This article covers a sample Median Housing Price Prediction Model for D. M. Pan National Real Estate Company.

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## Median Housing Price Prediction Model for D. M. Pan National Real Estate Company

## Introduction

A variety of factors influence the price of real estate. Aspects such as a locationâ€™s demographics, investment decisions, and the marketâ€™s interest rates of e often been evaluated when setting the housing prices for houses. While the above factors might give the general idea of how the houses are supposed to be sold, they do not give the investmentâ€™s exact value. For instance, the regionâ€™s economic status informs investors of the general price of houses in the area. However, the information does not relay at what price houses of different sizes in the same area should be sold. The report, therefore, seeks to determine the influence of house size on their pricing. Size in this particular case is looked at from the measurement of the house square footage. The research is guided by the following research question: Determining the association between housing footages and median pricing.

The answer to the researchâ€™s question is significant for D.M Pan National Real Estate Company. It will allow the organization to predict how the 2019 housing prices were affected by the square footage parameter. The knowledge will then be used in determining how to price their houses in the future.

There exists some information detailing diverse aspects of median house pricing, the median $ per square feet, and the median square feet. Data from the national survey of U.S houses indicate that the average median listing price for houses in 2019 was $ 288,407. The median $ per square foot was $ 142, with the housesâ€™ median square feet being $ 1944.

Despite the availability of the above descriptive statistics, there is no means to make predictions. The data only provides general information that cannot be used for decision making. Therefore, it is significant that a statistical model showing the association between house pricing and footage be obtained to allow the company to make accurate investment predictions.

## Data Collection

A random sampling method was deployed in the research exercise. A set of 30 observations was picked from a population size, n=978 recorded from the 2019 national housing statistics. The population was randomized in an excel worksheet. The generated random numbers were then sorted according to the numbers. The first 30 entries of the randomized data were picked to form the sample. The use of random sampling was encouraged as it promoted the chances of every variable to be selected. The random sample, therefore, eliminated the possibility of bias. Also, each observation had equal chances for selection meant that the data provided a uniform view of the real estate industry in the United States. The sample size, n=30, was chosen because it made the research significant by allowing representations of the entire populationâ€™s objectives.

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Data from the sample was entered into an excel worksheet for computation. Two variables were depicted as crucial in providing D.M Pan National Real Estate Company with the necessary information to predict housing prices. The variables are the median house pricing and the median square feet. Determining the relationship between the two variables was considered crucial in producing a particular pattern.

A scatter plot graph was drawn using values from the median house pricing and median square feet. The graph was in the form of median house pricing against median square feet. A line of best fit connecting most of the graphâ€™s points was drawn, and the resulting equation was generated. Using the excel functions, a regression equation was generated. The median house pricing, the dependent variable, is denoted by y. The median square feet, the independent variable, on the other hand, is represented by X.

**Scatterplot**

## Data Analysis

The linear regression requires that the variables have a linear relationship. The predictor variable is the one that influences a particular outcome and, in this case, is the median square feet. The response variable is the one whose outcome is determined by the predictor and happens to be the median house pricing. Also, the variables must be multivariate normal. There should be no auto relation in the variables.

**Histogram**

Median House Pricing. Scale 1:10,000

**Summary statistics**

Median Square Feet Summary Statistics

Median House Pricing Summary Statistics

**Interpret the graphs and statistics**

The median depicts the center of the data. The median house pricing is $ 209031, with that of square feet being 1783. The same is depicted by the mean scores of $ 212092 and 1934 for the median house pricing and square feet.

The shape of the data distribution for the median square feet is right-skewed as more data lies towards the left. The same is seen in the median housing graph, with most of the data lying at the center and decreasing towards the right. A key outlier in the graphs is seen in the median square feet, where there is a set of data that lies to the extreme right away from the rest of the data.

The range and the standard deviation give the spread of data for the variables. For instance, the median house pricing has its data widely distributed as indicated by the high range of 283449 and standard deviation of 75268. However, the median square feet are not that spread,d meaning the data sets are close together as seen in a range of 2011 and standard deviation of 476.

The summary statistics can be compared to those of the national statistics. The national data had a median house pricing list of 288407, a standard deviation of 163,986, a minimum of 75,309, a 256,936 median, and a maximum of 1 653, 763. On the other hand, the median square feet had a mean of 1944, the standard deviation of 367, a minimum of 697, a 1901 median, and a maximum of 3945. The data can be compared to the sampleâ€™s median house pricing mean of 212092, the median of 20903, a standard deviation of 75268, a minimum of 94,994, and a 378443 maximum. On the other hand, the median square feet median had a mean of 1934, 1783 median, a standard deviation of 476, a minimum of 1470, and 3482 maximum.

The sample represents the national image due to its reliance on random samples from the population.

## The Regression Model

[**Scatterplot:**

A regression model can be generated from the scatter plot diagram using excel functions to provide an equation.

**Discuss associations**

The modelâ€™s r-value of 0.778461 shows that the median house pricing and median square feet have a strong positive relationship. The two influence each other in the same direction, with an increase in one leading to a corresponding similar effect on the other.

**Find r:**

The positive r-value of 0.778461 means that the two variables, median house pricing and median square feet, influence each other in the same direction. An increase in one results in a corresponding effect on the other. The relationship between the two variables is further affirmed by the high r-value, which approaches 1. It shows that the relationship is a strong one. The correlation between the median house pricing and median square feet signifies that the two variables greatly influence each other hence act as ideal factors to evaluate when determining house prices.

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## The Line of Best Fit

**Regression equation**

y= 122.91x â€“ 25669

**Interpret regression equation**

According to the model, the regression equation is y= 122.91x â€“ 25669. The model had an r-value of 0.778461. R2 was 0.6060 with a 122.9095 slope and Y-intercept of-25669.2. The equation means that house pricing is the dependable variable. The median square feet, X, is the independent variable. The houseâ€™s pricing is influenced by the square feet figures keeping the other factors constant. The positive r value means that the two variables, that is, median house pricing and median square feet influence each other in the same direction. An increase in one results in a corresponding effect on the other.

The company can also make predictions regarding house prices by using the regression model slope. The researchâ€™s slope of 122.9095 represents the median house pricing changes following adjustments in the median square foot by one unit. An increase of one square foot results in a rise in housing price by $ 122.9095, with a decrease resulting in the opposite effect. Therefore, the housing prices can be determined by figuring out the number of changes in units of the median square feet. The Y-intercept of -25669.2 predicts the price of a house when there are no median square feet.

**Strength of the equation**

The R2 value of the model means that 60% of the regression variables can be explained. The R2 value, therefore, makes the model a significant one in explaining the changes.

**Use the regression equation to make predictions**

An example of using data for the prediction can be seen in Xâ€™s use at 2050 square feet. Using the equation, the house pricing can be predicted by the formula:

y= 122.91x â€“ 25669.

= 122.91 (2050) â€“ 25669

= $ 226,296.5

## Conclusions

The research focused on identifying a statistical approach that D.M Pan National Real Estate Company can use to make predictions on house pricing. In particular, the company wants to determine the association between house pricing and square footages. The use of statistical regression has been highlighted as the ideal approach for the company. A regression analysis facilitates the identification of relationships between variables and how they influence each other. The variables used in this particular research were median housing price and median square foot. The research established that there is a relationship between the two variables.

The relationshipâ€™s nature is strong and positive, as indicated by the correlation value, r, of 0.778461. The price of a house, therefore, relies on its size in terms of square footage. The more the square footage, the higher the price. The precise prediction regarding the pricing of a house is given by the regression model y= 122.91x â€“ 25669. D.M Pan National Real Estate Company should compute the calculation using the size of square footage to get the actual value for houses. By understanding changes in the square footage, they will develop a corresponding effect on the pricing. The organization should therefore initiate another primary research to ensure they capture all variables influencing house pricing for precise valuations. Despite the proof of a positive relationship between median house pricing and median square foot, there was no significance test. The company should therefore determine to what extend does the model hold by testing its significance level.