AE 16: Houses in Duke Forest

Application exercise

In this application exercise, we use bootstrapping to construct confidence intervals.

Packages

We will use tidyverse and tidymodels for data exploration and modeling, respectively, and the openintro package for the data, and the knitr package for formatting tables.

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-…

Bootstrap confidence interval

1. Calculate the observed fit (slope)

observed_fit <- duke_forest |>
  specify(____ ~ _____) |>
  fit()

observed_fit

2. Take n bootstrap samples and fit models to each one.

Fill in the code, then set eval: true .

n = 100
set.seed(1234)

boot_fits <- duke_forest |>
  _____(price ~ area) |>
  ______(reps = _____, type = ______) |>
  fit()

boot_fits

Why do we set a seed before taking the bootstrap samples?
Make a histogram of the bootstrap samples to visualize the bootstrap distribution.

boot_fits |>
  filter(_____  == _______) |>
  ggplot(aes(x = ______ )) +
  geom_histogram()

3. Compute the 95% confidence interval as the middle 95% of the bootstrap distribution

get_confidence_interval(
  boot_fits, 
  point_estimate = _____, 
  level = ______,
  type = ______
)

Changing confidence level

Modify the code from Step 3 to create a 90% confidence interval.

get_confidence_interval(
  boot_fits, 
  point_estimate = observed_fit, 
  level = ____,
  type = "percentile"
)

Modify the code from Step 3 to create a 99% confidence interval.

get_confidence_interval(
  boot_fits, 
  point_estimate = observed_fit, 
  level = _____,
  type = "percentile"
)

Which confidence level produces the most accurate confidence interval (90%, 95%, 99%)? Explain
Which confidence level produces the most precise confidence interval (90%, 95%, 99%)? Explain
If we want to be very certain that we capture the population parameter, should we use a wider or a narrower interval? What drawbacks are associated with using a wider interval?