**Chapter 17: Statistical Analysis
in Appraisal**

**Statistical analysis is an appraiser's tool not a substitute for
judgment.**

**Statistical analysis involves six steps:**

## u Defining
the appropriate statistical procedure for the task at hand.

## u Identifying
the appropriate data population.

## u Delineating
the correct procedure for data collection.

## u Collecting
sample data from the data population.

## u Applying
the appropriate procedure to the collected data.

## u Making
judgments about the nature of the data population.

**Measures of central tendency**

## u Mean

### u Advantages:
most widely used and understood

### u Disadvantages:
effected by extreme values

## u Median

### u Advantages:

### u Disadvantages:

## u Mode

### u Advantages:

### u Disadvantages:

**Mean**

## u Formulation

_ _{i=1}

X = ∑ __X___{i}

^{ n n}

## u Keystrokes

### u Clear All

### u Enter 1st
number, press S+, display
shows 1

### u Repeat for
all other numbers, the press

_

X

**Measures of Dispersion**

**Range**

## u Formulation:

### u Lowest
value to highest value

### u Or highest
value - lowest value

## u Application

### u Quick
measure

### u Reality
based (actual observations)

**Variance**** **(σ^{2}
if a population variance or S^{2} if a sample variance)

## u Formulation:

_{ n }_

S (X_{i} - X)^{2}

^{i=1}

## u Is useful
only in the calculation of subsequent statistics

**Standard Deviation **(σ if a
population standard deviation or s if a sample standard deviation.)

## u Formulation:

_{}

_{________
}Keystrokes:

### u Clear All

### u Enter 1st
number, press S+, display
shows 1

_{u
}Repeat for all other numbers, the press

s_{x},s_{y}

**Standard Deviation (cont.)**

## u Power
application requires the assumption of a symmetrical distribution. If the distribution is not symmetrical,
there may be adjustments that can be made to compensate.

## u Special
properties

### u The mean ± 1 standard
deviation includes the “true” value about 68% of the time.

### u The mean ± 2 standard
deviation includes the “true” value about 95% of the time.

### u The mean ± 3 standard
deviation includes the “true” value about 99% of the time.

**Application of Statistical Properties**

## u Market
research indicates that the mean (expected) price for lots in a subdivision is
$20,000 with an indicated standard deviation of $1,500.

## u The
probability that the lots will sell for above $23,000 is less than 2.5%. (The probability that the “true value” is
between $17,000 and 23,000.
Consequently, the probability that the property would not bring at least
$17,000 is less than 2.5% and that it will bring above $23,000 is also less
than 2.5%.)

**Measures of Association**

## u Correlation

### u Keystrokes

### u Application

## u Linear
regression

### u Keystrokes

### u Application

## u Reliability

**Multiple Linear Regression**

## u Regression
equation

### u α +
+ β_{1}X_{1} +
β_{ 2}X_{2} + β_{ 3}X_{3} + . . .
β_{n}X_{n} + ε

### u α
coefficient (or sometimes called β_{
0}): Intercept

### u β_{
1… . }Coefficients show the marginal contribution for each variable

### u ε is the
error term

## u Regression
traps

### u Multicolinearity

### u Autocorrelation

### u Singular
matrix with dummy variables