MAT 240 Module Three Assignment - D.McKenzie 091723

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Housing Price Prediction Model for D.M. Pan Real Estate Company Desiree McKenzie Southern New Hampshire University

Median Housing Price Prediction Model for D.M. Pan National Real Estate Company 2 Module Two Notes Real estate is a fast-paced industry in which data analysis can offer a competitive advantage in helping resourceful agencies stay ahead of the game. Although it is important for real estate agents to study the physical attributes of the properties they show, it is equally as important for them to have extended knowledge of those homes in order for them to understand the relationship between factors such as home price, square footage, location, age of the home, and comparable home values. The purpose of this report is to provide D.M Pan Real Estate Company with a method to help predict the business environment to provide the best service to their clients. To do this, I’ve created a random sample of 30 properties from a particular region and will be analyzing the relationship between the selling price of the properties and their square footage. Regression Equation 1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500 5,000 5,500 6,000 $200,000 $250,000 $300,000 $350,000 $400,000 $450,000 $500,000 $550,000 $600,000 $650,000 $700,000 $750,000 $800,000 f(x) = 102.36 x + 160349.87 R² = 0.81 Real Estate Sample The sample data being presented is of 30 properties randomly selected from the Mountain region. For this particular region, the regression equation is y = 102.36x + 160350.

Median Housing Price Prediction Model for D.M. Pan National Real Estate Company 3 Determine r The correlation coefficient (r) measures the dependence between the predictor variable and the response variable which then provides information about the strength and direction of the relationship. To calculate r, I chose to use the ‘=CORREL” function in excel, pulling in the listing price and square footage data. From this calculation, the strength of the correlation can also be determined by how close the correlation coefficient is to the number +1.00, with +1.00 being the strongest correlation (see the table below) and the direction of the association is identified by the sign of the correlation coefficient. Positive associations will have a plus sign and a negative association will have a minus sign. For the Mountain region, the calculation came to r = 0.9023 which is very close to +1.00, so for these two variables, there is a strong positive association. Examine the Slope and Intercepts If the regression equation is y = 102.36x + 160350, the slope is 102.36 and means that for every additional one square foot of a home, the listing price will increase an average of $102.36. The intercept means that when square footage of a home is zero, the listing price is $160,350. The intercept would not make practical sense for a home to have zero square footage, but in the context of this problem, the intercept does make sense because it provides the value of the land on its own, which would be $160,350 representing the minimum price for property in this region.

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Median Housing Price Prediction Model for D.M. Pan National Real Estate Company 4 R -squared Coefficient R-squared is the coefficient determination and is used as another means of depicting how well a regression equation represents its data by measuring the variation in the response variable that can be explained by the variation in the explanatory variable. For this analysis we previously calculated that r = 0.9023, so to find the coefficient determination, we would find the square root of r, which is R^2 = 0.8142. These results indicate that approximately 81.42% of the variation in listing price is explained by square feet of the property, which means square footage is a good predictor of listing price. Conclusions In conclusion, the sample analysis affirms a strong, positive, and linear relationship between listing price and square footage which can provide well founded estimates of listing prices for homes. Results from this analysis seem to be in line with overall homes listed for sale in the United States and the regression equation can be used to help identify price changes. For example, if we wanted to know how much the price of a home would increase for every 100 square feet, we could input 100 in place of x in the regression equation: y = 102.36*100 = $10,236/every 100 square feet. And lastly, for the most reliable results, it will be best to keep the square footage range between 1,400 – 5,800 square feet as it’s within the data range limits of the sample regression model, any data outside of that range would need to be carefully analyzed.

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