library(readxl)
AgeHeight <- read_excel("~/Downloads/CS 583/AgeHeight.xlsx")
View(AgeHeight)
lmHeight <- lm(height~age, data = AgeHeight)
lmHeight
##
## Call:
## lm(formula = height ~ age, data = AgeHeight)
##
## Coefficients:
## (Intercept) age
## 64.928 0.635
summary(lmHeight)
##
## Call:
## lm(formula = height ~ age, data = AgeHeight)
##
## 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
lmHeight2 <- lm(height ~ age + no_siblings, data = AgeHeight)
lmHeight2
##
## Call:
## lm(formula = height ~ age + no_siblings, data = AgeHeight)
##
## Coefficients:
## (Intercept) age no_siblings
## 64.90554 0.63751 -0.01772
summary(lmHeight2)
##
## Call:
## lm(formula = height ~ age + no_siblings, data = AgeHeight)
##
## 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
library(readxl)
insurance <- read.csv("~/Downloads/CS 583/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$charges)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1122 4740 9382 13270 16640 63770
hist(insurance$charges)
table(insurance$region)
##
## northeast northwest southeast southwest
## 324 325 364 325
table(insurance$sex)
##
## female male
## 662 676
table(insurance$smoker)
##
## no yes
## 1064 274
cor(insurance[c('age', 'bmi', 'children', 'charges')])
## age bmi children charges
## age 1.0000000 0.1092719 0.04246900 0.29900819
## bmi 0.1092719 1.0000000 0.01275890 0.19834097
## children 0.0424690 0.0127589 1.00000000 0.06799823
## charges 0.2990082 0.1983410 0.06799823 1.00000000
pairs(insurance[c('age','bmi','children','charges')])
library(psych)
pairs.panels(insurance[c('age', 'bmi','children','charges')])
ins_model<- lm(charges~age + children + bmi + sex + smoker + region, data = insurance)
#the period character(.) can be used to specify all features excluding those already specified
#in the formula so the code can be re-written as this:
ins_model<-lm(charges~.,data= insurance)
ins_model
##
## Call:
## lm(formula = charges ~ ., data = insurance)
##
## Coefficients:
## (Intercept) age sexmale bmi
## -11938.5 256.9 -131.3 339.2
## children smokeryes regionnorthwest regionsoutheast
## 475.5 23848.5 -353.0 -1035.0
## regionsouthwest
## -960.1
summary(ins_model)
##
## Call:
## lm(formula = charges ~ ., data = insurance)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11304.9 -2848.1 -982.1 1393.9 29992.8
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -11938.5 987.8 -12.086 < 2e-16 ***
## age 256.9 11.9 21.587 < 2e-16 ***
## sexmale -131.3 332.9 -0.394 0.693348
## bmi 339.2 28.6 11.860 < 2e-16 ***
## children 475.5 137.8 3.451 0.000577 ***
## smokeryes 23848.5 413.1 57.723 < 2e-16 ***
## regionnorthwest -353.0 476.3 -0.741 0.458769
## regionsoutheast -1035.0 478.7 -2.162 0.030782 *
## regionsouthwest -960.0 477.9 -2.009 0.044765 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6062 on 1329 degrees of freedom
## Multiple R-squared: 0.7509, Adjusted R-squared: 0.7494
## F-statistic: 500.8 on 8 and 1329 DF, p-value: < 2.2e-16
#improve model by adding non linear variable
insurance$age2<-insurance$age^2
#transformation_ convertign a numeric variable to a binary indicator
insurance$bmi30<-ifelse(insurance$bmi>=30, 1, 0)
#model specification- adding interaction effects
charges ~bmi30*smoker
## charges ~ bmi30 * smoker
charges~bmi30 + smokeryes + bmi30:smokeryes
## charges ~ bmi30 + smokeryes + bmi30:smokeryes
#putting all together-an improved regression model
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
#making predictions
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