As usual, all code below should follow the style guidelines from the lecture slides.

  1. Use the code below to read in data from a survey of 55 Duke University students about their study habits and grades. You can read more about this data at https://www.openintro.org/data/index.php?data=gpa.
grades_data <- read.csv("https://www.openintro.org/data/csv/gpa.csv")

  1. Create a scatter plot with GPA on the y-axis and and hours studied per week on the x-axis. What do you observe?

  2. Use the lm function to regress gpa upon studyweek. What are the estimated coefficients? What are their interpretations?

  3. Use the lm function to regress gpa upon sleepnight and studyweek. What are the estimated coefficients? What are their interpretations?

  4. We can write the model used in question 4 as \[\mathbf{Y}=\mathbf{X}\boldsymbol\beta+\boldsymbol\epsilon\]. What is \(\mathbf{Y}\) here? What is \(\mathbf{X}\) here. Create the matrix \(X\) in your .Rmd file and print out the first six rows.