Abstract

This study, conducted by Claudio Urbani for Texas Realty Insights, analyzes the dynamics of the Texas real estate market using historical sales data from the “Real Estate Texas.csv” dataset. The analysis examines key variables – including sales, transaction volumes, median prices, active listings, and months of inventory – across cities, years, and months. Results highlight significant geographic and temporal disparities: some cities display higher median prices and stability, while others are characterized by volatility and larger transaction volumes. The study also identifies seasonal and cyclical patterns consistent with national real estate trends. These insights provide Texas Realty Insights with data-driven guidance to optimize sales strategies, evaluate listing effectiveness, and target areas with the greatest growth potential.

Keywords: Texas real estate market trends, Texas housing market analysis, Texas property sales data, Texas home sales historical data, Texas real estate statistics, Texas housing market insights, Texas real estate data visualization, Texas property market research, Texas real estate sales trends, Texas home prices trends, Texas real estate market forecast, Texas housing supply and demand analysis, Texas real estate sales optimization, Texas real estate listings analysis, Texas property market dynamics, Texas real estate analytics, Texas home sales trends by city, Texas real estate big data analysis, Texas real estate investment trends, Texas housing market dashboards

1. Introduction and Variable Analysis

1.1 Statistical Variable Classification

# Variable classification (theoretical definition based on dataset structure)
variable_types <- data.frame(
  Variable = c("city", "year", "month", "sales", "volume", "median_price", "listings", "months_inventory"),
  Statistical_Type = c(
    "Categorical Nominal",
    "Quantitative Discrete (Temporal)",
    "Quantitative Discrete (Temporal)", 
    "Quantitative Discrete",
    "Quantitative Continuous",
    "Quantitative Continuous",
    "Quantitative Discrete",
    "Quantitative Continuous"
  ),
  Measurement_Scale = c("Nominal", "Ordinal", "Ordinal", "Ratio", "Ratio", "Ratio", "Ratio", "Ratio"),
  Possible_Analysis = c(
    "Frequencies, mode, chi-square tests",
    "Temporal trends, seasonality, autocorrelation",
    "Seasonal cycles, monthly patterns",
    "All indices, correlations, regressions",
    "All indices, correlations, distributive analysis",
    "All indices, correlations, price analysis", 
    "All indices, correlations, supply-demand analysis",
    "All indices, correlations, inventory cycle analysis"
  ),
  stringsAsFactors = FALSE
)

kable(variable_types,
      caption = "Variable Classification and Applicable Analysis Types")
Variable Classification and Applicable Analysis Types
Variable Statistical_Type Measurement_Scale Possible_Analysis
city Categorical Nominal Nominal Frequencies, mode, chi-square tests
year Quantitative Discrete (Temporal) Ordinal Temporal trends, seasonality, autocorrelation
month Quantitative Discrete (Temporal) Ordinal Seasonal cycles, monthly patterns
sales Quantitative Discrete Ratio All indices, correlations, regressions
volume Quantitative Continuous Ratio All indices, correlations, distributive analysis
median_price Quantitative Continuous Ratio All indices, correlations, price analysis
listings Quantitative Discrete Ratio All indices, correlations, supply-demand analysis
months_inventory Quantitative Continuous Ratio All indices, correlations, inventory cycle analysis

Temporal Dimension Considerations

The year and month variables constitute a structured temporal dimension that enables time series analysis. The combination of these variables allows for: - Monthly time series to identify trends and seasonality - Autocorrelation analysis to verify temporal dependence - Seasonal decomposition to isolate trend, seasonal, and irregular components - Stationarity analysis to validate statistical stability assumptions

1.2 Dataset Structure

# Load data
df <- read_csv("texas_data.csv", show_col_types = FALSE)

# Verify dataset structure after loading
cat("Dataset Information:\n")
## Dataset Information:
cat("- Observations:", nrow(df), "\n")
## - Observations: 240
cat("- Variables:", ncol(df), "\n")
## - Variables: 8
cat("- Period:", min(df$year), "-", max(df$year), "\n")
## - Period: 2010 - 2014
cat("- Cities:", length(unique(df$city)), "\n")
## - Cities: 4
# Check variable structure
str(df)
## spc_tbl_ [240 × 8] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
##  $ city            : chr [1:240] "Beaumont" "Beaumont" "Beaumont" "Beaumont" ...
##  $ year            : num [1:240] 2010 2010 2010 2010 2010 2010 2010 2010 2010 2010 ...
##  $ month           : num [1:240] 1 2 3 4 5 6 7 8 9 10 ...
##  $ sales           : num [1:240] 83 108 182 200 202 189 164 174 124 150 ...
##  $ volume          : num [1:240] 14.2 17.7 28.7 26.8 28.8 ...
##  $ median_price    : num [1:240] 163800 138200 122400 123200 123100 ...
##  $ listings        : num [1:240] 1533 1586 1689 1708 1771 ...
##  $ months_inventory: num [1:240] 9.5 10 10.6 10.6 10.9 11.1 11.7 11.6 11.7 11.5 ...
##  - attr(*, "spec")=
##   .. cols(
##   ..   city = col_character(),
##   ..   year = col_double(),
##   ..   month = col_double(),
##   ..   sales = col_double(),
##   ..   volume = col_double(),
##   ..   median_price = col_double(),
##   ..   listings = col_double(),
##   ..   months_inventory = col_double()
##   .. )
##  - attr(*, "problems")=<externalptr>
# Display structure
head(df) %>% kable(caption = "Dataset Structure - First 6 Observations")
Dataset Structure - First 6 Observations
city year month sales volume median_price listings months_inventory
Beaumont 2010 1 83 14.162 163800 1533 9.5
Beaumont 2010 2 108 17.690 138200 1586 10.0
Beaumont 2010 3 182 28.701 122400 1689 10.6
Beaumont 2010 4 200 26.819 123200 1708 10.6
Beaumont 2010 5 202 28.833 123100 1771 10.9
Beaumont 2010 6 189 27.219 122800 1803 11.1

The dataset contains 240 monthly observations for 4 Texas metropolitan areas in the period 2010-2014.

Variables analyzed: - sales: Number of monthly sales - volume: Transaction volume (millions USD) - median_price: Median housing price (USD) - listings: Number of active listings - months_inventory: Months of available inventory

2. Statistical-Descriptive Analysis

2.1 Summary Statistics

# Calculate descriptive statistics
quant_vars <- c("sales", "volume", "median_price", "listings", "months_inventory")

stats_summary <- data.frame(
  Variable = quant_vars,
  Mean = round(sapply(quant_vars, function(x) mean(df[[x]], na.rm = TRUE)), 2),
  Median = round(sapply(quant_vars, function(x) median(df[[x]], na.rm = TRUE)), 2),
  Std_Dev = round(sapply(quant_vars, function(x) sd(df[[x]], na.rm = TRUE)), 2),
  Coeff_Variation = round(sapply(quant_vars, function(x) {
    mean_val <- mean(df[[x]], na.rm = TRUE)
    sd_val <- sd(df[[x]], na.rm = TRUE)
    if(mean_val != 0) (sd_val / mean_val) * 100 else NA
  }), 2)
)

# Rename variables for presentation
stats_summary$Variable <- c("Monthly Sales", "Transaction Volume ($M)", 
                           "Median Price ($)", "Active Listings", "Months Inventory")

kable(stats_summary,
      caption = "Descriptive Statistics - Core Market Variables",
      col.names = c("Variable", "Mean", "Median", "Std Dev", "Coeff Variation (%)"))
Descriptive Statistics - Core Market Variables
Variable Mean Median Std Dev Coeff Variation (%)
sales Monthly Sales 192.29 175.50 79.65 41.42
volume Transaction Volume (\(M) | 31.01| 27.06| 16.65| 53.71| |median_price |Median Price (\)) 132665.42 134500.00 22662.15 17.08
listings Active Listings 1738.02 1618.50 752.71 43.31
months_inventory Months Inventory 9.19 8.95 2.30 25.06 
# Identify most variable
most_variable_var <- quant_vars[which.max(stats_summary$Coeff_Variation)]
max_coefficient_variation <- max(stats_summary$Coeff_Variation, na.rm = TRUE)

Distributional Insights

The analysis reveals that transaction volume presents the highest relative dispersion (CV = 53.71%), consistent with real estate cycle literature that documents high volume elasticity to macroeconomic conditions.

2.2 Price Distribution Analysis

# Price distribution analysis
price_data <- df$median_price

# Calculate Gini coefficient for price distribution
calculate_gini_coefficient <- function(x) { 
  x <- sort(x) 
  n <- length(x) 
  gini_value <- (2 * sum((1:n) * x)) / (n * sum(x)) - (n + 1) / n 
  return(gini_value) 
} 
gini_index <- round(calculate_gini_coefficient(price_data), 4)

# Dynamic interpretation based on calculated Gini value
concentration_level <- if(gini_index > 0.7) "HIGH" else if(gini_index > 0.4) "MODERATE" else "LOW"
concentration_level_lower <- tolower(concentration_level)

# Histogram
hist(price_data, 
     breaks = 15,
     main = "Empirical Distribution of Median Prices",
     xlab = "Median Price (USD)",
     ylab = "Frequency",
     col = "lightsteelblue", 
     border = "navy",
     prob = FALSE,
     xaxt = "n")

# Custom x-axis with readable labels
axis(1, at = seq(80000, 200000, 20000), 
     labels = paste0("$", seq(80, 200, 20), "K"))

# Overlay density curve (scaled to histogram)
hist_data <- hist(price_data, breaks = 15, plot = FALSE)
density_data <- density(price_data)
density_scaled <- density_data$y * length(price_data) * diff(hist_data$breaks)[1]
lines(density_data$x, density_scaled, col = "red", lwd = 2)

cat("Concentration Index:", gini_index, "\n")
## Concentration Index: 0.0968
cat("Interpretation:", 
    if(gini_index > 0.7) "HIGH Concentration" else if(gini_index > 0.4) "MODERATE Concentration" else "LOW Concentration")
## Interpretation: LOW Concentration

The Gini coefficient (0.097) indicates low concentration in price distribution.

3. Geographic Analysis

3.1 Performance by Metropolitan Area

# Analysis by city
city_analysis <- df %>%
  group_by(city) %>%
  summarise(
    n_observations = n(),
    mean_sales = round(mean(sales, na.rm = TRUE), 1),
    mean_median_price = round(mean(median_price, na.rm = TRUE), 0),
    total_volume = round(sum(volume, na.rm = TRUE), 1),
    mean_listings = round(mean(listings, na.rm = TRUE), 0),
    cv_sales = round((sd(sales, na.rm = TRUE) / mean(sales, na.rm = TRUE)) * 100, 2),
    .groups = 'drop'
  ) %>%
  arrange(desc(mean_median_price))

# Performance table
city_performance <- city_analysis %>%
  select(city, mean_median_price, mean_sales, total_volume, cv_sales) %>%
  mutate(
    price_rank = row_number(),
    volume_rank = rank(desc(total_volume))
  )

kable(city_performance,
      caption = "Comparative Performance by Metropolitan Area",
      col.names = c("MSA", "Median Price ($)", "Average Sales", "Total Volume ($M)", 
                    "Volatility (%)", "Price Rank", "Volume Rank"))
Comparative Performance by Metropolitan Area
MSA Median Price (\()| Average Sales| Total Volume (\)M) Volatility (%) Price Rank Volume Rank
Bryan-College Station 157488 206.0 2291.5 41.26 1 2
Tyler 141442 269.8 2746.0 22.97 2 1
Beaumont 129988 177.4 1567.9 23.39 3 3
Wichita Falls 101743 116.1 835.8 19.09 4 4 
# Identify leaders dynamically
price_leader_city <- city_analysis$city[1]
price_leader_value <- city_analysis$mean_median_price[1]
volume_leader_city <- city_analysis$city[which.max(city_analysis$total_volume)]
volume_leader_value <- max(city_analysis$total_volume)
# Visualization of prices by city
ggplot(city_analysis, aes(x = reorder(city, mean_median_price))) +
  geom_col(aes(y = mean_median_price/1000), fill = "#1f77b4", alpha = 0.8, width = 0.6) +
  geom_text(aes(y = mean_median_price/1000, 
                label = paste0("$", format(round(mean_median_price/1000), big.mark = ","), "K")), 
            hjust = -0.1, size = 3.5, fontface = "bold") +
  coord_flip() +
  labs(
    title = "Median Price Stratification by Metropolitan Area",
    subtitle = "Observation period: 2010-2014",
    x = NULL,
    y = "Median Price (thousands USD)",
    caption = "Source: Analysis of Texas MLS data"
  ) +
  theme_minimal() +
  theme(
    plot.title = element_text(size = 14, face = "bold"),
    plot.subtitle = element_text(size = 11),
    plot.caption = element_text(size = 9, color = "gray60")
  )

Bryan-College Station emerges as a premium market ($157,488 median price), while Tyler dominates in transaction volumes ($2,746M).

3.2 Growth Analysis

# Calculate growth rates
annual_city_data <- df %>%
  group_by(city, year) %>%
  summarise(
    annual_median_price = median(median_price, na.rm = TRUE),
    .groups = 'drop'
  )

growth_analysis <- annual_city_data %>%
  arrange(city, year) %>%
  group_by(city) %>%
  mutate(
    price_growth_rate = ((annual_median_price - lag(annual_median_price)) / lag(annual_median_price)) * 100
  ) %>%
  ungroup()

growth_summary <- growth_analysis %>%
  filter(!is.na(price_growth_rate)) %>%
  group_by(city) %>%
  summarise(
    avg_growth_rate = round(mean(price_growth_rate, na.rm = TRUE), 2),
    years_data = n(),
    .groups = 'drop'
  ) %>%
  arrange(desc(avg_growth_rate))

kable(growth_summary,
      caption = "Annual Price Growth Rates by MSA",
      col.names = c("Metropolitan Area", "Average Growth (%)", "Years of Data"))
Annual Price Growth Rates by MSA
Metropolitan Area Average Growth (%) Years of Data
Tyler 3.12 4
Bryan-College Station 3.05 4
Wichita Falls 1.49 4
Beaumont 1.11 4 
# Identify growth leader dynamically
growth_leader_city <- growth_summary$city[1]
growth_leader_value <- growth_summary$avg_growth_rate[1]

4. Temporal Analysis

# Aggregate annual trends
annual_analysis <- df %>%
  group_by(year) %>%
  summarise(
    mean_median_price = round(mean(median_price, na.rm = TRUE), 0),
    total_sales = sum(sales, na.rm = TRUE),
    total_volume = round(sum(volume, na.rm = TRUE), 2),
    cv_price = round((sd(median_price, na.rm = TRUE) / mean(median_price, na.rm = TRUE)) * 100, 2),
    .groups = 'drop'
  ) %>%
  arrange(year)

# Temporal evolution chart
ggplot(annual_analysis, aes(x = year, y = mean_median_price)) +
  geom_line(color = "#1f77b4", size = 1.5, alpha = 0.8) +
  geom_point(color = "#1f77b4", size = 3) +
  geom_text(aes(label = paste0("$", format(round(mean_median_price/1000), big.mark = ","), "K")), 
            vjust = -0.7, size = 3.5) +
  labs(
    title = "Evolution of Aggregate Median Price",
    subtitle = "All metropolitan areas",
    x = "Year", 
    y = "Median Price (USD)"
  ) +
  theme_minimal() +
  scale_y_continuous(labels = function(x) paste0("$", format(x/1000, big.mark = ","), "K")) +
  scale_x_continuous(breaks = annual_analysis$year)

# Trend table
kable(annual_analysis,
      caption = "Annual Market Evolution",
      col.names = c("Year", "Median Price ($)", "Total Sales", "Total Volume ($M)", "Price CV (%)"))
Annual Market Evolution
Year Median Price (\()| Total Sales| Total Volume (\)M) Price CV (%)
2010 130192 8096 1232.44 16.76
2011 127854 7878 1207.58 16.67
2012 130077 8935 1404.84 16.48
2013 135723 10172 1687.32 15.99
2014 139481 11069 1909.07 18.37

5. Advanced Visualizations

5.1 Boxplot Analysis

# Boxplot 1: Median price distribution by city
price_boxplot <- ggplot(df, aes(x = reorder(city, median_price, median), y = median_price/1000)) +
  geom_boxplot(aes(fill = city), alpha = 0.7, show.legend = FALSE) +
  geom_jitter(width = 0.2, alpha = 0.3, size = 0.8) +
  labs(title = "Median Price Distribution by City",
       subtitle = "Comparison of intra-urban variability",
       x = "Metropolitan Area", 
       y = "Median Price (thousands USD)") +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1))

print(price_boxplot)

# Boxplot 2: Sales distribution by city
sales_boxplot <- ggplot(df, aes(x = reorder(city, sales, median), y = sales)) +
  geom_boxplot(aes(fill = city), alpha = 0.7, show.legend = FALSE) +
  labs(title = "Monthly Sales Distribution by City",
       subtitle = "Analysis of sales volume variability",
       x = "Metropolitan Area", 
       y = "Monthly Sales (units)") +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1))

print(sales_boxplot)

# Boxplot 3: Sales by city and year (temporal comparison)
temporal_boxplot <- ggplot(df, aes(x = city, y = sales, fill = factor(year))) +
  geom_boxplot(alpha = 0.8, position = "dodge") +
  labs(title = "Sales Distribution Evolution: Cities vs Years",
       subtitle = "Comparison of temporal volatility by geographic area",
       x = "Metropolitan Area", 
       y = "Monthly Sales (units)",
       fill = "Year") +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1))

print(temporal_boxplot)

# Boxplot 4: Transaction volume by year
volume_boxplot <- ggplot(df, aes(x = factor(year), y = volume)) +
  geom_boxplot(aes(fill = factor(year)), alpha = 0.7, show.legend = FALSE) +
  geom_jitter(width = 0.2, alpha = 0.4) +
  labs(title = "Transaction Volume Distribution by Year",
       subtitle = "Evolution of variability over time",
       x = "Year", 
       y = "Transaction Volume (millions USD)") +
  theme_minimal() +
  scale_y_continuous(labels = function(x) paste0("$", x, "M"))

print(volume_boxplot)

5.2 Seasonal Analysis

# Data preparation for seasonality
monthly_data <- df %>%
  group_by(month, city) %>%
  summarise(total_sales = sum(sales), 
            avg_sales = mean(sales),
            .groups = 'drop')

# Chart 1: Stacked bars for seasonality
seasonal_stacked <- ggplot(monthly_data, aes(x = factor(month), y = total_sales, fill = city)) +
  geom_col(position = "stack", alpha = 0.8) +
  labs(title = "Seasonal Sales Patterns: Composition by City",
       subtitle = "Relative contribution of each MSA to monthly total",
       x = "Month", 
       y = "Total Sales (units)",
       fill = "Metropolitan Area") +
  theme_minimal() +
  scale_x_discrete(labels = month.abb) +
  scale_y_continuous(labels = function(x) format(x, big.mark = ","))

print(seasonal_stacked)

# Chart 2: Normalized bars (percentages)
seasonal_normalized <- ggplot(monthly_data, aes(x = factor(month), y = total_sales, fill = city)) +
  geom_col(position = "fill", alpha = 0.8) +
  labs(title = "Percentage Sales Composition by Month",
       subtitle = "Relative share of each city on monthly total",
       x = "Month", 
       y = "Proportion (%)",
       fill = "Metropolitan Area") +
  theme_minimal() +
  scale_x_discrete(labels = month.abb) +
  scale_y_continuous(labels = scales::percent_format())

print(seasonal_normalized)

# Chart 3: Multi-annual seasonal patterns
yearly_monthly <- df %>%
  group_by(year, month, city) %>%
  summarise(avg_sales = mean(sales), .groups = 'drop')

multi_annual_seasonal <- ggplot(yearly_monthly, aes(x = factor(month), y = avg_sales, fill = city)) +
  geom_col(position = "dodge", alpha = 0.7) +
  facet_wrap(~year, labeller = label_both) +
  labs(title = "Multi-Annual Seasonal Patterns by City",
       subtitle = "Evolution of seasonal cycles in the 2010-2014 period",
       x = "Month", 
       y = "Average Sales (units)",
       fill = "MSA") +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1, size = 8),
        strip.text = element_text(size = 9, face = "bold")) +
  scale_x_discrete(labels = month.abb[1:12]) +
  scale_y_continuous(labels = function(x) format(x, big.mark = ","))

print(multi_annual_seasonal)

5.3 Line Charts

# Time series data preparation
ts_data <- df %>%
  mutate(time_period = year + (month - 1)/12) %>%
  arrange(city, year, month)

# Line Chart 1: Median price evolution by city
price_evolution <- ggplot(ts_data, aes(x = time_period, y = median_price/1000, color = city)) +
  geom_line(size = 1.2, alpha = 0.8) +
  geom_smooth(method = "loess", se = FALSE, size = 0.8, linetype = "dashed") +
  labs(title = "Temporal Evolution of Median Prices",
       subtitle = "Trends and smooth curves for cyclical pattern identification",
       x = "Year", 
       y = "Median Price (thousands USD)",
       color = "Metropolitan Area") +
  theme_minimal() +
  scale_x_continuous(breaks = seq(2010, 2014, 1), 
                     labels = c("2010", "2011", "2012", "2013", "2014")) +
  scale_y_continuous(labels = function(x) paste0("$", x, "K"))

print(price_evolution)

# Line Chart 2: Transaction volume dynamics
volume_dynamics <- ggplot(ts_data, aes(x = time_period, y = volume, color = city)) +
  geom_line(size = 1.1, alpha = 0.7) +
  geom_point(size = 1.5, alpha = 0.6) +
  labs(title = "Transaction Volume Dynamics by City",
       subtitle = "Identification of temporal shocks and recovery patterns",
       x = "Year", 
       y = "Transaction Volume (millions USD)",
       color = "Metropolitan Area") +
  theme_minimal() +
  scale_x_continuous(breaks = seq(2010, 2014, 1), 
                     labels = c("2010", "2011", "2012", "2013", "2014")) +
  scale_y_continuous(labels = function(x) paste0("$", x, "M"))

print(volume_dynamics)

# Line Chart 3: Composite activity indicator
activity_index <- ts_data %>%
  group_by(city) %>%
  mutate(
    sales_normalized = scale(sales)[,1],
    volume_normalized = scale(volume)[,1],
    activity_index = sales_normalized + volume_normalized
  ) %>%
  ungroup()

composite_activity <- ggplot(activity_index, aes(x = time_period, y = activity_index, color = city)) +
  geom_line(size = 1.3, alpha = 0.8) +
  geom_hline(yintercept = 0, linetype = "dashed", alpha = 0.5) +
  labs(title = "Composite Market Activity Index",
       subtitle = "Normalized synthesis of sales and volumes for relative comparisons",
       x = "Year", 
       y = "Activity Index (standardized)",
       color = "Metropolitan Area") +
  theme_minimal() +
  scale_x_continuous(breaks = seq(2010, 2014, 1), 
                     labels = c("2010", "2011", "2012", "2013", "2014")) +
  scale_y_continuous(labels = function(x) round(x, 1))

print(composite_activity)

6. Correlation Analysis

# Correlation matrix calculation
correlation_vars <- c("sales", "volume", "median_price", "listings", "months_inventory")
correlation_matrix <- df %>%
  select(all_of(correlation_vars)) %>%
  cor(use = "complete.obs")

# Visualization
corrplot(correlation_matrix, 
         method = "color",
         type = "upper", 
         order = "hclust",
         tl.col = "black",
         tl.srt = 45,
         addCoef.col = "black",
         number.cex = 0.8)

# Dynamic correlation interpretation
sales_volume_corr <- round(correlation_matrix["sales", "volume"], 3)
sales_inventory_corr <- round(correlation_matrix["sales", "months_inventory"], 3)

kable(round(correlation_matrix, 3),
      caption = "Correlation Matrix - Market Variables")
Correlation Matrix - Market Variables
sales volume median_price listings months_inventory
sales 1.000 0.976 0.590 0.621 0.147
volume 0.976 1.000 0.704 0.570 0.055
median_price 0.590 0.704 1.000 0.396 -0.035
listings 0.621 0.570 0.396 1.000 0.735
months_inventory 0.147 0.055 -0.035 0.735 1.000

The correlations observed confirm expected economic mechanisms: Sales-Volume (r = 0.976) shows strong direct relationship.

7. Probability Analysis

# Calculate probabilities dynamically
total_observations <- nrow(df)

probability_events <- data.frame(
  Event = c("City = Beaumont", "Month = July", "December 2012"),
  Probability = c(
    round(sum(df$city == "Beaumont") / total_observations, 4),
    round(sum(df$month == 7) / total_observations, 4),
    round(sum(df$month == 12 & df$year == 2012) / total_observations, 4)
  ),
  Count = c(
    sum(df$city == "Beaumont"),
    sum(df$month == 7),
    sum(df$month == 12 & df$year == 2012)
  ),
  Total = rep(total_observations, 3)
) %>%
  mutate(Percentage = round(Probability * 100, 2))

kable(probability_events,
      caption = "Probability Analysis of Key Events")
Probability Analysis of Key Events
Event Probability Count Total Percentage
City = Beaumont 0.2500 60 240 25.00
Month = July 0.0833 20 240 8.33
December 2012 0.0167 4 240 1.67

8. Derived Variables

# Calculate derived variables
df_enhanced <- df %>%
  mutate(
    average_transaction_value = ifelse(sales > 0, (volume * 1000000) / sales, NA),
    market_efficiency_ratio = ifelse(listings > 0, sales / listings, NA),
    inventory_turnover_rate = ifelse(months_inventory > 0, 1 / months_inventory, NA)
  )

# Summary of derived variables
derived_summary_stats <- df_enhanced %>%
  summarise(
    avg_transaction_mean = round(mean(average_transaction_value, na.rm = TRUE), 0),
    efficiency_mean = round(mean(market_efficiency_ratio, na.rm = TRUE), 3),
    turnover_mean = round(mean(inventory_turnover_rate, na.rm = TRUE), 3),
    correlation_derived_median = round(cor(average_transaction_value, median_price, use = "complete.obs"), 3)
  )

derived_variables_table <- data.frame(
  Indicator = c("Average Transaction Value", "Market Efficiency Ratio", "Inventory Turnover Rate"),
  Mean = c(
    paste0("$", format(derived_summary_stats$avg_transaction_mean, big.mark = ",")),
    derived_summary_stats$efficiency_mean,
    derived_summary_stats$turnover_mean
  ),
  Interpretation = c(
    "Average value per transaction",
    "Listing-to-sale conversion efficiency", 
    "Inventory rotation speed"
  )
)

kable(derived_variables_table,
      caption = "Derived Performance Indicators")
Derived Performance Indicators
Indicator Mean Interpretation
Average Transaction Value $154,320 Average value per transaction
Market Efficiency Ratio 0.119 Listing-to-sale conversion efficiency
Inventory Turnover Rate 0.117 Inventory rotation speed 
cat("Correlation Average Transaction Value vs Median Price:", derived_summary_stats$correlation_derived_median)
## Correlation Average Transaction Value vs Median Price: 0.946

9. Key Results

9.1 Market Leadership

  • Price Leadership: Bryan-College Station with $157,488
  • Growth Leadership: Tyler with 3.12% annually
  • Volume Leadership: Tyler with $2,746M

9.2 Statistical Characteristics

  • Most volatile variable: Transaction volume (CV = 53.71%)
  • Price concentration: LOW (Gini index = 0.0968)
  • Sales-volume correlation: 0.976 (strong direct relationship)

10. Conclusions

This comprehensive analysis of the Texas real estate market (2010-2014) reveals distinct geographic and temporal patterns. The identification of Bryan-College Station as price leader and Tyler as volume leader provides clear strategic direction for market positioning.

The methodology developed provides a replicable framework for ongoing market analysis and strategic decision-making in regional real estate markets.

Analysis conducted using R v4.3.0. Complete reproducible methodology with automated insights generation.

Report generated: 2025-08-16 | Author: Claudio Urbani | Texas Realty Insights