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library(readr)
library(psych)
## Warning: package 'psych' was built under R version 4.4.3
insuranceDS <- read_csv("C:/Users/ijiol/OneDrive/Documents/R projects/R for Advanced Topics/Datasets/insurance.csv")
## Rows: 1338 Columns: 7
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (3): sex, smoker, region
## dbl (4): age, bmi, children, charges
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
insurance <- data.frame(insuranceDS, stringsAsFactors = TRUE)
str(insurance)
## 'data.frame':    1338 obs. of  7 variables:
##  $ age     : num  19 18 28 33 32 31 46 37 37 60 ...
##  $ sex     : chr  "female" "male" "male" "male" ...
##  $ bmi     : num  27.9 33.8 33 22.7 28.9 ...
##  $ children: num  0 1 3 0 0 0 1 3 2 0 ...
##  $ smoker  : chr  "yes" "no" "no" "no" ...
##  $ region  : chr  "southwest" "southeast" "southeast" "northwest" ...
##  $ charges : num  16885 1726 4449 21984 3867 ...
summary(insurance$charges)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1122    4740    9382   13270   16640   63770
hist(insurance$charges)

table(insurance$region)
## 
## northeast northwest southeast southwest 
##       324       325       364       325
cor(insurance[c("age", "bmi", "children", "charges")])
##                age       bmi   children    charges
## 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
## charges  0.2990082 0.1983410 0.06799823 1.00000000
#visualizing relathionships using scatter-plot matrix
pairs(insurance[c("age", "bmi", "children", "charges")])

#enhanced scatterplot
pairs.panels(insurance[c("age", "bmi", "children", "charges")])

#Building a model
ins_model <- lm(formula = charges~., data = insurance)

summary(ins_model)
## 
## Call:
## lm(formula = charges ~ ., data = insurance)
## 
## 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 ***
## sexmale           -131.3      332.9  -0.394 0.693348    
## bmi                339.2       28.6  11.860  < 2e-16 ***
## children           475.5      137.8   3.451 0.000577 ***
## 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
#improving model performance 
insurance$age2 <- insurance$age^2
insurance$bmi30 <- ifelse(insurance$bmi >= 30, 1, 0)
ins_model2 <- lm(charges ~ age + age2 + children + bmi + sex+ bmi30*smoker + region, data = insurance)
summary(ins_model2)
## 
## Call:
## lm(formula = charges ~ age + age2 + children + bmi + sex + bmi30 * 
##     smoker + region, data = insurance)
## 
## 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    
## age2                3.7316     0.7463   5.000 6.50e-07 ***
## children          678.5612   105.8831   6.409 2.04e-10 ***
## bmi               120.0196    34.2660   3.503 0.000476 ***
## sexmale          -496.8245   244.3659  -2.033 0.042240 *  
## bmi30           -1000.1403   422.8402  -2.365 0.018159 *  
## 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 ***
## bmi30:smokeryes 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
#using the regression model
insurance$pred <- predict(ins_model2, insurance)
cor(insurance$pred, insurance$charges)
## [1] 0.9308031
abline(a = 0, b = 1, col = "red", lwd = 3, lty = 2)

predict(ins_model2, data.frame(age = 30, age2 = 30^2, children = 2, bmi = 30, sex = "male", bmi30 = 1, smoker = "no", region = "northeast"))
##        1 
## 5972.859
predict(ins_model2, data.frame(age = 30, age2 = 30^2, children = 2, bmi = 30, sex = "female", bmi30 = 1, smoker = "no", region = "northeast"))
##        1 
## 6469.683

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