Method for estimating the value of real property

A method for estimating the price of real property such as a single family residence. A set of real estate properties comparable to the subject property is retrieved. The comparable properties and the subject property are characterized by a plurality of common attributes each having a respective value. Each attribute value from the comparable properties are evaluated to the same attribute value of the subject property on a fuzzy preference scale indicating desirable and tolerable deviations from an ideal match with the subject property. A measurement of similarity between each comparable property and the subject property is then determined. Next, the price of the comparable properties are adjusted to the value of the subject property and the best properties are extracted for further consideration. The extracted comparable properties are then aggregated into an estimate price of the subject property.

FIELD OF THE INVENTION
 This invention relates generally to real estate appraisals and more
 particularly to a method for estimating the value of real property.
 Real estate appraisals are used to estimate the defined value of a real
 property interest in real estate. The real estate appraisals are quite
 useful in many types of real estate transactions. However, a problem with
 real estate appraisals is that they take a lot of time to perform and are
 expensive. Typically, an appraiser is sent to a subject property (i.e. a
 property to be appraised) to inspect and determine an estimate price at
 which the property would most likely sell in the market under certain
 specified conditions. In order to estimate the price, the real estate
 appraiser finds recent sales that are comparable to the subject property.
 Then the most relevant units of comparison for each sale are determined
 from the comparables. Next, the sales prices of the comparables are
 adjusted to reflect their differences from the subject property. The
 adjusted sales prices are then reconciled to the comparables in order to
 derive a single value estimate of the subject property, which is a
 reflection of the probable price that would be agreed upon between
 knowledgeable parties acting without duress in a competitive market. This
 real estate appraisal process typically takes about four days to finish,
 which may be too long in many of today's fast paced real estate
 transactions. In addition, this appraisal process does not provide much
 insight on how to select comparable properties, which often results in
 estimates that do not accurately reflect the best price. Therefore, there
 is a need for a method that speeds up the appraisal process of a subject
 property and that provides a better estimate.
 SUMMARY OF THE INVENTION
 Thus, in accordance with this invention, there is provided a
 computer-implemented method for estimating the price of a subject
 property. The method comprises retrieving a set of real estate properties
 comparable to the subject property from a case base. The comparable
 properties and the subject property are characterized by a plurality of
 common attributes each having a respective value. Each attribute value
 from the comparable properties are evaluated to the same attribute value
 of the subject property on a fuzzy preference scale indicating desirable
 and tolerable deviations from an ideal match with the subject property.
 Each evaluation generates a preference vector having a value between 0 and
 1. A measurement of similarity between each comparable property and the
 subject property is then determined. Next, comparable properties are
 extracted according to a predetermined threshold. The price of the
 extracted comparable properties are then adjusted to the value of the
 subject property by evaluating additional characteristics between the
 comparable properties and the subject property. Comparable properties are
 then extracted according to predetermined selection criteria. The
 extracted comparable properties are then aggregated into an estimate price
 of the subject property.
 While the present invention will hereinafter be described in connection
 with an illustrative embodiment and method of use, it will be understood
 that it is not intended to limit the invention to this embodiment.
 Instead, it is intended to cover all alternatives, modifications and
 equivalents as may be included within the spirit and scope of the present
 invention as defined by the appended claims.

DETAILED DESCRIPTION OF THE INVENTION
 This invention estimates the value of a subject property by using
 case-based reasoning principles. In particular, case-based reasoning is
 used to automate the steps of finding recent sales comparable to the
 subject property, determining the most relevant units of comparison,
 comparing the subject property with the comparables, adjusting the sales
 price of the comparables to reflect the differences from the subject, and
 reconciling the adjusted sales prices of the comparables to derive an
 estimate of the subject. This invention includes two modules. The first
 module is case retrieval, where recent sales of properties most comparable
 to the subject property are retrieved. The second module is case
 adaptation, where the selection of comparable properties is further
 refined and prices of these properties are then adjusted to reflect the
 differences with the subject property. Both the case retrieval and case
 adaptation modules are explained below in further detail.
 FIG. 1 is a flow chart setting forth the case retrieval and case adaptation
 operations performed according to this invention. Referring now to FIG. 1,
 an initial set of real properties that are comparable to the subject
 property are retrieved at 10. The initial set of comparable real
 properties and the subject property are both characterized by a plurality
 of common attributes each having a respective value. The attributes
 include transaction characteristics such as location of the property, date
 of sale of the property, the living area, the lot size, the number of
 bedrooms, and the number of bathrooms. Although the illustrative
 embodiment is described with reference to these attributes, it is within
 the scope of this invention to use other attributes such as type of
 construction of the property, parking spaces, location influence of the
 property, foundation of the property, the roof type and roof cover of the
 property, garage or carport, style of the property, etc. Each attribute
 value from the comparable properties is then evaluated to the same
 attribute value of the subject property and a measure of similarity is
 then generated at 12. The price of each of the comparable properties is
 then adjusted at 14 to reflect the value of the subject property by
 applying a set of modification rules. The modification rules evaluate
 additional characteristics between the comparable properties and the
 subject property and adjust the price of the property accordingly. In the
 illustrative embodiment, the additional characteristics are the number of
 fireplaces, pools, the effective age of the properties, the quality of the
 properties, and the condition of the properties. After price adjustment, a
 smaller set of more closely related comparable properties is then
 extracted at 16. The extracted comparable properties are then aggregated
 at 18 into an estimate price of the subject property. After the estimate
 price has been generated, a measurement of confidence indicating the
 reliability of the estimated value is generated 20.
 FIG. 2 shows a system 22 for performing the case retrieval and case
 adaptation operations according to this invention. The system 22 includes
 a comparable property database 24, which is preferably a case base having
 a plurality of properties. The system 22 also includes an adjustment rules
 database 26 containing rules for adjusting the prices of the comparable
 properties in the comparable property case base 24. A personal computer or
 work station 28 having a hard drive 30, an input device such as a keyboard
 32 and a mouse 34, and an output device such as a display 36 and a printer
 38, is connected to the case base 24 and the database 26. The computer 28
 uses SQL queries to retrieve the comparable properties from the case base
 24 and performs a series of case adaptation operations to the properties
 according to the adjustment rules.
 The case retrieval and case adaptation operations are shown in further
 detail in the flow diagram of FIG. 3. After information about the subject
 property has been acquired, similar comparable properties are selected at
 40 from the case base 24. In the illustrative embodiment, the case base 24
 contains about 600,000 real estate properties, with each property being
 characterized by about 166 attributes. Typically, the selection at 40
 returns anywhere from four to one hundred comparable properties. The
 selection is performed by comparing specific attributes (i.e., location,
 date of sale, living area, lot size, number of bedrooms, and number of
 bathrooms) of the subject property with the same attributes of each
 comparable properties. All of the retrieved potential comparable
 properties have values that are within allowable deviations for the
 subject property. If the size of the comparable set of properties is too
 small (e.g., less than 10), then the allowable deviations can be adjusted
 so that more comparables of lesser quality can be obtained.
 After the initial set of comparable properties has been retrieved, each of
 the values for the attributes (i.e., location, date of sale, living area,
 lot size, number of bedrooms, and number of bathrooms) are evaluated
 against the same attributes of the subject property on a fuzzy preference
 scale that indicates desirable and tolerable deviations from an ideal
 match. For example, in the illustrative embodiment, the maximum allowable
 deviations for the attributes are within one mile for the location
 attribute, 12 months for the date of sale attribute, plus or minus 25% for
 the living area attribute, plus 100% or minus 50% for the lot size
 attribute, plus or minus two percent for the number of bedrooms attribute,
 and plus or minus two percent for the number of bathrooms attribute. After
 each attribute is evaluated, a preference vector having a value between 0
 and 1 inclusive, is generated, with 1 being the best value. These values
 represent the partial degree of membership of each attribute value in the
 fuzzy sets and fuzzy relations representing the preference criteria
 provided in the fuzzy preference scales.
 An understanding of the above preference criteria for the first four
 attributes (i.e., the date of sale, the distance from subject property,
 the living area, and the lot size) is graphically described in FIG. 4.
 Each of the attributes in FIG. 4 have a trapezoidal shape representing its
 criteria evaluation functions. For each attribute, the broader base of the
 trapezoidal shape represents the range of tolerable values and corresponds
 to the interval-value used in the preliminary retrieval query. The smaller
 top or core of the trapezoidal shape represents the most desirable range
 of values. An attribute value falling inside the most desirable region
 will receive a preference value of 1. As the feature value moves away from
 the most desirable range, its associated preference value will decrease
 from 1 to 0. At the end of this evaluation, each comparable will have a
 preference vector, with each element taking values in the [0,1] interval.
 These values represent the partial degree of membership of each attribute
 value in the fuzzy sets and fuzzy relations representing the preference
 criteria provided in the fuzzy preference scales. Typically, comparable
 properties selected in the preliminary retrieval that have attribute
 values falling outside the tolerable value range will not be evaluated.
 In the illustrative embodiment, the preference distribution for the
 date-of-sale attribute for a comparable property that was sold within
 three months of the present date is 1. If the date of sale of the
 comparable property was 6 months ago, its preference value will be 0.67.
 If the date of sale of the comparable property was 9 months ago, its
 preference value will be 0.33. Any comparable property with a date of sale
 of more than 12 months is given a preference value of zero. For the
 distance from the subject property attribute, comparable properties
 located within 0.25 miles from the subject property have a preference
 value of 1. If the comparable property is located a half of a mile from
 the subject property, then its preference value will be 0.67. If the
 comparable property is located three quarters of a mile from the subject
 property, then its preference value will be 0.33. Any comparable property
 located more than one mile from the subject property is given a preference
 value of zero. For the living area attribute, a comparable property having
 a living area that is within 94% to 106% of the living area of the subject
 property will have a preference value of 1. If the comparable property has
 a living area that is within 75% to 94% or within 106% to 125% of the
 living area of the subject property, then the comparable property is given
 a preference value between zero and 1. If the comparable property has a
 living area that is less than 75% or greater than 125% of the living area
 of the subject property, then the comparable property is given a
 preference value of zero. For the lot size attribute, a comparable
 property having a lot size that is within 87.5% to 112.5% of the lot size
 of the subject property will have a preference value of 1. If the
 comparable property has a lot size that is within 50% to 87.5% or within
 112.5% to 150% of the lot size of the subject property, then the
 comparable property is given a preference value between zero and 1. If the
 comparable property has a lot size that is less than 50% or greater than
 150% of the lot size of the subject property, then the comparable property
 is given a preference value of zero. The tolerable and desirable ranges of
 values for the five attributes are illustrative of possible values for use
 with the present invention and are not intended to be limiting.
 The remaining two attributes not shown in FIG. 4, the number of bedrooms
 and the number of bathrooms, have preference functions which are
 illustrated in Tables 1 and 2, respectively. For example, if the subject
 property has five bedrooms, then Table 1 will provide a preference value
 of 1 for comparable properties having five bedrooms. However, if the
 comparable property has six or more bedrooms, then the comparable will be
 given a preference value of 0.80. Also, Table 1 indicates that a
 comparable property having four bedrooms will have a preference value of
 0.60, three bedrooms will have a preference value of 0.50, and two or less
 bedrooms will receive a preference value of zero.
 TABLE 1
 Preference Function for Number of Bedrooms
 Comparable's
 # Bedrooms 1 2 3 4 5 6+
 Subject's 1 1.00 0.50 0.05 0.00 0.00 0.00
 # Bedrooms 2 0.20 1.00 0.50 0.05 0.00 0.00
 3 0.05 0.30 1.00 0.60 0.05 0.00
 4 0.00 0.05 0.50 1.00 0.60 0.20
 5 0.00 0.00 0.05 0.60 1.00 0.80
 6+ 0.00 0.00 0.00 0.20 0.80 1.00
 Table 2 can be used in a similar manner to generate preference functions
 for the number of bathrooms attribute. For example, if the subject
 property has 2 bathrooms, then Table 2 will provide a preference value of
 1 for comparable properties having two bathrooms. However, if the
 comparable property has two and a half bathrooms, then the comparable will
 be given a preference value of 0.70. Also, Table 2 indicates that a
 comparable property having three bathrooms will have a preference value of
 0.25, three and half bathrooms will have a preference value of 0.05, four
 or more bathrooms will have a preference value of zero. In addition, Table
 2 indicates that a comparable property having one and a half bathrooms
 will have a preference value of 0.70 and one bathroom will have a
 preference of 0.1.
 TABLE 2
 Preference Function for Number of Bathrooms
 Comparable
 Subject 1 1.5 2 2.5 3 3.5 4 4.5 5+
 1 1.00 0.75 0.20 0.05 0.01 0.00 0.00 0.00 0.00
 1.5 0.60 1.00 0.60 0.25 0.10 0.05 0.00 0.00 0.00
 2 0.10 0.70 1.00 0.70 0.25 0.05 0.00 0.00 0.00
 2.5 0.05 0.20 0.75 1.00 0.75 0.20 0.05 0.00 0.00
 3 0.01 0.10 0.40 0.80 1.00 0.80 0.40 0.10 0.05
 3.5 0.00 0.05 0.15 0.45 0.85 1.00 0.85 0.45 0.30
 4 0.00 0.00 0.05 0.20 0.50 0.90 1.00 0.90 0.70
 4.5 0.00 0.00 0.00 0.10 0.30 0.70 0.95 1.00 0.95
 5+ 0.00 0.00 0.00 0.05 0.15 0.35 0.75 0.95 1.00
 After each attribute of the comparable properties has been evaluated
 against the subject property and a preference vector has been generated,
 the measurement of similarity between each comparable and the subject
 property is determined. The measurement of similarity is a function of the
 preference vector computed above and of the priorities of the attributes,
 which are reflected by a set of predetermined weights. The predetermined
 weights for the illustrative embodiment are shown in Table 3 under the
 weight column. In the illustrative embodiment, the living area attribute
 has a weight of 0.3, the date of sale and distance attributes both have a
 weight of 0.2, the lot size attributes have a weight of 0.1, while the
 number of bedrooms and bathrooms attributes have a weight of 0.05.
 The measurement of similarity for a comparable property is determined by
 multiplying the predetermined weight by the preference vector generated
 for each attribute. This product results in a weighted preference value.
 After all of the weighted preference values have been determined, the
 weighted preferences are summed together to generate the measurement of
 similarity. An example of a measurement of similarity computation between
 a comparable property and a subject property is provided in Table 3. In
 the example provided in Table 3, the subject property has a living area of
 2000 square feet, a lot size of 20,000 square feet, three bedrooms, and
 two and a half bathrooms. The comparable property was sold six months ago,
 is located 0.2 miles from the subject property, has a living area of 1800
 square feet, a lot size of 35,000 square feet, three bedrooms and two
 bathrooms. A comparison between the subject property and the comparable
 property is provided in the fourth column for each attribute. In Table 3,
 the living area comparison is 90%, the lot size comparison is 175%, and
 the number of bedroom comparison is 0%. As described above, each
 comparison results in a preference which is multiplied by the
 predetermined weight. The weighted preferences for each attribute for the
 comparable property are listed in the weighted preference column and the
 measurement of similarity is the sum of the weighted preferences. In Table
 3, the measurement of similarity for this particular comparable property
 is 0.7915.
 TABLE 3
 Computation of the Measurement of Similarity
 Weighted
 Attribute Subject Comparable Comparison Preference Weight
 Preference
 Date of Sale x 6 months 6 months 0.67 0.2 0.134
 Distance x 0.2 miles 0.2 miles 1 0.3 0.3
 Living Area 2000 1800 90% 0.79 0.3 0.237
 Lot Size 20000 35000 175% 0.33 0.1 0.033
 # Bedrooms 3 3 3 .fwdarw. 3 1 0.05 0.05
 # Bathrooms 2.5 2 2.5 .fwdarw. 2 0.75 0.05 0.0375
 Similarity 0.7915
 After the measurement of similarities have been computed for all of the
 comparable properties, the comparables are then sorted in decreasing order
 of similarity. After sorting, the comparables are arranged in a preference
 distribution as shown in FIG. 5, with the comparable property having the
 highest measurement of similarity placed at one end of the distribution
 and the comparable property having the lowest measurement of similarity
 placed at the opposite end of the distribution. The comparable properties
 are then compared against a predetermined threshold that reflects
 desirable and tolerable deviations of an ideal match with the subject
 property. More specifically, the comparable properties that have a
 measurement of similarity above the predetermined threshold will be
 extracted for further review, while the comparable properties below the
 threshold are removed from further consideration. FIG. 5 shows two
 possible similarity distributions for two different retrievals. In these
 distributions, a value of 0.5 is used as the predetermined threshold.
 Therefore, comparable properties having a measurement of similarity above
 0.5 are extracted for further review, while the comparables with
 measurements of similarities less than 0.5 are removed and no longer
 considered. In FIG. 5, retrieval number one has 11 comparable properties
 having a measurement of similarity above 0.5, while retrieval number two
 has five comparable properties with a measurement of similarity above 0.5.
 Instead of using a predetermined threshold to determine which retrieval
 provides the best results, an alternative approach is to take the average
 of the similarity values of the retrieved comparables. This corresponds to
 the area under the curve of the distributions and is determined by taking
 the average measurement of similarity. For example, the average similarity
 measure for retrievals one and two in FIG. 5 would be determined as
 follows:
 Average Similarity Measure Subject 1 (from best 8 comps):
 (1+1+0.85+0.8+0.7+0.7+0.7+0.5)/8=0.78125
 Average Similarity Measure Subject 2 (from best 8 comps):
 (1+0.9+0.8+0.7+0.7+0.4+0.035+0.25)/8=0.6375
 Referring again to FIG. 3, the comparable properties that have been
 selected for further review at 40 are then adjusted to reflect the value
 of the subject property at 42. In particular, any difference between the
 subject property and the comparable properties that would cause the
 comparables to be more or less valuable than the subject property will
 require an adjustment. Thus, if a comparable property is superior to the
 subject property, then an adjustment is needed to decrease the price of
 the comparable. However, if the comparable property is inferior to the
 subject property, then an adjustment is needed to increase the price of
 the comparable.
 The adjustments to the price of the comparable properties are performed by
 using the plurality of adjustment rules stored in the adjustment rule
 database 26. The adjustment rules are generated from the plurality of
 attributes stored in the case base 24 for all of the comparable
 properties. As mentioned earlier, there are approximately 166 attributes
 available for the subject property and the comparable properties in the
 illustrative embodiment. A illustrative listing of the attributes are
 presented below. The attributes described with a # are numeric and the
 remaining attributes are textual. The numeric attributes are described
 with a number and the textual attributes are described with text. For
 example, the attribute total room is described with a number such as
 three, four, or the like, and the pool attribute is described with a text
 format such as indoor, spa, etc.

SFRFireplaces (subject - comp) * 2000
 SFRStyle ?
 SFRBedrooms see Table 5
 TABLE 5
 Adjustment Function for Number of Bedrooms
 Comp
 Subject 1 2 3 4 5 6+
 1 0.00 0.00 -3.50 N/A N/A N/A
 2 0.00 0.00 0.00 -2.50 N/A N/A
 3 4.00 0.00 0.00 0.00 -4.00 N/A
 4 N/A 4.00 0.00 0.00 0.00 `(@-1)*3.5
 5 N/A N/A 4.00 0.00 0.00 `(@-1)*3.5
 6+ N/A N/A N/A `(@-1)*3.5 `(@-1)*3.5 0.0
 In order to accommodate for even more or less bedrooms, Table 5 takes the
 difference between the subject property and the comparable property (i.e.,
 @) and subtracts the difference by one and multiplies the difference by
 3.5. For example, if the subject property has six bedrooms and the
 comparable has four, then the adjustment would be 3.5 [[(6-4)-1]*3.5]. If
 the subject property has four bedrooms and the comparable has six, then
 the adjustment would be -3.5 [[(6-4)-1]*-3.5].

Pool $10000 for a pool
 LotArea (subject - comp)
 BuildingArea (subject - comp) * (22 +
 (sales_price_closing_of_comp * .00003))
 NumberOfUnits ?
 NumbeOfStories ?
 ParkingSpaces ?
 LocationInfluence no adjustment between comps in same level
 (B - ocean, F - lake/pond, A - positive view, C
 - bay front = + 10%, D - canal, E - river, G - wooded, H -
 golf, L - greenbelt = + 5%
 K - cul-de-sac, J - corner = no adjust
 I - corner lot/sound, N - negative = -5%)
 TypeOfConstruction?
 Foundation ?
 YearBuilt use only if no effective year built w *
 (Age_comp_Age_subject) * (SalePrice_comp/1000)
 if (Age_subject + Age_comp) / 2 &lt; 5 then w = 3.2
 else if (Age_subject + Age_comp) / 2 &lt; 9 then w =
 2.4 else if (Age_subject + Age_comp) / 2 &lt; 12 then w = 1.6 else if
 (Age_subject + Age_comp) / 2 &lt; 20 then w = .8 else w = .4
 max of 10% of salePrice
 EffectiveYearBuilt w * (Age_comp-Age_subject) *
 (SalePrice_comp/1000)
 if (Age_subject + Age_comp) / 2 &lt; 4 then w = 4
 else if (Age_subject + Age_comp) / 2 &lt; 6 then w = 3 else if
 (Age_subject + Age_comp) / 2 &lt; 8 then w = 2 else if
 (Age_subject + Age_comp) / 2 &lt; 15 then w = 1 else w = .5 max of
 10% of salePrice Quality(.02 * sale price) for each
 level of difference
 (Luxury &gt; Excellent &gt; Good &gt; Average &gt; Fair &gt;
 Poor) Condition (.02 * sale price) for each l evel of
 difference (Excellent &gt; Good&gt; Average &gt; Fair &gt; Poor)
 AirCondition (.01 * sale price) for each level of difference
 (Central &gt; Evaporative, Heat pump, waLl, Yes, Z-
 chill water &gt; None, Office only, Partial, Window,)
 Heating (.01 * sale price) for each level of difference
 (Z - Central, B - forced air &gt; A - gravity, C
 - floor furnace, D - wall furnace, E - hot water, F - ele
 bboard, G - heat pump, H - steam, I -
 radiant, J - space heater, K - solar, Y - yes &gt; L - none, P -
 partial)
 ParkingType ?
 BasementArea if not finished 1/4 to 1/2 value of living area
 if finished 1/2 to 1 value of living area
 RoofType ?
 RoofCover ?
 Frame ?
 GargageCarportSqFt?
 latitude none
 longitude none
 These adjustment rules are then applied to the comparable properties
 selected at 40 in order to adjust for the value of the subject property.
 An example of an adjustment for a comparable property is provided in Table
 6. In the example provided in Table 6, the comparable property has a sale
 price of $175,000 dollars. However, the comparable property has a building
 area of 1800 square feet, while the subject property has a building area
 of 2000. Using the adjustment rules for the attribute building area, the
 price of the comparable is adjusted by $5450 (i.e.,
 22+(175000*0.00003)=$27.25 per square foot which is (200*$27.25=$5450)).
 Also, the price of the comparable is adjusted for the lot area since the
 comparable has a larger lot size. In Table 6, the lot area attribute is
 adjusted by $1/sq ft for a total of -$5000. Since the comparable has two
 bathrooms and the subject property has two and a half bathrooms, the price
 needs to be adjusted by using the rules provided in Table 4, which turns
 out to be $2000. There are no adjustments necessary for the bedroom
 attribute because both the subject property and the comparable property
 have the same number of bedrooms. Since the comparable does not have a
 fireplace and the subject property has one, the price needs to be adjusted
 accordingly. Using the adjustment rule for fireplaces, the price is
 adjusted $2000. If the adjustment rules are used for the effective year,
 quality, condition, and pool attributes for the subject and comparable
 property, the rules will generate an adjustment of $2800, $3500, $0, and
 $10,000, respectively. All of the adjustments are then summed with the
 sale price of the comparable property to arrive at the adjusted price. In
 Table 6, the adjusted price of the comparable property is $195,750.
 TABLE 6
 Example of an Adjustment
 Attribute Subject Comparable Adjustment
 SalePrice ? 175000 175000
 BuildingArea 2000 1800 5450
 LotArea 20000 25000 -5000
 SFRTotalBaths 2.5 2 2000
 SFRBedrooms 3 3
 SFRFireplaces 1 0 2000
 EffYearBuilt 93 89 2800
 Quality Good Average 3500
 Condition Average Average
 Pool Yes No 10000
 195750
 Referring again to FIG. 3, after all of the adjustments are applied to the
 sales price of the comparable properties, another set of comparable
 properties that more closely match the subject property are extracted at
 44. In the illustrative embodiment, 4-8 comparables are selected at 44. If
 less than four comparables are selected, then the comparables may not
 correctly reflect the market and if more than eight comparables are used,
 then some of the comparables may not be similar enough to the subject
 property. If it is not possible to find four comparables similar to the
 subject property, then no value estimate may be calculated for the subject
 property. However, if there are many comparables (i.e. about 100 hundred),
 then it is necessary to filter out the poorer comparables. In the
 illustrative embodiment, the best results are attained by keeping
 comparable properties that have no single adjustment larger than 10% of
 the sale price, a net adjustment that does not exceed 15% of the sale
 price, a gross adjustment that does not exceed 25% of the sale price, and
 a dollar per square foot that does not vary more than 15%. Basically, all
 of the adjusted comparable properties are excluded from further
 consideration if any comparable has a single adjustment larger than 10%, a
 net adjustment larger than 15% or a gross adjustment larger than 25%.
 The best (i.e. four to eight) of the remaining adjusted comparable
 properties are selected by sorting and ranking each of the comparables'
 measurement of similarity, the net adjustment, and the gross adjustment,
 in the manner as shown in Table 7. In particular, the comparables having
 the highest measurement of similarity score are placed at the top of the
 list and ranked in descending order. In Table 7, comparable property
 113-012 has the highest measurement of similarity score and is ranked one,
 while comparable property 331-018 has the lowest measurement of similarity
 score and is ranked nine. Next to the measurement of similarity score and
 rank are the net and gross adjustment and respective rankings for the
 comparable properties. The rankings for the net and gross adjustment are
 attained in the same manner as the measurement of similarity. The rankings
 for the measurement of similarity, net adjustment, and gross adjustment,
 for each comparable are then summed across the board to produce a total
 ranking. The comparables with the lowest total rank are considered the
 best. In Table 7, comparables 113-012, 306-008, and 334-010, are the three
 best comparables.
 TABLE 7
 Selection of the best Comparables
 Gross
 Comparable Score rank Net Adjust rank Adjust rank total
 113-012 0.95 1 1344 2 5924 4 7
 306-018 0.88 2 3586 5 4186 1 8
 093-011 0.78 3 5686 7 8191 7 17
 305-006 0.67 4 6150 8 6160 6 18
 685-046 0.64 5 3139 3 6099 5 13
 847-984 0.58 6 -948 1 5670 3 10
 873-005 0.53 7 -5261 6 9261 8 21
 431-023 0.48 8 3546 4 4410 2 14
 331-018 0.44 9 9310 9 11300 9 27
 After the comparables have been ordered, it is necessary to determine how
 many of these comparables are to be used. Generally, the sales prices of
 the comparables should bound the sales price that will be estimated for
 the subject property. Therefore, it would be favorable to select
 comparables with both a negative and positive net adjustment. A comparable
 property with a negative net adjustment is likely to have an unadjusted
 price over the final estimate and a comparable with a positive net adjust
 is likely to have an unadjusted price under the final estimate. So, in
 order to do this, a temporary set of comparables is created by repeatedly
 adding the comparable with the best similarity score to the set until
 there are at least four comparables in the set and there is at least one
 comparable of each sign (negative and positive) net adjustment. In Table
 7, the comparables with the top six similarity scores would be included in
 the set. All other comparables are discarded. Of the comparables in the
 set only four of each sign net adjustments are retained. The four retained
 are the four comparables with the lowest total rank. In the example,
 comparable 305-006 would be discarded since there are four comparables
 with a positive net adjustment and lower total rank. The five comparables
 selected form the final set of comparables.
 Referring again to FIG. 3, after the best of the adjusted comparables have
 been selected, the adjusted prices of the selected comparables are
 aggregated into an estimate price of the subject property at 46. The
 aggregated estimated price is determined by multiplying the adjusted price
 of the comparable properties to their respective measurement of similarity
 and summed together to generate a total weighted price. Next, the total
 weighted price is divided by the total of the similarity measurements for
 the comparable properties. The result is an estimate price of the subject
 property. An example of the aggregation for the comparables provided in
 Table 7 is shown in Table 8. In this example, the total weighted price is
 $757,640 and the total similarity score is 3.83. Thus, dividing $757,640
 by 3.83 results in an estimate price of 199,900 for the subject property.
 TABLE 8
 Comparable Aggregation
 Comparable Adjusted Price Score Weighted Price
 113-012 197000 0.95 187150
 306-008 202000 0.88 177760
 093-011 196500 0.78 153270
 685-046 192000 0.64 122880
 847-984 201000 0.58 116580
 total 3.83 757640
 final estimate = 757640/ 3.83 = 199900
 After producing the final estimate of the value of the subject property, a
 measurement of confidence indicating the reliability is generated. In
 particular, the confidence measurement in the estimate can be obtained by
 averaging the similarity scores of the comparables in the final selection,
 or by averaging the number of comparables over a threshold in the primary
 retrieval. The estimate is justified by displaying the comparables in
 enough detail so that they can be shown to be similar to the subject.
 It is therefore apparent that there has been provided in accordance with
 this invention, a method for estimating the price of a real property that
 fully satisfy the aims and advantages and objectives hereinbefore set
 forth. The invention has been described with reference to several
 embodiments, however, it will be appreciated that variations and
 modifications can be effected by a person of ordinary skill in the art
 without departing from the scope of the invention.