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Introduction

• The housing crisis in 2025 has been a big topic of concern in media and the news
• Definition of key terms:
  • Dwellings: Buildings that are primarily designed for long-term residential purposes
  • Housing stress: housing costs that exceed 30% of the average income for low-income households
  • Housing affordability: Relationship between housing costs and household income, can vary between locations
  • Affordable housing: housing provided at discounted market rates, typically targeted towards households that are part of the low-middle income class.
  • Social housing: Government or community managed housing typically provided to those who are unable to access affordable, adequate housing in the market.
  • Overcrowding: The number of residents that live within the dwelling exceeding the designed capacity due to affordability challenges or housing shortages.

Introduction cont.

• Key findings from Australia’s National Housing Supply and Affordability Council (2025) include:
  • Rises in housing prices and rent outpaced the rise in the median household income
  • Housing affordability deteriorating
  • Supply of housing is near its lowest levels in a decade
• Key findings from CBRE Investment Management (2025) on the state of housing in the United States include:
  • Home prices reaching historical highs
  • Income required to buy a home has doubled since 2019
  • Key problem is the difference in supply and demand of houses in the US
    • Not enough housing, wrong types of houses being supplied for current demand
  • Regulatory barriers include:
    • Local zoning regulations
    • Higher cost of capital, goods and labour
    • Rising interest rates, which significantly decreased development activity despite strong consumer demand for housing

Problem Statement

• How do the different variables (i.e. property prices, furnishing statuses, salaries, etc.) interact with purchasing decision of properties?
• Statistics will be employed to:
  • Explore the average property prices across different countries
  • Explore the differences in purchasing decisions between countries
  • Explore the relationship between monthly salary and property prices
  • Explore the relationship between property price and buyer decisions
  • Explore the relationship between furnishing status and buyer decisions

Data

• I went to Kaggle.com and searched for a recently updated housing dataset.
• Open Data Reference: https://www.kaggle.com/datasets/mohankrishnathalla/global-house-purchase-decision-dataset
• List of important variables in the dataset:
  • Property_type describes the type of the developed property, such as a studio, an apartment, a townhouse, etc.
  • Furnishing_status describes the furninshing condition of the developed property, such as unfurnished or furnished
  • The price describes the price of the property in the local currency
  • Monthly_expenses describes the monthly expenses of the customer that is looking to buy the property
  • Customer_salary describes the monthly salary of the customer looking to buy the property

Data cont.

• Some of the pre-processing done to the data set includes:
  • Converted the decision variable into a factor, with 0 being No and 1 being Yes
    • This helps with plotting, as well as treating purchase decision as a numerical outcome
  • Converted all dollar values from local currency to USD for easier comparison

ds <- read.csv("global_house_purchase_dataset.csv")
ds$decision <- ds$decision %>% factor(levels = c(0,1), labels = c("No", "Yes"))
ds$furnishing_status <- ds$furnishing_status %>% factor(levels = c("Unfurnished", "Semi-Furnished", "Fully-Furnished"), ordered=TRUE)
ds_filtered <- subset(ds, !country %in% c("Brazil", "China", "India", "Germany","Japan", "South Africa", "UAE"))
currency_pairs <- c("AUDUSD=X", "CADUSD=X", "EURUSD=X", "SGDUSD=X", "GBPUSD=X")

exchange_data <- getQuote(currency_pairs)
exchange_rates <- exchange_data$Last

currency_codes <- c("AUD", "CAD","EUR", "SGD", "GBP")
names(exchange_rates) <- currency_codes

exchange_rates <- c("USD" = 1, exchange_rates)
country_currency <- c("Australia" = "AUD", "Canada" = "CAD", "France" = "EUR","Singapore" = "SGD", "UK" = "GBP", "USA" = "USD")
ds_filtered$currency <- country_currency[ds_filtered$country]
ds_filtered$price_usd <- ds_filtered$price * exchange_rates[ds_filtered$currency]
ds_filtered$salary_usd <- ds_filtered$customer_salary*exchange_rates[ds_filtered$currency]
ds_filtered$loan_amt_usd <- ds_filtered$loan_amount*exchange_rates[ds_filtered$currency]
ds_filtered$monthly_exp_usd <-ds_filtered$monthly_expenses*exchange_rates[ds_filtered$currency]

Descriptive Statistics and Visualisations

• The table below summarises the mean and median prices of homes in USD for each country
• It also describes the mean salary in USD for each country in the data set

country_summary <- ds_filtered %>%
  group_by(country) %>%
  summarise(avg_price_usd = mean(price_usd, na.rm = TRUE),
    median_price_usd = median(price_usd, na.rm = TRUE),
    avg_salary_usd = mean(salary_usd, na.rm = TRUE))
knitr::kable(country_summary)

Descriptive Statistics and Visualisations cont.

# Boxplot: Price comparison by Country
ggplot(ds_filtered, aes(x = country, y = price_usd, fill = country)) +
  geom_boxplot(fill = "white", color = "black") +
  xlab("Country") +  ylab("Property Price (USD)") +  theme_classic() +
  labs(title = "Boxplot of Property Prices by Country") +
  scale_y_continuous(labels = dollar) +  
  theme(legend.position = "none", axis.text.x = element_text(angle = 90, size = 10),
    axis.title.x = element_text(size = 12), axis.title.y = element_text(size = 12),
    plot.title = element_text(size = 16))

• The boxplot below describes the prices of properties across the different countries being analysed in the data set.
• Looking at the boxplot, the median property price (solid black line) is higher in countries like Singapore, the UK, US, and France compared to countries like Australia and Canada.

Descriptive Statistics and Visualisations cont.

ggplot(ds_filtered, aes(x = country, fill = decision)) +
  geom_bar(position = "dodge") + labs(title = "Decision to Buy by Country", 
  x = "Country", y = "Count of Decisions", fill = "Decision") + theme_minimal()

• The bar plot describes the difference in each country’s buyer decisions
• It can be seen that buyers in Singapore and the US are less likely to commit to buying a property
• There are the largest number of buyers in the US who ended up backtracking on their decision to buy a property

Descriptive Statistics and visualisations cont.

property_counts <- ds_filtered %>% group_by(country, constructed_year, property_type) %>% summarise(count = n()) 
filtered_counts <- property_counts %>% filter(property_type %in% c("Apartment", "Independent House"))
ggplot(filtered_counts, aes(x = constructed_year, y = count, colour = property_type)) +
  geom_line(size=0.75) + facet_wrap(~ country)+
  labs(title = "Number of apartments and townhouses built by year in each country",
       x = "Constructed Year", y = "Number of Properties", color = "Property Type") + theme_minimal() + 
  theme(legend.text = element_text(size = 8), legend.title = element_text(size = 9), legend.position = "bottom")

• Based on the chart above, it can be seen that over years, some countries (i.e. Canada, France, UK) are building more apartments and less independent houses
  • This could indicate that the population of people who are moving into the main city area to live are getting bigger
• Other countries like Australia, Singapore, and the US are showing a slow-down in the building of both property types
  • This could indicate broader issues within their economies, such as an increase in the cost of building materials in general, or regulatory issues

Hypothesis testing: Welch 2-sample t-test

• The welch 2-sample t-test was chosen to analyse the difference in property prices between the 2 decision gorups

yes_prices <- ds_filtered$price_usd[ds_filtered$decision == "Yes"]
no_prices <- ds_filtered$price_usd[ds_filtered$decision == "No"]

par(mfrow=c(1,2))
yes_prices %>% qqnorm()
no_prices %>% qqnorm()

• Using qqnorm() function to check for normality, both lines show an s-curve, indicating that normality assumptions are violated
  • However, since the sample size in the data set is large ( > 30), sampling distributions will approximate a normal distribution

Welch 2-sample t-test cont.

leveneTest(price_usd ~ decision, data = ds_filtered)

## Levene's Test for Homogeneity of Variance (center = median)
##          Df F value    Pr(>F)    
## group     1  196.24 < 2.2e-16 ***
##       92441                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

t.test(yes_prices, no_prices)

## 
##  Welch Two Sample t-test
## 
## data:  yes_prices and no_prices
## t = -21.082, df = 37695, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -144894.7 -120244.3
## sample estimates:
## mean of x mean of y 
##   1240507   1373076

• Using Levene Test to check for homogeneity of variances, results show that the homogeneity of variances is violated
  • the p-value reported is < 2.2e-16, therefore is statistically significant
• The results of the Welch 2-sample t-test show that the mean property price of those who ended up purchasing houses is USD1,242,744, whereas the mean property price of those who did not buy a house is USD1,375,326.
• The t-value is -21.059, a degree of freedom of 37689, and a p-value of < 2.2e-16
• Results of the Welch 2-sample t-test are statistically significant, indicating that there is a strong evidence of a difference in house prices between the 2 decision groups
• Properties that buyers buy is on average cheaper than properties that buyers decided not to buy

Regression analysis: Linear regression

• Statement: Is the home loan amount a good predictor of property prices?

cor.test(ds_filtered$price_usd, ds_filtered$loan_amt_usd, method="pearson")

## 
##  Pearson's product-moment correlation
## 
## data:  ds_filtered$price_usd and ds_filtered$loan_amt_usd
## t = 771.39, df = 92441, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.9294711 0.9312047
## sample estimates:
##       cor 
## 0.9303431

• Pearson’s correlation test first performed to check if linear regression analysis is appropriate
  • Results of correlation test: p-value < 0.05 and correlation calculated is 0.93, indicating a high correlation

Linear regression cont.

lm_model <- lm(price_usd ~ loan_amt_usd, data = ds_filtered)
summary(lm_model)

## 
## Call:
## lm(formula = price_usd ~ loan_amt_usd, data = ds_filtered)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -741484 -196411  -71887  144676 1236356 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.802e+05  1.811e+03   99.48   <2e-16 ***
## loan_amt_usd 1.385e+00  1.796e-03  771.39   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 305800 on 92441 degrees of freedom
## Multiple R-squared:  0.8655, Adjusted R-squared:  0.8655 
## F-statistic: 5.95e+05 on 1 and 92441 DF,  p-value: < 2.2e-16

• Results of the linear regression model:
  • \(R^2\) value: 0.8564, F(1,92441) = 594500
  • P-value < 0.05, indicating statistical significance
• Conclusion: Results of the linear regression model is statistically significant. There is a significant relationship between the amount of the home loan and the price of the property.

Linear regression cont.

par(mfrow=c(2,2))
plot(lm_model)

• Looking at the diagnostic plot:
  • residuals vs fitted plot show a triangular shape, but follows the shape of the red line, therefore indicating heteroscedascity
  • Q-Q plot shows slight deviations from normality at the tail end of the curve
  • Scale-location plot also shows non-flat red line, further indicating heteroscedascity
• Conclusion: Key assumptions of homoscedascity and normality of residuals are violated, therefore interpretation of linear regression analysis should be reviewed.

Categorical association

• Statement: Does furnishing status influence the buying decision of a given property?
• Null hypothesis: There is no association between furnishing status and the buying decision
• Alternative: There is an association between the furnishing status and buying decision

furnishing_decision_table <- table(ds_filtered$furnishing_status, ds_filtered$decision)
chi_result <- chisq.test(furnishing_decision_table)
chi_result

## 
##  Pearson's Chi-squared test
## 
## data:  furnishing_decision_table
## X-squared = 4.81, df = 2, p-value = 0.09026

• p-value: 0.09026 (> 0.05) therefore we fail to reject the null hypothesis
• Conclusion: Results of chi-squared tests are not statistically significant. There is therefore not enough evidence to conclude that furnishing status influences the buying decision of a property.

Categorical association cont.

• Statement: Do buyers in certain countries have higher purchase rates than others?
• Null hypothesis: There is no association between a buyer’s country and their purchase decisions
• Alternative: There is an association

country_decision_table <- table(ds_filtered$country, ds_filtered$decision)
chi_result <- chisq.test(country_decision_table)
chi_result

## 
##  Pearson's Chi-squared test
## 
## data:  country_decision_table
## X-squared = 487.55, df = 5, p-value < 2.2e-16

• p-value: 2.2e-16 (< 0.05), therefore we reject the null hypothesis
• Conclusion: Results of the chi-squared tests are statistically significant. There is therefore enough evidence to conclude that a buyer’s purchase rates differ by country.

Categorical association cont.

• Statement: Are certain property types more likely to be furnished or not?
• Null hypothesis: There is no association between the furnishing status and property types
• Alternative: There is an association

property_furnishing_table <- table(ds_filtered$property_type, ds_filtered$furnishing_status)
chi_result <- chisq.test(property_furnishing_table)
chi_result

## 
##  Pearson's Chi-squared test
## 
## data:  property_furnishing_table
## X-squared = 7.8341, df = 10, p-value = 0.645

• p-value: 0.645 (> 0.05), fail to reject the null hypothesis
• Conclusion: Results of the chi-squared tests are not statistically significant. There is therefore not enough evidence to prove that a given property type has a higher chance of being furnished over another.

Discussion

• Median property prices in places like Singapore and the US are higher than in places like Australia and Canada
  • Land size of Singapore is significantly smaller than other countries listed in this analysis
  • Places like Los Angeles and San Francisco have good job opportunities and good weather due to its location near the Pacific Ocean, leading to intense competition in those areas (Fitzgerald, 2025)
• Similarly, potential buyers in Singapore and the US are less likely to commit to buying a property
  • This is shown in the bar plot, with the US and Singapore having a higher ratio of buyers not committing to the purchase
• Statistically significant findings:
  • Difference in property prices between those who ended up purchasing a house (USD$1242744) vs those who did not (USD$1375326)
    • This indicates that affordability is a big factor in buyer decisions
  • Country-specific buying rates were different, indicating there are broader influences that are affecting the decisions of buyers within the specific countries
  • There is a strong correlation between the amount of the home loan given and the price of the property
    • This indicates that buyers who typically require a larger home loan are looking at buying more expensive properties
• Conclusion: Based on the statistical findings, the most important factors that play into a buyer’s decision to commit to a home is most likely the affordability of the home, as well as the loan they require
  • Factors like furnishing statuses and crime cases reported on property play a less significant role in buyer decisions.

References

• CBRE Investment Management. (2025, August 14). Digging out of the U.S. housing affordability crisis. https://www.cbreim.com/insights/articles/digging-out-of-the-us-housing-affordability-crisis
• Fitzgerald, R. (2025, April 16). Average house prices by state in 2025: The least and most affordable U.S. states. Raleigh Realty. https://raleighrealty.com/blog/least-and-most-affordable-states
• National Housing Supply and Affordability Council. (2025, May 21). State of the housing system 2025. https://nhsac.gov.au/reports-and-submissions/state-housing-system-2025
• Thalla, M. K. (2025, September). Global house purchase decision dataset. Kaggle. https://www.kaggle.com/datasets/mohankrishnathalla/global-house-purchase-decision-dataset