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  = ∑ Xi
              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 2 if a population variance or S2 if a sample variance)

u  Formulation:
  n                  _
 
S (Xi - 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
sx,sy

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 + +  β1X1 + β 2X2 + β 3X3 + . . . βnXn +  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