homework 1: review of linear models

• homework is due in Dropbox on Avenue on Weds 12 September.
• your homework should be saved as R code with comments (.R), R markdown (.Rmd), or Sweave (.Rnw)
• none of the following functions should appear in your solution:
  • setwd()
  • rm(list=ls())
  • attach()
• the TA or I should be able run your code from scratch without any problems.

Pick a data set and perform the following steps. (For each step, either write R code or text (commented-out if you’re writing R code).

• Read the help page for your data set. If you’re using your own data set (i.e. one not built into R), give us a brief description of where you got it and what it means.
• Create univariate plots of the response variable with respect to each of the predictor variables (scatterplots for continuous predictors, boxplots for categorical predictors)
• Write a brief description (not more than a few sentences) of the patterns you see. Does there seem to be any strong evidence of weirdness in the data at this point (e.g. outliers, strong nonlinearity …)
• Fit a linear model to the data using lm(). In comments/text, explain why you chose a particular model (i.e. including or excluding predictors, including or excluding interactions).
• Write code to do graphical diagnostics of the model (typically: fitted vs. residual plot, scale-location plot, Q-Q plot, influence plot). Describe whether you see any cause for concern in the diagnostic plots.
• Summarize the model results; interpret what the parameters mean.
• optional: try dotwhisker::dwplot(your_model), library(effects); plot(allEffects(your_model)), or sjPlot::plot_model(your_model) to summarize your model.

Do not do any model/variable selection steps (we’ll talk about this in class).

Some data sets you could try:

• rock: perm is the response variable. Do you notice any concerns with non-independence in the data?
• mtcars: mpg is the response variable. It is suggested that you pick one or two predictor variables to work with (do not do stepwise selection), e.g. disp, cyl, and am. If you do use all possible predictor variables, comment on why this might not give good results.
• prostate (in the faraway package): lpsa is the response variable.
• swiss: Fertility is the response variable.

You can also see help(package="datasets") or install.packages("carData"); help(package="carData") for more options (obviously, not all of these data sets will be suitable examples for linear regression).