model2 <- lm(Expences ~ age + children + bmi + Gender + smoker + region + age2 +bmi30*smoker,
data = df)
summary(model2)
##
## Call:
## lm(formula = Expences ~ age + children + bmi + Gender + smoker +
## region + age2 + bmi30 * smoker, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -17296.4 -1656.0 -1263.3 -722.1 24160.2
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 134.2509 1362.7511 0.099 0.921539
## age -32.6851 59.8242 -0.546 0.584915
## children 678.5612 105.8831 6.409 2.04e-10 ***
## bmi 120.0196 34.2660 3.503 0.000476 ***
## Gendermale -496.8245 244.3659 -2.033 0.042240 *
## smokeryes 13404.6866 439.9491 30.469 < 2e-16 ***
## regionnorthwest -279.2038 349.2746 -0.799 0.424212
## regionsoutheast -828.5467 351.6352 -2.356 0.018604 *
## regionsouthwest -1222.6437 350.5285 -3.488 0.000503 ***
## age2 3.7316 0.7463 5.000 6.50e-07 ***
## bmi30 -1000.1403 422.8402 -2.365 0.018159 *
## smokeryes:bmi30 19810.7533 604.6567 32.764 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4445 on 1326 degrees of freedom
## Multiple R-squared: 0.8664, Adjusted R-squared: 0.8653
## F-statistic: 781.7 on 11 and 1326 DF, p-value: < 2.2e-16
test <- data.frame(35,"female",32,2,"no","northeast",30000,1225,1)
colnames(test) <- c("age","Gender","bmi","children","smoker","region","Expences","age2","bmi30")
pred <- predict(object = model2 , newdata = test)
pred
## 1
## 7759.058