MAT 240 Project One
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Median Housing Price Prediction Model for D. M. Pan National Real Estate Company
1
Report: Housing Price Prediction Model for D. M. Pan National Real Estate Company
Natalie Ann Merle Donate
Southern New Hampshire University
Median Housing Price Model for D. M. Pan National Real Estate Company
2
Introduction
This report has the purpose of determining if using the square footage of a house is appropriate to predict the selling price of houses in the US. We will use a sample data of the population to do our analysis. Using a model of linear regression can help us understand the how strong the relationship is between two variables, if there is one, and whether this relationship is positive or negative, which is appropriate for the purpose of our report. From our sample data, we will create a scatterplot which we expect to show a trend in listing price as it relates to the square footage. Square footage will be our predictor variable, meaning that the square feet of houses will help us estimate listing price. On the other hand, our response variable is listing price, which means that the value of houses will be dependent on square feet. Data Collection
A random sample is necessary in order to prevent any bias, so we selected a random sample of 50 data values using the excel function “
=rand()
”
in our worksheet. Our predictor variable will be square feet, as it will help us predict listing price, and our response
variable is listing price, as this will be responding to a change in square feet. We expect these two to be related, which we will analyze more in depth later on.
Median Housing Price Model for D. M. Pan National Real Estate Company
3
Region
State
County
square feet listing price
New England
vt
rutland
4,162
523,600
West South Central
la
vernon
2,256
255,900
Mid Atlantic
md
frederick
1,246
263,600
West South Central
tx
brazos
1,835
242,500
East North Central
in
marion
3,408
323,300
Northeast
ny
st. lawrence
1,734
256,900
New England
nh
hillsborough
1,744
331,300
New England
vt
rutland
2,280
344,200
West South Central
tx
grayson
1,837
248,700
Northeast
pa
adams
1,566
247,000
West North Central
mn
crow wing
1,602
263,200
South Atlantic
nc
cleveland
1,681
250,700
West South Central
la
calcasieu
1,871
214,300
Northeast
pa
indiana
1,713
284,600
New England
vt
franklin
3,747
489,900
Mountain
ut
davis
2,351
486,700
New England
nh
grafton
2,491
358,200
West North Central
mn
blue earth
1,518
315,900
Pacific
ca
butte
1,875
406,200
South Atlantic
nc
davidson
2,571
504,500
Pacific
or
lane
1,845
404,600
Pacific
ca
marin
1,856
420,800
Northeast
ny
chautauqua
1,905
336,400
Northeast
pa
franklin
1,363
277,700
Northeast
ny
schenectady
2,031
331,300
East North Central
mi
ionia
1,416
193,600
West South Central
la
st. tammany
1,869
280,300
Northeast
ny
monroe
1,545
318,400
East South Central
ms
lee
2,066
273,100
East North Central
oh
muskingum
1,999
188,300
New England
me
york
1,991
370,000
South Atlantic
fl
miami-dade
4,810
792,900
East South Central
tn
greene
1,950
226,000
East North Central
in
allen
3,525
398,000
Mountain
id
twin falls
1,892
319,000
New England
vt
franklin
1,892
341,300
Pacific
ca
san diego
2,081
421,400
West South Central
la
bossier
2,177
305,500
South Atlantic
sc
berkeley
1,913
351,900
South Atlantic
fl
martin
3,919
592,000
West North Central
ia
cerro gordo
1,869
361,000
Mid Atlantic
nj
hudson
3,168
444,400
Mid Atlantic
va
roanoke
2,054
348,200
Pacific
wa
grays harbor
1,393
395,300
Mid Atlantic
md
wicomico
1,335
353,900
South Atlantic
ga
laurens
1,694
275,900
Northeast
ny
niagara
1,517
261,400
Pacific
hi
hawaii
4,927
856,600
West North Central
mo
cape girardeau
1,798
292,100
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Median Housing Price Model for D. M. Pan National Real Estate Company
4
Median Housing Price Model for D. M. Pan National Real Estate Company
5
Square Feet
Listing Price
Mean
2,190
353,929
$ Median
1,892
331,300
$ Std Dev
871.69
131,971.56
$ Min
1,246
188,300
$ Max
4,927
856,600
$ Spread
3,681
668,300
$ The histograms above provide a lot of valuable information represented in a visual way for an easier interpretation. We can see that the data is not in normal distribution, so we do not have a “
center.
” The center would normally be identified if we have a normal distribution, in which the
bars in the histogram would be bell-shaped. Instead, we have a right-skewed graph which means
that most houses are within the lower price range (left side). Given our selected random sample, square feet ranges from a low of 1,246 to a high of 4,927 – within this range, or “
spread
” is where we can most accurately predict house prices. We can see that the average listing price is $353,929. Standard deviation tells us how far values are to that mean, or average. When compared to the national population, we can see that our numbers are fairly close which means that our sample is representative of the national housing market.
Median Housing Price Model for D. M. Pan National Real Estate Company
6
Develop Regression Model
Data Analysis
As we can see in the above scatterplot, this is an appropriate model as most data points follow the trend line fairly close. We can clearly identify an increase in listing price as the square feet increases, which gives us a positive (upward) relationship between the square feet and listing price of houses. Some outliers were identified and removed from our data in order to have a stronger model, since they do not properly represent the national average. Keeping these outliers
in our model could prevent us from having a more accurate prediction given that these are the exception to the rule when it comes to our data, and could weaken the correlation between square
feet and pricing. Outliers can be easily identified visually; they are the dots that are furthest away from the trendline, and also in our histogram they are the bars next to the gap. By removing the one identified outlier, our correlation coefficient went from 0.78
to our current 0.817
– any correlation above 0.80 is considered strong. We can also see that this correlation is
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Median Housing Price Model for D. M. Pan National Real Estate Company
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supported by our scatterplot given that it’s evident that as square feet increase, listing price does so as well in a very similar way, generally speaking. Using this scatterplot as a confirmation is a great way to validate our data. This is a strong model and an appropriate one for our analysis.
Determine the Line of Best Fit
Our regression equation is “
y_hat = 123.73x + 83024
”
which we obtained from our worksheet in excel using the square feet as the variable “
x
” and listing price as variable “
y
.” This
equation is what we will be using to predict listing price. In this regression model, the number next to “
x
” is considered the “
slope
” and it tells us how much the listing price will increase with each unit increase of square feet. The number on the right, considered the “
intercept” tells us the
square feet when house listing price is “
$0
”, which is not really of value in this context as house listing price is never zero. R
-squared is 0.6679
provided our model. This means that 66.79%
of the listing price of a house can be explained (or predicted) by the square feet. We can say that this is a great indicator for us to use when determining the listing price of a house based on square feet.
Prediction using our regression model “
y_hat = 123.73x + 83024
”
:
Square Feet
Listing Price
1,500
$268,619.00
Median Housing Price Model for D. M. Pan National Real Estate Company
8
Conclusions
Based on our analysis, we can determine that the model selected is an appropriate one to use when predicting the listing price of houses. Our model helped us identify that square feet is strongly correlated to selling price and hence it’s a great tool to use for our predictions. The equation developed can confidently help us estimate the selling house of a price. The sample we used was representative of the national house market, which otherwise could have given us different results. Before we analyzed our data, we did expect the square feet and house pricing to have a positive relationship, which were our findings in this report along with few exceptions or outliers. Figuratively, if we were to flip the numbers, perhaps a city developer or contractor could use listing price around a certain area to determine the size houses that they should build. This could be another problem that this type of analysis could help solve, if there was a need.
As a follow up, I would suggest considering what factors would contribute to a higher house price, if we wanted to list it outside of our findings?
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500
450
400
350
300
250
200
150
100
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0
0
Demand
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Graph Input Tool
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- You own the only pharmacy in the small town of Jackson City, which has 40,000 residents. You would like to get a sense of what the local demand is for seasonal allergy medicine so you can determine how many packages to keep in stock and what price to charge. You conduct a survey of four residents of Jackson City, asking them about the quantity of allergy medicine they would buy each allergy season at various prices. Their responses are shown in the accompanying table. Estimate and graph the demand for the entire town of Jackson City. Price Lee June Carlotta Eric $8 8 5 6 9 $10 6 4 5 5 $12 4 3 4 3 $14 2 2 2 1 $18 0 1 1 0arrow_forwardYou own the only pharmacy in the small town of Jackson City, which has 40,000 residents. You would like to get a sense of what the local demand is for seasonal allergy medicine so you can determine how many packages to keep in stock and what price to charge. You conduct a survey of four residents of Jackson City, asking them about the quantity of allergy medicine they would buy each allergy season at various prices. Their responses are shown in the accompanying table. Estimate and graph the demand for the entire town of Jackson City. Price Lee June Carlotta Eric $8 8 5 6 9 $10 6 4 5 5 $12 4 3 4 3 $14 2 2 2 1 $18 0 1 1 0 I submitted this question earlier and I understand how to add up the market demand for each individual but I don't understand how to estimate the entire market demand for Jackson city which has 40,000 residents including the individuals listed in the chart. If you could please answer this specifically I would appreciate it.arrow_forwardWhat is the relationship between the $ price of paint and the gallon demand for this paint? A random sample of (price, quantity) data for 7 days of operation was obtained. Construct a plot and describe the relationship between quantity and price, with emphasis on any unusual observations.(10, 100) (8, 120) (5, 200) (4, 200) (10, 90) (7, 110) (6, 150)arrow_forward
- The Wall Street Journal’s website, www.wsj.com, reported the number of cars and light-duty trucks sold through October of 2014 and October of 2015. The top sixteen manufacturers are listed here. The sales information for all manufacturers can be accessed in a data file below. Sales data are often reported in this way to compare current sales to last year’s sales. Year-to-Date Sales Manufacturer Through October 2015 Through October 2014 General Motors Corp. 2,562,840 2,434,707 Ford Motor Company 2,178,587 2,065,612 Toyota Motor Sales USA Inc. 2,071,446 1,975,368 Chrysler 1,814,268 1,687,313 American Honda Motor Co Inc. 1,320,217 1,281,777 Nissan North America Inc. 1,238,535 1,166,389 Hyundai Motor America 638,195 607,539 Kia Motors America Inc. 526,024 489,711 Subaru of America Inc. 480,331 418,497 Volkswagen of America Inc. 294,602 301,187 Mercedes-Benz 301,915 281,728 BMW of North America Inc.…arrow_forwardThe Australian Government has developed a survey to enable it to gauge the views of the Australian public regarding "Climate Change". The survey consists of a sample of 400 Australian Citizens and Permanent Residents regarding their views on a wide range of Climate Change topics. The Government intends to use the results of the survey to assist in the formulation of government policy for the next 30 years. The variables used in the dataset are as follows: Variable Name Explanation Options Cars Number of motor vehicles in your household Income Your income in Dollars ($) Support Belief that Australia should financially support developing countries in their efforts to address Climate Change (Yes, No) Cause Who/what you think is most responsible for Climate Change (Mostly Human, Mostly Natural, There is no Climate Change, Unsure/Undecided} Solar_Panels Willingness to Install Solar Panels For each of the scenarios outlined below, describe a type of Visualisation (i.e. a Chart/Table/Graph)…arrow_forwardYour boss would like your help on a marketing research project she is conducting on the relationship between the price of soda and the quantity of soda demanded. She hands you the following document: Price of Soda Quantity of Soda Demanded (Dollars per can) (Billions of cans) 0.50 2,000 0.75 1,500 1.00 1,000 1.25 750 Your task is to take this and construct a graphical representation of the data. In doing so, you determine that as the price of soda rises, the quantity of soda demanded decreases. This confirms thearrow_forward
- Construct a histogram that represents the following data regarding the score ranges for the extrovertive tendencies of respondents to a personality questionnaire. Personality Questionnaire Class Frequency 16-19 9 20-23 3 24-27 8 28-31 7 32-35 7 Copy Dataarrow_forwardThe Fearless Champions Outdoor Company is a catalogue sales operation that specializes in outdoor recreational clothing. Demand for its items is very seasonal, peaking during the holiday season and during spring. It has accumulated the following data for order per quarter (their seasons) during the past 3 years (year 3 being the most recent). First determine the demand for year 4 (next year) using the Least Squares method. What is the seasonal demand for the fourth quarter of year 4? Note: Orders are in the 1000's Year Quarter 1 1 38 2 3 4 8888 34 29 56 3428N 33 52 3 40 45 44 75 75.71 79.89 72.02 Fearless! Just like the Red Raiders! 77.67arrow_forwardPlease answer and show complete solution. Thank you!arrow_forward
- If incorrect then 10 downvotes Read the following statements. i. As a result of globalisation, companies are increasingly making acquisitions around the world. ii . In the world of financial reporting, companies have increasingly moved from historical cost to fair value accounting. iii. In the new age economy, intellectual property is becoming an important driver of a company's value. Which of the above has contributed to the growth of business valuation in recent years? Pick the best answer. Question 7Select one: a. (iii) only b. (1) & (ii) only c. (i) & (ii) only d. All of the abovearrow_forwardplease answer in text form and in proper format answer with must explanation , calculation for each part and steps clearlyarrow_forwardYpsilanti Market Research conducted a survey to find out whether people who earn more money purchase more expensive goods. The following graph indicates the relationship between income the survey subjects earned and the price of the car that they purchased. The variable shown on the vertical axis is __________ (options: thousands of dollars per car, thousands of dollars per year, income, thousands of dollars, price, number of goods). The units for the variable on the horizontal axis are _________ (options: thousands of dollars per car, thousands of dollars per year, income, thousands of dollars, price, number of goods). There are two ways to view the information presented on the graph. First, the graph tells us the amount a person with a certain income is likely to spend on a car, and second, it tells us the probable income of a person who spent a certain amount on a car. For example, if an individual earned $50,000 last year and purchased a new car, you would expect that person to…arrow_forward
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