assignment - regression
Tomasz Dabrowski
28 05 2021
Body Fat prediction
knitr::opts_chunk$set(
echo = TRUE,
message = TRUE,
warning = TRUE
)
library(mplot)## Warning: package 'mplot' was built under R version 4.0.5data(bodyfat)
Bodyfat= bodyfat$Bodyfat
Neck = bodyfat$Neck
Chest = bodyfat$Chest
Abdo = bodyfat$Abdo
Hip = bodyfat$Hip
Thigh = bodyfat$Thigh
Knee = bodyfat$Knee
Ankle = bodyfat$Ankle
Bic = bodyfat$Bic
Fore = bodyfat$Fore
Wrist = bodyfat$Wrist
bf.lm <- lm(Bodyfat ~ Neck + Chest + Abdo + Hip + Thigh + Knee + Ankle + Bic + Fore + Wrist, data=subset(bodyfat,select=-Id))
summary(bf.lm)##
## Call:
## lm(formula = Bodyfat ~ Neck + Chest + Abdo + Hip + Thigh + Knee +
## Ankle + Bic + Fore + Wrist, data = subset(bodyfat, select = -Id))
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.0414 -2.5037 -0.1783 2.7166 9.5073
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -10.34859 9.07550 -1.140 0.2565
## Neck -0.68341 0.30776 -2.221 0.0283 *
## Chest -0.03297 0.11898 -0.277 0.7822
## Abdo 0.96013 0.10562 9.090 3.01e-15 ***
## Hip -0.27401 0.16515 -1.659 0.0998 .
## Thigh 0.03553 0.17675 0.201 0.8410
## Knee -0.12257 0.27596 -0.444 0.6577
## Ankle -0.24841 0.47587 -0.522 0.6027
## Bic 0.03025 0.23880 0.127 0.8994
## Fore 0.33694 0.26239 1.284 0.2016
## Wrist -0.26845 0.67340 -0.399 0.6909
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.054 on 117 degrees of freedom
## Multiple R-squared: 0.7487, Adjusted R-squared: 0.7272
## F-statistic: 34.86 on 10 and 117 DF, p-value: < 2.2e-16As we can see the values are present:
Neck = -0.68341
Chest = -0.03297
Abdo = 0.96013
Hip = -0.27401
Thigh = 0.03553
Knee = -0.12257
Ankle = -0.24841
Bic = 0.03025
Fore = 0.33694
Wrist = -0.26845
Plot
knitr::opts_chunk$set(
echo = TRUE,
message = TRUE,
warning = TRUE
)
library(ggplot2)
predicted <- predict.lm(bf.lm)
ggplot(bodyfat) + geom_point(aes(x=Id, y=Bodyfat, colour=c("red"))) + geom_point(aes(x=Id, y=predicted), colour=c("blue")) + theme(legend.position="none") + ylab("Bodyfat") + xlab("Person ID")
Red dots are real values of bodyfat and blue dots are predicted values.
Regression analysis
library(leaps)
my_summ <- summary(regsubsets(Bodyfat ~ Age + Weight + Height + Neck + Chest + Abdo + Hip + Thigh + Knee + Ankle + Bic + Fore + Wrist, data = bodyfat, nbest = 12))
my_summ## Subset selection object
## Call: regsubsets.formula(Bodyfat ~ Age + Weight + Height + Neck + Chest +
## Abdo + Hip + Thigh + Knee + Ankle + Bic + Fore + Wrist, data = bodyfat,
## nbest = 12)
## 13 Variables (and intercept)
## Forced in Forced out
## Age FALSE FALSE
## Weight FALSE FALSE
## Height FALSE FALSE
## Neck FALSE FALSE
## Chest FALSE FALSE
## Abdo FALSE FALSE
## Hip FALSE FALSE
## Thigh FALSE FALSE
## Knee FALSE FALSE
## Ankle FALSE FALSE
## Bic FALSE FALSE
## Fore FALSE FALSE
## Wrist FALSE FALSE
## 12 subsets of each size up to 8
## Selection Algorithm: exhaustive
## Age Weight Height Neck Chest Abdo Hip Thigh Knee Ankle Bic Fore Wrist
## 1 ( 1 ) " " " " " " " " " " "*" " " " " " " " " " " " " " "
## 1 ( 2 ) " " " " " " " " "*" " " " " " " " " " " " " " " " "
## 1 ( 3 ) " " "*" " " " " " " " " " " " " " " " " " " " " " "
## 1 ( 4 ) " " " " " " " " " " " " "*" " " " " " " " " " " " "
## 1 ( 5 ) " " " " " " " " " " " " " " "*" " " " " " " " " " "
## 1 ( 6 ) " " " " " " " " " " " " " " " " " " " " "*" " " " "
## 1 ( 7 ) " " " " " " " " " " " " " " " " "*" " " " " " " " "
## 1 ( 8 ) " " " " " " "*" " " " " " " " " " " " " " " " " " "
## 1 ( 9 ) " " " " " " " " " " " " " " " " " " " " " " " " "*"
## 1 ( 10 ) " " " " " " " " " " " " " " " " " " "*" " " " " " "
## 1 ( 11 ) " " " " " " " " " " " " " " " " " " " " " " "*" " "
## 1 ( 12 ) "*" " " " " " " " " " " " " " " " " " " " " " " " "
## 2 ( 1 ) " " "*" " " " " " " "*" " " " " " " " " " " " " " "
## 2 ( 2 ) " " " " " " "*" " " "*" " " " " " " " " " " " " " "
## 2 ( 3 ) " " " " " " " " " " "*" "*" " " " " " " " " " " " "
## 2 ( 4 ) " " " " " " " " " " "*" " " " " " " " " " " " " "*"
## 2 ( 5 ) " " " " " " " " " " "*" " " " " " " "*" " " " " " "
## 2 ( 6 ) " " " " " " " " " " "*" " " " " "*" " " " " " " " "
## 2 ( 7 ) " " " " " " " " " " "*" " " "*" " " " " " " " " " "
## 2 ( 8 ) " " " " "*" " " " " "*" " " " " " " " " " " " " " "
## 2 ( 9 ) " " " " " " " " " " "*" " " " " " " " " "*" " " " "
## 2 ( 10 ) " " " " " " " " "*" "*" " " " " " " " " " " " " " "
## 2 ( 11 ) "*" " " " " " " " " "*" " " " " " " " " " " " " " "
## 2 ( 12 ) " " " " " " " " " " "*" " " " " " " " " " " "*" " "
## 3 ( 1 ) " " " " " " "*" " " "*" "*" " " " " " " " " " " " "
## 3 ( 2 ) " " "*" " " "*" " " "*" " " " " " " " " " " " " " "
## 3 ( 3 ) " " "*" " " " " " " "*" " " " " " " " " " " " " "*"
## 3 ( 4 ) " " "*" " " " " " " "*" " " " " " " " " " " "*" " "
## 3 ( 5 ) " " " " " " " " " " "*" "*" " " " " " " " " " " "*"
## 3 ( 6 ) " " " " " " "*" " " "*" " " " " " " "*" " " " " " "
## 3 ( 7 ) " " " " " " "*" " " "*" " " " " "*" " " " " " " " "
## 3 ( 8 ) " " "*" " " " " " " "*" "*" " " " " " " " " " " " "
## 3 ( 9 ) " " "*" "*" " " " " "*" " " " " " " " " " " " " " "
## 3 ( 10 ) " " "*" " " " " " " "*" " " " " " " "*" " " " " " "
## 3 ( 11 ) " " "*" " " " " "*" "*" " " " " " " " " " " " " " "
## 3 ( 12 ) "*" "*" " " " " " " "*" " " " " " " " " " " " " " "
## 4 ( 1 ) " " "*" " " "*" " " "*" " " " " " " " " " " "*" " "
## 4 ( 2 ) " " " " " " "*" " " "*" "*" " " " " " " " " "*" " "
## 4 ( 3 ) " " " " " " "*" " " "*" "*" " " " " " " "*" " " " "
## 4 ( 4 ) " " "*" " " "*" " " "*" "*" " " " " " " " " " " " "
## 4 ( 5 ) " " " " " " "*" " " "*" "*" " " "*" " " " " " " " "
## 4 ( 6 ) " " " " " " "*" " " "*" "*" " " " " "*" " " " " " "
## 4 ( 7 ) " " " " " " "*" " " "*" "*" " " " " " " " " " " "*"
## 4 ( 8 ) " " " " " " "*" " " "*" "*" "*" " " " " " " " " " "
## 4 ( 9 ) " " " " "*" "*" " " "*" "*" " " " " " " " " " " " "
## 4 ( 10 ) "*" " " " " "*" " " "*" "*" " " " " " " " " " " " "
## 4 ( 11 ) " " " " " " "*" "*" "*" "*" " " " " " " " " " " " "
## 4 ( 12 ) " " "*" " " " " " " "*" " " " " " " " " " " "*" "*"
## 5 ( 1 ) " " "*" " " "*" " " "*" "*" " " " " " " " " "*" " "
## 5 ( 2 ) " " "*" "*" "*" " " "*" " " " " " " " " " " "*" " "
## 5 ( 3 ) " " "*" " " "*" " " "*" " " " " " " " " " " "*" "*"
## 5 ( 4 ) " " "*" " " "*" " " "*" " " " " " " "*" " " "*" " "
## 5 ( 5 ) " " " " " " "*" " " "*" "*" " " " " "*" " " "*" " "
## 5 ( 6 ) " " "*" " " "*" "*" "*" " " " " " " " " " " "*" " "
## 5 ( 7 ) " " " " " " "*" " " "*" "*" " " "*" " " " " "*" " "
## 5 ( 8 ) " " " " " " "*" " " "*" "*" " " " " " " " " "*" "*"
## 5 ( 9 ) " " "*" " " "*" " " "*" " " " " "*" " " " " "*" " "
## 5 ( 10 ) " " "*" " " "*" " " "*" " " "*" " " " " " " "*" " "
## 5 ( 11 ) " " "*" " " "*" " " "*" " " " " " " " " "*" "*" " "
## 5 ( 12 ) "*" "*" " " "*" " " "*" " " " " " " " " " " "*" " "
## 6 ( 1 ) " " "*" " " "*" " " "*" "*" " " " " " " " " "*" "*"
## 6 ( 2 ) " " "*" " " "*" " " "*" "*" " " " " "*" " " "*" " "
## 6 ( 3 ) " " "*" "*" "*" "*" "*" " " " " " " " " " " "*" " "
## 6 ( 4 ) " " "*" "*" "*" " " "*" "*" " " " " " " " " "*" " "
## 6 ( 5 ) " " "*" " " "*" " " "*" "*" " " " " " " "*" "*" " "
## 6 ( 6 ) " " "*" " " "*" " " "*" "*" "*" " " " " " " "*" " "
## 6 ( 7 ) " " "*" " " "*" " " "*" "*" " " "*" " " " " "*" " "
## 6 ( 8 ) " " "*" " " "*" "*" "*" "*" " " " " " " " " "*" " "
## 6 ( 9 ) "*" "*" " " "*" " " "*" "*" " " " " " " " " "*" " "
## 6 ( 10 ) " " "*" "*" "*" " " "*" " " " " " " " " " " "*" "*"
## 6 ( 11 ) " " "*" "*" "*" " " "*" " " " " " " "*" " " "*" " "
## 6 ( 12 ) " " "*" " " "*" "*" "*" " " " " " " " " " " "*" "*"
## 7 ( 1 ) " " "*" "*" "*" " " "*" "*" " " " " " " " " "*" "*"
## 7 ( 2 ) " " "*" "*" "*" "*" "*" " " " " " " " " " " "*" "*"
## 7 ( 3 ) " " "*" " " "*" " " "*" "*" " " " " "*" " " "*" "*"
## 7 ( 4 ) " " "*" "*" "*" "*" "*" "*" " " " " " " " " "*" " "
## 7 ( 5 ) " " "*" " " "*" " " "*" "*" " " " " " " "*" "*" "*"
## 7 ( 6 ) " " "*" "*" "*" "*" "*" " " " " " " " " "*" "*" " "
## 7 ( 7 ) " " "*" "*" "*" " " "*" "*" " " " " " " "*" "*" " "
## 7 ( 8 ) " " "*" "*" "*" "*" "*" " " "*" " " " " " " "*" " "
## 7 ( 9 ) " " "*" "*" "*" " " "*" "*" " " " " "*" " " "*" " "
## 7 ( 10 ) " " "*" " " "*" "*" "*" "*" " " " " " " " " "*" "*"
## 7 ( 11 ) " " "*" " " "*" " " "*" "*" " " "*" " " " " "*" "*"
## 7 ( 12 ) " " "*" " " "*" " " "*" "*" "*" " " " " " " "*" "*"
## 8 ( 1 ) " " "*" "*" "*" "*" "*" "*" "*" " " " " " " "*" " "
## 8 ( 2 ) " " "*" "*" "*" "*" "*" "*" " " " " " " " " "*" "*"
## 8 ( 3 ) " " "*" "*" "*" "*" "*" "*" " " " " " " "*" "*" " "
## 8 ( 4 ) " " "*" "*" "*" " " "*" "*" " " " " " " "*" "*" "*"
## 8 ( 5 ) " " "*" "*" "*" "*" "*" " " " " " " " " "*" "*" "*"
## 8 ( 6 ) " " "*" "*" "*" " " "*" "*" "*" " " "*" " " "*" " "
## 8 ( 7 ) " " "*" "*" "*" " " "*" "*" " " " " "*" " " "*" "*"
## 8 ( 8 ) " " "*" "*" "*" "*" "*" " " "*" " " " " " " "*" "*"
## 8 ( 9 ) " " "*" "*" "*" " " "*" "*" "*" " " " " " " "*" "*"
## 8 ( 10 ) " " "*" "*" "*" "*" "*" "*" " " " " "*" " " "*" " "
## 8 ( 11 ) " " "*" "*" "*" " " "*" "*" " " " " "*" "*" "*" " "
## 8 ( 12 ) " " "*" "*" "*" " " "*" "*" " " "*" " " " " "*" "*"