Part two math Project

MAT240.docx 3/19/22, 6:05 AM

Selling Price and Area Analysis for D.M. Pan National Real Estate Company ​1

Report: Selling Price and Area Analysis for D.M. Pan National Real Estate Company

[Your Name]

Southern New Hampshire University ​ Median Housing Price Prediction Model for D. M. Pan National Real Estate Company ​9

Introduction D. M. Pan National Real Estate Company's CEO aims to assist their real estate agents in estimating home prices based on square feet. As a junior data analyst employee, I've been asked to write a research on how square footage influences housing values in the country. According to studies, the square footage of a home is closely proportional to its price. As a result, the bigger the square footage, the more expensive the residence. This report uses data from all house prices in the United States in 2019 to create a regression model that predicts home prices using square footage, with the goal of proving if the hypothesis is correct. Because the variables in the frequency plots from the National Statistics and Graph Document are normally distributed, linear regression is acceptable for this study. The x and y variables are also included in the variables. The square footage is the independent or predictor variable, while the home listing prices are the dependent or predicted variable, represented by the y variable. The scatter plot should show a rising trend to the right, showing a positive relationship. The response variable is a dependent variable which is influenced by the predictor variable, whereas the predictor variable is an independent variable which is unaffected by other variables. The predictor variable in this scenario is square footage while the responder variable is listing prices, which are influenced by square footage.

Data Collection From a total population of 1000 households, a sample of 50 homes was chosen to be analyzed in the research. The sample was chosen using a simple random sampling in which 20 residences were chosen from the population's data received from the 2019 Real Estate County statistics. The study's key variables are the listing price which is the dependent variable and square feet which is the independent variable. Figure 1 depicts a scatter plot of home listing prices vs square footage in sample populations of homes sold in the United States in 2019. Figure 1.

Data Analysis

The histograms in Figures 1 and 2 are based on sample data of listing prices and square feet, respectively. Figure 2.

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Figure 3.

The summary statistics for both the square feet and listing prices variables are shown in Table 1 below. Table 1. square feet listing price Mean 2566.92 342574 Standard Error 211.5122 16572.59 Median 1977 333250 Mode 5284 265400 Standard Deviation 1495.617 117185.9 Sample Variance 2236871 1.37E+10 Kurtosis 0.714474 3.96408 Skewness 1.471359 1.713201 Range 5275 575800 Minimum 1145 169700 Maximum 6420 745500 Sum 128346 17128700 Count 50 50

The sigma curve form of the histogram on the sample data of listing prices is somewhat skewed to the left. Its shape is similar to the median listing price frequency table in the National statistics graphs article. The means of the population and sample data, however, diverge, as seen in the summary statistics tables. The histogram also indicates a gap between 609700 and 719700, indicating that the listing prices in that range were either absent or relatively low. The listed prices ranged from 169,700 to 745,500 dollars. The histogram for square feet illustrates that the majority of the often occurring square feet in the sample are on the right side of the graph, with the number of square feet decreasing as the number of square feet increases. As shown in the National statistics graphics paper, the histogram's shape differs from that of the population. The population data exhibits a normal distribution with a perfect sigma curve. There is a gap between 2545 and 3945 square feet, according to the sample statistics histogram. Since the sample mean is 2566.92 and the population mean is 1944, there is also a disparity between the sample mean and the population mean.

The Regression Model

Scatter plot of square feet versus listing prices containing the trend line, r-square and regression equation is shown in figure 4. Figure 4.

Figure 4 demonstrates that the majority of the data points do not deviate from the trend line, and the trend line rises to the right. The data pattern indicates that the dependent variable, may be projected, and hence a regression model for prediction can be created. This can be done by forming the equation using the trend line or by running a regression analysis. The scatter plot reveals a substantial positive relationship between home square feet and listing prices. The positive correlation indicates that when the square footage of a home increases, so does the listing price, indicating that the variables are directly proportionate. The trend line's angle indicates the strength of the relationship and that the majority of data points lie around the line of best feet. The output summary of the regression analysis for the two variables is shown in Table 2.

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Table 2. Regression Statistics Multiple R 0.904239 R Square 0.817648 Adjusted R Square 0.813849 Standard Error 81024.21 Observations 50

The variables exhibit a high positive connection with an r-value of 0.904. This backs up the scatter plot's visualization conclusions that there is a large positive association between listing prices and the sample's square footage.

The Line of Best Fit The regression equation to be used in this study is derived from table 3 below. This is because the table contains the coefficients and the constant. Table 3.

Coefficients Standard

Error t Stat P-value Intercept 102058.7 22933.67 4.450168 5.09E-05 square feet 113.5389 7.739204 14.67062 2.31E-19

Therefore, the regression equation derived is in the form;

Y = 113.5389X + 102058.7 Where X = Square feet

Y = Listing price The slope is 113.5389. The Y-intercept, where the line of best fit crosses the Y axis, is 10258.7. The independent variable square feet explains 81.78 percent of total differences in listing price variables, according to R-squared of 0.8178. By substituting the value of square feet in X, the regression equation may forecast the listing price of a home using square feet. Using a square foot of 7000 as an example, we may forecast the following listing price:

Y = 113.5389(7000) + 102058.7 Y = 794772.3 + 102058.7

Y = 896831 As a result, when the square foot is 7000, the listing price is expected to be 8996831.

Conclusions According to this study, square footage is directly proportional to property listing prices in the United States. The histogram of square feet produced unexpected results, as it was expected to be closer to normal than the population's frequency table. However, because of a strong positive correlation of 0.9042, which is extremely close to 1, it has a significant impact on a home's listing price. The study raises the intriguing question of whether there are other characteristics that influence property listing prices and whether they may be utilized to anticipate them.

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