Real Property Modeling Concepts

COURSE 311

Real Property Modeling Concepts

Solutions Set

Real Property Modeling Concepts | Course 311

Solutions Set 2

© 2020 International Association of Assessing Officers

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Chapter 1 - Solutions Set 3


Chapter 1 | Introduction to Mass Appraisal

REVIEW QUESTIONS – Chapter 1 SOLUTION

1. The definition of mass appraisal is the systematic appraisal of groups of properties, as of a given date,

using standardized procedures and statistical testing.

2. Characteristics of mass appraisal that are different from single property appraisal are the use of

valuation tables, schedules, and models.

3. Economic, social, and environmental data are termed market data, while off-site features and

improvement data are termed property analysis data.

4. The appraisal principle which states “land cannot be valued on the basis of one use, while

improvements are valued on the basis of another use” is the principle of consistent use.

5. Selecting appropriate valuation approaches and specifying the variables to be used is called model

specification.

6. Developing adjustment weights from measurable supply and demand factors, including quantitative

and qualitative factors, is called model calibration.

7. According to modern price theory, value in exchange is determined by the interaction of supply and

demand.

8. List the three determinants of supply and the five determinants of demand.

Supply Demand

Price Price

Availability and cost of related goods Consumers’ income

Technology Price of related commodities

Consumer expectations

Consumer tastes and preferences

9. V = bo + b1 × SFLA + b2 × #baths + b3 × GARSQFT … is an example of a/an additive model.


Chapter 1 - Solutions Set 4




Chapter 2 – Solutions Set 5


Chapter 2 | Data Collection and Management

Exercise 2-1: Creation of Binary Variables – Solution

You are appraising an area where lot size requires an adjustment based on size ranges. Your analysis has

indicated the following:

• Undersized lot = Less than 8,000 sq. ft.

• Standard lot = 8,000 to 12,000 sq. ft.

• Large lot = 12,001 to 16,000 sq. ft.

• Extra-large lot = 16,001 to 20,000 sq. ft.

• Double lot = Greater than 20,000 sq. ft.

1. How many binary variables are necessary to model the above lot sizes?

Five binary variables are created, but only four binary variables are necessary for these lot

sizes, for modeling purposes. In this problem, the presumption is that the standard lot is typical.

Variables for the other lot sizes are created and included in the model. The reference for these

coefficients will be the standard lot.

2. If the condition were met, how would you code the variable?

If the condition were met, the variable would be coded a 1.

3. If the condition were not met, how would you code the variable?

If the condition were not met, the variable would be coded a 0.








Exercise 2-2: Creation of Scalar Variables – Solution

1. Develop scalar variables for each neighborhood for use in a multiplicative or hybrid model.

Since neighborhood 300 is considered the typical neighborhood, the scalar variables for a

multiplicative or hybrid model are developed by dividing each of the neighborhood’s average

sale price per square foot by the average sale price per square foot for Neighborhood 300. This

produces the following relative values:

Neighborhood 500 41 ÷ 50 = 0.82

Neighborhood 100 44 ÷ 50 = 0.88

Neighborhood 300 50 ÷ 50 = 1.00

Neighborhood 200 57.50 ÷ 50 = 1.15

Neighborhood 400 62.50 ÷ 50 = 1.25

2. Develop scalar variables for an additive model.

To create scalar variables for an additive model the values would be centered on 0 (by

subtracting 1.00) as follows:

Neighborhood 500 0.82 – 1.00 = -0.18

Neighborhood 100 0.88 – 1.00 = -0.12

Neighborhood 300 1.00 – 1.00 = 0

Neighborhood 200 1.15 – 1.00 = + 0.15

Neighborhood 400 1.25 – 1.00 = + 0.25








1. Assume that the standard home is 1,500 square feet. Compute a size multiplier for the following

benchmark parcels by raising square foot of living area to the power of 0.90 and expressing the

results relative to the standard home. (Note: This requires a calculator with a power key.)

SQFT SQFT0.90 MULTIPLIER

1,000 501 0.694

1,500 722 1.000

2,000 935 1.295

2,500 1,143 1.583

3,000 1,347 1.866

Sample equation: 1,0000.90 = 501 ÷ 722 = 0.694

2. Assume that property values are heavily influenced by their proximity to the ocean and that the effect

can be approximated by raising distance to the power of -0.50. Compute the appropriate multiplier

for the following distances. (Note: If you don't have a calculator with power key, take the square root

and then the reciprocal of the result).

MILES MILES-0.50

0.10 3.162

0.25 2.000

0.50 1.414

1.00 1.000

2.00 0.707

5.00 0.447

Exercise 2-3: Exponential Transformations – Solution








Exercise 2-4: Logarithmic Transformations – Solution

Find the natural logs of the following depths and express the result relative to the standard depth (100

feet).

DEPTH NATURAL LOG FACTOR

50 3.912 0.850

75 4.317 0.937

100 4.605 1.000

125 4.828 1.048

150 5.011 1.088

175 5.165 1.122

200 5.298 1.150

Each doubling of the amount of depth provides an equal increase in the logarithm. For example, a

change from a depth of 50 feet to a depth of 100 feet equals 0.693 (4.605 - 3.912 = 0.693) and a

change from a depth of 100 feet to a depth of 200 feet equals 0.693 as well (5.298 - 4.605 = 0.693).









1. List the four market forces that must be analyzed.

Economic Governmental Social Physical / Environmental

2. Items such as building codes, planning, and zoning are considered governmental forces.

3. The most effective, yet most expensive, method of gathering income and expense data is personal

interviews.

4. Potential gross income (PGI) is based on market rent, which reflects current rents and typical

management.

5. Net operating income is the income that is typically capitalized into an indication of value in mass

appraisal.

6. Typically, a gross lease requires the owner to pay all operating expenses, while a net lease requires

the tenant to pay all operating expenses.

7. Qualitative data, also known as "discrete" data, relate to features or attributes of the property.

8. Quantitative data, also known as "continuous" data, are based on measuring or counting.

9. Scalar transformation converts a discrete variable to relative values or numerical ratings.

10. When property characteristics affect value interactively, a multiplicative transformation captures the

interactive effects.

11. A pilot study helps evaluate what data to collect and the best way to collect them.

12. IAAO standards recommend routine property inspections at least every six (6) years.

13. List four methods of obtaining income and expense data:

Mail questionnaires Telephone interview

Personal interview Industry and trade publications

14. The square foot area of a residence is considered continuous (quantitative) data while the condition

rating is considered discrete (qualitative) data.

15. Binary data are qualitative items that have only two possibilities: yes or no.

16. The result of a depreciation analysis shows that the effect of age or value is: % good = Age-0.l0. The

percent good for 20 years of age would be 0.741 while the percent good for 40 years of age would

be 0.692.

17. The natural log for a lot with a depth of 150 feet would be 5.011. The adjustment factor for this lot

relative to a base lot of 100 feet would be 1.088.

18. A multiplicative transformation helps address the interactive relationship of a size-related variable

with a quality-related variable.

19. The division of one variable by another, for example square feet by number of rooms, is termed a

quotient transformation.








Chapter 3 | Market Analysis

INTERVAL NUMBER OF

OCCURRENCES

FREQUENCY DISTRIBUTION

(% OF SALES)

1940 and Before 3 6%

1941–1950 6 12%

1951–1960 8 16%

1961–1970 16 32%

1971–1980 7 14%

1981–1990 6 12%

1991 and After 4 8%

Exercise 3-1: Constructing A Frequency Distribution – Solution








DATA # SALE PRICE $ K = (p)(n) + p

1 89,500

2 91,000

3 93,000

4 95,500

5 97,000 25%

(.25)(20) + .25 = 5.25

1500 x .25 = 375 + 97,000 = 97,375 6 98,500

7 99,500

8 100,000

9 100,800

10 101,400

11 102,500

12 103,200 60% (.60)(20) + .60 = 12.60

800 x .60 = 480 + 103,200 = 103,680 13 104,000

14 105,000

15 107,000 75% (.75)(20) + .75

1500 x .75 = 1,125 + 107,000 = 108,125 16 108,500

17 110,000

18 112,000

19 114,000

20 116,000

Exercise 3-2: Calculation of Percentile – Solution








Exercise 3-3: Computing Measures of Central Tendency and Dispersion – Solution

MEAN

PROPERTY

NUMBER

EFFECTIVE AGE EFFECTIVE AGE DIFFERENCE

FROM MEAN

DIFFERENCE

SQUARED

1 24 30 -6 36

2 26 30 -4 16

3 28 30 -2 4

4 29 30 -1 1

5 30 30 -0- -0-

6 30 30 -0- -0-

7 31 30 +1 1

8 32 30 +2 4

9 34 30 +4 16

10 36 30 +6 36

TOTAL 300 114

Median effective age: (30 + 30) ÷ 2 = 30

Mean effective age: 300 ÷ 10 = 30

Range: 36 – 24 = 12

Variance: 114 ÷ 9 = 12.67

Standard Deviation: 67.12 = 3.56








Exercise 3-4: Confidence Intervals – Solution

PARCEL EFFECTIVE

AGE MEAN DIFF

SQRD

DIFF

1 20 30.20 -10.20 104.04

6 21 30.20 -9.2 84.64

2 22 30.20 -8.2 67.24

3 25 30.20 -5.2 27.04

7 29 30.20 -1.2 1.44

4 30 30.20 -0.2 .04

10 30 30.20 -0.2 .04

13 30 30.20 -0.2 .04

8 31 30.20 0.8 .64

14 31 30.20 0.8 .64

11 33 30.20 2.8 7.84

9 36 30.20 5.8 33.64

15 38 30.20 7.8 60.84

5 38 30.20 7.8 60.84

12 39 30.20 8.8 77.44

Sum 453 Sum 526.40

Median effective age: 30.00

Mean effective age: 30.20

Standard deviation: 6.13




Exercise 3-4: Confidence Intervals – Solution (continued)

The confidence interval for the mean is:

�̅� ± 𝑡 × (𝑆 ÷ √𝑛)

30.20 ± 2.145 × (6.13 ÷ 3.87)

30.20 ± 3.40

The lower confidence limit is 30.20 – 3.40 = 26.80

The upper confidence limit is 30.20 + 3.40 = 33.60

The confidence interval for the median is:

𝑗 =1.96 × √15

2

𝑗 =1.96 × 3.87

2

j = 3.79 or 4

The lower confidence interval is 25.

The upper confidence interval is 36.




Exercise 3-5: Hypothesis Tests – Solution

SALE

NUMBER

SALE

DATE

SALE

PRICE $

SALE

DATE

SALE

PRICE $

AMOUNT

OF

CHANGE

MONTHLY

RATE OF

CHANGE

1 16 months 118,300 current 132,000 0.1158 0.0072

2 15 months 110,500 current 123,900 0.1213 0.0081

3 14 months 145,100 current 174,000 0.1992 0.0142

4 11 months 138,600 current 149,000 0.0750 0.0068

5 19 months 149,700 current 187,000 0.2492 0.0131

6 22 months 120,300 1 month 134,900 0.1214 0.0058

7 19 months 144,500 1 month 150,000 0.0381 0.0021

8 21 months 148,300 3 months 166,600 0.1234 0.0069

9 33 months 120,900 1 month 128,000 0.0587 0.0018

10 34 months 111,000 3 months 123,000 0.1081 0.0035

SUM 0.0695

AVERAGE 0.00695

The t-test formula is: Average = mean of monthly rates ± 𝑡 × (𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 ÷ √𝑛)

Average = 0.00695 ± 1.833 × (0.00415 ÷ √10)

Where 1.833 is the one-tailed t-value corresponding to the 95% confidence interval with 9 degrees of

freedom.

Average = 0.00695 ± 1.833 × (0.00415 ÷ 3.162)

Average = 0.00695 ± 1.833 × .0013124

Average = 0.00695 ± 0.0024077

0.00695 – 0.0024077 = 0.00454

0.00695 + 0.0024077 = 0.00936

Confidence Interval = 0.00454 to 0.00936

Since the computed confidence interval is above zero and positive, we reject Ho.








Exercise 3-6 Hypothesis Tests – Solution

Average sale price ± t × (standard deviation ÷ square root of number of observations)

�̅� ± 𝑡 × (𝑆 ÷ √𝑛)

$97,000 ± 1.96 × (15,000 ÷ √225)

$97,000 ± 1.96 × (15,000 ÷ 15)

$97,000 ± 1.96 × 1,000

$97,000 ± 1,960

$95,040 to $98,960

Because the range in sales prices does not include $100,000, you must reject the null hypothesis and

accept the alternative hypothesis.









1. Market or economic areas are broad geographic areas subject to similar economic influences.

2. Subareas or neighborhoods are groups of properties that share similar location amenities.

3. Market areas are used primarily in the development of MRA models, while subareas are used to

develop regression variables.

4. Stratification criteria to be considered, in addition to property type and location, can include such things as

size, age, condition, and quality.

5. A method of stratification operating on the principle of minimizing differences within groups and

maximizing differences among groups is known as cluster analysis.

6. A histogram is a bar chart or graph of a frequency distribution.

7. Percentiles are those values that include given percentages of the data set.

8. Quartiles are those values that include one-fourth, one-half, three-fourths, and 100 percent of the

data, respectively.

9. When data are normally distributed, approximately 68 percent lie within one standard deviation, 95

percent within two standard deviations, and 99 percent within three standard deviations of the mean.

10. Common measures of central tendency in market analysis are the mean, median, and mode.

11. Two common measures of dispersion in market analysis are the range and the standard deviation.

12. Cross-tabulation shows the relationship between two qualitative variables or grouped quantitative

variables.

13. Correlation analysis quantifies the degree of linear relationship between two variables.

14. Polygons also called line charts can be used to show several variables simultaneously.

15. The analysis of a continuous variable with two qualitative variables can be accomplished using

contingency tables or three-dimensional plots.

16. One of the most common statistical tests that is used to determine whether the mean equals a given

value is the t-test.

17. In testing variables, two primary statistical tests can be used. However, a parametric test assumes

that the data are normally distributed, while a non-parametric test requires no assumption about the

distribution of the data.

18. A polygon plots summary statistics for a continuous variable against a second or third variable.

19. Confidence intervals are valuable to assessors, because they provide meaningful information about

the probable range of the true measures of central tendency.








Chapter 4 | Ratio Studies

Exercise 4-1: Calculating Measures of Central Tendency – Solution

Sale

Number

Appraised

Value

Sale Price Ratio

4 $ 90,000 $120,000 0.75

3 $79,900 $94,000 0.85

2 $82,800 $92,000 0.90

7 $95,000 $100,000 0.95

5 $102,900 $98,000 1.05

6 $109,200 $104,000 1.05

1 $126,500 $110,000 1.15

TOTALS $686,300 $718,000 6.70

Mean Ratio: 6.70 ÷ 7 = 0.957

Median Ratio: 0.950

Weighted Mean Ratio: 686,300 ÷ 718,000 = 0.956








Exercise 4-2: Calculating the Coefficient of Dispersion – Solution

Use the data from Exercise 4-1 and compute the coefficient of dispersion based on the median ratio.

Sale

No. Ratio

Median

Ratio

Average Absolute

Deviation

4 0.75 0.95 0.20

3 0.85 0.95 0.10

2 0.90 0.95 0.05

7 0.95 0.95 0.00

5 1.05 0.95 0.10

6 1.05 0.95 0.10

1 1.15 0.95 0.20

--- --- --- 0.75

Averaged Absolute Deviation: 0.75 ÷ 7 = 0.107

Coefficient of Dispersion: (0.107 ÷ 0.95) × 100 = 11.26%








Exercise 4-3: Calculating the Coefficient of Variation – Solution

SALE

NO. RATIO

DIFF.

FROM

MEAN

DIFF.

SQUARED

SALE

NO. RATIO

DIFF.

FROM

MEAN

DIFF.

SQUARED

1 0.79 -0.17 0.0289 11 0.97 0.01 0.0001

2 0.88 -0.08 0.0064 12 0.70 -0.26 0.0676

3 1.06 0.10 0.0100 13 0.75 -0.21 0.0441

4 1.15 0.19 0.0361 14 1.02 0.06 0.0036

5 0.99 0.03 0.0009 15 1.05 0.09 0.0081

6 0.99 0.03 0.0009 16 1.12 0.16 0.0256

7 0.90 -0.06 0.0036 17 1.20 0.24 0.0576

8 0.96 0.00 0 18 1.15 0.19 0.0361

9 0.85 -0.11 0.0121 19 1.05 0.09 0.0081

10 0.75 -0.21 0.0441 20 0.95 -0.01 0.0001

TOTAL 0.3940

Standard deviation: 0.3940 ÷ 19 (n-1) = 0.0207

√𝟎. 𝟎𝟐𝟎𝟕 = 0.144

Coefficient of variation: (0.144 ÷ 0.96) × 100 = 15.00%








Exercise 4-4: Calculating Sales Ratio Statistics – Solution

SALE NO. SALE RATIO

ARRAYED MEDIAN

ABSOLUTE

DEVIATION

MEDIAN

MEAN DEVIATION DEVIATION

SQUARED

4 0.70 0.98 0.28 0.95 -0.25 0.0625

9 0.75 0.98 0.23 0.95 -0.20 0.0400

7 0.79 0.98 0.19 0.95 -0.16 0.0256

5 0.90 0.98 0.08 0.95 -0.05 0.0025

1 0.97 0.98 0.01 0.95 +0.02 0.0004

10 0.99 0.98 0.01 0.95 +0.04 0.0016

3 1.02 0.98 0.04 0.95 +0.07 0.0049

8 1.06 0.98 0.08 0.95 +0.11 0.0121

2 1.12 0.98 0.14 0.95 +0.17 0.0289

6 1.20 0.98 0.22 0.95 +0.25 0.0625

TOTAL 9.50 ---- 1.28 TOTAL ---- 0.2410

Mean: 9.50 ÷ 10 = 0.95

Median: (0.97 + 0.99) ÷ 2 = 0.98

Weighted mean: 952,750 ÷ 1,025,000 = 0.93 (rounded)

Coefficient of dispersion: 1.28 ÷ 10 = 0.128 (Average Absolute Deviation)

(0.128 ÷ 0.98) × 100 = 13.06%

Coefficient of variation: 0.2410 ÷ 9 = 0.0268

√0.0268 = 0.1637 (SD)

(0.1637 ÷ 0.95) × 100 = 17.23%

Price-related differential: 0.95 ÷ 0.93 = 1.02 (rounded)









1. List three uses for ratio studies:

Testing compliance with legal or administrative standards

Identifying groups of properties requiring reappraisal or adjustments

Evaluating the effectiveness of various appraisal procedures

Monitoring the work of individual appraisers

Gauging the merit of taxpayer appeals

2. The preferred measure of assessment level in most ratio studies is the median.

3. Which measure of the central tendency weights each ratio in proportion to its sale price?

the weighted mean

4. The coefficient of dispersion (COD) is the most widely used measure of uniformity in ratio studies.

5. The IAAO standard for the coefficient of dispersion (COD) for residential properties is between 5 and

10 for properties in newer relatively homogeneous areas and between 5 and 15.0 in older

heterogeneous areas.

6. The coefficient of variation (COV) expresses the standard deviation as a percentage, making

comparisons among groups easier.

7. The predictive power of the coefficient of variation (COV) depends on the extent the data are

normally distributed.

8. A scatter diagram depicting the relationship between sales ratio and effective age that portrays a

downward sloping trend indicates a negative correlation which reflects lower ratios for older

residences.

9. The price-related differential (PRD) is calculated by dividing the mean by the weighted mean.

10. PRDs greater than 1.03 indicate relative under appraisal of higher value parcels while PRDs less than

0.98 indicate relative over appraisal of higher value parcels.

11. The price-related differential relates to equality between lower and higher value parcels.








Chapter 5 | Cost Approach


1. In the cost approach model, construction costs represent the supply side of the market, while

depreciation represents the demand side of the market.

2. The first step in specifying cost models is to stratify improvements into homogeneous groups.

3. In developing a cost table, a scatter diagram is used to develop the relationship between the cost

per square foot and area.

4. Adjustments for variations from base specifications in the cost model can take the form of

multipliers, dollars per square foot, other per unit costs, or lump sum dollar costs.

5. List three types of sales that should be excluded when deriving depreciation schedules from the

market:

Mixed-use parcels

Parcels with additional buildings

Parcels with extreme land-to-building ratios

6. After plotting percent good or accrued depreciation against effective age, a curve can be fitted to the

data using any one of the following three ways:

Visually by hand

Using graphics software

Using multiplicative or nonlinear MRA

7. Market calibration of cost models is best accomplished by using ratio studies or through multiple

regression analysis (MRA).

8. The cost approach attempts to replicate the workings of the real estate market, since the current cost

of construction represents the supply side and depreciation and variations in location represent the

demand side of the market.

9. In the following cost model V = GQ [LV + (RCN-D)], GQ represents general qualitative factors.

10. In structuring models for commercial properties, stratification is usually based on structure type and

number of floors.

11. For commercial properties, construction costs are usually divided between structural and interior

costs.

12. In the following cost model, V = πGQ × [1-BQD) × RCN +LV], the symbol BQD represents

depreciation.

13. To calibrate a model to produce Replacement Cost New (RCN), replacement costs must include all

direct and indirect costs.

14. Cost schedules should be tested to ensure that estimated costs are consistent with actual (local)

costs.




15. Formula-driven cost models are an equation that expresses additive adjustments as multipliers.

16. In developing building depreciation schedules, percent good or accrued depreciation is plotted

against effective age.


Quiz 1 – Solutions Set 41


Quiz 1 Solutions

1. Scalar values are best centered on 1.00 in:

A. Additive models

B. Multiplicative models

C. Hybrid models

D. All of the above

2. Which of the following statistical techniques would be most appropriate for

grouping similar subdivisions for modeling purposes?

A. Multiple regression analysis

B. Location Value Response Surface Analysis

C. Adaptive estimation procedure

D. Cluster analysis

3. Assume that the average age of homes in a neighborhood is 25 years and that the

standard deviation is 3 years. Assuming the data are normally distributed,

approximately 95% of the homes will fall in what age bracket?

A. 22-26

B. 22-28

C. 19-31

D. 16-34




4. A scatter diagram shows that there is a loose negative correlation between sale

price and distance to the central business district. Which of the following

correlation coefficients would be consistent with the scatter diagram?

A. Zero

B. -2.00

C. -.20

D. .50

5. Which of the following best defines the coefficient of dispersion (COD)?

A. Average deviation from the chosen measure of central tendency

B. Standard deviation of the ratios expressed as a percentage of the mean

C. The range which contains 50 percent of the ratios

D. Average percentage deviation from the median

6. The IAAO standards for the COD for older, heterogeneous residential property is:

A. 5.0 or less

B. 10.0 or less

C. 15.0 or less

D. 20.0 or less




7. Assessors need skills in single property appraisal to:

A. Develop valuation models

B. Test values

C. Defend values

D. All of the above

8. In a statistical test, the statement or conclusion that is accepted in the absence of

sufficient evidence to the contrary is known as the:

A. First hypothesis

B. Alternative hypothesis

C. Confidence level

D. Null hypothesis

9. Consider the following ratios: .89, .96, 1.08, 1.14, and 1.20. What is the coefficient of

variation (COV)?

A. 10.6

B. 11.4

C. 12.1

D. 13.3

10. In the cost approach model, construction costs represent the ____________ side of

the market and depreciation represents the _____________ side of the market.

A. demand - supply

B. supply - demand

C. supply – supply

D. demand - demand




11. The cost approach is closely related to a/an:

A. Additive model structure

B. Multiplicative model structure

C. Hybrid model structure

D. Least square model structure

12. Which of the following is not one of the seven major steps in the mass appraisal

process?

A. Preliminary survey and analysis

B. Defend value estimates

C. Valuation

D. Correlation of values, model testing, and quality control

13. _________________________ is the process of quantifying and evaluating the reliability

of value estimates by comparing values to a representative sample of sales.

A. Model specification

B. Model calibration

C. Model testing

D. Model infusion

14. In modern price theory, which of the following is not a determinant of demand?

A. Consumer incomes

B. Price of related commodities

C. Consumer expectations

D. Availability and cost of goods used in the production process




15. The following model structure: V = b0 + (b1*1) + (b2*X2) + (b3*X3)...

is what type of model?

A. Additive

B. Multiplicative

C. Hybrid

D. None of the above

16. Which of the following is the most effective but expensive means of collecting

income and expense data?

A. Mail questionnaire

B. Personal interview

C. Telephone

D. Assessment appeals

17. In a net lease the owner pays:

A. All expenses

B. Only operating expenses

C. A pre-specified percentage of operating expenses

D. No operating expenses

18. A lease indexed to the Consumer Price Index is an example of:

A. A percentage lease

B. An adjustable lease

C. A graduated lease

D. A net lease




19. Interactive effects, in which the impact of certain property characteristics upon

value is interrelated, are best handled by:

A. Additive MRA

B. Stepwise MRA

C. Exponential transformations

D. Multiplicative and quotient transformations

20. Which of the following can best be used to present visually the contents of a

frequency distribution?

A. Array

B. Bar chart (histogram)

C. Scatter diagram

D. Box plot

21. The IAAO Standard on Ratio Studies calls for a price-related differential in what

range?

A. 0.95 to 1.05

B. 0.95 to 1.10

C. 0.98 to 1.03

D. 0 to 0.15

22. Costs used in mass appraisal are typically:

A. Reproduction costs

B. Replacement costs

C. Historical costs

D. Trended historical costs




23. Which of the following does not apply to the development of depreciation tables?

A. Use only arm's-length sales

B. Exclude parcels with extreme land-to-building ratios

C. Include mixed-use parcels

D. Exclude parcels with additional buildings

24. In the market calibration of cost models, market adjustments can be developed

using ratio studies by:

A. Construction class

B. Size

C. Age groups

D. All of the above








Chapter 6 | Sales Comparison Approach

Exercise 6-1: Calculating an Additive Model – Solution

Characteristics of the subject property:

Main living area 1,800 square feet

Finished basement area 1,200 square feet

Unfinished basement area 400 square feet

Garage area 528 square feet

Grade 3

Fireplace 1

Effective age 20

Location Neighborhood 2

Determine a value for the subject property by using the model given in Practical Application 6-1.

Then:

V = 20,965 + (43.19 × 1,800) + (22.96 × 1,200) + (10.04 × 400) + (19.40 × 528) + (6,444 × 3) +

(3,900 × 1) – (798 × 20) – (5,679 × NBHD2)

V = 20,965 + 77,742 + 27,552 + 4,016 + 10,243 +19,332 + 3,900 – 15,960 – 5,679 = $142,111

V = $142,111 (or $142,100 when rounded)








Exercise 6-2: Calculating a Multiplicative Model – Solution

Characteristics of the subject parcel:

Main living room 2,040 square feet

Finished basement 1,600 square feet

Unfinished basement 440 square feet

Garage 480 square feet

Fireplace 1

Quality grade 4

Effective age 15

Neighborhood 3

Use the model in Practical Application 6-2 to determine a value for the subject property.

Then:

EFFSQFT = 2,040 + (0.66 × 1,600) + (0.33 × 440) + (0.45 × 480) = 3,457

LINGRADE = 1.25

PCTGOOD = 1 - (15 ÷ 100) = 0.85

Value of subject parcel:

V = 59.49 × 34570.986 × 1.251.072 × 1.0521 × 0.850.680 × 1.1041

V = 59.49 × 3,084 × 1.27 × 1.052 × 0.895 × 1.104

V = $242,198 (or $242,200 when rounded)








Exercise 6-3 Calculating a Hybrid Model – Solution

The subject parcel has the following characteristics:

Main living room 1,500 square feet

Finished basement 800 square feet

Unfinished basement 700 square feet

Garage 440 square feet

Quality grade 2

Effective age 30 years

Neighborhood 2

Lot size 7,200 square feet

Use the model given in Practical Application 6-3 to determine a value for the subject property.

Then:

LINGRADE = 0.80

PCTGOOD = 1 - (30 ÷100) = 0.70

Value of subject parcel:

V = 0.9331 × 1.1220 × [((.80.977 × 0.70.895) × (39.16 × 1,500) + (24.11 × 800) + (12.98 × 700))) +

(24.99 × 0) + (24.99 × 440) + (1.29 × 7,200))]

V = 0.933 × [(.5843 × (58,740 + 19,288 + 9,086)) + (10,996 + 9,288)]

V = 0.933 × ((.5843 × 87,114) + 20,284)

V = 0.933 × (50,901 + 20,284)

V = 0.933 × 71,185

V = $66,416 (or $66,400 when rounded)








Exercise 6-4: Classification of Model Structure – Solution

1. Multiplicative

2. Hybrid

3. Additive

4. Hybrid

5. Multiplicative

6. Additive

7. Hybrid

8. Multiplicative








Exercise 6-5: Measures of Goodness of Fit – Solution

1. 71.3 percent (as indicated by R-square)

2. COV = SEE ÷ Average value of Dependent Variable

3. $22.24 per square foot or 41.0%

4. Fair








Exercise 6-6: Measures of Variable Importance – Solution

1. All the variables are significant at the 95% confidence level except LOTSIZE, PATIO, NBHD02, and

SITEAMEN.

2. An approximate 95 percent confidence interval for FIREPL can be computed as follows:

Lower 95% limit = 3402.099 - 2 × 654.902 = 2,092

Upper 95% limit = 3402.099 + 2 × 654.902 = 4,712

3. The three variables that have the greatest percentage impact on sale price, based on their beta values,

are SQFEET, QUAL, and NBHD05.








1. No, it must first be converted to log format.

2. ln(SP)

3. ln(SQFT), ln(LINGRAD), ln(PCTGOOD), ln(LINHEAT), DOWNTOWN, CORNER

4. DOWNTOWN and CORNER

5. ex Where: e = base e

and x = 4.312

e4.312 or Exp (4.312) = 74.59

6. Yes (since b1 < 1.00)

7. Too much (since b3 < 1.00)

8. ex Where: e = base e

and x = 0.233

e.233 or Exp (.233) = 1.262

9. Yes (since b6 > 0)

10. SP = 74.59 × SQFT.977 × LINGRAD1.067 × PCTGOOD.751 × HEATING1.209 × 1.262DOWNTOWN ×

1.103CORNER

Exercise 6-7: Calibrating and Interpreting Multiplicative Models – Solution








General qualitative = πGQ = 1.07

Building qualitative = πBQ = 1.08 × 1.12 = 1.2096

Building additive = ΣBA = (35.24 × 1,620) + (510 × 8) + (3,400 × 2) = 67,969

Land qualitative = πLQ = 1.15 × 1.00 = 1.15

Land additive = ΣLA = 1.43 × 9,000 = 12,870

Market value = πGQ × (πBQ × ΣBA + πLQ × ΣLA)

Market value = 1.07 × [(1.2096 × 67,969 + 1.15 × 12,870)] = $103,806

Building value = 1.07 × 1.2096 × 67,969 = $87,970

Land value = 1.07 × 1.15 × 12,870 = $15,836

Exercise 6-8: Estimating Value Using Feedback – Solution








ATTRIBUTE SUBJECT

PROPERTY

SALE

PROPERTY DIFFERENCE

STANDARD

DEVIATION

Living area 1500 1660 -160 225.7

Age 8 4 4 4.1

Quality class 4 5 -1 0.9

ATTRIBUTE STANDARDIZED

DIFFERENCE

APPRAISER

ASSIGNED

WEIGHT

WEIGHTED

STD. DIFF.

SQUARED

WEIGHTED

STD. DIFF.

Living area -0.71 2 -1.42 2.02

Age 0.98 1 0.98 0.96

Quality class -1.11 1 -1.11 1.23

Sum 4.21

The metric value for this property is 4.21.

Exercise 6-9: Comparable Sales Algorithm – Solution









1. In mass appraisal, the sales comparison approach uses either the additive, multiplicative, or hybrid

model formats to arrive at final value estimates.

2. Multiple regression analysis (MRA) is a statistical technique for estimating unknown data based on

known and available data.

3. In regression statistics, the t-value is the ratio of a regression coefficient to its standard error (the

higher the ratio, the more significant the variable).

4. In an additive MRA model, bo represents the constant and X1 X2 ... XP represent the independent

variables.

5. The successful application of MRA models in mass appraisal require accurate property

characteristics data, adequate sales, good model building skills and variables to capture significant

location influences.

6. The regression statistic R-square is the percentage of the variation in sales price explained by the

model.

7. In regression statistics, the standard deviation of the regression error is termed the standard error of

estimate (SEE).

8. List three strengths and three limitations to feedback.

Strengths Limitations

Calibrates the generic model directly Lacks the rich diagnostics of MRA

Not overly affected by outliers Algorithms are proprietary and not

completely documented

Provides separate land and building values Software is relatively limited

9. Automated comparable sales provide a method of finding a given number of sales most comparable

to the subject parcel. It is based on a comparable sale algorithm. The user must be able to determine

the:

Sales to be searched

Variables used to define comparability

Relative weight given to each variable

10. The basic structure of the sales comparison model is V = Sc + ADJc.

11. An additive model structure for income properties in the sales comparison approach is V/UNIT = b0 +

(b1 × X1) + (b2 × X2) + (b3 × X3)...

12. In multiplicative models, in the sales comparison approach for income properties, sales prices are

converted to logarithms before calibration, making a per unit transformation unnecessary.

13. When calibrating an additive model, in the sales comparison approach for income properties, the

dependent variable is usually expressed on a per unit basis.




14. List four requirements for effective MRA mass appraisal models.

Accurate property characteristics data

Location and proximity data

Adequate sales

Good modeling procedures

15. In regression statistics, the adjusted R-square adjusts for degrees of freedom providing an unbiased

estimate of R-square.

16. List five measures of variable importance that can be considered in regression analysis.

Coefficient of correlation

Correlation matrix

t-value

F-value

Beta-value

17. List five advantages of multiplicative MRA for income properties:

Captures interactive affects

Captures nonlinearities

Makes percentage adjustments

Taking logarithms reduces the span of the dependent variables

Retains the use of additive MRA for calibration purposes




Chapter 7 | Income Approach

Exercise 7-1: Gross Rent Per Unit – Office Buildings – Solution

BLDG.

NO.

GROSS

RENT/S.F. MEDIAN

ABSOLUTE

DIFF. MEAN DIFF. DIFF. SQ.

2 $16.00 $19.50 $3.50 $19.30 $3.30 $10.89

6 $17.00 $19.50 $2.50 $19.30 $2.30 $5.29

5 $17.50 $19.50 $2.00 $19.30 $1.80 $3.24

1 $18.50 $19.50 $1.00 $19.30 $0.80 $0.64

3 $19.00 $19.50 $0.50 $19.30 $0.30 $0.09

10 $20.00 $19.50 $0.50 $19.30 $-0.70 $0.49

4 $20.50 $19.50 $1.00 $19.30 $-1.20 $1.44

8 $21.00 $19.50 $1.50 $19.30 $-1.70 $2.89

9 $21.50 $19.50 $2.00 $19.30 $-2.20 $4.84

7 $22.00 $19.50 $2.50 $19.30 $-2.70 $7.29

$193.00 $17.00 $37.10

The mean and median are very close. The median is the best choice since it is not influenced by the

extremes. The standard deviation shows about a $2.00 variation away from the mean. The COD indicates

an 8.72% variation from the median or about $1.70 per square foot. The reliability of the suggested gross

rent is good since the mean and median are close and all indications of variation are low.

Median $19.50 (19.00 + 20.00) ÷ 2

Mean $19.30 (193.00 ÷ 10)

Average Absolute Deviation $1.70 (17.00 ÷ 10)

Standard Deviation 2.03 Sqrt. of (37.10 ÷ 9)

Coefficient of Dispersion (COD) 8.72 (1.70 ÷ 19.50) × 100








Exercise 7-2: Gross Rent Per Unit – Retail Store – Solution

Rents per square foot stratified by square foot area. (There is no consistent pattern relative to age.)

BLDG.

NO.

SQFT

AREA

RENT

PER SF

BLDG.

NO.

SQFT

AREA

RENT

PER SF

BLDG.

NO.

SQFT

AREA

RENT

PER SF

2 7,000 $16.00 1 11,200 $11.75 19 17,500 $7.75

6 7,700 $15.50 4 11,900 $11.50 3 18,200 $7.50

11 8,400 $15.00 13 12,600 $11.25 12 19,600 $7.25

15 9,100 $15.00 7 13,300 $11.00 18 20,300 $7.00

17 9,800 $14.75 16 14,000 $10.75 5 21,000 $6.75

8 10,500 $14.25 10 15,400 $10.50 14 22,400 $6.50

20 16,100 $10.25 9 23,800 $6.25

Median 15.00 Median 11.00 Median 7.00

Mean 15.08 Mean 11.00 Mean 7.00

Standard deviation 0.61 Standard deviation 0.54 Standard deviation 0.548

Typical gross rent $15.00 sqft Typical

gross rent $11.00 sqft

Typical

gross rent $7.00 sqft

In each case, the mean and median are the same or very close, indicating no outliers. In addition, the

standard deviation indicates a variation of just over $0.50 for two-thirds of the rents. Therefore, the

stratification by size has produced a reliable indicator of the typical rent per square foot.








Exercise 7-3: Developing Gross Income Multipliers (GIMs) – Solution

Properties Arrayed by GIM

SALE

NO.

SALE

PRICE

GROSS

INCOME

EFF AGE

GIM

MEDIAN

ABS DEV

12 $280,000 $48,700 35 5.75 7.13 1.38

11 $264,000 $44,000 34 6.00 7.13 1.13

9 $372,000 $59,520 34 6.25 7.13 0.88

4 $320,000 $49,230 32 6.50 7.13 0.63

2 $272,000 $40,300 32 6.75 7.13 0.38

1 $256,000 $36,550 25 7.00 7.13 0.13

7 $432,000 $59,590 24 7.25 7.13 0.12

5 $336,000 $44,800 22 7.50 7.13 0.37

3 $360,000 $46,450 20 7.75 7.13 0.62

6 $304,000 $38,000 13 8.00 7.13 0.87

8 $248,000 $29,180 12 8.50 7.13 1.37

10 $310,000 $35,430 10 8.75 7.13 1.62

9.50

Median 7. 13

Mean 7.17

COD 11.11 (9.50 ÷ 12 = 0.792) (0.792 ÷ 7.13 × 100 = 11.11)

Although the mean and median are very close, there is a greater than 10% spread as indicated by the

COD. Stratifying the GIMs by age groups (10 to 19, 20 to 29, and 30 to 39) would produce the following:

GROUP 1

30–39

GROUP 2

20–29

GROUP 3

10–19

Mean 6.25 7.38 8.42

Median 6.50 7.38 8.50

COD 4.80 3.39 2.94

In each case, the mean and median remain the same or close. However, the COD has dropped

significantly. Therefore, there is a greater amount of reliability in the GIM, if it is selected based on this age

grouping.








Exercise 7-4: Interpreting a GIM Model – Solution

1. 4.815 + 0.566 + 0.442 – (Sq. root of 20,000) × 0.004673)

4.815 + 0.566 + 0.442 – 0.661 = 5.162

2. Area 04

3. Decrease (as indicated by the negative coefficient for SQRSIZE)

4. 2 × 0.566 = 1.132

5. AGE did not enter the model because the condition variables (COND-GD and COND-PR) account

for effective age.

6. 65.97% (R-Square)

7. 100 × (.83961 ÷ 4.975) = 16.9








Exercise 7-5: Expense Ratio Analysis – Solution

Apartment Buildings

CMPLEX

NO

AGE

EXP RATIO

ARRAYED

CMPLEX

NO

AGE

EXP RATIO

ARRAYED

84 25 20.5 44 39 38.0

34 20 35.0 140 31 42.1

312 21 35.5 38 37 43.2

20 23 36.0 91 31 44.4

66 24 36.3 65 34 45.3

122 29 38.2 85 32 46.0

72 23 42.5 75 36 65.0

Median 36.0 Median 44.4

Mean 34.8 Mean 46.3

Trimmed mean 36.2 Trimmed mean 44.2

Standard dev: 6.83 Standard dev: 8.67

Standard dev:

(Trimmed mean)

1.22

Standard dev:

(Trimmed mean)

1.57

CMPLEX

NO

AGE

EXP RATIO

ARRAYED

19 45 38.5 Median 52.0

300 47 50.0 Mean 53.9

89 42 51.2 Trimmed mean 52.4

37 41 52.0 Standard dev: 11.37

130 48 53.5 Standard dev:

(Trimmed mean)

2.06

95 43 55.3

71 47 76.5

Excluding the outliers provides a mean that is close to the median. In addition, the standard deviation

drops significantly with the elimination of the outliers. This ensures the reliability of the estimated typical

expense ratio.








Exercise 7-6: Retail Expense Ratio Model – Solution

1. A fair grade retail store with an effective age of 10 years, in REGION 1 has an expense ratio of

47% .

0.333099 + (-1 × -0.045630) + (10 × 0.002952) + 0.058028 = 0.466277

2. A very good grade retail store with an effective age of 3 years, in REGION 6 has an expense ratio

of 23% .

0.333099 + (2 × -0.045630) + (3 × 0.002952) - 0.023731 = 0.226964

3. An average grade retail store with an effective age of 12 years, in REGION 4 has an expense ratio

of 37% .

0.333099 + (0 × -0.045630) + (12 × 0.002952) = 0.368523

4. Which location variable has the lowest significance? REGION4

5. Which location variable is used as the reference location variable? REGION3

6. The coefficient of variation for the model is 7.48% .

0.02639 ÷ 0.35270 = 0.0748228 × 100 = 7.48228

7. What is the confidence level for the REGION5 variable? 98%

1 - 0.0197 = 0.9803








Exercise 7-7: Calculating a Vacancy Ratio – Solution

Eight centers arrayed by vacancy ratio:

PARCEL NUMBER

SQUARE FEET

NET LEASABLE

AREA

SQUARE FEET

CURRENT VACANT

AREA

VACANCY

RATES

4632-193-05-122 95,000 2,850 0.030

4632-061-01-072 86,000 3,440 0.040

4632-262-28-012 86,000 3,870 0.045

4632-124-02-013 88,000 4,225 0.048

4632-291-12-112 85,000 4,420 0.052

4632-082-18-030 90,000 4,950 0.055

4632-144-14-056 92,000 5,520 0.060

4632-301-10-090 91,000 13,650 0.150

Minimum 0.030

Maximum 0.150

Range 0.120

Median 0.050

Mean 0.060

Trimmed mean 0.050

Selected vacancy ratio 0.050








Exercise 7-8: Evaluating OARs – Solution

1. The following do not fit the expected pattern:

a) Class A building in declining areas (only 2 sales)

b) Class B building in appreciating areas (4 sales)

2. OARs for these two strata could be changed to numbers that fall in the following ranges:

a) 0.150–0.160

b) 0.135–0.140








Exercise 7-9: Example of OAR Model – Solution

1. (0.02031 ÷ 0.1033) × 100 = 19.7

2. -0.020 to +0.020

3. LINGRADE, CONVERSN, NBHD102

4. EFFAGE, NBHD105, SQRUNITS

5. OAR = 0.09980 + 0.00039 × 15 - 0.00571 + 0.00117 × 8 = 0.109









1. When estimating market rents either potential or effective gross income is used.

2. One of the characteristics by which properties are grouped is location.

3. One of the modeling considerations for gross income models is that the dependent variable is on a

per unit basis.

4. The two basic methods of developing GIMs are stratification and multiple regression.

5. GIM = sale price divided by gross income.

6. The reliability of GIMs developed through stratification is evaluated by examining:

Sample size

Measures of dispersion

Consistency among strata

7. The two basic methods for developing per unit rents, expense ratios, GIMs, and OARs are

stratification and multiple regression.

8. OAR = net income divided by sale price (value).

9. Potential gross income less vacancy and collection losses equals effective gross income.

10. The dependent variable in the gross income model is gross income per unit.

11. The dependent variable in a GIM model is sale price/gross income.

12. The dependent variable in an OAR model is net income/sale price.

13. The measure of goodness-of-fit that is used in direct sale price models but is less useful in income

models is R-square.

14. Vacancy and collection losses reflect typical management.




15. Consider the following ten expense ratios:

0.112 0.375

0.156 0.401

0.231 0.455

0.277 0.570

0.327 0.732

A. Compute the median and trimmed mean ignoring the two lowest and two highest values.

Median: (0.327 + 0.375) ÷ 2 = 0.351

Trimmed mean: (0.231 + 0.277 + 0.327 + 0.375 + 0.401 + 0.455) ÷ 6 = 0.34

B. Calculate the COD of the 10 ratios.

Ratio Abs Dev

0.112 0.239

0.156 0.195

0.231 0.120

0.277 0.074

0.327 0.024

0.375 0.024

0.401 0.050

0.455 0.104

0.570 0.219

0.732 0.381

______

Sum 1.430

COD = 100 × (1.430 ÷ 10) / 0.351 = 40.7




C. Calculate the standard deviation and COV about the trimmed mean (ignoring the two highest and

lowest values).

Ratio Dev from Trimmed

Mean

Dev

Squared

0.231 -0.113 0.0128

0.277 -0.067 0.0045

0.327 -0.017 0.0003

0.375 0.031 0.0010

0.401 0.057 0.0032

0.455 0.111 0.0123

Sum 0.341

STD DEV = SQRT (0.0341 ÷ 5) = 0.0825

COV = 100 × (0.0825 ÷ 0.344) = 24.0








Chapter 8 | Value Review and Maintenance

Exercise 8–1: Interpretation of Sales Ratio Results – Solution

Neighborhoods 500 and 501:

• Within an acceptable range; do not require further attention.

Neighborhood 502:

• The median is below the acceptable range. In addition, the PRD of 1.07 indicates an under

valuation of higher value properties.

• If the cost approach was used, this may indicate a problem with the depreciation table.

• If the sales comparison approach was used, this may indicate a problem with the sales model or

the sales base used to develop the values.

Neighborhood 503:

• Shows a median that is outside the range. The COD is acceptable; therefore, this neighborhood

could be trended.

Neighborhood 504:

• There is a problem with both the median and the COD. In addition, the PRD of 1.04 suggests that

there may be a slight bias toward high value properties. A field review is necessary for this

neighborhood to ensure correct physical characteristics are in the database.









1. Pilot studies are used when implementing a new CAMA system or valuation techniques, because

they provide a test on a sample or test area.

2. Once preliminary values are produced, an office review is an essential first step in quality control.

3. Sales ratio studies are one of the best tools to measure the quality of new appraised values during

the review process.

4. List three items that are required for an effective field review.

Assessment maps

Property record cards

Valuation reports

5. List three aspects of value acceptability.

Accuracy

Stability

Explainability

6. Two goodness-of-fit statistics used to evaluate accuracy when using multiple regression are:

R-square

Standard error of estimate

7. List three steps that are used to promote a greater understanding of multiple regression

other than conversion to the base home approach.

Simplified models

Stepwise MRA

Constrained MRA

8. List four update strategies that are typically used by an assessor’s office.

Full recalibration

Cyclical recalibration with interim adjustments

Partial recalibration

Use of previous year’s values








Quiz 2 Solutions

1. V = bo + '(b1 * Xl) + (b2 * X2) + (b3 * X3) ... is an example of a/an model structure for

the sales comparison approach.

A. Additive

B. Hybrid

C. Multiplicative

D. Adaptive Estimation

2. Consider the following regression statistics:

N=349

Adjusted R-Square = .879

Standard Error of Estimate (SEE) = 9800

Average sale price = $100,000

On a percentage basis, approximately two-thirds of the regression errors would fall

within what range:

A. -9.8% to +9.8%

B. -12.1% to +12.1%

C. -19.6% to +19.6%

D. 0% to 12.1%

3. In regression statistics, the most accurate measure of the percentage of variation in

sales prices explained by the model is the

A. R-square

B. Adjusted R-square

C. Standard Error of Estimate (SEE)

D. Coefficient of variation




4. In regression statistics, the ____________________ is the ratio of a regression

coefficient to its standard error (the higher the ratio, the more significant the

variable).

A. R-square

B. Adjusted R-square

C. Standard Error of Estimate (SEE)

D. t-value

5. In multiple regression analysis, _______________ represents the difference between

actual and predicted sales prices.

A. Standard error of estimate

B. Coefficient of variation

C. Residuals


6. Which of the following employs the Euclidean distance metric:

A. Automated comparable sales

B. Location value response surface analysis

C. Adaptive estimation procedure

D. Multiplicative MRA

7. During the office review of values, the reasonableness, consistency and credibility of

values can be gauged through:

A. Ratio studies

B. Benchmark values

C. Average change in values

D. All of the above




8. Materials required for an effective field review of values include:

A. Assessment maps and property record cards

B. Sales ratio reports

C. Average value change reports

D. All of the above

9. Aspects of value acceptability are:

A. Accuracy

B. Stability

C. Explainability

D. All of the above

10. Which of the following maximizes accuracy versus stability?

A. Full recalibration

B. Cyclical recalibration with interim adjustments

C. Partial recalibration

D. All of the above




11. In mass appraisal, multiple regression analysis (MRA) works on the principle of:

A. Passing the sales file multiple times until the process stabilizes and the

coefficients converge on their "optimal" values

B. Minimizing the sum of the absolute errors between actual sales prices and

predicted prices

C. Minimizing the squared errors between actual and predicted sales prices

D. Finding the best comparables through a predefined metric (e.g., Euclidean

distance metric) and adjusting the comparables to the subject

12. The ________________________ model is the most flexible model structure; however, it

is the most difficult to calibrate.

A. Additive model

B. Multiplicative model

C. Hybrid model


13. When modeling income properties, sample sizes can best be expanded by:

A. Extending the period from which sales are drawn

B. Combining property types

C. Using non-market sales

D. Supplementing sales with prior year values




14. Which of the following is the most appropriate calibration tool for a multiplicative

model?

A. Additive MRA

B. Feedback

C. Nonlinear MRA

D. Loglinear MRA

15. Which of the following measures the significance of independent variables in the

regression model?

A. Correlation coefficient

B. t-value

C. Adjusted R square

D. Standard Error of Estimate

16. Consider the following model:

SP/SQFT = 61.85 * SQFT.977 * PCTGOOD.652

Which of the following is true?

A. The model is hybrid in form.

B. The contribution of SQFT to value is linear.

C. The model is multiplicative in form.

D. The effect of SQFT and PCTGOOD upon value is additive.




17. Consider the following indicated gross income multipliers:

Sales Median COD

GIM

Superior Economic Area

Newer Apartments 9 6.5 10.1

Mid-Age Apartments 5 6.3 12.4

Older Apartments 3 6.0 15.6

Average Economic Area

Newer Apartments 4 6.7 17.4

Mid-Age Apartments 11 5.9 14.1

Older Apartments 2 5.4 23.6

Which of the multipliers is inconsistent with prior expectations based on appraisal

theory and thus most likely to require override?

A. The multiplier of 6.0 for older apartments in the superior economic area

B. The multiplier of 6.7 for newer apartments in the average economic area

C. The multiplier of 5.9 for mid-age apartments in the average economic area

D. The multiplier of 5.4 for older apartments in the average economic area




18. In developing gross income models for a large metropolitan area, it would be most

important to stratify properties by:

A. Economic area

B. Size, stories, or number of units

C. Value

D. Use class

19. Which of the following is least effective in evaluating the reliability of an expense

ratio model?

A. R-square

B. Standard Error of Estimate

C. Coefficient of variation

D. Coefficient of dispersion

20. Which of the following is an important component of the field review of values?

A. Assessment maps

B. Property record cards

C. Valuation reports

D. All of the above

21. Cyclical recalibration with interim adjustments:

A. Tends to maximize accuracy

B. Tends to maximize stability

C. Sacrifices stability

D. Maintains reasonable accuracy while emphasizing stability




22. What would be the value of an office building with 2,500 square feet using the

following income model? Round to the nearest hundred dollars.

Rent $15.00/sf

Vacancy & collection loss 5%

Expenses 15%

Miscellaneous income 2%

Capitalization Rate 8%

A. $370,900

B. $378,500

C. $386,500

D. $398,400


Solutions Set



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Real Property Modeling Concepts