MAT 240 Project One Final

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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 Tiarre Crawford Southern New Hampshire University

Median Housing Price Model for D. M. Pan National Real Estate Company 2 Introduction The purpose of this report is to analyze real estate data to determine the relationship between the median listing price of a property and its median square footage. Doing so by selecting data from 50 random samples of properties in different regions. Then to convey findings on to the likes of scatter plots, histograms, and statistics charts to govern the strength of the correlation between the two variables in question. Liner regression in this case will be most appropriate when predicting the outcome of the response variable (y) that is based off the predictor variable (x). Thus, I expect that change in one variable will impact the change of the other. Data Collection I stared off randomizing the samples given by using the =Rand function in excel. From there I chose 50 properties and regions from within that data. I then had to identify what my variables would be. In which I labeled my predictor variable (x) to represent the median square feet and my response variable (y) to represent the median listing price.

Median Housing Price Model for D. M. Pan National Real Estate Company 3 Data Analysis Sample Data Listing Price Square feet Mean 326,958 1,982 Median 316,450 1,840 Std. Dev 108,861 853

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Median Housing Price Model for D. M. Pan National Real Estate Company 4 For the first histogram that represents median square feet, has a shape that is skewed right and is non symmetric. Most of the square feet data occurs to the left of the graph. Its peeking point representing a high frequency of thirty-three shows that majority of the properties has square footage that range between 1,201 and 2,011. This histogram is centered at its median of 1,840 square feet. The range or spread for this histogram is 4,744 which is the difference between the first and the last points of data. There are two gaps in this graph that act for points in which there was no data reported. The second histogram of median listing price also has a shape that is skewed right. There are no outliers or gaps present. The graph is center at its median of $316,450. The range of this graph can be depicted at $421,700 which is the difference between the highest listing point and the lowest. The listing price peeks at a frequency of twenty-two showing that a lot of the properties were listed between 239,200 and 339,200. National Listing price Square feet Mean 342,365 2,111 Median 318,000 1,881 Std. Dev 125,914 921 Data in the chart above is from the National Housing market. The national data shows that the mean has about a $15,000 difference in listing prices and a 129 difference in square feet arear than the sample. Its standard deviation for listing price is about $17,000 more than the sample and has about 68ft more. Yet the medians of the two are not that far off in comparison of

Median Housing Price Model for D. M. Pan National Real Estate Company 5 the numbers. The sample data could be a representation of the national housing market seeing as though the numbers are not drastically far off. The Regression Model Based on my graph above, a regression model can be developed. Hence there is a clear liner relationship between response variable (y) and the predictor variable (x). Associations in the scatter plot already proven above shares a liner relationship between variables, so for every value of Y there is also a value of X. The scatterplot also shows that the association is strong and is going in a positive direction R=0.749616914(Correlation Coefficient) The correlation coefficient that was determined is closer to one and it aligns with the finding on the scatterplot showing that it is indeed has a strong and positive liner relationship between its two variables. The Line of Best Fit Regression Equation: Y=95.576x +137499

Median Housing Price Model for D. M. Pan National Real Estate Company 6 The slope represents the change in listing price where there is a unit change in the square feet area. Therefore, if the square feet were to increase by one unit the estimated listing price would then go up by 95.576. The intercept shows that when X (square feet) is zero then Y (listing price) should be 137,499. [ Strength of the equation: Interpret the strength of the regression equation, R -squared.] Based off the regression equation I could predict that if there was a square footage of 2,500 the listing price would be $366,881. I could also predict that if the square footage was at 900 then the listing price would be $223,517. Predictions 2500sq ft $366,881 900 sq ft $223,517 Conclusions After analyzing all the data, I could see how the listing price could be affected by the square footage of a property. Although the fifty samples where random they still shared a representation of what the housing market could look like next to those on the national level. The histogram and scatter plot gave a more visual approach to the data by concretely showing the margins of where both the listing prices and square foot area lined up. I concluded that D. M. Pan National Real Estate Company could use my findings as a benchmark to help their agents in the future to show how a property in one area or region could differentiate between that said property’s listing price and its square footage. Despite the fact I still have questions as to what other variables plays apart in the actual listing price, such as does these properties have extended land, do the have a built-in pool in doors or out, does the properties have appliances already or do they come furnished.

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