STAT330/430 -Assignment 2 Solved

Question 1
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Question 2
The net reproductive rate (R0) of an animal is defined as the total number of offspring that an individual can produce during its lifetime and can be calculated as follows:

∞

R0 = X(lxmx)

x=0

where lx is the proportion of females surviving to each age and mx is the average number of offspring produced at each age. Hence, if you had data on two different time-periods or ages you would calculate (R0) as:

R0 = (l1m1) + (l2m2)

The aphid data-set contains records of the number of eggs produced on three different days by each of 20 aphids.

Variable
Description
ID
Individual aphid in the experiment
Day1
Number of eggs produced on Day 1
Day2
Number of eggs produced on Day 2
Day3
Number of eggs produced on Day 3
Note: NA indicates that the animal has died.

Using the aphid data-set:

(a)    Create a function to calculate R0 for the population.

(b)    Estimate a boot-strapped standard error and 95% confidence interval of R0 using 100,000 replicates.

(c)     Provide a brief summary of your result as well as fully annotated code in your R Script file.

Question 3
The Body dataset contains 21 body dimension measurements as well as age, weight, height, and gender on 507 individuals. The 247 men and 260 women were primarily individuals in their twenties and thirties that all reported to exercise on a regular basis.

Variable
Description
BA_diam
Biacromial diameter
PB
Biliac diameter, or “pelvic breadth”
BI_diam
Bitrochanteric diameter
Chest_dep
Chest depth between spine and sternum at nipple level
Chest_diam
Chest diameter at nipple level, mid-expiration
Elbow_diam
Elbow diameter, sum of two elbows
Wrist_diam
Wrist diameter, sum of two wrists
Knee_diam
Knee diameter, sum of two knees
Ankle_diam
Ankle diameter, sum of two ankles
Shoulder_g
Shoulder girth over deltoid muscles
Chest_g
Chest girth
Waist_g
Waist girth, narrowest part of torso below the rib cage
Navel_g
Navel (or “Abdominal”) girth at umbilicus and iliac crest
Hip_g
Hip girth at level of bitrochanteric diameter
Thigh_g
Thigh girth below gluteal fold
Bicep_g
Bicep girth, flexed
Forearm_g
Forearm girth, extended, palm up
Knee_g
Knee girth over patella, slightly flexed position
Calf_g
Calf maximum girth
Ankle_g
Ankle minimum girth
Wrist_g
Wrist minimum girth
Age
Age (years)
Weight
Weight (kg)
Height
Height (cm)
Gender
Gender (1 - male, 0 - female)
(a)    Produce some appropriate exploratory graphics of the Body dataset. Given the number of variables ensure that all graphics are easily readable and understandable. Provide a general summary of the trends seen in your graphics. Note: These graphics do not have to be exhaustive, just useful.

(b)    Split the Body data-set into 50:50 testing:training data-sets. Use the validation set approach to implement forward or backward selection to select an optimal subset of predictors of Weight. Provide a summary of your results which includes (but is not limited to) appropriate tables, metrics and commentary on the relative accuracy of your results.

Using the testing and training data-sets created in (b) use ridge or lasso regression to constrain or regularise the predictors of Weight. You should employ cross-validation to tune the value of λ during the training phase of your model. Provide a summary of your results which includes (but is not limited to) appropriate tables, metrics and commentary on the relative accuracy of your results