**Housing Price Prediction Model for D.M. Pan Real Estate Company**

**The Pattern**

The simple linear regression model is used in establishing the relationship between listing price and area in square feet. The listing price assumes the dependent variable (Y), while the area in square feet assumes the independent variable (X), where the area in square feet will be used to estimate the price of real estate. The relationship between the two variables can be described as a strong positive relationship. This is evidenced by a positive gradient scatter plot of the two variables. Additionally, a linear regression of the two variables generates a positively sloped scatter plot. Both the R^{2 }and the adjusted R^{2} are greater than 78%, implying that more than 78% of changes in listing prices can be explained by changes in the square feet area. Do you need help with your assignment ? Get in touch with us at eminencepapers.com.

There exist several outliers in the data set whose values are significantly larger than the rest of the values in the data set. The outliers may exist due to the strength of other factors influencing listing prices not included in the model in certain areas (Yusof & Ismael, 2012). However, the outliers align with the general direction of the slope.

If one had an 1800 square foot house, the price may be estimated using the regression as:

*Price = 72930 + 89.763*1800*

*Price = 72930 + 161573.4 = $ 234503.4*

The house can be sold at a price of $ 234503.4, where $ 72930 of the price is the fixed price irrespective of the size of the house, and $ 234503.4 of the price can be attributed to the area in square feet.

**Regression Equation**

The regression equation is obtained as follows:

** Y = 72930 + 89.763X**.

**Determine ***r*

*r*

The listing price assumes the dependent variable (Y), while the area in square feet assumes the independent variable (X), where the area in square feet will be used to estimate the price of real estate. The relationship between the two variables can be described as a strong positive relationship. This is evidenced by a positive *multiple r *(0.89). The r-value indicates a positive linear relationship between the variables (Salkind, 2015). Also, the gradient scatter plot of the two variables shows a strong positive correlation. The relationship is an almost strong positive relationship. The direction of the association between the two variables is determined by the correlation coefficient and the slope of the line. In this case, the slope of the line shows a positive gradient in that an increase in the explanatory variable leads to an increase in the response of another variable. Therefore, the direction of the correlation is towards 1, which is a strong positive correlation.

**Examine the Slope and Intercepts**

**Slope: **

For Y intercept= taking the regression equation, y=mx + c, the y-intercept becomes;

** Y = 72930 + 89.763X**.

Therefore, *Y= 72930*

For x-intercept, from the equation,

** Y = 72930 + 89.763X**.

72930=89.763X

Therefore, *X = 812.473*

The slope of the line from the equation can be obtained as 89.763. Considering the slope of the line, the slope implies a true indication of the slope. The price of the land can be obtained by making the footage of the house zero. Alternatively, the footage of the house can be obtained by calculating the price of the land at zero. Therefore, the x and y-intercepts give the value of one variable by obscuring the value of the other variable in a two-variable equation. Looking at the line of best fit, the intercept makes sense. The value of the land is given by the y-intercept, which is obtained as 72930.

*R*-squared Coefficient

*R*-squared Coefficient

The R-squared value is 0.79, which implies that the model explains 79% of the change in the outcome variable (price listing) due to the change in square feet. The R-squared value shows the percentage of the points that fall on the scatter plot regression line. In other words, 79% of the values fit the model (Turner, 2020). In this analysis, the change in a land’s area in square feet explains 79% of the change in pricing.

**Conclusions**

The mean sales price for the land is 342,365. Four hundred and nine (409) states have listing prices greater than the mean listing price. This implies that a greater number of states have listing prices below the mean listing prices. Fifty-seven (57) states have listing prices greater than 581,800. Generally, an increase in the area of the farm leads to an increase in prices, which may depend on other factors, such as the area where the land is located. The regression equation can be used to identify price changes by substituting the values of the cost per square foot to the regression equation. This can be used to identify the corresponding listing prices. Descriptive statistics for the square feet data can be obtained to determine the ranges of the different variables. Particularly, a graph of minimum value and the maximum value for square feet would indicate the range and would be best suited to inform square footage ranges.

**References**

Salkind, N. (2015). *Excel Statistics: A Quick Guide*. Third Edition. SAGE Publications.

Turner, D. P. (2020). Sampling Methods in Research Design. *Headache: The Journal of Head and Face Pain, 60*(1), 8–12.

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**Question**

Overview

Recall that samples are used to generate statistics, which businesses use to estimate population parameters. You have learned how to take samples from populations and use them to produce statistics. For two quantitative variables, businesses can use scatterplots and the correlation coefficient to explore a potential linear relationship. Furthermore, they can quantify the relationship in a regression equation.

**Prompt**

**This assignment picks up where the Module Two assignment left off and will use components of that assignment as a foundation.**

You have submitted your initial analysis to the sales team at D.M. Pan Real Estate Company. You will continue your analysis of the provided Real Estate Data spreadsheet using your selected region to complete your analysis. You may refer back to the initial report you developed in the Module Two Assignment Template to continue the work. This document and the National Statistics and Graphs spreadsheet will support your work on the assignment.

**Note: In the report you prepare for the sales team, the dependent or response variable (y) should be the listing price, and the independent or predictor variable (x) should be the square feet.**

Using the Module Three Assignment Template, specifically address the following:

**Regression Equation:**Provide the regression equation for the line of best fit using the scatterplot from the Module Two assignment.**Determine**Determine*r*:*r*and what it means. (What is the relationship between the variables?)- Determine the strength of the correlation (weak, moderate, or strong).
- Discuss how you determine the direction of the association between the two variables.
- Is there a positive or negative association?
- What do you see as the direction of the correlation?

**Examine the Slope and Intercepts:**Examine the slopeb1{“version”: “1.1”, “math”:”<math xmlns=”http://www.w3.org/1998/Math/MathML”><msub><mi>b</mi><mn>1</mn></msub></math>”} and intercept b0{“version”: “1.1”, “math”:”<math xmlns=”http://www.w3.org/1998/Math/MathML”><msub><mi>b</mi><mn>0</mn></msub></math>”}.- Draw conclusions from the slope and intercept in the context of this problem.
- Does the intercept make sense based on your observation of the line of best fit?

- Determine the value of the land only.

**Note:**You can assume that when the square footage of the house is zero, the price is the value of just the land. This happens when*x*=0, which is the*y-intercept*. Does this value make sense in context?

- Draw conclusions from the slope and intercept in the context of this problem.
**Determine the**Determine the*R*-squared Coefficient:*R*-squared value.- Discuss what
*R*-squared means in the context of this analysis.

- Discuss what
**Conclusions:**Reflect on the Relationship: Reflect on the relationship between square feet and sales price by answering the following questions:- Is the square footage for homes in your selected region different from that for homes overall in the United States?
- For every 100 square feet, how much does the price go up (i.e., can you use slope to help identify price changes)?
- What square footage range would the graph be best used for?