Mr. Aristotle is a Vice President at Bayou City Real Estate Investment Trust (REIT) and he has presented a
proposal to the board to consider an investment of $200 million in the Houston market. To support his
recommendation, Mr. Aristotle had a forecast model developed for the Houston rental market. Venus, a
Financial Analyst at Bayou City, presented a regression model to forecast the average rent in the Houston
market with an R-square of 0.9918 and said, “We can confidently invest in the Houston market because we have
a ‘perfect’ model to predict future rents.” The REIT’s board wants to conduct further analysis and has hired your
Consulting team to evaluate the proposal and Venus’ model.
Venus used a number of predictive variables in her regression model. She included Vacancy Rate (percentage of
rental properties that are vacant) and Renter Fraction (percentage of renting households as a fraction of total
households). She also included home sales data like the median and average home sales price and number of
single-family home sales. Lastly, she included the WTI crude price and unemployment rate bringing the total to
seven (7) predictor variables. Table 1 shows the data used by Venus to develop her multiple regression model.
TABLE 1: Houston Rental Market Data
Year Average
Rent
Vacancy
Rate
Renter
Fraction
Total
property sales
Average Home
Sales Price
Home Median
Sales Price
WTI_Crude
Price
Unemployment
Rate
2019 $1,176 8.59% 39.92% 102,593.00 $305,959 $245,000 56.99 3.8
2018 $1,150 9.49% 39.70% 98,323.00 $298,982 $237,500 64.94 4.4
2017 $1,091 9.73% 39.26% 94,818.00 $291,340 $229,900 50.80 5.0
2016 $1,084 7.28% 40.83% 91,530.00 $283,133 $221,000 43.29 5.3
2015 $1,069 6.46% 41.33% 88,764.00 $280,290 $212,000 48.66 4.6
2014 $1,020 7.13% 40.94% 91,439.00 $270,182 $199,000 93.17 5.0
2013 $964 8.39% 39.87% 88,080.00 $248,591 $180,000 97.98 6.1
2012 $956 10.17% 38.65% 74,116.00 $225,330 $164,500 94.05 6.6
2011 $941 11.64% 38.44% 63,606.00 $213,723 $155,000 94.88 8.1
2010 $961 13.76% 37.16% 61,005.00 $211,765 $153,990 79.48 8.3
2009 $984 12.27% 37.74% 63,803.00 $203,626 $153,000 61.95 7.5
2008 $971 12.55% 36.63% 69,336.00 $208,266 $152,000 99.67 4.8
2007 $924 13.57% 36.12% 83,736.00 $206,393 $152,000 72.34 4.3
2006 $913 10.91% 36.52% 87,574.00 $198,410 $149,079 66.05 5.1
The Bayou City board was concerned about the predictive nature of the variables chosen by Venus and whether
they were truly independent. They also question why some of the variables were considered good predictors of
Houston rents. Venus was confident because her model had an excellent R-square and the F-statistic was well
above the 4.0 required to be considered a good model. Venus’ regression results are shown in Table 2. Mr.
Aristotle was initially happy with the model, but he started to waver under the questioning of some of the board
members. He thought an independent evaluation would help determine if the model was as good as it looked
and whether they could predict Houston rents effectively.
TABLE 2: Venus’ Regression Model
The Bayou City board made several specific requests of your team to help them assess the model and make a
decision on a significant investment in the Houston rental market.
Questions:
1. Review the regression output in Table 2 and provide your critique of the results. What are your
concerns about Venus’ model? (20 pts)
2. Use the data in Table 1 to recreate the regression results in Table 2. (15 pts)
3. Develop a correlation matrix for the data in Table 1. Comment on the values in your matrix and whether
there are any concerns in using these variables in Venus’ multiple regression model. (20 pts)
4. Based on your correlation results, what one (1) variable regression model would give you the best model
from among the seven (7) parameters chosen by Venus? Build a 1-variable regression model with this
variable, write out your equation, and comment on the results. (30 pts)
5. Perform a step-wise regression to reduce the number of independent variables and produce a final
regression model. Write out the forecast equation for your final model. (45 pts)
6. Now that you have a final model, present a pitch as to why your model is better than Venus’ model and
whether Bayou City should use your model to invest in the Houston market. (20 pt
