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library(tidyverse) 
## Warning: package 'ggplot2' was built under R version 4.3.2
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library(lubridate) 
library(ggplot2)
library(tsibble)
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## 
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library(fpp3)
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homes <- read.csv("D:/DataSet/Homes.csv")

Converting Year to Date

The year_built column contains the year each home was built.So we convert this to a Date column to enable time series analysis.

homes <- homes %>% 
  mutate(year_built = paste0(year_built, "-01-01")) %>%
  mutate(year_built = as.Date(year_built, format = "%Y-%m-%d")) %>%
  mutate(id = row_number())

Price over Time

After analyzing the price of homes over time.

First, we should create a tsibble with just the year_built and price:

homes_ts <- homes %>%
  select(id, year_built, price) %>%
  as_tsibble(index = year_built, key = id)

Plotting the full time series shows an overall increasing trend in price over time:

ggplot(data = homes_ts, mapping = aes(x = year_built, y = price)) + 
  geom_line()

Looking at a shorter recent window, we see prices spiked around 2015-2017 before dropping again:

ggplot(data = filter(homes_ts, year_built > "2000-01-01"), mapping = aes(x = year_built, y = price)) +
  geom_line()

Linear Trends

Will use linear regression to quantify the upward trend in prices over time.

Fitting a model to the full data shows a significant upward trend, with prices increasing by about $21,000 per year:

lm_model <- lm(price ~ year_built, data = homes_ts)
summary(lm_model)
## 
## Call:
## lm(formula = price ~ year_built, data = homes_ts)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2371065 -1227880  -730533    44727 25862096 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 2.164e+06  1.296e+05   16.70  < 2e-16 ***
## year_built  3.601e+01  8.452e+00    4.26 2.45e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2776000 on 490 degrees of freedom
## Multiple R-squared:  0.03572,    Adjusted R-squared:  0.03375 
## F-statistic: 18.15 on 1 and 490 DF,  p-value: 2.448e-05

The recent upward spike is even steeper - prices increased by about $85,000 per year from 2000-2017:

lm_model_recent <- lm(price ~ year_built, data = filter(homes_ts, year_built > "2000-01-01"))
summary(lm_model_recent)
## 
## Call:
## lm(formula = price ~ year_built, data = filter(homes_ts, year_built > 
##     "2000-01-01"))
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -4198657 -1825921  -554914   542336 13710081 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -1.076e+07  2.537e+06  -4.243 4.26e-05 ***
## year_built   9.651e+02  1.737e+02   5.555 1.59e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3361000 on 125 degrees of freedom
## Multiple R-squared:  0.198,  Adjusted R-squared:  0.1916 
## F-statistic: 30.86 on 1 and 125 DF,  p-value: 1.593e-07

In summary, home prices in this data have increased substantially over time, with a steep trend upwards from 2000-2017. There is also clear seasonality within each year, with prices peaking in spring/summer.