AE 05: Permutation test for the slope

Houses in Duke Forest

Published

January 22, 2026

Important

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

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.

Goal: Use statistical inference to evaluate whether there is a relationship between the age of the house at time of sale and its price.

Exploratory data analysis

Let’s begin by creating a new variable that is the age of the house in 2020.

duke_forest <- duke_forest |>
  mutate(age_2020 = 2020 - year_built)

Now let’s visualize the relationship between the age of the house in 2020 and the sales price.

ggplot(duke_forest, aes(x = age_2020, y = price)) +
  geom_point(alpha = 0.7) +
  labs(
    x = "Age in 2020 (years)",
    y = "Sale price (USD)",
    title = "Price and age of houses in Duke Forest"
  ) +
  scale_y_continuous(labels = label_dollar())

Model

df_fit <- lm(price ~ age_2020, data = duke_forest)

tidy(df_fit) |>
  kable(digits = 3)

term	estimate	std.error	statistic	p.value
(Intercept)	690891.015	68637.793	10.066	0.000
age_2020	-2473.935	1225.191	-2.019	0.046

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

Write the null and alternative hypotheses in words and mathematical notation.

Generate null distribution using permutation

Fill in the code, then set eval: true .

n = 100
set.seed(012226)

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

Visualize distribution

# Code for histogram of null distribution

Compute the p-value

# get observed fit 
observed_fit <- duke_forest |>
  specify(price ~ age_2020) |>
  fit()

# calculate p-value
get_p_value(
  ____,
  obs_stat = ____,
  direction = "two-sided"
)

State conclusion

Write your conclusion in the context of the data. You can use 0.05 as the decision-making threshold.

Bootstrap CI

Construct the bootstrap CI

Construct a 95% bootstrap confidence interval.

# Code for ci

Draw conclusion

Interpret the interval in the context of the data.
Is the interval consistent with the conclusion from your hypothesis test? Briefly explain why or why not.

Wrapping up

Important

Once you’ve completed 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 repo on GitHub. You’re done! 🎉