Homework 4

Due 3/10/23 @ 11:59 PM

Use an RMD Notebook file from to create the assignment.

Update inqstools for new template format.

remotes::install_github("inqs909/inqstools")

You will need to knit the document if you use “M408 Alternative”.

You must comment all your code to receive credit.

Submit the *nb.html or *.html file to canvas.

Problem 1

The faithful data set in R contains information on eruptions time and waiting time. Describe the relationship between waiting (independent) and eruptions (dependent).

You must provide descriptive statistics, visuals, and model.

Problem 2

The cats data set from the MASS package contains information of cat body weight (kg; Bwt) and heart weight (g; Hwt). Fit a model to see if there is a significant association between body weight (predictor) and heart weight (outcome).

You must provide descriptive statistics, visuals, and model.

Problem 3

When estimating the \(\beta\) coefficients, we are minimizing the sum of error squares:

\[ \sum^n_{i=1}(y_i-(\beta_0+\beta_1x_i))^2 \]

We square the errors to make sure we do not lose information when summing up all the values. However, what if we try to use an absolute value:

\[ \sum^n_{i=1}|y_i-(\beta_0+\beta_1x_i)| \]

Simulate a data set, estimate the coefficients, and compare the results. Are they the same or different?

Problem 4

Conduct a simulation assessing which case from problem 3 is better.

To assess which case is better compare the mean and standard deviations of the simulated-estimated coefficients.