Predicting Market Activity: A Linear Regression Analysis of Texas Housing Inventory (2010 – 2015)
by: Erin Novoa
Project Overview
Data Source: txhousing dataset built in ggplot2 package in RStudio
Objectives
- Exploratory Data Analysis
- Hypotheses Testing
- Linear Regression Model Analysis
- Model Validity
You can also view the pdf of this project on my GitHub.
This project analyzes the relationship between housing inventory and market liquidity across Texas (2010 – 2015) using the txhousing dataset in the ggplot2 package in R. I developed a linear regression model revealing that active listings explain 63.4% of sales volume variation (R^2 = 0.6342), with each additional listing generating approximately $46,987 in market value. While highly significant (p < 0.001), residual diagnostics indicate that market predictability is highest in small to mid-sized cities but faces increased volatility in high-growth metropolitan hubs like Houston and Dallas.
Setup R for the analysis
library(ggplot2)
1. Data Exploration (EDA)
# view txhousing data
head(txhousing)
## # A tibble: 6 × 9
## city year month sales volume median listings inventory date
## <chr> <int> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Abilene 2000 1 72 5380000 71400 701 6.3 2000
## 2 Abilene 2000 2 98 6505000 58700 746 6.6 2000.
## 3 Abilene 2000 3 130 9285000 58100 784 6.8 2000.
## 4 Abilene 2000 4 98 9730000 68600 785 6.9 2000.
## 5 Abilene 2000 5 141 10590000 67300 794 6.8 2000.
## 6 Abilene 2000 6 156 13910000 66900 780 6.6 2000.
years <- unique(txhousing$year)
years
## [1] 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014
## [16] 2015
# save a subset of the txhousing data for the years 2010 - 2015, inclusive
txhousing_after_2010 <- txhousing[txhousing$year >= 2010,]
txhousing_after_2010
## # A tibble: 3,082 × 9
## city year month sales volume median listings inventory date
## <chr> <int> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Abilene 2010 1 73 9130783 112200 868 6.4 2010
## 2 Abilene 2010 2 93 10372904 98300 830 6.1 2010.
## 3 Abilene 2010 3 133 16517713 114000 854 6.3 2010.
## 4 Abilene 2010 4 161 18788002 103600 859 6.3 2010.
## 5 Abilene 2010 5 200 22804393 99300 914 6.5 2010.
## 6 Abilene 2010 6 169 23216943 127900 932 6.7 2010.
## 7 Abilene 2010 7 159 22363123 127300 915 6.6 2010.
## 8 Abilene 2010 8 144 17504580 122000 936 6.7 2011.
## 9 Abilene 2010 9 116 15475763 121300 899 6.5 2011.
## 10 Abilene 2010 10 111 14570529 111900 863 6.4 2011.
## # ℹ 3,072 more rows
The summary statistics of the dataset.
summary(txhousing_after_2010)
## city year month sales
## Length:3082 Min. :2010 Min. : 1.000 Min. : 6.0
## Class :character 1st Qu.:2011 1st Qu.: 3.000 1st Qu.: 81.0
## Mode :character Median :2012 Median : 6.000 Median : 160.0
## Mean :2012 Mean : 6.239 Mean : 541.8
## 3rd Qu.:2014 3rd Qu.: 9.000 3rd Qu.: 436.8
## Max. :2015 Max. :12.000 Max. :8945.0
## NA's :8
## volume median listings inventory
## Min. :1.019e+06 Min. : 55000 Min. : 0.0 Min. : 0.000
## 1st Qu.:1.150e+07 1st Qu.:119325 1st Qu.: 638.8 1st Qu.: 4.400
## Median :2.441e+07 Median :139750 Median : 1173.0 Median : 6.800
## Mean :1.214e+08 Mean :146639 Mean : 2636.4 Mean : 7.893
## 3rd Qu.:7.837e+07 3rd Qu.:168075 3rd Qu.: 2343.5 3rd Qu.: 9.500
## Max. :2.568e+09 Max. :304200 Max. :40409.0 Max. :55.900
## NA's :8 NA's :8 NA's :46 NA's :49
## date
## Min. :2010
## 1st Qu.:2011
## Median :2013
## Mean :2013
## 3rd Qu.:2014
## Max. :2016
##
boxplot(txhousing_after_2010$listings, horizontal = TRUE)
boxplot(txhousing_after_2010$volume, horizontal = TRUE)
The data is heavily right-skewed due to larger cities like Houston/Dallas vs smaller markets. We can see the difference in the cities like Houston and Dallas versus other cities in Texas by viewing the barplot below. We can see our “Big Four” Cities like Houston, Dallas, San Antonio, and Austin all having more total active listings compared to other cities in Texas.
# 2. Sum the listings by city
sum_listings <- aggregate(listings ~ city, data = txhousing_after_2010,
FUN = sum, na.rm = TRUE)
# 3. Sort by total listings (descending)
sum_listings <- sum_listings[order(sum_listings$listings, decreasing = TRUE), ]
sum_listings
## city listings
## 20 Houston 1794158
## 12 Dallas 1115936
## 37 San Antonio 694922
## 4 Austin 543026
## 16 Fort Worth 235063
## 14 El Paso 233039
## 10 Collin County 224539
## 15 Fort Bend 220107
## 5 Bay Area 212130
## 30 Montgomery County 203907
## 43 Tyler 191440
## 32 NE Tarrant County 150614
## 13 Denton County 146426
## 28 McAllen 145491
## 11 Corpus Christi 144598
## 25 Longview-Marshall 113632
## 6 Beaumont 111620
## 19 Harlingen 105974
## 23 Killeen-Fort Hood 96789
## 9 Bryan-College Station 94070
## 26 Lubbock 91456
## 45 Waco 90773
## 2 Amarillo 86834
## 3 Arlington 84245
## 41 Temple-Belton 68325
## 17 Galveston 61410
## 1 Abilene 61007
## 46 Wichita Falls 60134
## 40 South Padre Island 56308
## 39 Sherman-Denison 54463
## 22 Kerrville 51278
## 42 Texarkana 44934
## 8 Brownsville 43156
## 35 Port Arthur 41407
## 7 Brazoria County 37021
## 24 Laredo 36968
## 29 Midland 36891
## 21 Irving 35563
## 18 Garland 33976
## 36 San Angelo 33296
## 27 Lufkin 26231
## 34 Paris 22528
## 44 Victoria 21289
## 33 Odessa 19929
## 31 Nacogdoches 17455
## 38 San Marcos 9654
par(mar = c(8, 7, 4, 2))
par(mgp = c(4.5, 1, 0))
# 4. Plot the top 10
barplot(height = sum_listings$listings[1:10] / 1000,
names.arg = sum_listings$city[1:10],
las = 2,
col = "seagreen",
cex.names = 0.8,
main = "Total Active Listings (2010-2015) for Top 10 cities",
ylab = "Total Listings (in Thousands)")
The Texas housing market, the “Big Four” cities (Houston, Dallas, San Antonio, and Austin) account for a vast majority of the state’s inventory. This concentration explains the high number of outliers in the initial boxplot analysis and suggests that a single linear model may be heavily influenced by these metropolitan hubs.
Examining the strength of the relationship between the number of active listings and the volume of sales for the years of 2010 to 2015.
plot(txhousing_after_2010$listings, txhousing_after_2010$volume,
ylab = "Volume of Sales ($)",
xlab = "Number of Active Listings",
main = "Number of Active Listings vs. Volume of Sales, 2010 - 2015")
There appears to be a positive correlation between the two quantitative variables.
cor(txhousing_after_2010$listings, txhousing_after_2010$volume, use = "complete.obs")
## [1] 0.7963502
The two quantitative variables, listings and volume, have a correlation value of 0.7963502 rounded to 0.8 have a positive strong linear association.
2. Formal Hypotheses
To determine the validity of this model, I tested the following to see whether the slope for the linear regression model was different from zero:
Ho: β1 = 0 and there is no relationship between listings and volume
Ha: β1 ≠ 0 and there is a significant relationship between listings and volume
3. The Model: Linear Regression
model <- lm(volume ~ listings, data = txhousing_after_2010)
plot(txhousing_after_2010$listings, txhousing_after_2010$volume,
ylab = "Volume of Sales ($)",
xlab = "Number of Active Listings",
main = "Number of Active Listings vs. Volume of Sales, 2010 - 2015")
# add regression line, "line of best fit"
abline(model, col="red", lwd=2)
However, is the linear model a good fit for these two variables and how well does it predict the outcome?
model
##
## Call:
## lm(formula = volume ~ listings, data = txhousing_after_2010)
##
## Coefficients:
## (Intercept) listings
## -1163195 46987
The linear model is predicting the volume of sales given the number of active listings.
The y-intercept of the linear model is -1,163,195. It mathematically represents the predicted volume of sales at zero listings, however, it is outside the observable range of the data (extrapolation) and not a possible value that we would realistically encounter. Therefore, we will focus on the slope for the remainder of this analysis.
The slope is 46,987, which means that for every single additional listing added to the market, the total volume of sales is predicted to increase by $46,987, on average.
summary(model)
##
## Call:
## lm(formula = volume ~ listings, data = txhousing_after_2010)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.054e+09 -4.288e+07 -1.949e+07 -2.413e+05 1.448e+09
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1163195.4 3591551.0 -0.324 0.746
## listings 46987.2 647.9 72.523 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 174100000 on 3034 degrees of freedom
## (46 observations deleted due to missingness)
## Multiple R-squared: 0.6342, Adjusted R-squared: 0.6341
## F-statistic: 5260 on 1 and 3034 DF, p-value: < 2.2e-16
The Reliability of the Model:
Looking at the R^2 value, 0.6342, we can say that 63.4% of the variation in the total sales volume is explained by the number of listings. However, there is around 36.6% of the story still missing that likely comes from other factors that this model did not include.
The Statistical Significance:
Since the P-value is less than 2e^-16, and it is less than 0.05 and the slope was not equal to 0, we reject the Null Hypothesis. We believe we have convincing evidence that there is a statistical significance with the relationship between the listings and volume variables in the Texas housing market.
4. Model Accuracy (Residuals Plot)
plot(model, which = 1)
This model appears to have a fan shape indicating it is not very accurate for the Texas market as a whole. It is more accurate for small to mid-size markets but loses precision as the total number of listings increase (or the city size increases like Houston or Dallas that have higher numbers of active listings, as we saw in our barplot in section 1).
Conclusion:
Between 2010 and 2015, the Texas housing market followed a predictable pattern: for every new listing added, the market generated on average approximately $46,987 in total volume. While this model is highly significant (p < 2e^-16), the R^2 of 0.634 suggests that inventory alone doesn’t tell the whole story. Investors should look at listings as a ‘baseline’ indicator, but must supplement this with local economic or additional housing data to account for the remaining 36.6% of market volatility.
Future Project Expansion:
Future iterations of this model could use Multiple Regression to see if adding another variable like, ‘Year’ improves the R^2 above 0.634.