Assignment Format

Setup

Load packages

  • Make sure that the dplyr, ggplot2, and arm packages are downloaded on the machine you’re using
    • You can check this by clicking on the Packages tab in the Files, Plots, Packages… panel and scrolling down
    • If you need to download the package, copy the following code into your Console panel and run it **Do not put it in your homework script*
    • install.packages("dplyr")
  • Copy the following code into the beginning of your homework script to load the dplyr package:
# load libraries
library(arm)
library(tidyverse)

Data

For this homework assignment, we will once again be working with the real finch data from the Galapagos Islands collected by the Grants. This time, we will just focus on the Geospiza scandens data which was collected on Daphne Major Island in 1975 and 2012. We will use a simple linear model to determined of the beak depth changed across the time period.

Load and wrangle the data

Be sure to download the data galapago-finches.csv and from D2L and place them both in your data/ folder in your R project.

Copy the following code and put it at the top of your homework script:

# read in full data set
finch <- read_csv("data/galapago-finches.csv")
# filter out scandens data and make a tibble
scandens <- finch %>%
  filter(species == "scandens") 

# change the year column to a character data type
scandens$year <- as.character(scandens$year)

Exercises Homework 06: Linear Models

All of the following questions relate to the scandens object NOT the finch object.

Problem 1: Intercept only

  1. Print out the names(), and dim() of the columns in your scandens data object.
  2. Use distinct() or unique() to show each of the values in both the year and species column. Each value in both columns should only be printed once.
  3. Make a scatter plot of the blength variable in the complete data set, ignoring any grouping variables (i.e., set x = 0)
  4. Fit an intercept-only model using the lm() function, and save it in an object called flm0 (short for “finch linear model 0”).
  5. Use the display() function to show the results of flm0.
  • hint: if display(flm0) doesn’t work, either the arm package was not successfully installed or loaded, OR you did not save the output from the lm() function properly.
  1. Write a comment in your script with the value for each of the following:
  1. the global mean
  2. the SE for the global mean
  3. the sample size
  4. the number of parameters estimated in the model
  5. the residual standard deviation
  6. the value of R^2

  1. Calculate and print the global mean of blength. Is this in agreement with the global mean you wrote in problem 1.6a above?

  2. Calculate and print the sd for blength. Is this in agreement with the global mean you wrote in problem 1.6e above?

Problem 2: Categorical predictor

  1. Make a scatter plot of the blength observations separated by year.
  2. Make the same plot as in 2.1 above but “jitter” the points. Make sure to set width = 0.1 and height = 0
  3. Use lm() to fit a model which includes year as a predictor variable. Save this model output in an object called flm1, and use display() to print out the results in your console.
  4. Based on the information from 2.4 above, what is the mean beak length for the scandens species in 1975?
  5. Using the information displayed in 2.4 above, write out a calculation which shows the mean beak length for scandens in 2012.
  6. Make a scatter plot of this data which separates the observations by year, and includes an point for the estimated group means.
  • In the stat_summary() function, set shape = 18 and size = 6.

Problem 3: Confidence Intervals

  1. Using confint(), calculate and display a 95% confidence interval for the estimated difference in beak length between 1975 and 2012.

  2. Use coefplot() to display a graphical representation of the approximate 95% CI for the estimated difference in beak length between 1975 and 2012.

  3. Use a comment in your script to interpret the results of problem 3.1 and 3.2. Are these interpretations in agreement with each other?

  4. Use confint() to calculate and display a 99% CI for the estimated difference in beak length between 1975 and 2012.

  5. Use a comment to interpret the results of problem 3.4 above. How are the 95% and 99% CI’s different? How does our interpretation change when discussing a 95% and 99% CI?

Problem 4: Assumptions

  1. Make a Q-Q plot to test the assumption of normally distributed residuals for the blength variable in the scandens data set.
  • Hint make sure to use aes(sample = blength) inside the ggplot() function.
  1. Use a comment to interpret the graph you made in problem 4.1 above.
  2. Test the assumption of equal variance in the flm1 model output.
  • Hint make sure to use the model output and not the raw data.
  • Be sure to include aes(x = .fitted, y = .resid) inside the ggplot() function.
  1. Use a comment to interpret the graph you made in problem 4.3 above.

Problem 5: Relevel year variable (optional)

  1. Copy the scandens data set into a new object called scandens_factor. Make the year column a factor and order the levels so that 2012 is first. Fit the same linear model as in problem 2.3 but use the new scandens_factor data object as the input, and display the results of this new model.