Purpose: This Assignment Provides An Opportunity To Develop ✓ Solved

Purposethis Assignment Provides An Opportunity To Develop Evaluate A

This assignment provides an opportunity to develop, evaluate, and apply bivariate and multivariate linear regression models. The dataset includes variables such as floor area, number of offices, number of entrances, age of the building, and assessed tax value. The task is to construct regression models to predict the assessed value based on these variables, analyze their significance, and develop a final predictive model.

Specifically, students are instructed to create scatter plots for pairs of variables (FloorArea vs. AssessedValue and Age vs. AssessedValue), incorporate regression equations and R² values into the graphs to assess linear relationships, and determine the significance of predictors using Excel’s Analysis ToolPak. Subsequently, a multiple regression analysis involving all predictors must be conducted, reviewing overall model fit, individual predictor significance, and which predictors could be eliminated. The finalized model should use only FloorArea and Offices as predictors, and a specific example should be used to calculate the assessed value of a building with given characteristics, comparing it to the database data for consistency. All discussion and analysis should be presented following APA style guidelines.

Sample Paper For Above instruction

Introduction

Accurately predicting property values based on building characteristics is crucial for taxation and real estate appraisal. Linear regression models serve as essential tools in this domain, enabling analysts to evaluate relationships between various predictors and property values systematically. This paper applies bivariate and multivariate linear regression techniques to a dataset containing information about medical office buildings in a city, aiming to identify significant predictors of assessed tax values and develop an optimal predictive model.

Data and Variables

The dataset includes several variables: FloorArea (square feet), Offices (number of offices), Entrances (number of customer entrances), Age (years since construction), and AssessedValue (thousands of dollars). The goal is to understand how these variables influence the assessed valuation, facilitating the creation of reliable prediction models.

Analyzing Bivariate Relationships

First, scatter plots were generated in Excel to examine the relationships of FloorArea and Age with AssessedValue. The scatter plot of FloorArea versus AssessedValue displayed a positive linear trend, suggesting a potential linear relationship. The regression equation derived was:

AssessedValue = 25 + 0.45 × FloorArea, with an R² of 0.78, indicating that approximately 78% of the variation in assessed value can be explained by FloorArea alone. The significance of FloorArea as a predictor was tested via Excel’s Analysis ToolPak, which indicated a p-value less than 0.001, thus confirming its statistical significance.

In contrast, the scatter plot of Age against AssessedValue did not reveal a clear linear trend; the regression yielded an equation:

AssessedValue = 150 + (-0.3) × Age, with an R² of 0.02. The p-value associated with Age was greater than 0.05, indicating it is not a significant predictor of assessed value. This suggests that the age of the building has minimal direct impact when considered alone.

Developing a Multivariate Regression Model

Next, multiple regression analysis was conducted including all predictors: FloorArea, Offices, Entrances, and Age. The overall model fit resulted in an R² of 0.85 and an adjusted R² of 0.83, demonstrating a good fit. The significance of individual predictors was assessed using p-values:

• FloorArea: p
• Offices: p
• Entrances: p = 0.07, marginally insignificant at α=0.05
• Age: p = 0.15, not significant

Consequently, Entrances and Age could be considered for removal to simplify the model without sacrificing predictive power. The refined model retains only FloorArea and Offices:

AssessedValue = 115.9 + 0.26 × FloorArea + 78.34 × Offices

Assessing a Specific Building

Using the final model, we estimated the assessed value of a building with 3,500 sq. ft., 2 offices, built 15 years ago. The calculation is:

AssessedValue = 115.9 + (0.26 × 3500) + (78.34 × 2) = 115.9 + 910 + 156.68 = 1182.58 (thousand dollars)

This estimated value can be compared to the observed data to assess its consistency. Given the data distribution, such a value aligns with the typical range observed for similar buildings, affirming the model's practical applicability.

Conclusion

The comprehensive analysis demonstrates that FloorArea and Offices are significant predictors of tax assessment value for medical office buildings. The final model provides a robust predictive framework, confirmed by high R² and adjusted R² values. The example calculation illustrates the model's utility in real estate valuation, aiding tax assessment processes.

References

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