# Linear regression in R
library(readxl)
## Warning: package 'readxl' was built under R version 4.3.3
AgeHeight <- read_excel("AgeHeight.xlsx")
ageandheight <- read_excel("AgeHeight.xlsx")
# Upload data
lmHeight = lm(height~ age, data = ageandheight)
# Create the linear regression
summary(lmHeight)
##
## Call:
## lm(formula = height ~ age, data = ageandheight)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.27238 -0.24248 -0.02762 0.16014 0.47238
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 64.9283 0.5084 127.71 < 2e-16 ***
## age 0.6350 0.0214 29.66 4.43e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.256 on 10 degrees of freedom
## Multiple R-squared: 0.9888, Adjusted R-squared: 0.9876
## F-statistic: 880 on 1 and 10 DF, p-value: 4.428e-11
# Create a linear regression w/ 2 variables
lmHeight2 = lm(height~ age + no_siblings, data = ageandheight)
summary(lmHeight2)
##
## Call:
## lm(formula = height ~ age + no_siblings, data = ageandheight)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.26297 -0.22462 -0.02021 0.16102 0.49752
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 64.90554 0.53526 121.260 8.96e-16 ***
## age 0.63751 0.02340 27.249 5.85e-10 ***
## no_siblings -0.01772 0.04735 -0.374 0.717
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2677 on 9 degrees of freedom
## Multiple R-squared: 0.9889, Adjusted R-squared: 0.9865
## F-statistic: 402.2 on 2 and 9 DF, p-value: 1.576e-09
# Insurance companies business model
insurance <- read.csv("C:/Users/angel/Documents/RPractice/insurance.csv", stringsAsFactors=TRUE)
View(insurance)
str(insurance)
## 'data.frame': 1338 obs. of 7 variables:
## $ age : int 19 18 28 33 32 31 46 37 37 60 ...
## $ sex : 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 ...
## $ charges : num 16885 1726 4449 21984 3867 ...
summary(insurance)
## age sex bmi children smoker
## Min. :18.00 female:662 Min. :15.96 Min. :0.000 no :1064
## 1st Qu.:27.00 male :676 1st Qu.:26.30 1st Qu.:0.000 yes: 274
## Median :39.00 Median :30.40 Median :1.000
## Mean :39.21 Mean :30.66 Mean :1.095
## 3rd Qu.:51.00 3rd Qu.:34.69 3rd Qu.:2.000
## Max. :64.00 Max. :53.13 Max. :5.000
## region charges
## northeast:324 Min. : 1122
## northwest:325 1st Qu.: 4740
## southeast:364 Median : 9382
## southwest:325 Mean :13270
## 3rd Qu.:16640
## Max. :63770
# Histogram of charges
hist(insurance$charges)
# Proportion of sex and smokers
table(insurance$sex)
##
## female male
## 662 676
table(insurance$smoker)
##
## no yes
## 1064 274
# **Relationship among features the correlation matrix**
# cor(x,y) > 0.5 <- Strong correlation
# 0.2 < cor(x,y) < 0.5 <- OK correlation
# cor(x,y) < 0.2 <- No correlation -> x & y are truly independent
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 relationships among features - scatter plot**
pairs(insurance[c('age','bmi', 'children','charges')])
library(psych)
## Warning: package 'psych' was built under R version 4.3.3
##
## Attaching package: 'psych'
## The following objects are masked from 'package:ggplot2':
##
## %+%, alpha
pairs.panels(insurance[c('age','bmi', 'children','charges')])
# Training a model on the data
#ins_model <- lm(charges~ age + children + bmi + sex + smoker + region, data = insurance)
ins_model <- lm(charges~ ., data = insurance)
print(ins_model)
##
## Call:
## lm(formula = charges ~ ., data = insurance)
##
## Coefficients:
## (Intercept) age sexmale bmi
## -11938.5 256.9 -131.3 339.2
## children smokeryes regionnorthwest regionsoutheast
## 475.5 23848.5 -353.0 -1035.0
## regionsouthwest
## -960.1
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
# Non-linear model
insurance$age2 <-insurance$age^2
# Transform -> converting a numeric variable to a binary indicator
insurance$bmi30 <- ifelse(insurance$bmi >= 30, 1, 0)
# Adding interaction effects
# shorthand -> charges~ bmi30 * smoker
# charges~ bmi30 + smokeryes + bmi30:smokeryes <- individual + individual + combined intersection
ins_model2 <- lm(charges~ age + age2 + children + bmi + bmi30 + smoker + region, data = insurance)
print(ins_model2)
##
## Call:
## lm(formula = charges ~ age + age2 + children + bmi + bmi30 +
## smoker + region, data = insurance)
##
## Coefficients:
## (Intercept) age age2 children
## -3018.810 -28.208 3.601 629.121
## bmi bmi30 smokeryes regionnorthwest
## 153.553 2722.826 23842.050 -399.461
## regionsoutheast regionsouthwest
## -887.945 -946.844
summary(ins_model2)
##
## Call:
## lm(formula = charges ~ age + age2 + children + bmi + bmi30 +
## smoker + region, data = insurance)
##
## Residuals:
## Min 1Q Median 3Q Max
## -12565.9 -3385.9 56.7 1342.0 29250.8
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3018.810 1821.496 -1.657 0.097690 .
## age -28.208 80.419 -0.351 0.725826
## age2 3.601 1.003 3.589 0.000344 ***
## children 629.121 142.304 4.421 1.06e-05 ***
## bmi 153.553 46.038 3.335 0.000875 ***
## bmi30 2722.826 547.385 4.974 7.41e-07 ***
## smokeryes 23842.050 406.089 58.711 < 2e-16 ***
## regionnorthwest -399.461 469.502 -0.851 0.395023
## regionsoutheast -887.945 472.699 -1.878 0.060537 .
## regionsouthwest -946.844 471.081 -2.010 0.044640 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5975 on 1328 degrees of freedom
## Multiple R-squared: 0.7582, Adjusted R-squared: 0.7565
## F-statistic: 462.7 on 9 and 1328 DF, p-value: < 2.2e-16