WFA8433-HW2.Rmd

Homework 2: 
Assignment due: Homework-01: Blind review of a personal means network
Careeer objectives has been anonymized and a assigned to a reviewer in the table below.
Review your assigned network and provide a 1 paragraph review.
Work through your assigned network and see if you can follow the logic.
Ask the questions ‘how do I achieve this’ and ‘why is this important’ as you move through the network.
Was there anything missed? Is there a way to meet the fundamental objectives that was not specified?
Submit your review by 12 pm February 15th as a pdf.
Name the pdf file as “lastname-firstinitial-homework-01.pdf”. For example I would name mine colvin-m-homework-01.pdf.
SUBMIT your review TO: https://dropitto.me/WFA8433 (the upload password is ‘critter’)



1) Working with stochastic values and expectations
a. Generate  a vector named `Y` with 1001 stochastic replicates for a normal distribution
with mean 10 and standard deviation of 1.
b. Calculate the mean and standard deviation of `Y` and assign them as `Y_mean` and `Y_sd` respectively.
c. Make a histogram of `Y`, labeling the x-axis as `Y values` and the y-axis as `Frequency`
d. Calculate the probability that `Y` is less than 11. (HINT: you can use the `sort()` function
to sort a vector in ascending order; `?sort`)

2) Making a function to do useful things
a. Make a function that multiplies an input vector by 2 and returns the sum of the 
vector times 2.
b. Run the function created in 2a on the vector `Y` created in 1a.
c. Create another function called `risk` that returns the probability of an achieving
an expected outcome or less from a vector of stochastic replicates. (HINT: `subset()`
and `length()` functions might be useful.
d. Run the function crated in 2d on the vector `Y` created in 1a for an outcome of 11.
How does it compare to the value for 1d?

3) Linear modeling and prediction
a. Read in the dataset `elevation-counts.csv` and assign it as `ele_data`.
b. Plot counts (y-axis) versus elevation (x-axis) and label each axis as you see fit.
c. Create the same plot as above, but make group 1 red, group 2 blue, and group 3 green.
d. Fit a linear model that predicts counts from elevation, group, and an interaction of 
group and elevation.
e. Plot the residuals (y-axis) versus the predicted to evaluate whether you have 
violated any assumptions and a plot of the observed `count` versus the fitted values.  (HINT: recall `resid()` and `fitted()`?)
f. Now create another field in `ele_data`  named `lcount` that is the natural log of counts.
g. Refit the linear model from 3.a. using `lcount`.
h. Plot the residuals (y-axis) versus the predicted (x-axis) to evaluate whether you have 
violated any assumptions and a plot of the observed `lcount` versus the fitted values.
i. Create a dataset named `predicted_data` using the `expand.grid()` function to predict values for the range 
of elevations in `ele_data` in increments of 1 and each group.
k. Add columns to `predicted_data` for the predicted value, lower 95% prediction interval and 
upper 95% prediction interval.
l. Make a plot of predicted values and 95% prediction intervals for group 2 as lines. The line for 
the predicted value should be solid and the lines for the prediction intervals should by dotted.
(Recall that `lty=1` is a solid line and `lty=2` is a dotted line)