Using Regression Analysis to Predict Single Family Home Values/Prices in the Belmont/Eastside Areas of Pueblo

Transcription

1 Using Regression Analysis to Predict Single Family Home Values/Prices in the Belmont/Eastside Areas of Pueblo Sarah Mize Colorado State University - Pueblo Honors Program Senior Thesis 2017

2 1 Abstract The way that home values are established today is not statistically robust. Appraisers evaluate only three comparable properties to set a value, or price, for a house up for sale which is not as significant as one would think. Given the hundreds of property sales that occur in one year, it is logical to evaluate and analyze the sales from multiple previous years in a certain area to establish a more accurate value/selling price for a house in that specific area. Regression analysis is a statistical approach of modeling the relationship between one or more independent variables, or characteristics of a house or neighborhood, and a dependent variable, such as the value or selling price of the house. A model was created using regression analysis in which independent variables were analyzed and used to predict selling prices of properties in the Belmont and Eastside neighborhoods of Pueblo. The model proved to be successful as it provided accurate selling price estimates of houses in these neighborhoods which were sold in January and February of 2017; the estimates from the model for the majority of the properties were really close to what the houses actually sold for. The model created has proven that using regression analysis is a viable way to better establish an estimate of the true value of a house.

3 2 Acknowledgements I would like to thank my mentor, Dr. Justin Holman, for his help with this project. Without his guidance and advice, and assistance with gathering and analyzing the data used, I would not have been able to create anywhere near as accurate of a model as was our final output. Not only am I extremely grateful for him being my mentor for this thesis, but I am also very fortunate to be able to call him my friend and what I like to call my life coach for all of his thoughtfulness, advice, and support that he has given me throughout the past few years which I truly believe has led me in the right direction throughout my college career. If you ve never had him as an instructor, or simply have never met him, you are missing out.

4 3 Table of Contents Abstract 1 Acknowledgments..2 Introduction..4 Background.6 Executing the Project...13 Data..13 Methods...15 Results: Testing the Model...19 Conclusion.20 Appendix...21 References...24

5 4 Introduction During the Fall semester of 2015, I was enrolled in Dr. Justin Holman s Advanced Business Statistics course which was where I was first introduced to regression analysis. It was in this class, that I found out I enjoyed working with data and lots of numbers because of how much information they provide and what they have to offer in terms of predicting things. By using regression analysis, lots of things can be predicted including the selling price of a home, which is what we are doing here, or the amount of quantity demanded of something, or even how much snowfall to expect next ski season. This type of analysis is something that is extremely useful, and knowing how to conduct said research and analysis is something that could serve a college student well when searching for a job. With this thesis, I m hoping to give business students who are enrolled in a statistics course an explanation of regression analysis and how to use it effectively, and also instill in them the fact that it is extremely useful and and can be beneficial for forecasting a number of different things. By evaluating things that have happened in the past and using regression analysis, you can practically predict what is going to happen in the future. Of course, it will never be 100% accurate, but the potential level of accuracy can be fascinating. What is regression analysis? Regression analysis is defined by Ken Black as the process of constructing a mathematical model or function that can be used to predict or determine one variable by another variable or other variables (Black, 475). It is a form of predictive analysis, or forecasting something based on things that have occurred in the past. Black continues to explain that the variable to be predicted is called the dependent variable and is designated as y, and the predictors are called the independent variables, or explanatory variables, and are designated as x variables. Simple regression analysis includes strictly two variables: one variable is predicted by another variable. For this thesis, multiple regression is being used as there are more than one independent variables being utilized. Regression analysis is able to establish how well this set of predictor variables (independent variables) predicts an outcome variable (dependent variable), and it will also establish which of these independent variables are most significant at predicting the dependent variable (Statistics Solutions). For this thesis, using regression analysis

6 5 will allow us to establish how much of an impact housing characteristics, or neighborhood characteristics (the independent variables), have on the selling price of a single family house (the dependent variable; what is being predicted). The independent variables can be a number of things including number of bedrooms, total gross square footage of the house, number of bathrooms, median household income, median household value, etc., and the dependent variable will be selling price. By incorporating these and other variables and executing a regression analysis, it is possible to accurately predict 2017 selling prices of houses in the Belmont and Eastside neighborhoods of Pueblo, Colorado. The So What? Question Why is it so important to be able to predict the selling price or true value of a home? Well, imagine you are trying to buy a house. You wouldn t want to pay more than what it s actually worth would you? Also, if you are trying to sell your home, you don t want to sell yourself short and miss out on potential profit because you don t know how valuable your home really is compared to other properties. Regression analysis should typically be able to provide a true value of the house so you ensure that you are getting your money s worth if it is used correctly and carefully. This is just one reason. Furthermore, the way that properties are appraised currently is not statistically robust; the process is not as good as it should be. From talking with Linda Hedrick, a real estate agent in Pueblo, and from speaking with Dr. Holman, it was discovered that appraisers only look at three comparable properties to establish a value and selling price for the house in question. With the hundreds of real estate sales that occur every year, it is irrational to only look at three comparable properties. With such vast amounts of data out there, there is a better way to set selling prices for single family homes, and that is made possible by using regression analysis.

7 6 Background How Real Estate Agents Typically Value Homes When the thought to use regression analysis to predict home values in the Belmont and Eastside neighborhoods of Pueblo first appeared, an interest in how real estate agents typically value homes also came into question. Have agents ever used, or thought about using, regression analysis to set a selling price? Three real estate agents were interviewed for this thesis, and they were asked a variety of questions in order to gain an insight into the life of a real estate agent, why a career as an agent attracted them, and what methods or programs they use to set selling prices of homes. The first real estate agent interviewed by face-to-face interaction was Linda Hedrick of Re/Max in Pueblo, Colorado. Questions and Responses from Linda Hedrick: 1. What interested you about being a real estate agent? I originally wanted to become a real estate attorney which is something my parents suggested initially because of certain personality characteristics they saw in me. I have one degree in the legal field, and I have a lot of successful salespeople in my family who have great social skills. When I was young I was able to sell things successfully, and this great interest in being a real estate attorney eventually grew into becoming a real estate agent. 2. How did you become an agent? Some things are meant to be. I was told by many friends and family that it would be a great fit for me and they were right. I went through all the processes and took the tests and have enjoyed it ever since. 3. How long have you been an agent? I have been an agent for 22 years. The first year, I was awarded the Rookie of the Year award and was also titled the #2 real estate agent of the year by Re/Max of Pueblo last year.

8 7 4. Do you only sell single-family houses? Or do you also sell apartments, duplexes, etc.? No, I also sell multi-family homes, or dwellings, and apartments, duplexes, triplexes, and vacant land. 5. Who else do you talk with to set a sale price for a house? (banker/mortgage lender/appraiser/broker) I will talk to someone else I know that has sold the property before; on rare occasion I will speak with an appraiser. 6. How do you value a home and establish a selling price? I look at three other locations that are similar to the home. Also, if a home is on the market too long and isn t selling, that is a sign that the selling price should be decreased. 7. What characteristics of the house do you take into account when establishing a price? (square footage, # of bedrooms, # of bathrooms, age of the house, location such as upper, lower, or middle class neighborhoods, selling price of comparables, etc.) All of these characteristics are looked at, but the comparable properties are the main things that are evaluated to establish a selling price. However, we will also take into account if the home has a nice view, such as a view of the mountains, and also conduct inspections, such as HVAC inspections. My goal is to get the highest price/value for the seller. 8. Do you use any software to help set a selling price? Yes, we use a website called Navica to look at comparable properties and characteristics of other homes. Navica will show what houses have sold for which is the most important thing to look at. The bank will provide a current market value. 9. How do you set a range of prices that you try to sell within? (estimates vs actual selling price it sold for) Again, this is mainly by looking at Navica and taking into account other characteristics of the house and location.

9 8 10. How have websites such as Zillow and Trulia affected your role as a real estate agent? How are Zestimates taken into account? Do you believe these websites are capable of accurate prices? Living here, these websites haven t affected me much; they aren t as experienced with the local real estate and they re not as accurate. These websites don t have what a real estate agent has day-by-day access to. It is a subjective price, and their formula for price is not based on the appraised value. They take the characteristics of the house into account as much as they can, but they will not be as effective as an agent. The second real estate agent interviewed by questionnaire was Mark Sannita of Re/Max in Geneva, Illinois. Questions and Responses from Mark Sannita: 1. What interested you about being a real estate agent? I saw the opportunity to own my own business with little initial investment. I also liked the opportunity to help people with the biggest investment they may have. 2. How did you become an agent? I attended a pre-licensing class offered by Century 21 in Upon completion and passing of that class, I went on to take the Illinois Real Estate Licensing test. After passing this test, I began my career with Century 21 Kanute Real Estate in St Charles, IL. 3. How long have you been an agent? I have been a full time Real Estate agent for 21 years. 4. Do you only sell single-family houses? Or do you also sell apartments, duplexes, etc.? We are licensed to sell all types of properties. The list includes detached single family homes, attached single family homes, 2-4 unit buildings, commercial property, businesses with or without Real Estate, mobile homes, modular homes and vacant land. We can also help people secure residential and commercial rentals. Even though we

10 9 are licensed to sell all of these types of Real Estate, 95% of our business is from Detached and Attached single family homes. 5. Who else do you talk with to set a selling price for a house? (banker/mortgage lender/appraiser/broker) 95% of the time we set the list price for a property with the owner. Occasionally there may be a 3 rd party involved such as a relocation company or bank. Once the home is under contract, in almost every instance, there will be an appraisal to determine if the home is worth the contract price. 6. How do you value a home and establish a selling price? We utilize closed sales, active sales and active listings in the area. Just to be clear, we generally will not determine the actual sale price, only the list price. The actual sale price is determined through negotiations between the seller and the buyer. We will help with these negotiations and counsel our client, buyer or seller, to help them make the best decision possible. 7. What characteristics of the house do you take into account when establishing a price? (square footage, # of bedrooms, # of bathrooms, age of the house, location such as upper, lower, or middle class neighborhoods, selling price of comparables, etc.) We will utilize all of these characteristics in some form. However, much of the time it will boil down to simple supply and demand. 8. Do you use any software to help set a selling price such as Navica? I believe Navica is some type of Multiple Listing Service we do not use. We use Midwest Real Estate Data Multiple Listing Service. We also utilize a Case Schiller Model, an appraisal based Comparative Market Analysis model and tax records. 9. How do you set a range of prices that you try to sell within? (estimates vs actual sale price it sold for) We do our best to present the seller with a range of value based on current condition and improved condition. We utilize a professional stager/interior designer to help us determine improvements that might increase the potential sale price.

11 How have websites such as Zillow and Trulia affected your role as a real estate agent? How are Zestimates taken into account? Do you believe these websites are capable of accurate prices? Websites such as these have hurt us as agents as there is just too much information available to the general public. Some of the information is good and accurate, however there is too much of the information that is not. Zestimates can be a good benchmark, however, most of the time they are extremely inaccurate. I do not believe websites are capable of accurate pricing because they cannot always take into account characteristics such as improvements or condition. 11. What is your favorite thing about being a realtor? Helping people make sound business decisions. The third real estate agent interviewed by questionnaire was Cole Tibbs of Re/Max in Pueblo, Colorado. Questions and Responses from Cole Tibbs: 1. What interested you about being a real estate agent? I chose a career in real estate because I saw a lot of advantages in it. The first thing that attracted me to the profession is the fact that performance and productivity are correlated. The more effort you give, the more positive results you will see. Another attraction is the flexible hours. I can set my schedule how I prefer, so that I am able to still have a social life outside of my career. The main reason I chose a career in real estate is because it is very familiar to me. Real Estate has been a part of my life since I was very young. My grandfather and father are realtors as well, and I grew up working and learning the ins and outs of houses. 2. How did you become an agent? I was a grad student at CSU-Pueblo when I realized real estate was the profession for me. A Wealth Creation class influenced me to choose a career that put the ability to obtain success in my own hands. Once I graduated, I took a real estate licensee class in Pueblo. It took about three months, and then I took the exam to receive my real estate broker license.

12 11 3. How long have you been an agent? I have been a real estate broker for about two months now. 4. Do you only sell single-family houses? Or do you also sell apartments, duplexes, etc.? I have the ability to sell any type of home. My emphasis is residential real estate, but I would like to eventually sell commercial real estate as well. 5. Who else do you talk with to set a selling price for a house? (banker/mortgage lender/appraiser/broker) We as realtors set prices based on the market. We complete a Comparative Market Analysis to find a good listing price. We generally look at the characteristics of the house, the neighborhood it is located, and the sale of houses in the past six months in that area in order to set a listing price. Since I am fairly new to being a realtor, I ask my managing broker for advice when setting a listing price. 6. How do you value a home and establish a selling price? I mentioned above that we create a Comparative Market Analysis when determining the price of a home. The value of a home can actually be determined by the market depending on if it is a Seller s Market or a Buyer s Market. The area the home is located, the square footage, the condition of the home, and uniqueness of the home are also factors that determine value. 7. What characteristics of the house do you take into account when establishing a price? (square footage, # of bedrooms, # of bathrooms, age of the house, location such as upper, lower, or middle class neighborhoods, selling price of comparables, etc.) Characteristics when establishing price: Housing market, selling price of comparable homes, square footage, age of the home, location, current condition, and listing price of similar homes in the area. 8. Do you use any software to help set a selling price such as Navica?

13 12 Navica is our Multiple Listing Service (MLS) and yes, Navica is a great resource. We use Navica to publicly post houses for sale in the Pueblo area. We also use it to create Comparative Market Analyses to determine the correct prices of houses. 9. How do you set a range of prices that you try to sell within? (estimates vs actual sale price it sold for) First, I create a CMA to determine the price the house would sell for in the market. I then would ask the seller if they have a certain price they want to sell their house for. I then show them the CMA to give evidence of what their home s value is at. There is not a set rule for determining the Listing price of a home though. Some seller s may not need to sell their home right away, so they are fine with setting the listing price a little above what the home is worth. There are also seller s that set the listing price at or below value in order to sell quickly. As always, the market helps determine the amount of time a property is for sale. 10. How have websites such as Zillow and Trulia affected your role as a real estate agent? How are Zestimates taken into account? Do you believe these websites are capable of accurate prices? This is an interesting topic. A lot of realtors have different opinions on the matter. From what I understand, Zillow is a site that is not beneficial to realtors. Realtor.com is a good site for realtors from what I ve heard. I do know that Zillow is not an honest site to potential buyers. The site shows some houses for sale that are actually no longer available or are already Under Contract. I am not sure if the price Zillow puts on properties is accurate, but I know that the mortgage quotes given are not always accurate. As a realtor, I suggest potential buyers to use Realtor.com or talk to an agent in the area. We have the ability to send you automatic s with properties you are interested in depending on your preferences. 11. What is your favorite thing about being a realtor? My favorite thing about being a realtor is that I truly enjoy waking up in the morning and going to work. My great coworkers are irreplaceable, and the office morale is priceless.

14 13 Executing the Project Data The focus area for this thesis was the Belmont and Eastside neighborhoods of Pueblo County. Neighborhoods included in this area include: Bonnymede, Belmont, Outer Belmont, East Fountain, Upper East Side, Outer East Side, and Lower East Side. From Dr. Holman s personal website, a map of these neighborhoods can be found:

15 14 Each neighborhood corresponds to a specific census tract. A map of census tracts was obtained from the United States Census Bureau: Knowing which neighborhood corresponded to which census tract enabled more data to be obtained and allowed for better independent variable creation, which will be discussed later. After selecting the focus area, a large amount of data was obtained from the Multiple Listing Service ( MLS.com ). From this website, 2014, 2015, and 2016 single-family household property sales in the Belmont and Eastside neighborhoods of Pueblo were able to be found, and resulted in a combined total of 709 individual datum. When a request for this data is placed, the Multiple Listing Service website provides a file of all 709 properties which includes: address, MLS ID, list price (what the homeowner put the home on the market for), number of bedrooms, number of bathrooms, total gross

16 15 square footage, selling date, and selling price (what the home actually sold for). Refer to Figure 1 in the Appendix. After obtaining this information, geocoding the properties was necessary in able to find the specific, aligned census tracts. Texas A&M University Geoservices ( ) was used to match each of the 709 addresses to a census tract in Pueblo. After additional evaluation, some properties were eliminated from the data pool due to being extreme outliers or that they would not add value to the regression model. A new total of 696 sold properties was then used and were able to be geocoded into seven census tracts: 8, 9.02, 9.04, 9.05, 10, 11, and 12. Using this data, additional information was uncovered using the U.S. Census Bureau website ( ), and using 2015 estimates based on the 2010 census, average variables per census tract were discovered. The top three findings that were used in the regression analysis of this project were median household income, median household value, and percentage Hispanic per census tract examined. Methods Once all this information was gathered and sorted into a single file in Google Sheets, the Google Sheets Add-on XLMiner Analysis ToolPak was used to conduct the regression analysis. During the first run of regression, each variable found above (median household income, median household value, and percentage Hispanic) was used separately with total gross square footage as the independent, or x, variables and the dependent, or y, variable was selling price of the properties; this will always be the dependent variable because it is what is being predicted and it is what is affected by changes in the independent variables, or the housing/neighborhood characteristics of the properties. When using the Google Sheets Add-on, and selecting said columns of data for the X- and Y-ranges, it provides a regression summary output:

17 16 From running three runs of regression, it was found that out of the three variables, median household value was the most significant. Refer to Figures 2 and 3 in the Appendix. This is allowed to be said by looking at multiple items from the output. The first thing to be looked at is R Square, or the coefficient of determination. This is defined by Black as the proportion of variability of the dependent variable ( y ) accounted for or explained by the independent variable ( x ) (Black, 493). It portrays the accuracy of the model, or the quality of fit provided by the forecast compared with the actual data, which in this case is the actual selling price of the home. The closer to a value of one R Square is, the more accurate the model is. The next value to be looked at is the F stat. This is the ratio of two sample variances and is used to find out if the means between two populations are significantly different (Black, 388). It shows the overall significance of the model and if a group of variables are jointly significant. The higher the F stat, or the further away from zero it is, the more significant the model. The T stats should also be as far away from zero as possible. These show how significant each of the independent variables are by themselves. The last two items that are absolutely essential to examine are Significance F and P-values. These two show how likely the results of the model are to happen by chance, so they should be zero, or as close to zero as possible to ensure statistically significant results. Given the above image was the first run, a better model was bound to ensue. A new regression was ran using median household income, percentage Hispanic, and median household value as the independent variables and this was the resulting output:

18 17 The value of R Square increased a small amount to 76%; this signifies that the independent variables chosen explain 76% of the variance of selling price, while the remaining 24% is due to housing characteristics, such as number of beds or baths. The F stat decreased quite significantly however. Although not a direct cause of said decrease in the F stat, it was discovered that the problem of multicollinearity was present in the model. Multicollinearity is defined by Black as a problematic condition that occurs when two or more of the independent variables of a multiple regression model are highly correlated (Black, 582). This was discovered by running a correlation analysis using Google Sheets; refer to Figure 4 in the Appendix. It was discovered that median household income and median household value were highly correlated, meaning they produced similar results and did not add value to the model as they both correlated with total gross square footage and selling price. Median household income was eliminated due to median household value being more significant based on the information found when the initial first three outputs were generated. During the next run, a binary variable labeled Q1 was created to create a value for homes that were sold in Quarter 1 of the year, meaning they sold in January, February, or March only. Homes sold in these months were assigned a value of 1 while all other homes sold in the remaining months of the year were given a value of 0. This variable was created because homes typically sold in Q1 generally have a much lower selling price as this is a time when not a lot of homes are bought and sold. More people prefer to get out and look at houses during nicer, warmer months and, as a result, there is more demand for homes which lead to higher selling prices. This is the resulting output from using the independent variables of total gross square footage, percentage Hispanic, median household value, and Q1:

19 18 This signified quite a respectable model, but one more step was taken to create the final output, what should be given the name The Golden Output as it was the model that was chosen to predict single family home values in the Belmont and Eastside areas of Pueblo given its accuracy and significance. For this model, one last independent variable was created which also replaced total gross square footage: an average price per square foot per census tract multiplied by total gross square footage. This was the result: This model resulted in the highest R Square value, positive F and T stats, and zero, or very close to zero, values for Significance F and P-values. From this model, a y-hat equation may be formed to hypothesize the selling prices of 2017 single family home sales in the focus area that were sold in Q1, or January, February, and March; sales from Q1 accounted for the only data available given the time period when the project was conducted. The y-hat equation is formed using the coefficients found in the output, and for the sake of simplicity, average price per square foot per census tract multiplied by total gross square footage was labeled as X1, percentage Hispanic as X2, median household value as X3, and Q1 as X4. The resulting y-hat equation is: Y^ = X X X X4

20 19 Results: Testing the Model Using the Multiple Listing Service again, 32 properties were found to be sold in the focus area of Pueblo, Colorado in the months of January, February, and March of Using the y-hat equation, the average price per square foot per census tract multiplied by total gross square footage for the new data was multiplied by the corresponding coefficient, the percentage Hispanic value for each property in each census tract was multiplied by its corresponding coefficient, and so on. When all 32 properties were inputted into the y-hat equation, the model proved to be very accurate, further proving that regression analysis can be used predict home values/selling prices. The following figures show estimated selling price for a home, each followed by its actual sale price: $176,576_$183,500; $43,737_$35,000; $27,358_$29,000; $44,409_$45,000. It is fascinating how accurate the model was. However, forecasting is never going to be 100% accurate given the multiple additional variables and characteristics of homes and neighborhoods, and special circumstances that occur in the real estate market. For example, for two properties located on Norwood Avenue, the forecasted selling price was drastically lower that what it actually sold for. These two properties were researched on the Pueblo County Assessor s website ( Pueblo.org ), and it was discovered that the two homes were brand new; they were built in 2016, therefore having a logical explanation for having such a high sell price. Additionally, one house on East 10th Street had a forecasted selling price of $39,251, but surprisingly only sold for $10,000. This is the result of special circumstances such as the home needs major repairs, or perhaps it was a family transfer where the seller did not want to charge a high price to their family member. A scatter plot comparing actual vs forecasted selling price was created to visually show the accuracy of the model.

21 20 Conclusion Forecasting is never going to be 100% perfect and it is not going to be able to replace human judgment especially in the field of real estate, but it is a good second opinion that can and should be used in conjunction with the evaluation of the three comparable properties that are currently looked at to produce a more accurate representation of the true value of a home. It is a good baseline to use for setting a sell price. The Golden Output that resulted in the best model that was used to predict selling prices explains 78% of the variance of selling price of Quarter 1, 2017 single family home sales in the Belmont and Eastside neighborhoods of Pueblo, while the other 22% is most likely due to age of the structure and overall quality of the structure. Although conducting an experiment like this is very taxing, and requires extensive data collection, sorting, and crunching, when completed correctly it can be a very useful and beneficial tool for real estate agents, appraisers, and even the buyers and sellers who wish to make sound buying and selling decisions.

22 21 Appendix Figure 1 Figure 2 Figure 3

23 22 Figure 4 Figure S Norwood Avenue Figure S Norwood Avenue

24 Figure 6, continued 23

25 24 References Black, K. (2012). Business Statistics for Contemporary Decision Making. Hoboken, NJ: John Wiley & Sons, Inc. Cole Tibbs, communication, March 15, Holman, J. (2014, May 14). Pueblo Neighborhoods 1.0. Retrieved from Linda Hedrick, personal communication, February 9, Mark Sannita, communication, March 6, Multiple Listing Service. (2017). Colorado Real Estate and Homes for Sale. Retrieved from Pueblo.org. (2017). Assessor. Retrieved from Statistics Solutions. (2013). What is Linear Regression? Retrieved from Texas A&M GeoServices. (2017). TAMU GeoServices. Retrieved from United States Census Bureau. (2017). American Fact Finder. Retrieved from