Median Housing Price Prediction Model for D. M. Pan National Real Estate Company 1
Report: Housing Price Prediction Model forD. M. Pan National Real Estate Company
Emily Higdon
Southern New Hampshire University
Median Housing Price Model for D. M. Pan National Real Estate Company 2
Introduction
The purpose of this report will be to provide a model for predicting housing prices based
on square footage in order for the real estate agents at D.M. Pan National Real Estate Company
to better determine the use of square footage as a benchmark for listing prices on homes. The
data I am going to be presenting will be based on real estate data that is categorized by region
and county and then compared to the National Summary Statistics and Graphs. I am going to use
scatter plots, histograms, and tables to present the information I find.
When attempting to forecast a continuous dependent variable based on one or more
independent variables and the relationship between the two can be best represented by a straight
line, then linear regression is the most appropriate. When using linear regression, the data in your
scatterplot should form almost a straight line. The difference between predictor (x) and response
(y) variables is that the predictor variable should be something that you believe causes a change
in the response variable. The response variable should be the outcome that you are trying to
predict.
Data Collection
To get a random sample of 50 houses, I began by making a new column labeled random
and entered in the equation =RAND(). This generated random numbers for every single cell in
that column. After that, I highlighted every single column and cell so I could sort them by the
random column. Lastly, I selected the first 50 countries that are on the data sheet. For my data,
the predictor (x) variable is the square feet, and the response variable (y) is the listing price. The
image below is a scatterplot created based on my predictor and response variables.
Median Housing Price Model for D. M. Pan National Real Estate Company 3
Data Analysis
Median Housing Price Model for D. M. Pan National Real Estate Company 4
Listing Price Square Feet
Median Housing Price Model for D. M. Pan National Real Estate Company 5
Mean $341,306 2,122
Median $330,650 2,011
Standard Deviation $98,382 758.67
We can use the above sample statistics and graphs to interpret the center, spread, shape,
and any other unusual characteristics for the listing price and square footage. The center of a
dataset is made up of the mean and median. For listing price, the mean is $341,306 and the
median is $330,650, which indicates the center of the listing price is around these values. For
square feet, the mean is 2,122 and the median is 2,011, which indicates the center of square
footage is around these values. Based on the scatterplot, there are a few outliers, and that could
be because a lot of the houses from my random sample of 50 all have close to the same amount
of square footage, which would make the prices more similar.
National Summary: Listing Price Square Footage
Mean $342,365 2,111
Median $318,000 1,881
Standard Deviation $125,914 921
The above table is from the National Summary Statistics and Graphs. We can see that the
mean and median for the listing price from my sample and from the National Summary are
around the same, making the center around the same value. For square footage, the mean and
median from my sample are a bit lower, which would make the center lower. On the histogram
for median listing price, we can see for my sample that it is unimodal while the National
summary is right-skewed. Right-skewed indicates that most of the data points are on the left side,
Median Housing Price Model for D. M. Pan National Real Estate Company 6
while unimodal means only one mode exists in my sample histogram. For square feet, the
histogram from my random sample of 50 is skewed right and the National summary histogram is
also skewed right.
The standard deviation for the listing price is lower in my sample than the national
population, meaning less variability in house prices in the national population. The standard
deviation is lower in my sample than in the national population, meaning less variability in house
sizes in the sample. When taking a look at the two histograms from the National summary, there
do not appear to be any outliers. On the histogram for square footage from my sample histogram,
we can see there might be a potential outlier towards the right.
Develop Regression Model
When the points on a scatterplot appear to follow a straight line, then a regression
model would be appropriate. From what we can see on the scatterplot from my random sample
of 50, a regression model would be appropriate. Based on the scatterplot, we can see that there is
Median Housing Price Model for D. M. Pan National Real Estate Company 7
a positive direction, as the overall trend is moving upwards. To find the strength of the
scatterplot, we can use the correlation coefficient. The correlation coefficient for my sample
scatterplot is 0.79 which would mean the strength is strong. The form of my sample scatter plot
is linear because when one variable increases, the other variable increases as well.
When looking at my sample scatterplot, there is only one potential outlier, but because it
still follows the same pattern as the line of best fit, it will not have an impact on the correlation.
Since the outlier still follows the pattern as the line of best fit, I will be keeping the outlier which
will have no impact on my model. As I mentioned above, the correlation coefficient ( r) is 0.79,
which supports the strong positive correlation we can see in my sample scatter plot. [
Determine the Line of Best Fit
The regression equation for my sample scatter plot is y=101*x+127410 and the slope
would be 101. The slope represents the change in listing price when there is a change in the
square footage. Basically, if the square footage increased by 1, then the listing price would go up
by 101. The intercept would be if the slope was equal to zero, then the listing price would be
127,410.This suggests that above the zero value, the regression line crosses the y-axis. R-squared
is a measurement of how close the data in the scatterplot are to the regression line. R-squared for
my sample is 0.604, which means that approximately 60.4% of the variation in the listing price
can be explained by the square footage. Using my regression equation to predict how much I
should list my home for based on the assumed square footage of my home at 1,500 square feet,
the listing price would be $278,910.
Conclusions
After gathering all the data and graphs, I have come to the conclusion that real estate
agents can use the square footage of a house in order to determine the listing price. When the
Median Housing Price Model for D. M. Pan National Real Estate Company 8
square footage of a house increases, the listing price will also increase. Based on previous reports
similar to this one, the results were exactly what I was expecting. One change that I feel would
support different results would be to add in another variable, such as the amount of acres that
come with the house. One question that could be interesting for follow-up research could be,
“How much would the area that a house is in affect the listing price?”. For example, a house
being listed in a neighborhood where there is a higher amount of crime and a lot of poverty.
