---
title: "Housing Prices"
author: "Mine Çetinkaya-Rundel"
format: pdf
---

## Introduction

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.

```{r}
#| label: load-pkgs
#| code-summary: "Packages"
#| message: false

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 @sec-eda and the regression model in @sec-model.

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## Exploratory data analysis {#sec-eda}

The data contains `{r} nrow(duke_forest)` houses.
As part of the exploratory analysis let's visualize and summarize the relationship between areas and prices of these houses.

### Data visualization

@fig-histogram shows two histograms displaying the distributions of `price` and `area` individually.

```{r}
#| label: fig-histogram
#| fig-cap: "Histograms of individual variables"
#| fig-subcap:
#|   - "Histogram of `price`s"
#|   - "Histogram of `area`s" 
#| layout-ncol: 2

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")
```

@fig-scatterplot displays the relationship between these two variables in a scatterplot.

```{r}
#| label: fig-scatterplot
#| fig-cap: "Scatterplot of price vs. area of houses in Duke Forest"

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

### Summary statistics

@tbl-stats displays basic summary statistics for these two variables.

```{r}
#| label: tbl-stats
#| tbl-cap: "Summary statistics for price and area of houses in Duke Forest"

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))
```

## Modeling {#sec-model}

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

\[ADD EQUATION HERE\]

@tbl-lm shows the regression output for this model.

```{r}
#| label: tbl-lm
#| tbl-cap: "Linear regression model for predicting price from area"

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

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