13 pts total

Problem 1

A - 1pt

howell <- read.table("http://hompal-stats.wabarr.com/datasets/Howell_craniometry.txt", header=TRUE, sep=",")
library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

B - 1pt

howell <- howell %>% 
  dplyr::select(ID, Sex, Population, BNL, MDH, EKB, ZOR, BAA, NBA) %>%
  dplyr::filter(Population %in% c("BUSHMAN", "PERU", "NORSE", "ZULU"))
head(howell)
##   ID Sex Population BNL MDH EKB ZOR BAA NBA
## 1  1   M      NORSE 100  31 100  81  39  76
## 2  2   M      NORSE 102  19  96  84  35  79
## 3  3   M      NORSE 102  28  97  82  38  72
## 4  4   M      NORSE 100  25  99  79  46  75
## 5  5   M      NORSE  97  26  97  79  42  80
## 6  6   M      NORSE 106  29  98  88  39  77

C

1pt

cov(howell[,4:9])
##           BNL       MDH        EKB       ZOR        BAA       NBA
## BNL 31.990992  8.122307 15.9348763 21.629802 -1.5687912 -2.261421
## MDH  8.122307 16.495175  5.4709631  3.281787  4.9648033  1.509080
## EKB 15.934876  5.470963 20.0245801 13.425144 -0.6598362 -2.085858
## ZOR 21.629802  3.281787 13.4251439 24.084470 -4.6930390 -6.212397
## BAA -1.568791  4.964803 -0.6598362 -4.693039 11.3239096  3.836069
## NBA -2.261421  1.509080 -2.0858584 -6.212397  3.8360691 10.873610
#gives the same results
var(howell[,4:9])
##           BNL       MDH        EKB       ZOR        BAA       NBA
## BNL 31.990992  8.122307 15.9348763 21.629802 -1.5687912 -2.261421
## MDH  8.122307 16.495175  5.4709631  3.281787  4.9648033  1.509080
## EKB 15.934876  5.470963 20.0245801 13.425144 -0.6598362 -2.085858
## ZOR 21.629802  3.281787 13.4251439 24.084470 -4.6930390 -6.212397
## BAA -1.568791  4.964803 -0.6598362 -4.693039 11.3239096  3.836069
## NBA -2.261421  1.509080 -2.0858584 -6.212397  3.8360691 10.873610

Problem 2

A - 1pt

distMat <- dist(x = howell[,4:9], method = "euclid")

B - 1pt

HowellClust <- hclust(d = distMat, method = "average")

C - 1pt

plot(HowellClust)