Linear Regression Analysis – Lansink Appraisals

Posted: August 26th, 2021

Linear Regression Analysis – Lansink Appraisals

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Linear Regression Analysis – Lansink Appraisals

Introduction

Regression analysis is an important statistical method for determining the effect that different independent variables have on the dependent variables. For instance, companies can use the method to assess the impact that certain training program has had on their employees in a given period. At the same time, the method can be useful for appraisal of real estate facilities for the purposes of determining the adjustment value. In this case, property sales of a similar real estate facility are used for determining the actual value of a property under question. In this study, the paper applies the concept of regression analysis to appraise a real estate facility. The problem analyzed emerged following a dispute over the value of 817 Saint Stephen Street property. The issue is currently a court case being represented by Penfield Associates (plaintiff)and Croxall Law Partners (accused) law firm that has requested Ben Lansink, a real estate appraiser in London, Ontario. The source of dispute is the disagreement on the parking spaces included within the property. Croxall Law Partners have hired Hamilton Appraisals who prepared a report using regression analysis. Their appraised value is higher than the value attained by Lansink. After disputing the regression analysis results obtained by Croxall Law Partners, Lansink requested raw data to perform regression analysis. Therefore, the paper seeks to show how Lansink would disapprove of the results from Croxall Law Partners using the linear equation in the subsequent parts of the paper.

Methodology and Analysis

Methodology

The study uses regression analysis to conduct an appraisal assessment for the property. The method utilizes the raw data provided by Croxall Law Partners to build a regression model. The results are then compared against Croxall Law Partners’ results before making a final recommendation. The dependent variable was the sales price while other variables such as age, brick, lanes, location and medical, among other variables as listed under Table 1 below;

Variable Name	Definition
at	Average annual daily traffic volume in/ from of the property
age	Age of the building
Area_sf	The area of the building in square feet
Brick	Categorical variable; brick = 1, if the building is brick, brick =0, otherwise.
lanes	Number of lanes on the road in front of the building
location	Categorical variable; location =1 if the location is below average, location =2 if the location is average, and location =3 if the location is very good.
Medical	Categorical variable; medical =1 if the building is used for medical purposes, medical =0 otherwise
Park_min	Categorical variable; park _min=1 if there is a minimal amount of parking in front of the building, park_min = 0 otherwise
Num_park	Number of parking spaces
Sales date	The sale date for the property
Sales_price	The sales price of the property
Street_park	Categorical variable; street_park =1 if there are parking spaces on the street adjacent to the building, street_park =0 otherwise.
Use	Categorical variable; use =1 if the building is used for medical purposes, use =2 if the building is used for general purposes, and use = 3 if the building is used for retail.

            The raw data for each of these variables is in the Excel Sheet.

Regression Analysis

The following is thehypothesized regression model used in implementing the analytical appraisal for the building;

The hypothesis of the model is as follows;

H₀ : Bⁿ = 0

H_a: Bⁿ ≠ 0

Whereby, B is the coefficient of the independent variable while n is the position of the coefficient where n = 0, 1, 2, 3…n depending on the number of independent coefficients in the model. According to the null hypothesis, when the slope of the independent variable is equal to zero, it is probably not significant. However, the variable is significant when the slope is not equal to zero.  The model has twelve (12) independent variables.  represents a constant value as a measure of coefficient factors of the variables. Table 2 below is a summary of regression results.

Table 2: Summary Regression

	Coefficients	P-value
Intercept	-35278.32	0.94
aadt	-0.14	0.80
age	379.36	0.09
area_sf	42.57	0.00
brick	21280.04	0.15
lanes	5929.93	0.33
location	27745.33	0.00
medical	-8124.85	0.51
num_park	5909.68	0.00
park_min	51864.50	0.00
park_min_med	6439.77	0.30
sales_date	-255.55	0.96
street_park	-22430.94	0.07
use	-15390.31	0.05

 R-Square,

Based on the data above, the complete regression model is as follows:

The model implies that at any time, when all factors are constant, selling the property will lead to a loss of $ 35278.32, as indicated by the model intercept. The coefficient of the average annual daily traffic flow in and from the property has a negative coefficient of 0.14 implying that the variable has a tendency to reduce the sales price by 0.14 units whenever there are changes in annual traffic flow. The same applies to medical, sales date, street_park and use variables with negative coefficients of 8,124.85, 255.55, 224,430.50 and 15,490.31 respectively. These negative coefficients confirm that a unit increase in any of them is likely to reduce the sales price of the facility by their correspondent coefficients. However, the park_min, num_park, lanes, location and park_min_med all have positive coefficients of 51,654.80, 5908.60, 27745.33 and 6439.77 respectively. Accordingly, this implies that a unit increase in the value of any of this positive independent variable within the facility, the sales price is likely to s increase with the respective amount of coefficients. 

Testing the Model

The coefficient test evaluates the significance of each coefficient in the model using the probability value (p-value). The p-value proves or disapproves of the hypothesis tests whereby p-value <= 0.05 shows strong evidence against the null hypothesis while p-value >=0.05 implies that the evidence that the variable is significant is weak. The results show that almost all the variables are significant. However, variables use, location, num_park and park_min have a p-value <=0.05 implying that they hold strong influence in the model compared to other independent variables. Lastly, the R² value was equal to 0.8859, that is, 88.59%. The value implies that 88.59% of all the changes in price is explained by the variables in the model. However, the remaining 13.01% are explained by factors outside the model. Equally, the model is significant according to the results of a plot of Y against predicted Y, which shows close-fitting with a thin confidence band.

Conclusion and Recommendations

The coefficient of num_park as established in the model is 5908.68, implying that an increase in the number of parking will contribute $ 5,908.68 or $ 5, 900 to the selling price of the property. The value proposed by Croxall Law Partners is $ 11, 200, which is an excess of $ 5,300. Therefore, it is true that Croxall Law Partners exaggerated the actual value of the property. The recommendation is that Croxall Law Partners should review or recheck their argument.