AE 05: Mathematical Models

Songs on Spotify

Important

• Open RStudio and create a subfolder in your AE folder called “AE-05”

• Go to the Canvas and locate your AE 05 assignment to get started.

• Upload the ae-05.qmd and spotify-popular.csv files into the folder you just created. The .qmd and PDF responses are due in Canvas no later than Saturday, September 14 at 11:59pm.

library(tidyverse)
library(ggformula)
library(broom)
library(knitr)
library(patchwork) #arrange plots in a grid

Data

The data set for this assignment is a subset from the Spotify Songs Tidy Tuesday data set. The data were originally obtained from Spotify using the spotifyr R package.

It contains numerous characteristics for each song. You can see the full list of variables and definitions here. This analysis will focus specifically on the following variables:

variable	class	description
track_id	character	Song unique ID
track_name	character	Song Name
track_artist	character	Song Artist
track_popularity	double	Song Popularity (0-100) where higher is better
energy	double	Energy is a measure from 0.0 to 1.0 and represents a perceptual measure of intensity and activity. Typically, energetic tracks feel fast, loud, and noisy. For example, death metal has high energy, while a Bach prelude scores low on the scale. Perceptual features contributing to this attribute include dynamic range, perceived loudness, timbre, onset rate, and general entropy.
valence	double	A measure from 0.0 to 1.0 describing the musical positiveness conveyed by a track. Tracks with high valence sound more positive (e.g. happy, cheerful, euphoric), while tracks with low valence sound more negative (e.g. sad, depressed, angry).

spotify <- read_csv("spotify-popular.csv")

Are high energy songs more positive? To answer this question, we’ll analyze data on some of the most popular songs on Spotify, i.e. those with track_popularity >= 80. We’ll use linear regression to fit a model to predict a song’s positiveness (valence) based on its energy level (energy).

Below are plots as part of the exploratory data analysis.

p1 <- gf_histogram(~valence, data = spotify) |>  
  gf_labs(title = "Distribution of Valence", 
       subtitle = " for Popular songs on Spotify", 
       x = "Valence")

p2 <- gf_histogram(~energy, data = spotify) |> 
  gf_labs(title = "Distribution of Energy", 
       subtitle = "for Popular songs on Spotify", 
       x = "Energy")
p1 + p2 # The patchwork package will arrange your plots for you

gf_point(valence ~ energy, data = spotify) |> 
  gf_labs(title = "Valence vs. Energy", 
       subtitle = "Popular songs on Spotify", 
       x = "Energy", 
       y = "Valence")

Exercise 1

Fit a model using the energy of a song to predict its valence, i.e. positiveness. Include the 90% confidence interval for the coefficients, and display the output using 3 digits.

## add code

Exercise 2

In words interpret the estimate and confidence interval for the slope in the previous exercise.

Exercise 3

Interpret the p-value from Exercise 1.

Exericse 4

Predict what the average valence for a song with an energy score 0.5 is. Report and interpret a 90% confidence interval for the average valence.

Exericse 5

Report and interpret a 90% confidence interval for a single song with energy score 0.8.

Important

To submit the AE:

• Render the document to produce the PDF with all of your work from today’s class.
• Upload your qmd and pdf files to the Canvas assignment.