## Lab Worksheet 7

In 1898, Hermon Bumpus, an American biologist working at Brown University, collected data on one of the first examples of natural selection directly observed in nature. Immediately following a bad winter storm, he collected 136 English house sparrows, Passer domesticus, and brought them indoors. Of these birds, 64 had died during the storm, but 72 recovered and survived. By comparing measurements of physical traits, Bumpus demonstrated physical differences between the dead and living birds. He interpreted this finding as evidence for natural selection as a result of this storm:

bumpus <- read.csv("http://wilkelab.org/classes/SDS348/data_sets/bumpus_full.csv")
head(bumpus)
##    Sex   Age Survival Length Wingspread Weight Skull_Length Humerus_Length
## 1 Male Adult    Alive    154        241   24.5         31.2           17.4
## 2 Male Adult    Alive    160        252   26.9         30.8           18.7
## 3 Male Adult    Alive    155        243   26.9         30.6           18.6
## 4 Male Adult    Alive    154        245   24.3         31.7           18.8
## 5 Male Adult    Alive    156        247   24.1         31.5           18.2
## 6 Male Adult    Alive    161        253   26.5         31.8           19.8
##   Femur_Length Tarsus_Length Sternum_Length Skull_Width
## 1         17.0          26.0           21.1        14.9
## 2         18.0          30.0           21.4        15.3
## 3         17.9          29.2           21.5        15.3
## 4         17.5          29.1           21.3        14.8
## 5         17.9          28.7           20.9        14.6
## 6         18.9          29.1           22.7        15.4

The data set has three categorical variables (Sex with levels Male and Female; Age with levels Adult and Young; and Survival, with levels Alive and Dead) and nine numerical variables that hold various aspects of the birds’ anatomy, such as wingspread, weight, etc.

Split the bumpus data set into a random training and test set. Use 70% of the data as a training set.

set.seed(13)  # set the seed to make your partition reproductible

# your R code here

Fit a logistic regression model on the training data set, then predict the survival on the test data set, and plot the resulting ROC curves.

# model to use:
# Survival ~ Sex + Length + Weight + Humerus_Length + Sternum_Length

# your R code here

# 2. Area under the ROC curves

Calculate the area under the training and test curve for the following model.

# model to use:
# Survival ~ Weight + Humerus_Length

set.seed(13)  # set the seed to make your partition reproductible

# your R code here

# 3. What happens if we don’t use set.seed() to create reproducibility in the way we partition the dataset?

# your R code here (if the above was easy)