Application Exercise

1. Open Rstudio Server Pro
2. Create a new project
3. Click File > New File > R Markdown
4. Delete everything except for

---
title: "Untitled"
output: html_document
---

5. Give your work a sensible title
6. When you’ve finished, upload the .html file to Canvas

Generate some “fake” residuals under the following scenarios and plot the Q-Q plot and histogram for each. Describe what you see.

• Left-skewed data
• Right-skewed data
• Data generated under a lognormal distribution (use the rlnorm() function)
• Data generated under a t-distribution with 2 degrees of freedom (use the rt() function)

Copy the code below to create a design matrix, X and an outcome, y.

set.seed(1)
X <- matrix(c(rep(1, 100),
            rnorm(100)), ncol = 2)
y <- 2 + 3 * X[, 2] + 2 * X[, 2]^2 + 0.5 * X[, 2]^3 + rnorm(100)

• Add to this design matrix so you can fit a model with a 3rd degree polynomial.
• Fit this model using linear regression
• Calculate the expected change in Y given a change from the 25th percentile to the 75th percentile