AE 05: Randomization test for the slope

Houses in Duke Forest

Published

September 13, 2022

Important

Go to the course GitHub organization and locate your ae-05 repo to get started.

Render, commit, and push your responses to GitHub by the end of class. The responses are due in your GitHub repo no later than Saturday, September 16 at 11:59pm.

library(tidyverse)
library(tidymodels)
library(openintro)
library(knitr)

Data

The data are on houses that were sold in the Duke Forest neighborhood of Durham, NC around November 2020. It was originally scraped from Zillow, and can be found in the duke_forest data set in the openintro R package.

glimpse(duke_forest)
Rows: 98
Columns: 13
$ address    <chr> "1 Learned Pl, Durham, NC 27705", "1616 Pinecrest Rd, Durha…
$ price      <dbl> 1520000, 1030000, 420000, 680000, 428500, 456000, 1270000, …
$ bed        <dbl> 3, 5, 2, 4, 4, 3, 5, 4, 4, 3, 4, 4, 3, 5, 4, 5, 3, 4, 4, 3,…
$ bath       <dbl> 4.0, 4.0, 3.0, 3.0, 3.0, 3.0, 5.0, 3.0, 5.0, 2.0, 3.0, 3.0,…
$ area       <dbl> 6040, 4475, 1745, 2091, 1772, 1950, 3909, 2841, 3924, 2173,…
$ type       <chr> "Single Family", "Single Family", "Single Family", "Single …
$ year_built <dbl> 1972, 1969, 1959, 1961, 2020, 2014, 1968, 1973, 1972, 1964,…
$ heating    <chr> "Other, Gas", "Forced air, Gas", "Forced air, Gas", "Heat p…
$ cooling    <fct> central, central, central, central, central, central, centr…
$ parking    <chr> "0 spaces", "Carport, Covered", "Garage - Attached, Covered…
$ lot        <dbl> 0.97, 1.38, 0.51, 0.84, 0.16, 0.45, 0.94, 0.79, 0.53, 0.73,…
$ hoa        <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,…
$ url        <chr> "https://www.zillow.com/homedetails/1-Learned-Pl-Durham-NC-…

Exploratory data analysis

ggplot(duke_forest, aes(x = area, y = price)) +
  geom_point(alpha = 0.7) +
  labs(
    x = "Area (square feet)",
    y = "Sale price (USD)",
    title = "Price and area of houses in Duke Forest"
  ) +
  scale_y_continuous(labels = label_dollar())

Model

df_fit <- linear_reg() |>
  set_engine("lm") |>
  fit(price ~ area, data = duke_forest)

tidy(df_fit) |>
  kable(digits = 2)
term estimate std.error statistic p.value
(Intercept) 116652.33 53302.46 2.19 0.03
area 159.48 18.17 8.78 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(09132023)

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 <- duke_forest |>
  specify(price ~ area) |>
  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.
  • Push all your work to your ae-05 repo on GitHub. (You do not submit AEs on Gradescope).