AE 04: Randomization test for the slope

Bikeshare

Published

September 6, 2024

Important

  • Open RStudio and create a subfolder in your AE folder called “AE-04”

  • Go to the Canvas and locate your AE 04 assignment to get started.

  • Upload the ae-04.qmd and dcbikeshare.csv files into the folder you just created. The .qmd and PDF responses are due in Canvas no later than Thursday, September 12 at 11:59pm.

library(tidyverse)
library(infer)
library(ggformula)
library(broom)
library(openintro)
library(knitr)

Data

Our dataset contains daily rentals from the Capital Bikeshare in Washington, DC in 2011 and 2012 filtered to only contain the winter months. It was obtained from the dcbikeshare data set in the dsbox R package.

We will focus on the following variables in the analysis:

  • count: total bike rentals
  • temp_orig: Temperature in degrees Celsius
winter <- read_csv("../ae/data/dcbikeshare.csv") |>
  mutate(season = case_when(
    season == 1 ~ "winter",
    season == 2 ~ "spring",
    season == 3 ~ "summer",
    season == 4 ~ "fall"
  ),
  season = factor(season)) |>
  filter(season == "winter")
Rows: 731 Columns: 17
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
dbl  (16): instant, season, yr, mnth, holiday, weekday, workingday, weathers...
date  (1): dteday

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
glimpse(winter)
Rows: 181
Columns: 17
$ instant    <dbl> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, …
$ dteday     <date> 2011-01-01, 2011-01-02, 2011-01-03, 2011-01-04, 2011-01-05…
$ season     <fct> winter, winter, winter, winter, winter, winter, winter, win…
$ yr         <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$ mnth       <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,…
$ holiday    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,…
$ weekday    <dbl> 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4,…
$ workingday <dbl> 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1,…
$ weathersit <dbl> 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 2, 2,…
$ temp       <dbl> 0.3441670, 0.3634780, 0.1963640, 0.2000000, 0.2269570, 0.20…
$ atemp      <dbl> 0.3636250, 0.3537390, 0.1894050, 0.2121220, 0.2292700, 0.23…
$ hum        <dbl> 0.805833, 0.696087, 0.437273, 0.590435, 0.436957, 0.518261,…
$ windspeed  <dbl> 0.1604460, 0.2485390, 0.2483090, 0.1602960, 0.1869000, 0.08…
$ casual     <dbl> 331, 131, 120, 108, 82, 88, 148, 68, 54, 41, 43, 25, 38, 54…
$ registered <dbl> 654, 670, 1229, 1454, 1518, 1518, 1362, 891, 768, 1280, 122…
$ count      <dbl> 985, 801, 1349, 1562, 1600, 1606, 1510, 959, 822, 1321, 126…
$ temp_orig  <dbl> 14.110847, 14.902598, 8.050924, 8.200000, 9.305237, 8.37826…

Exploratory data analysis

gf_point(count ~ temp_orig, data = winter, alpha = 0.7) |> 
  gf_labs(
    x = "Temperature (C)",
    y = "Number of Bike Rentals",
  )

Model

model_fit <- lm(count ~ temp_orig, data = winter)

tidy(model_fit) |>
  kable(digits = 2)
term estimate std.error statistic p.value
(Intercept) -111.04 238.31 -0.47 0.64
temp_orig 222.42 18.46 12.05 0.00

Hypothesis test

Tip

For code chunks with fill-in-the-blank code, change code chunk option to #| eval: true once you’ve filled in the code.

State the null and alternative hypotheses

[Add hypotheses in mathematical notation]

Generate null distribution using permutation

Fill in the code, then set eval: true .

n = 100
set.seed(212)

null_dist <- _____ |>
  specify(______) |>
  hypothesize(null = "independence") |>
  generate(reps = _____, type = "permute") |>
  fit()

Visualize distribution

# Code for histogram of null distribution

Calculate the p-value.

# get observed fit 
observed_fit <- winter |>
  specify(count ~ temp_orig) |>
  fit()

# calculate p-value
get_p_value(
  ____,
  obs_stat = ____,
  direction = "two-sided"
)
  • What does the warning message mean?

State conclusion

[Write your conclusion in the context of the data.]

Important

To submit the AE:

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