Please use D2L to turn in both the HTML output and your R Markdown file in.

Q1. (50 pts)

For part a and b, simulate 100 points, create a plot to show the simulated data, and include a brief caption for each figure. Note your figure should be neat and contain appropriate titles, axes, and labels.

a.

Include a linear trend in time and a random component

b.

Include a linear trend, a seasonal cycle, and a random component

c. (STAT 536 only)

Write out the mathematical notation for the models in part a and part b.

Q2. (50 pts)

For this question use a dataset containing individual bike trips from the Capital Bike Share program in Washington, D.C. The data can be downloaded at http://math.montana.edu/ahoegh/teaching/stat408/datasets/biketrips2017.csv

a.

Using this dataset, create a plot of the number of bike trips by day. Include appropriate titles, labels, and a caption (a few sentences) to describe the figure.

b.

Does this dataset give enough information to visualize or estimate a trend, why or why not?

c.

Does this dataset give enough information to visualize or estimate a cyclical pattern, why or why not?

d. (STAT 536 only)

Redo, parts a - c, but now look at the number of trips by hour and day. You can reduce the dataset to only include the last 10 days.