Housing Prices

1 Introduction

price = \hat{\beta}_0 + \hat{\beta}_1 \times area + \epsilon \tag{1}

en nu inline:

een formule zoals deze price = \hat{\beta}_0 + \hat{\beta}_1 \times area + \epsilon is mooi!

zie ook (Waal, Goedegebuure, and Geradts 2011). we kunnen er nog eens naar verwijzen (Waal, Goedegebuure, and Geradts 2011).

zoals blijkt uit formule Equation 1

Testje, we kunnen Equation 1 nou moe …

This is a pretty incomplete analysis, but hopefully the document provides a good overview of some of the authoring features of Quarto!

Nu een call-out

In this analysis, we build a model predicting sale prices of houses based on data on houses that were sold in the Duke Forest neighborhood of Durham, NC around November 2020. Let’s start by loading the packages we’ll use for the analysis.

Packages

library(openintro)  # for data
library(tidyverse)  # for data wrangling and visualization
library(knitr)      # for tables
library(broom)      # for model summary

We present the results of exploratory data analysis in Section 2 and the regression model in Section 3.

2 Exploratory data analysis

The data contains 98 houses. As part of the exploratory analysis let’s visualize and summarize the relationship between areas and prices of these houses.

2.1 Data visualization

Figure 1 shows two histograms displaying the distributions of price and area individually.

Code

ggplot(duke_forest, aes(x = price)) +
  geom_histogram(binwidth = 50000) +
  labs(title = "Histogram of prices")

ggplot(duke_forest, aes(x = area)) +
  geom_histogram(binwidth = 250) +
  labs(title = "Histogram of areas")

(a) Histogram of prices

(b) Histogram of areas

Figure 1: Histograms of individual variables

Figure 2 displays the relationship between these two variables in a scatterplot.

Code

ggplot(duke_forest, aes(x = area, y = price)) +
  geom_point() +
  labs(title = "Price and area of houses in Duke Forest")

Figure 2: Scatterplot of price vs. area of houses in Duke Forest

2.2 Summary statistics

Table 1 displays basic summary statistics for these two variables.

Code

duke_forest %>%
  summarise(
    `Median price` = median(price),
    `IQR price` = IQR(price),
    `Median area` = median(area),
    `IQR area` = IQR(area),
    `Correlation, r` = cor(price, area)
    ) %>%
  kable(digits = c(0, 0, 0, 0, 2))

Table 1: Summary statistics for price and area of houses in Duke Forest

Median price	IQR price	Median area	IQR area	Correlation, r
540000	193125	2623	1121	0.67

3 Modeling

We can fit a simple linear regression model of the form shown in ?@eq-slr.

[ADD EQUATION HERE]

Table 2 shows the regression output for this model.

Code

price_fit <- lm(price ~ area, data = duke_forest)
  
price_fit %>%
  tidy() %>%
  kable(digits = c(0, 0, 2, 2, 2))

Table 2: Linear regression model for predicting price from area

term	estimate	std.error	statistic	p.value
(Intercept)	116652	53302.46	2.19	0.03
area	159	18.17	8.78	0.00

4 References

Waal, André de, Robert Goedegebuure, and Patricia Geradts. 2011. “The Impact of Performance Management on the Results of a Non-Profit Organization.” International Journal of Productivity and Performance Management 60 (8): 778–96. https://doi.org/10.1108/17410401111182189.