MAT 240 Project One Template

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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 Shaterria Johnson Southern New Hampshire University

Median Housing Price Model for D. M. Pan National Real Estate Company 2 Introduction I have been hired by D.M. Pan National Real Estate Company to provide a report to see if the housing prices based on square footage are appropriate. This will help real estate agents determine if square footage should be a benchmark for home listing prices. Using Linear regression is only appropriate if the relationship between the predictor variable (square footage) and the response variable(housing listing price) is linear. The response variable must be a continuous numeric variable. When using linear regression, I would expect the scatterplot to look like an upward continuous positive slope. The response variable is a random variable, while the predictor variable is assumed to be non- random or fixed and measured without error. The relationship between the response and predictor variables must be linear, given by the model y ^ = b 0 + b 1 x2. Data Collection I selected a random sample of 50 by first using the Excel function on the data spreadsheet =rand() for all houses listed. After successfully randomizing the houses, I sorted the list from smallest to largest and chose the first 50 houses listed. My predictor variable is the median square foot of the house and my response variable is the housing listing price.

Median Housing Price Model for D. M. Pan National Real Estate Company 3 - 1,000 2,000 3,000 4,000 5,000 6,000 - 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 Real Estate County Data 2019 Random Sample Square footage Median House listing price Data Analysis

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Median Housing Price Model for D. M. Pan National Real Estate Company 4 Summary Statistics Table Median House Listing Price Square Footage Mean 362742 Mean 2254.84 Standard Error 16899.33 Standard Error 154.037 7 Median 330950 Median 1896.5 Mode #N/A Mode #N/A Standard Deviation 119496.3 Standard Deviation 1089.21 1 Sample Variance 1.43E+10 Sample Variance 1186381 Kurtosis 2.275429 Kurtosis 2.63547 2 Skewness 1.304433 Skewness 1.93305 7 Range 598300 Range 4089 Minimum 188500 Minimum 1201 Maximum 786800 Maximum 5290 Sum 1813710 0 Sum 112742 Count 50 Count 50 The Center of the sample shows an average house listing price of $362,742 with an average square footage of 2254.84. It also shows a median of $330,950 for the listing price of

Median Housing Price Model for D. M. Pan National Real Estate Company 5 houses and a median square foot of 1896.5 with No mode. The spread shows a standard deviation of $119,496.30 for the house listing price and 1089.211 for the square footage of the houses. With a range of $598,300 for the listing price and 4,089 for square footage. When identifying the 1 st and 3 rd quartiles, the IQR, and lower bound and upper bound, I identified that there were no outliers present. The center of the sample data compared to the national data shows an average listing price of 6% more than the national average which is an over $20,000 increase. Whereas the median listing price shows a 4.1% increase. The Average square foot of my sample compared with the national average for square feet shows a 6.8% increase with a 1% increase associated with the median of square footage. The spread shows a 5.1% decrease when comparing the standard deviation of the median house listing price for the national data to my sample. With an 18% increase in standard deviation when comparing the national data to the random sample I created. With Percentages this small I would say it is a good representation of the housing market. Develop Regression Model

Median Housing Price Model for D. M. Pan National Real Estate Company 6 Based on my scatter plot the regression model has a strong linear relationship between house listing price and the square foot of that house. The coefficient of determination indicates a strong linear relationship of 71.61% of the house price listing can be explained by the square foot of the house. The scatterplot shows a positive linear correlation between house listing price and square footage. I see maybe one outlier but I don’t see it affecting the linear regression, seeing that the graph positively depicts a rise in house listing price can be determined by square footage of the house. I would keep the outlier with the outlier and examine it further. Using the =Correl function in Excel I was able to identify a correlation coefficient of 0.846 which is closer to 1 indicating a strong linear relationship between the two variables. Determine the Line of Best Fit

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Median Housing Price Model for D. M. Pan National Real Estate Company 7 Y=92.84x+153403. Y is the dependent variable which is the median house listing price of a random sample of 50. X is the independent variable which is square foot. The coefficient of the x variable is 92.84 whereas the coefficient of the intercept is 153403. The slope in the situation represents how much housing price goes up by 1 square foot. Y-intercept represents what the median house listing price is when the square foot of the house is 0. R-squared determines how well the regression model fits. In this situation, R squared is 71.61% meaning that 71.61% of the house price list can be explained by the square foot of the house. Based on the assumption that a house is 1500 square feet, I would list the house at $292,663. Conclusions By taking a random sample of 50 from the national county data, I was able to draw up a regression model that was appropriate to predict housing prices in 2019. My findings showed a strong positive correlation between the square feet of the houses and the house listing price. Even with minimal outliers present, we can predict an average house listing price of $362,742 accompanied by a house with an average square foot of 2254.84. 71.61% of the house pricing list can be explained by an increase in the square foot of the house. The listing price in this sample also shows a small 6% increase from the national average. Based on my findings square foot of the house can be a benchmark for house listing price.

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