Comparison of Multiple Linear Regression and Sales Comparison
The multiple linear regression model is more objective in determining the compensation due to property owners along Springbank Drive. As such, the method used to determine the amount due to each owner is verifiable and not biased. In addition, the multiple linear regression model can be used to determine compensation for several owners at the same time without significant investment in professional fees for valuation. In addition, the model is faster and easier to apply, as it generalizes all the properties in the neighborhood. Therefore, the multiple linear regression model is more cost effective compared to the sales comparison method.
Despite the cost effectiveness of the multiple linear regression model, it is unreliable for determining the value of property that has differing characteristics. These differing properties make it inappropriate to generalize their valuation using a linear model. Consequently, the sales comparison model is more appropriate as it offers adequate flexibility to include any unique features that affect the value of the property. In addition, the sales comparison method will enable a professional determination of the value of property, which will provide more depth and detail justifying the compensation. Moreover, the process of sales comparison method will encourage more discussion with the property owners, thereby overcoming the potential resistance in the acquisition process. Therefore, the sales comparison method is the most suitable method for determining the value of property.
A new multiple linear regression model was developed to determine the value of the property based on the available characteristics. This model used all the variables in the dataset except property number, address, sales date, sales year, and sales month. These variables were omitted because they were not discrete. The following are the model output using R software.
The resulting model is Sales price = 84524.67 + 3892.53 HSETYPE + 163.18 AGEYR + 0.50 LOTAREA + 59.41 LOTFRT + 32.37 LFA + 162.92 DISTCURB – 534.78 EXTAMEN -5566.67 EXTFINFACTOR -3403.62 GAR + 2456.32 STSCAPE + 105.42 CENAIR + 8822.93 POOL + 3758.96 INTCOND – 8181.07 BASEMT + 17.19 BSMTFINAREA – 335.83 BI AMEN APPL -679.55 LANESRD -0.58 TRAFCOUNT.
This model captures the 44.19% of the variation in sales price. The model is significant at 5% level, with F(18,85)=5.53, p<0.05. Therefore, the model is reliable in determining the compensation due to the residents.
The model selection has a major effect on the compensation claims due to three reasons. Firstly, adding more variables in the model makes it more reliable for determining the appropriate compensation. Secondly, excluding insignificant variables enhances its reliability in predicting the compensation. Lastly, inclusion of several variables takes into account the unique characteristic of each property in the neighbourhood. Therefore, the model selection has a major effect on the compensation claims.
Strength and Weaknesses of the Model
The model has two major strengths and three major weaknesses. The major strength is its relatively high level of reliability as indicated by the adjusted R-squared. The model captures nearly half of the variation in the compensation price. Secondly, the model is significant as determined by the F-test. However, most of the variables in the model are not significant. As such, only two of the variable (LFA and INCOTD) are significant. Secondly, the model does not explain most of the change in the sales price. It leaves 55.81% of the variation unexplained. Lastly, it assumed a linear relationship between these variables, which might not been the case. Therefore, it has significant shortcomings that could affect the accuracy of its predictions.
Fairness of Compensation
The coefficients were used to determine the appropriate compensation for each of the seven residents. Using the coefficients, a new column was added to list the predicted values. The code used the complainant dataset to calculate the compensation offered to the residents. The resulting output from the r code is as follows
The complainants received higher average compensation compared to the average population. Therefore, the complainants received better compensation and should not appeal to the council.
I could recommend the cist to use the sales comparison model in place of the linear regression model due to three key reasons. Firstly, the regression model does not consider some crucial qualitative factors such as the location, nearness to busy road intersections, and other factors that affect customer traffic to the affected properties. Secondly, the model is unreliable for determining the value of property with differing characteristics, which make it inappropriate to generalize their valuation using a multiple linear model. Notably, the data used is assumed to follow a normal distribution with minimal outliers. The presence of outliers in the dataset could affect the accuracy of the model, thereby skewing the results against the residents. Finally, input from a professional valuation expert could be the most appropriate means of avoiding compensation disputes with the residents. These disputes arise from the perceived inaccuracy of the valuation model. Use of expert opinions could arrest these disputes and make it easy for the council to proceed with the project.