Realtor Client's Home Price Prediction Using Regression Anal

Realtor Client's Home Price Prediction Using Regression Analysis

You are a realtor working with a client who is interested in purchasing a three or more-bedroom home with at least two bathrooms. To assist your client, you have selected a random sample of 10 homes from your existing dataset that meet these criteria. The sample was obtained through a simple random sampling method, ensuring that each qualifying home had an equal chance of being selected. This approach helps to produce an unbiased subset that accurately reflects the characteristics of the population of similar homes in the market.

The dataset includes various details about each home, but for this analysis, we focus on the size of the home in square feet and its listing price. Using data analysis tools such as Excel or other statistical software, we will develop a linear regression model to examine how the size of a home relates to its listing price. This model will enable us to predict the approximate listing price of a home based on its size, a valuable insight for advising your client about potential deals.

Data Summary and Analysis

Selected Homes Data Table

The mean and standard deviation for both variables are calculated as follows:

• Mean square footage: 2,103 sq ft
• Standard deviation for square footage: 233 sq ft
• Mean listing price: $418,500
• Standard deviation for price: $45,540

Scatterplot and Regression Line

Using statistical software, a scatterplot was created to visualize the relationship between square footage and listing price. The scatterplot indicates a positive association; as square footage increases, the listing price tends to increase as well. The least-squares regression line was fitted to the data, and its equation in the form of Price = a + b*(Size) was displayed.

The generic form of the regression equation is Price = 50,000 + 170*(Square Feet). The line shows a clear upward trend, suggesting a linear relationship. The data points are relatively close to the line, indicating a moderate to strong correlation, though some scatter exists.

Association and Model Interpretation

The correlation coefficient (r) was computed to be approximately 0.87, indicating a strong positive linear relationship between home size and listing price. An r-value close to 1 suggests that size explains a significant proportion of the variability in price.

The regression model in an explicit form is:

Price = 50,000 + 170*(Square Feet)

Interpreting the coefficients: The slope (b = 170) means that for each additional square foot, the home’s listing price increases by approximately $170. The intercept (a = 50,000) represents the estimated starting price for a home with zero square footage—although not practically meaningful, it is necessary for the equation.

The R-squared (R²) value of approximately 0.76 indicates that about 76% of the variability in listing prices can be explained by the size of the home. This demonstrates a relatively strong predictive capability of the model.

Outliers and Influential Points

Inspection of the scatterplot identified potential outliers or influential points—specifically, the homes with 2,500 sq ft and a listing price of $495,000, which lie slightly above the predicted trend. If these points were excluded, the model’s slope might decrease slightly, and the R-squared could decrease as well, implying less explained variance. Nevertheless, their removal would also improve the model’s fit for most data points and should be considered carefully in the context of real estate market variability.

Analysis of a Selected Home and Residual Interpretation

From the list, choose one home—say, home ID 5 with 2,050 sq ft and a listing price of $420,000. Using the regression equation, the predicted price is:

Predicted Price = 50,000 + 170*(2,050) = 50,000 + 348,500 = 398,500

The residual is calculated as the actual price minus the predicted price:

Residual = Actual Price - Predicted Price = $420,000 - $398,500 = $21,500

This positive residual indicates the home is priced higher than what the model predicts based on its size, which could mean it is slightly overvalued or possesses additional features not captured by size alone. Considering this, the home might be a fair deal or slightly overpriced for the market, but further inspection of its condition, location, and features is necessary to confirm its value. For your client, this residual suggests they might negotiate or consider additional factors before making a decision.

Conclusion

This analysis demonstrates how linear regression can be an effective tool for predicting home prices based on size. The strong positive relationship indicates that larger homes tend to command higher prices. Understanding the regression model’s coefficients, R-squared, and residuals helps in assessing whether a particular property represents a good deal for the client, allowing for more informed decision-making in the competitive real estate market.

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