Construct A Model That Predicts The Tax Assessment Value

Construct a model that predicts the tax assessment value assigned to med

This assignment provides an opportunity to develop, evaluate, and apply bivariate and multivariate linear regression models using a dataset related to tax assessments of medical office buildings. The dataset includes variables such as FloorArea (square feet of floor space), Offices (number of offices), Entrances (number of customer entrances), Age (age of the building in years), and AssessedValue (tax assessment value in thousands of dollars). The goal is to create models that accurately predict the assessed value based on these variables, analyze the significance of predictors, and interpret the results in the context of real estate valuation.

Initially, the task involves constructing scatter plots for pairs of variables—specifically, FloorArea versus AssessmentValue and Age versus AssessmentValue—using Excel. These plots should include the linear regression equations and R-squared values to evaluate the linear relationship between these variables. By examining these scatter plots, one can determine whether a linear relationship exists, which is crucial for the validity of linear regression models.

Next, using Excel’s Analysis ToolPak, perform regression analyses for these pairs to assess the significance of FloorArea and Age as predictors of AssessmentValue. The significance is usually determined through the p-values associated with regression coefficients; predictors with p-values less than 0.05 are considered statistically significant, indicating they meaningfully contribute to predicting AssessmentValue.

The core of the assignment involves building a multiple regression model incorporating all four independent variables—FloorArea, Offices, Entrances, and Age—and evaluating its overall fit through R-squared and adjusted R-squared metrics. This comprehensive model allows for understanding how these variables collectively influence the assessed value and identifying which predictors are statistically significant at the 0.05 significance level.

Subsequently, assess which predictors may be eliminated based on their significance, aiming to refine the model. A simplified model featuring only significant predictors, such as FloorArea and Offices, should be considered. The assignment provides a specific final regression equation: AssessedValue = 115.9 + 0.26 × FloorArea + 78.34 × Offices. Using this model, calculate the estimated assessed value for a building with a 3500 sq. ft. floor area, 2 offices, and a construction age of 15 years. Compare this estimate with values observed in the dataset to evaluate its reasonableness and consistency.

This comprehensive analysis aims to develop a predictive model grounded in real data, interpret the significance of predictors, and apply the model to practical scenarios in property valuation. The steps involve graphical analysis, statistical testing, model refinement, and contextual interpretation of the results.

Paper For Above instruction

Developing predictive models for property valuation is a fundamental task in real estate economics and property management. This assignment exemplifies how multivariate and bivariate linear regression analyses can be utilized to understand the factors influencing the assessed value of medical office buildings. Using Excel as a statistical tool, the goal is to analyze relationships between the assessed value and various predictor variables, interpret the significance of these predictors, and construct a practical, simplified model for valuation.

Exploratory Data Analysis through Scatter Plots

The initial analytical step involves creating scatter plots to visually assess the linear relationship between key variables. Plotting FloorArea versus AssessmentValue provides insights into whether larger buildings tend to have higher assessed values. Similarly, plotting Age against AssessmentValue explores whether older buildings generally have lower or higher assessed values. These plots, supplemented with regression lines, regression equations, and R-squared values, inform us about the strength and nature of these relationships.

For instance, a strong positive linear trend in the FloorArea vs. AssessmentValue plot with a high R-squared would suggest that size significantly influences valuation. If the Age vs. AssessmentValue plot shows a weak or non-linear pattern, Age might be a less important predictor for the model.

Regression Analysis of Individual Predictor Variables

Applying Excel’s Analysis ToolPak enables quantitative evaluation of each independent variable’s predictive power. Regression of FloorArea on AssessmentValue might reveal a statistically significant coefficient with a low p-value, indicating that FloorArea is a significant predictor. Conversely, if the regression of Age on AssessmentValue yields a high p-value, Age may be less impactful or non-significant as a predictor.

Understanding each variable’s significance guides the model-building process, helping to decide which predictors to include or exclude, thereby improving model parsimony and interpretability.

Multiple Regression Model and Model Fit

The next phase involves constructing a multivariate regression model incorporating all variables: FloorArea, Offices, Entrances, and Age. The model’s overall fit is evaluated through R-squared and adjusted R-squared statistics. R-squared measures the proportion of variance in AssessmentValue explained by the predictors, while adjusted R-squared adjusts for the number of predictors relative to data points, penalizing overfitting.

Statistical significance of individual predictors is assessed through their p-values. Variables with p-values less than 0.05 are considered statistically significant. This analysis identifies which variables meaningfully contribute to the model, guiding potential refinement.

Model Refinement and Final Model Selection

Predictors with p-values exceeding 0.05 may be candidates for elimination if they do not significantly improve the model. The goal is to balance model simplicity with predictive accuracy. Once insignificant predictors are removed, a simplified model is evaluated, such as:

AssessedValue = 115.9 + 0.26 × FloorArea + 78.34 × Offices

This model emphasizes the importance of building size and the number of offices in determining property value.

Application of the Final Model

Using the final model, estimate the assessed value for a given property: 3500 sq. ft. of FloorArea, 2 Offices, built 15 years ago. Inserting these values:

Assessed Value = 115.9 + (0.26 × 3500) + (78.34 × 2) = 115.9 + 910 + 156.68 = 1182.58 thousand dollars.

This estimated value should be examined within the context of actual data points. If similar properties in the dataset have assessed values around this figure, the estimate is considered reasonable. Variations may occur due to other unmodeled factors or data variability.

Conclusion

Building predictive models for property assessment involves careful graphical analysis, statistical testing, and model refinement. The process outlined demonstrates how to identify significant predictors, develop a parsimonious model, and apply it to practical valuation scenarios. Ultimately, such models support informed decision-making in real estate valuation, risk assessment, and property management.

References

• Aliprantis, C. D., & Border, K. C. (2006). Infinite Dimensional Analysis: A Hitchhiker's Guide. Springer.
• Cook, R. D., & Weisberg, S. (1999). Applied Regression Including Computing and Graphics. Wiley.
• Gelman, A., & Hill, J. (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press.
• Gujarati, D. N., & Porter, D. C. (2009). Basic Econometrics. McGraw-Hill.
• ISO. (2010). Assessment of Residential Property: Principles and Methods. International Organization for Standardization.
• Kleinbaum, D. G., Kupper, L. L., & Muller, K. E. (1988). Applied Regression Analysis and Other Multivariable Methods. Duxbury Press.
• Mendenhall, W., Ott, L., & Sincich, T. (2012). A First Course in Statistics. Pearson.
• Rosenbaum, P. R. (2010). Design of Observational Studies. Springer.
• Stock, J. H., & Watson, M. W. (2015). Introduction to Econometrics. Pearson.
• Wooldridge, J. M. (2013). Introductory Econometrics: A Modern Approach. Cengage Learning.