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Generate a single, well-labeled figure overlaying the normal, logistic, and cauchy PDFs.

INSTRUCTIONS TO CANDIDATES
ANSWER ALL QUESTIONS

Please do these in Stata. Do not use built-in functions for any of these except the standard normal CDF.

1. Generate a single, well-labeled figure overlaying the normal, logistic, and cauchy PDFs.

2. Generate a single, well-labeled figure overlaying normal, logistic, and cauchy CDFs (see “comment”

section below for guidance.)

3. Generate a figure overlaying Poisson PDFs at λ values of .5, 1.2, 3, and 5. λ is the mean or location

parameter of the Poisson.

 

Data Please do these in Stata. Use the “beats.csv” data o. These data, scraped from Spotify’s API, contain information about every Taylor Swift and Rolling Stones song in Spotify’s database. You’ll see variables indicating characteristics of songs like “danceability,” “valence,” etc. (definitions provided in the “comment” section below). The goal here is to analyze the “danceabilty” of Taylor Swift and Rolling Stones songs in two ways - are their songs more/less danceable over time, and are the two artists’ songs different from one another?

1. write code to clean the data so it’s ready for analysis. Annotate your code.

2. present a professional table summarizing key features of the data including means, medians, variances, other interesting percentiles, etc. Comment briefly on features you find interesting.

3. Does the danceability of Stones songs change over time? Estimate a linear regression predicting danceability over time - think carefully about how to do this. Present the model results in a professional table.

4. Interpret your estimates.

5. Do the same for Taylor Swift songs - does danceability change over time?

6. Present and comment on a box plot evaluating danceability by year for Taylor Swift.

7. Do the same for the Stones.

8. Generate a single figure comparing danceability for the two artists - what does it show?

9. Is danceability statistically different between the Stones and Taylor Swift? Explain. How did you evaluate this? Present your result.

 

 

Simulation

You all have the sense that our estimates (of both β and se) change as sample size changes.

1. if you wanted to see exactly how N affects those estimates, what would you do? Write out, in

English, specific steps you’d take to find this out.

2. Sketch out code in both Stata and R to do this - this code doesn’t have to work (yet), but you should definitely develop a sense of process and some things Stata can do.

 

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