Load Data

Here we load the data

# Check out packages
library(tidyverse)
library(dplyr)
#library(FNN)
#library(MASS)
#library(randomForest)
#library(caret)
#library(pdp)
#library(iml)

# Load data
df1 <- readRDS("~/Documents/D698/df.rds")

Remove Condos

We noticed that Condos have one record per unit instead of one record per building. We attempted to roll them up with the sum or non-missingness of their other column values, however we were missing a relevant record in the PLUTO database where condos are one record per building to identify which lot number to use. Also we were missing FINMKTTOT for condo records. An attempt to return to Coding Chunks 5 and 6 to resolve the issue upstream didn’t preserve FINMKTTOT so we’re removing condos to focus on co-ops and non-condo Class 2 buildings.

This led to rerunning previous chunks to both exclude Condos but widen the scope from zip code 10019 to all of Manhattan.


Missing Values

There are lots of missing values:

colSums(is.na(df1))
##                  PARID                   BORO                  BLOCK 
##                      0                      0                      0 
##                    LOT               EASEMENT                   YEAR 
##                      0                  13349                      0 
##              FINMKTTOT            FINTAXCLASS             BLDG_CLASS 
##                      0                      0                      0 
##                 ZONING               ZIP_CODE                LOT_FRT 
##                      1                      0                      0 
##                LOT_DEP              LOT_IRREG                BLD_FRT 
##                      0                     40                      0 
##                BLD_DEP                BLD_EXT              BLD_STORY 
##                      0                    195                      0 
##                 CORNER              LAND_AREA              NUM_BLDGS 
##                   9878                      0                      0 
##                YRBUILT                 YRALT1                 YRALT2 
##                      0                      0                      0 
##              COOP_APTS                  UNITS           CONDO_Number 
##                      0                      0                  13349 
##             GROSS_SQFT      OFFICE_AREA_GROSS RESIDENTIAL_AREA_GROSS 
##                      0                      0                      0 
##             FINTAXFLAG                     cd                bct2020 
##                      0                     37                     37 
##              bctcb2020             schooldist                council 
##                     37                     37                     37 
##               firecomp             policeprct   healthcenterdistrict 
##                     37                     37                     37 
##             healtharea              zonedist1                spdist1 
##                     37                     40                  11106 
##              ltdheight              bldgclass                landuse 
##                  13220                     16                     34 
##              easements               histdist               landmark 
##                     16                  10749                  13248 
##               builtfar               residfar                commfar 
##                     16                     16                     16 
##               facilfar                    bbl                condono 
##                     16                     16                  13349 
##              tract2010                 xcoord                 ycoord 
##                     37                     37                     37 
##            firm07_flag           pfirm15_flag               latitude 
##                  13027                  12807                     37 
##              longitude                    ASP 
##                     37                  11424


Significant Missingness

We’re dropping 37 records missing xcoord and ycoord. They presumably are the same records that have ~37 missing in the other columns.

We’re also dropping CONDO_Number, EASEMENT, and condono since they are all missing.

df2 <- df1 %>%
  filter(!is.na(xcoord))

df3 <- df2 %>%
  dplyr::select(-CONDO_Number, -EASEMENT, -condono)

names(df2)
##  [1] "PARID"                  "BORO"                   "BLOCK"                 
##  [4] "LOT"                    "EASEMENT"               "YEAR"                  
##  [7] "FINMKTTOT"              "FINTAXCLASS"            "BLDG_CLASS"            
## [10] "ZONING"                 "ZIP_CODE"               "LOT_FRT"               
## [13] "LOT_DEP"                "LOT_IRREG"              "BLD_FRT"               
## [16] "BLD_DEP"                "BLD_EXT"                "BLD_STORY"             
## [19] "CORNER"                 "LAND_AREA"              "NUM_BLDGS"             
## [22] "YRBUILT"                "YRALT1"                 "YRALT2"                
## [25] "COOP_APTS"              "UNITS"                  "CONDO_Number"          
## [28] "GROSS_SQFT"             "OFFICE_AREA_GROSS"      "RESIDENTIAL_AREA_GROSS"
## [31] "FINTAXFLAG"             "cd"                     "bct2020"               
## [34] "bctcb2020"              "schooldist"             "council"               
## [37] "firecomp"               "policeprct"             "healthcenterdistrict"  
## [40] "healtharea"             "zonedist1"              "spdist1"               
## [43] "ltdheight"              "bldgclass"              "landuse"               
## [46] "easements"              "histdist"               "landmark"              
## [49] "builtfar"               "residfar"               "commfar"               
## [52] "facilfar"               "bbl"                    "condono"               
## [55] "tract2010"              "xcoord"                 "ycoord"                
## [58] "firm07_flag"            "pfirm15_flag"           "latitude"              
## [61] "longitude"              "ASP"


Recategorize NAs

Next we replace NAs that should be flagged as zero or No. For example firm07_flag is either NA or 1 so we can replace the NAs with 0.

df4 <- df3 %>%
  mutate(firm07_flag = replace_na(firm07_flag, 0)) %>%
  mutate(pfirm15_flag = replace_na(pfirm15_flag, 0)) %>%
  mutate(landmark = replace_na(landmark, 'None')) %>%
  mutate(histdist = replace_na(histdist, 'None')) %>%
  mutate(spdist1 = replace_na(spdist1, 'None')) %>%
  mutate(CORNER = case_when(CORNER %in% c("CR", "NE", "SW", "NW", "SE") ~ "Yes", is.na(CORNER) | CORNER == "00" ~ "No")) %>%
  mutate(ltdheight = replace_na(ltdheight, "None")) %>%
  mutate(LOT_IRREG = replace_na(LOT_IRREG, "Unknown")) %>%
  mutate(BLD_EXT = replace_na(BLD_EXT, "N")) %>%
  mutate(landuse = replace_na(landuse, "Unknown"))

We’re left with 4 NAs in zoning fields out of 94 options and the significant missingness of ASP, or Average Sale Price, which is ok because we’ll only use that to interpret our model results or run the model to predict on just the subset with sales data.

df4 %>%
  is.na() %>%
  colSums() %>%
  .[. > 0]
##    ZONING zonedist1       ASP 
##         1         3     11389


Correlation Matrix

The correlation matrix is turning up a lot of extreme correlation. So we removed a lot of labeling like ZIP_CODE and YEAR, and duplicates like longitude and xcoord.

Note we also took out cd, council, policeprct and the two health care districts, because while they are numbers, they are factors or labels, not quantitative values.

Interestingly there is very little correlation to year of alteration (YRALT1 YRALT2), except a slight negative correlation between the first year of alteration and FINMKTTOT which could suggest owners who are able to rebuild buildings have the sophistication to protest, appeal or lobby for smaller market value assessments from the DOF, or possibly had tax incentives to

Many variables are highly correlated with each other, such as GROSS_SQFT, RESIDENTIAL_AREA_GROSS, and UNITS so we may need to handle multicollinearity.

Also, Average Sale Price has very low correlation with FINMKTTOT, and while this may be because we need to create a new field of average sale price times number of units, it could also indicate that this tax assessment process is truly diverged from market realities.

# Define the columns to exclude
exclude_cols <- c("bbl", "PARID", "BLOCK", "bctcb2020", "bct2020", 
                  "latitude", "longitude", "ycoord", "xcoord", "LOT", "BORO", "YEAR",
                  "COOP_APTS", "firm07_flag",   "pfirm15_flag", "LOT_DEP", "FINTAXCLASS", "ZIP_CODE", "LOT_FRT", "BLD_FRT", "BLD_DEP", "cd", "council", "policeprct", "healthcenterdistrict", "healtharea")

# Create correlation matrix excluding those columns
correlations <- cor(
  df4[, sapply(df4, is.numeric) & !names(df4) %in% exclude_cols],
  use = "pairwise.complete.obs"
)

# Plot the correlations
corrplot::corrplot(correlations, method = "square", type = "upper", order = "original", tl.cex = 0.6, tl.srt = 45)


Clean Dataset for Modeling

We’ve identified a number of variables to remove before modeling with linear regression so we take that step now.

Aliasing

Also, there are a number of the qualitative fields that have aliasing, where their values are linearly dependent on each other so we cannot include them with modeling. We add them to the columns to exclude below iteratively as they appear in the alias() test below.

# Define the columns to exclude
exclude_cols_lrmodel <- c("bbl", "PARID", "BLOCK", "LOT", "bctcb2020", "bct2020", 
                  "latitude", "longitude", "ycoord", "xcoord", "BORO", "YEAR",
                  "COOP_APTS", "firm07_flag",   "pfirm15_flag", "LOT_DEP", "FINTAXCLASS", "ZIP_CODE", "LOT_FRT", "BLD_FRT", "BLD_DEP", "cd", "council", "policeprct", "healthcenterdistrict", "healtharea", "spdist1", "firecomp", "zonedist1", "bldgclass", "landuse", "tract2010", "RESIDENTIAL_AREA_GROSS", "residfar", "commfar", "facilfar")

df5 <- df4 %>%
  dplyr::select(-all_of(exclude_cols_lrmodel))

lm_model_test <- lm(FINMKTTOT ~ ., data = df5)
alias(lm_model_test)$Complete
## NULL


Multicollinearity

Our Variance Inflation Factors (VIF) indicate there is still yet multicollinearity in our data, with RESIDENTIAL_AREA_GROSS, residfar, commfar and facilfar, which we’ve already removed.

We should be concerned with UNITS at 5.956, LAND_AREA at 4.499, and GROSS_SQFT at 3.218; and monitor BLD_STORY at 2.792 and builtfar at 2.690; however we’ll review the linear regression model summary first.

lm_model <- lm(FINMKTTOT ~ ., data = df5)
vif_values <- car::vif(lm_model)
vif_values
##                           GVIF Df GVIF^(1/(2*Df))
## BLDG_CLASS        8.367716e+01 13        1.185622
## ZONING            1.307562e+07 69        1.126078
## LOT_IRREG         1.513449e+00  2        1.109154
## BLD_EXT           1.419274e+00  3        1.060094
## BLD_STORY         7.796284e+00  1        2.792183
## CORNER            1.939321e+00  1        1.392595
## LAND_AREA         2.024974e+01  1        4.499971
## NUM_BLDGS         3.042013e+00  1        1.744137
## YRBUILT           2.332567e+00  1        1.527274
## YRALT1            1.210281e+00  1        1.100128
## YRALT2            1.223977e+00  1        1.106335
## UNITS             3.548436e+01  1        5.956875
## GROSS_SQFT        1.036134e+01  1        3.218904
## OFFICE_AREA_GROSS 1.242231e+00  1        1.114554
## FINTAXFLAG        1.206629e+00  1        1.098467
## schooldist        2.412102e+01  5        1.374800
## ltdheight         1.271544e+01  2        1.888352
## easements         1.261585e+00  1        1.123203
## histdist          1.650867e+07 51        1.176960
## landmark          2.875365e+00  1        1.695690
## builtfar          7.239698e+00  1        2.690669
## ASP               1.766568e+00  1        1.329123



Linear Regression Model Summary

The model is strong, with an Adjusted R-squared of 0.956. This suggests to us that the DOF may use linear regression as their statistical model, or that we’re overfit because of a number of near multicollinear variables measuring different facets of building size.

Almost every zoning label and building class are highly significant, this supports the domain knowledge that zoning and building class have a huge impact on the capitalization rate selected for determining the market value of a Class 2 property. It may be that when we look for comparables we should always look for properties with the same zoning and building class.

Being a landmark or historic district building doesn’t seem to impact market tax assessment. This makes sense because it wasn’t included as part of the DOF’s PVAD database but rather layered on with the PLUTO data. Also, they may handle different taxation for landmark or historic district buildings at the exemption and abatement level, after the market value has been assessed.

Even though year built (YRBUILT, YRALT1 and YRALT2), CORNER and LOT_IRREG are listed on the DOF’s annual individual statements with the development of their taxable property value, they and BLD_EXT don’t appear to have an impact on assessed market value.

Variables related to size such as GROSS_SQFT, UNITS, OFFICE_AREA_GROSS and builtfar are all significant for predicting assessed market value however they may be overlapping, which we will consider along with overfitting in our final XGBoost model.

summary(lm_model)
## 
## Call:
## lm(formula = FINMKTTOT ~ ., data = df5)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -132838164   -2835402     -79981    2736015   58882393 
## 
## Coefficients:
##                                                                       Estimate
## (Intercept)                                                          3.595e+07
## BLDG_CLASSC4                                                        -1.818e+06
## BLDG_CLASSC5                                                        -1.495e+06
## BLDG_CLASSC6                                                        -1.696e+06
## BLDG_CLASSC7                                                        -1.421e+06
## BLDG_CLASSD0                                                        -4.396e+06
## BLDG_CLASSD1                                                        -3.529e+06
## BLDG_CLASSD3                                                        -6.391e+06
## BLDG_CLASSD4                                                        -5.396e+06
## BLDG_CLASSD5                                                        -1.554e+06
## BLDG_CLASSD6                                                        -4.768e+06
## BLDG_CLASSD7                                                        -8.161e+06
## BLDG_CLASSD8                                                        -2.169e+07
## BLDG_CLASSD9                                                        -9.016e+05
## ZONINGC1-6                                                          -5.743e+07
## ZONINGC1-7                                                          -5.056e+07
## ZONINGC1-8                                                          -5.619e+07
## ZONINGC1-9                                                          -5.918e+07
## ZONINGC16A                                                          -5.621e+07
## ZONINGC17A                                                          -5.680e+07
## ZONINGC18A                                                          -5.901e+07
## ZONINGC18X                                                          -5.669e+07
## ZONINGC19A                                                          -5.466e+07
## ZONINGC2-6                                                          -5.474e+07
## ZONINGC2-7                                                          -5.486e+07
## ZONINGC2-8                                                          -5.694e+07
## ZONINGC26A                                                          -5.614e+07
## ZONINGC27A                                                          -5.930e+07
## ZONINGC28A                                                          -5.695e+07
## ZONINGC4-4                                                          -5.365e+07
## ZONINGC4-5                                                          -5.967e+07
## ZONINGC4-7                                                          -5.141e+07
## ZONINGC44A                                                          -5.672e+07
## ZONINGC44D                                                          -5.289e+07
## ZONINGC45A                                                          -5.634e+07
## ZONINGC46A                                                          -5.497e+07
## ZONINGC5-1                                                          -4.992e+07
## ZONINGC5-2                                                          -5.520e+07
## ZONINGC5-3                                                          -5.310e+07
## ZONINGC5-5                                                          -6.427e+07
## ZONINGC5-P                                                          -5.822e+07
## ZONINGC51A                                                          -5.679e+07
## ZONINGC52.5                                                         -5.600e+07
## ZONINGC6-1                                                          -5.409e+07
## ZONINGC6-2                                                          -5.248e+07
## ZONINGC6-2G                                                         -3.883e+07
## ZONINGC6-4                                                          -6.029e+07
## ZONINGC6-6                                                          -5.353e+07
## ZONINGC6-7                                                          -5.702e+07
## ZONINGC62A                                                          -5.459e+07
## ZONINGC62G                                                          -6.080e+07
## ZONINGC62M                                                          -5.087e+07
## ZONINGC63A                                                          -5.337e+07
## ZONINGC63X                                                          -5.668e+07
## ZONINGC64.5                                                         -5.889e+07
## ZONINGC64A                                                          -5.663e+07
## ZONINGC64M                                                          -5.445e+07
## ZONINGC64X                                                          -6.025e+07
## ZONINGC66.5                                                         -5.411e+07
## ZONINGC8-4                                                          -5.658e+07
## ZONINGM1-5                                                          -5.247e+07
## ZONINGM1-6                                                          -5.406e+07
## ZONINGM15M                                                          -5.708e+07
## ZONINGM15R7D                                                        -5.500e+07
## ZONINGM15R7X                                                        -5.075e+07
## ZONINGM15R9A                                                        -5.149e+07
## ZONINGM15R9X                                                        -5.322e+07
## ZONINGM16D                                                          -6.243e+07
## ZONINGR10                                                           -5.599e+07
## ZONINGR10A                                                          -5.672e+07
## ZONINGR10H                                                          -5.753e+07
## ZONINGR6                                                            -5.979e+07
## ZONINGR6A                                                           -5.187e+07
## ZONINGR7-2                                                          -5.960e+07
## ZONINGR7A                                                           -5.564e+07
## ZONINGR7B                                                           -5.664e+07
## ZONINGR7D                                                           -5.278e+07
## ZONINGR8                                                            -5.885e+07
## ZONINGR8A                                                           -5.723e+07
## ZONINGR8B                                                           -5.640e+07
## ZONINGR9                                                            -5.999e+07
## ZONINGR9A                                                           -5.940e+07
## ZONINGR9X                                                           -5.706e+07
## LOT_IRREGR                                                          -2.088e+05
## LOT_IRREGUnknown                                                     6.283e+06
## BLD_EXTEG                                                            1.376e+06
## BLD_EXTG                                                             4.302e+06
## BLD_EXTN                                                             7.431e+05
## BLD_STORY                                                            6.171e+05
## CORNERYes                                                            7.109e+05
## LAND_AREA                                                            2.020e+01
## NUM_BLDGS                                                           -1.276e+06
## YRBUILT                                                              9.134e+03
## YRALT1                                                               4.005e+02
## YRALT2                                                               2.981e+02
## UNITS                                                                3.328e+04
## GROSS_SQFT                                                           1.636e+02
## OFFICE_AREA_GROSS                                                    3.463e+02
## FINTAXFLAGT                                                          1.334e+06
## schooldist02                                                         5.853e+06
## schooldist03                                                         4.424e+06
## schooldist04                                                         2.077e+06
## schooldist05                                                        -2.533e+05
## schooldist06                                                        -1.493e+06
## ltdheightLH-1A                                                       7.803e+06
## ltdheightNone                                                        4.990e+06
## easements                                                            8.590e+06
## histdistCarnegie Hill Historic District                              4.562e+06
## histdistCentral Harlem West -- 130-132nd Street Historic District    1.470e+07
## histdistCentral Park West-76th Street Historic District              4.809e+06
## histdistCentral Park West-West 73rd - 74th Street Historic District  1.216e+07
## histdistCharlton-King-Vandam Historic District                       8.373e+06
## histdistChelsea Historic District                                    5.105e+06
## histdistChelsea Historic District Extension                          2.763e+06
## histdistDorrance Brooks Square Historic District                     1.315e+07
## histdistEast Village / Lower East Side Historic District             6.919e+06
## histdistExpanded Carnegie Hill Historic District                     7.919e+06
## histdistGansevoort Market Historic District                          9.198e+06
## histdistGramercy Park Historic District                              1.039e+07
## histdistGreenwich Village Historic District                          9.103e+06
## histdistGreenwich Village Historic District Extension                1.196e+07
## histdistGreenwich Village Historic District Extension II             7.063e+06
## histdistHamilton Heights / Sugar Hill Historic District              6.548e+06
## histdistHamilton Heights / Sugar Hill Northeast Historic District    7.079e+05
## histdistHamilton Heights / Sugar Hill Northwest Historic District    2.987e+06
## histdistHamilton Heights Historic District Extension                 1.708e+06
## histdistIndividual Landmark                                         -7.860e+06
## histdistLadies' Mile Historic District                               5.585e+06
## histdistLamartine Place Historic District                            4.252e+06
## histdistMadison Square North Historic District                       6.415e+06
## histdistMetropolitan Museum Historic District                        9.494e+06
## histdistMorningside Heights Historic District                        9.969e+05
## histdistMount Morris Park Historic District                          1.987e+06
## histdistMount Morris Park Historic District Extension                8.822e+06
## histdistMurray Hill Historic District                               -1.285e+06
## histdistMurray Hill Historic District Extension                      1.238e+06
## histdistNoHo East Historic District                                 -1.816e+06
## histdistNoHo Historic District                                       1.259e+06
## histdistNone                                                         4.780e+06
## histdistPark Avenue Historic District                                6.549e+06
## histdistRiverside-West End Historic District                         1.161e+06
## histdistRiverside-West End Historic District Extension I             3.252e+06
## histdistRiverside-West End Historic District Extension II           -1.330e+06
## histdistSoHo-Cast Iron Historic District                             2.839e+06
## histdistSoHo-Cast Iron Historic District Extension                   6.410e+06
## histdistSouth Village Historic District                              9.398e+06
## histdistSt. Mark's Historic District                                 1.675e+07
## histdistStuyvesant Square Historic District                          5.821e+06
## histdistSullivan-Thompson Historic District                          6.866e+06
## histdistTribeca East Historic District                               2.998e+06
## histdistTribeca West Historic District                               3.120e+06
## histdistTudor City Historic District                                -3.944e+06
## histdistUpper East Side Historic District                            6.709e+06
## histdistUpper East Side Historic District Extension                  5.496e+06
## histdistUpper West Side / Central Park West Historic District        8.049e+06
## histdistWeehawken Street Historic District                           5.103e+05
## histdistWest End-Collegiate Historic District                        7.719e+06
## histdistWest End-Collegiate Historic District Extension              3.860e+06
## landmarkNone                                                        -1.352e+07
## builtfar                                                             2.741e+05
## ASP                                                                  7.409e-02
##                                                                     Std. Error
## (Intercept)                                                          2.802e+07
## BLDG_CLASSC4                                                         2.070e+06
## BLDG_CLASSC5                                                         2.126e+06
## BLDG_CLASSC6                                                         1.431e+06
## BLDG_CLASSC7                                                         1.552e+06
## BLDG_CLASSD0                                                         1.970e+06
## BLDG_CLASSD1                                                         2.248e+06
## BLDG_CLASSD3                                                         2.940e+06
## BLDG_CLASSD4                                                         1.403e+06
## BLDG_CLASSD5                                                         5.891e+06
## BLDG_CLASSD6                                                         2.472e+06
## BLDG_CLASSD7                                                         2.892e+06
## BLDG_CLASSD8                                                         8.825e+06
## BLDG_CLASSD9                                                         2.854e+06
## ZONINGC1-6                                                           1.095e+07
## ZONINGC1-7                                                           1.091e+07
## ZONINGC1-8                                                           1.206e+07
## ZONINGC1-9                                                           1.070e+07
## ZONINGC16A                                                           1.084e+07
## ZONINGC17A                                                           1.337e+07
## ZONINGC18A                                                           1.087e+07
## ZONINGC18X                                                           1.075e+07
## ZONINGC19A                                                           1.091e+07
## ZONINGC2-6                                                           1.128e+07
## ZONINGC2-7                                                           1.343e+07
## ZONINGC2-8                                                           1.076e+07
## ZONINGC26A                                                           1.168e+07
## ZONINGC27A                                                           1.098e+07
## ZONINGC28A                                                           1.120e+07
## ZONINGC4-4                                                           1.171e+07
## ZONINGC4-5                                                           1.177e+07
## ZONINGC4-7                                                           1.129e+07
## ZONINGC44A                                                           1.099e+07
## ZONINGC44D                                                           1.240e+07
## ZONINGC45A                                                           1.341e+07
## ZONINGC46A                                                           1.084e+07
## ZONINGC5-1                                                           1.076e+07
## ZONINGC5-2                                                           1.036e+07
## ZONINGC5-3                                                           1.098e+07
## ZONINGC5-5                                                           1.139e+07
## ZONINGC5-P                                                           1.124e+07
## ZONINGC51A                                                           1.348e+07
## ZONINGC52.5                                                          1.164e+07
## ZONINGC6-1                                                           1.098e+07
## ZONINGC6-2                                                           1.080e+07
## ZONINGC6-2G                                                          1.536e+07
## ZONINGC6-4                                                           1.098e+07
## ZONINGC6-6                                                           1.159e+07
## ZONINGC6-7                                                           1.339e+07
## ZONINGC62A                                                           1.084e+07
## ZONINGC62G                                                           1.166e+07
## ZONINGC62M                                                           1.123e+07
## ZONINGC63A                                                           1.100e+07
## ZONINGC63X                                                           1.334e+07
## ZONINGC64.5                                                          1.160e+07
## ZONINGC64A                                                           1.114e+07
## ZONINGC64M                                                           1.144e+07
## ZONINGC64X                                                           1.346e+07
## ZONINGC66.5                                                          1.336e+07
## ZONINGC8-4                                                           1.206e+07
## ZONINGM1-5                                                           1.338e+07
## ZONINGM1-6                                                           1.092e+07
## ZONINGM15M                                                           1.261e+07
## ZONINGM15R7D                                                         1.485e+07
## ZONINGM15R7X                                                         1.209e+07
## ZONINGM15R9A                                                         1.576e+07
## ZONINGM15R9X                                                         1.246e+07
## ZONINGM16D                                                           1.337e+07
## ZONINGR10                                                            1.066e+07
## ZONINGR10A                                                           1.066e+07
## ZONINGR10H                                                           1.121e+07
## ZONINGR6                                                             1.085e+07
## ZONINGR6A                                                            1.142e+07
## ZONINGR7-2                                                           1.066e+07
## ZONINGR7A                                                            1.068e+07
## ZONINGR7B                                                            1.076e+07
## ZONINGR7D                                                            1.144e+07
## ZONINGR8                                                             1.064e+07
## ZONINGR8A                                                            1.074e+07
## ZONINGR8B                                                            1.062e+07
## ZONINGR9                                                             1.086e+07
## ZONINGR9A                                                            1.082e+07
## ZONINGR9X                                                            1.127e+07
## LOT_IRREGR                                                           4.867e+05
## LOT_IRREGUnknown                                                     4.851e+06
## BLD_EXTEG                                                            8.269e+06
## BLD_EXTG                                                             2.110e+06
## BLD_EXTN                                                             8.866e+05
## BLD_STORY                                                            8.012e+04
## CORNERYes                                                            5.309e+05
## LAND_AREA                                                            8.437e+00
## NUM_BLDGS                                                            2.674e+05
## YRBUILT                                                              1.233e+04
## YRALT1                                                               2.156e+02
## YRALT2                                                               3.992e+02
## UNITS                                                                5.286e+03
## GROSS_SQFT                                                           3.548e+00
## OFFICE_AREA_GROSS                                                    6.849e+01
## FINTAXFLAGT                                                          4.775e+05
## schooldist02                                                         1.145e+06
## schooldist03                                                         1.359e+06
## schooldist04                                                         2.521e+06
## schooldist05                                                         1.589e+06
## schooldist06                                                         1.396e+06
## ltdheightLH-1A                                                       9.308e+06
## ltdheightNone                                                        9.185e+06
## easements                                                            3.459e+06
## histdistCarnegie Hill Historic District                              7.640e+06
## histdistCentral Harlem West -- 130-132nd Street Historic District    9.685e+06
## histdistCentral Park West-76th Street Historic District              9.566e+06
## histdistCentral Park West-West 73rd - 74th Street Historic District  6.796e+06
## histdistCharlton-King-Vandam Historic District                       9.748e+06
## histdistChelsea Historic District                                    6.184e+06
## histdistChelsea Historic District Extension                          7.778e+06
## histdistDorrance Brooks Square Historic District                     9.700e+06
## histdistEast Village / Lower East Side Historic District             5.899e+06
## histdistExpanded Carnegie Hill Historic District                     5.066e+06
## histdistGansevoort Market Historic District                          9.816e+06
## histdistGramercy Park Historic District                              9.702e+06
## histdistGreenwich Village Historic District                          5.224e+06
## histdistGreenwich Village Historic District Extension                9.720e+06
## histdistGreenwich Village Historic District Extension II             6.204e+06
## histdistHamilton Heights / Sugar Hill Historic District              7.565e+06
## histdistHamilton Heights / Sugar Hill Northeast Historic District    6.240e+06
## histdistHamilton Heights / Sugar Hill Northwest Historic District    7.936e+06
## histdistHamilton Heights Historic District Extension                 8.596e+06
## histdistIndividual Landmark                                          5.982e+06
## histdistLadies' Mile Historic District                               6.775e+06
## histdistLamartine Place Historic District                            9.508e+06
## histdistMadison Square North Historic District                       1.019e+07
## histdistMetropolitan Museum Historic District                        5.526e+06
## histdistMorningside Heights Historic District                        5.233e+06
## histdistMount Morris Park Historic District                          9.638e+06
## histdistMount Morris Park Historic District Extension                7.790e+06
## histdistMurray Hill Historic District                                7.635e+06
## histdistMurray Hill Historic District Extension                      9.499e+06
## histdistNoHo East Historic District                                  8.226e+06
## histdistNoHo Historic District                                       1.120e+07
## histdistNone                                                         4.852e+06
## histdistPark Avenue Historic District                                5.123e+06
## histdistRiverside-West End Historic District                         5.147e+06
## histdistRiverside-West End Historic District Extension I             5.097e+06
## histdistRiverside-West End Historic District Extension II            5.029e+06
## histdistSoHo-Cast Iron Historic District                             7.758e+06
## histdistSoHo-Cast Iron Historic District Extension                   8.114e+06
## histdistSouth Village Historic District                              6.225e+06
## histdistSt. Mark's Historic District                                 9.629e+06
## histdistStuyvesant Square Historic District                          7.009e+06
## histdistSullivan-Thompson Historic District                          5.831e+06
## histdistTribeca East Historic District                               7.789e+06
## histdistTribeca West Historic District                               6.284e+06
## histdistTudor City Historic District                                 5.651e+06
## histdistUpper East Side Historic District                            5.032e+06
## histdistUpper East Side Historic District Extension                  5.478e+06
## histdistUpper West Side / Central Park West Historic District        4.968e+06
## histdistWeehawken Street Historic District                           9.735e+06
## histdistWest End-Collegiate Historic District                        5.942e+06
## histdistWest End-Collegiate Historic District Extension              5.101e+06
## landmarkNone                                                         2.625e+06
## builtfar                                                             1.254e+05
## ASP                                                                  2.756e-02
##                                                                     t value
## (Intercept)                                                           1.283
## BLDG_CLASSC4                                                         -0.878
## BLDG_CLASSC5                                                         -0.703
## BLDG_CLASSC6                                                         -1.184
## BLDG_CLASSC7                                                         -0.915
## BLDG_CLASSD0                                                         -2.232
## BLDG_CLASSD1                                                         -1.570
## BLDG_CLASSD3                                                         -2.174
## BLDG_CLASSD4                                                         -3.845
## BLDG_CLASSD5                                                         -0.264
## BLDG_CLASSD6                                                         -1.929
## BLDG_CLASSD7                                                         -2.822
## BLDG_CLASSD8                                                         -2.458
## BLDG_CLASSD9                                                         -0.316
## ZONINGC1-6                                                           -5.245
## ZONINGC1-7                                                           -4.634
## ZONINGC1-8                                                           -4.658
## ZONINGC1-9                                                           -5.533
## ZONINGC16A                                                           -5.184
## ZONINGC17A                                                           -4.248
## ZONINGC18A                                                           -5.427
## ZONINGC18X                                                           -5.275
## ZONINGC19A                                                           -5.009
## ZONINGC2-6                                                           -4.854
## ZONINGC2-7                                                           -4.085
## ZONINGC2-8                                                           -5.294
## ZONINGC26A                                                           -4.807
## ZONINGC27A                                                           -5.403
## ZONINGC28A                                                           -5.086
## ZONINGC4-4                                                           -4.583
## ZONINGC4-5                                                           -5.071
## ZONINGC4-7                                                           -4.554
## ZONINGC44A                                                           -5.163
## ZONINGC44D                                                           -4.265
## ZONINGC45A                                                           -4.200
## ZONINGC46A                                                           -5.071
## ZONINGC5-1                                                           -4.641
## ZONINGC5-2                                                           -5.326
## ZONINGC5-3                                                           -4.836
## ZONINGC5-5                                                           -5.642
## ZONINGC5-P                                                           -5.178
## ZONINGC51A                                                           -4.212
## ZONINGC52.5                                                          -4.810
## ZONINGC6-1                                                           -4.926
## ZONINGC6-2                                                           -4.858
## ZONINGC6-2G                                                          -2.528
## ZONINGC6-4                                                           -5.488
## ZONINGC6-6                                                           -4.620
## ZONINGC6-7                                                           -4.259
## ZONINGC62A                                                           -5.036
## ZONINGC62G                                                           -5.214
## ZONINGC62M                                                           -4.529
## ZONINGC63A                                                           -4.851
## ZONINGC63X                                                           -4.250
## ZONINGC64.5                                                          -5.075
## ZONINGC64A                                                           -5.086
## ZONINGC64M                                                           -4.761
## ZONINGC64X                                                           -4.476
## ZONINGC66.5                                                          -4.049
## ZONINGC8-4                                                           -4.689
## ZONINGM1-5                                                           -3.922
## ZONINGM1-6                                                           -4.949
## ZONINGM15M                                                           -4.525
## ZONINGM15R7D                                                         -3.704
## ZONINGM15R7X                                                         -4.199
## ZONINGM15R9A                                                         -3.268
## ZONINGM15R9X                                                         -4.271
## ZONINGM16D                                                           -4.669
## ZONINGR10                                                            -5.251
## ZONINGR10A                                                           -5.323
## ZONINGR10H                                                           -5.130
## ZONINGR6                                                             -5.509
## ZONINGR6A                                                            -4.542
## ZONINGR7-2                                                           -5.590
## ZONINGR7A                                                            -5.210
## ZONINGR7B                                                            -5.267
## ZONINGR7D                                                            -4.616
## ZONINGR8                                                             -5.533
## ZONINGR8A                                                            -5.331
## ZONINGR8B                                                            -5.311
## ZONINGR9                                                             -5.523
## ZONINGR9A                                                            -5.489
## ZONINGR9X                                                            -5.065
## LOT_IRREGR                                                           -0.429
## LOT_IRREGUnknown                                                      1.295
## BLD_EXTEG                                                             0.166
## BLD_EXTG                                                              2.039
## BLD_EXTN                                                              0.838
## BLD_STORY                                                             7.703
## CORNERYes                                                             1.339
## LAND_AREA                                                             2.395
## NUM_BLDGS                                                            -4.774
## YRBUILT                                                               0.741
## YRALT1                                                                1.857
## YRALT2                                                                0.747
## UNITS                                                                 6.295
## GROSS_SQFT                                                           46.117
## OFFICE_AREA_GROSS                                                     5.057
## FINTAXFLAGT                                                           2.793
## schooldist02                                                          5.112
## schooldist03                                                          3.255
## schooldist04                                                          0.824
## schooldist05                                                         -0.159
## schooldist06                                                         -1.070
## ltdheightLH-1A                                                        0.838
## ltdheightNone                                                         0.543
## easements                                                             2.484
## histdistCarnegie Hill Historic District                               0.597
## histdistCentral Harlem West -- 130-132nd Street Historic District     1.518
## histdistCentral Park West-76th Street Historic District               0.503
## histdistCentral Park West-West 73rd - 74th Street Historic District   1.790
## histdistCharlton-King-Vandam Historic District                        0.859
## histdistChelsea Historic District                                     0.826
## histdistChelsea Historic District Extension                           0.355
## histdistDorrance Brooks Square Historic District                      1.356
## histdistEast Village / Lower East Side Historic District              1.173
## histdistExpanded Carnegie Hill Historic District                      1.563
## histdistGansevoort Market Historic District                           0.937
## histdistGramercy Park Historic District                               1.071
## histdistGreenwich Village Historic District                           1.743
## histdistGreenwich Village Historic District Extension                 1.230
## histdistGreenwich Village Historic District Extension II              1.138
## histdistHamilton Heights / Sugar Hill Historic District               0.866
## histdistHamilton Heights / Sugar Hill Northeast Historic District     0.113
## histdistHamilton Heights / Sugar Hill Northwest Historic District     0.376
## histdistHamilton Heights Historic District Extension                  0.199
## histdistIndividual Landmark                                          -1.314
## histdistLadies' Mile Historic District                                0.824
## histdistLamartine Place Historic District                             0.447
## histdistMadison Square North Historic District                        0.629
## histdistMetropolitan Museum Historic District                         1.718
## histdistMorningside Heights Historic District                         0.191
## histdistMount Morris Park Historic District                           0.206
## histdistMount Morris Park Historic District Extension                 1.132
## histdistMurray Hill Historic District                                -0.168
## histdistMurray Hill Historic District Extension                       0.130
## histdistNoHo East Historic District                                  -0.221
## histdistNoHo Historic District                                        0.112
## histdistNone                                                          0.985
## histdistPark Avenue Historic District                                 1.278
## histdistRiverside-West End Historic District                          0.226
## histdistRiverside-West End Historic District Extension I              0.638
## histdistRiverside-West End Historic District Extension II            -0.264
## histdistSoHo-Cast Iron Historic District                              0.366
## histdistSoHo-Cast Iron Historic District Extension                    0.790
## histdistSouth Village Historic District                               1.510
## histdistSt. Mark's Historic District                                  1.740
## histdistStuyvesant Square Historic District                           0.831
## histdistSullivan-Thompson Historic District                           1.178
## histdistTribeca East Historic District                                0.385
## histdistTribeca West Historic District                                0.497
## histdistTudor City Historic District                                 -0.698
## histdistUpper East Side Historic District                             1.333
## histdistUpper East Side Historic District Extension                   1.003
## histdistUpper West Side / Central Park West Historic District         1.620
## histdistWeehawken Street Historic District                            0.052
## histdistWest End-Collegiate Historic District                         1.299
## histdistWest End-Collegiate Historic District Extension               0.757
## landmarkNone                                                         -5.150
## builtfar                                                              2.186
## ASP                                                                   2.688
##                                                                     Pr(>|t|)
## (Intercept)                                                         0.199754
## BLDG_CLASSC4                                                        0.379931
## BLDG_CLASSC5                                                        0.481864
## BLDG_CLASSC6                                                        0.236395
## BLDG_CLASSC7                                                        0.360224
## BLDG_CLASSD0                                                        0.025766
## BLDG_CLASSD1                                                        0.116702
## BLDG_CLASSD3                                                        0.029852
## BLDG_CLASSD4                                                        0.000125
## BLDG_CLASSD5                                                        0.791908
## BLDG_CLASSD6                                                        0.053875
## BLDG_CLASSD7                                                        0.004826
## BLDG_CLASSD8                                                        0.014068
## BLDG_CLASSD9                                                        0.752099
## ZONINGC1-6                                                          1.76e-07
## ZONINGC1-7                                                          3.84e-06
## ZONINGC1-8                                                          3.42e-06
## ZONINGC1-9                                                          3.62e-08
## ZONINGC16A                                                          2.43e-07
## ZONINGC17A                                                          2.26e-05
## ZONINGC18A                                                          6.53e-08
## ZONINGC18X                                                          1.49e-07
## ZONINGC19A                                                          6.02e-07
## ZONINGC2-6                                                          1.32e-06
## ZONINGC2-7                                                          4.60e-05
## ZONINGC2-8                                                          1.35e-07
## ZONINGC26A                                                          1.66e-06
## ZONINGC27A                                                          7.44e-08
## ZONINGC28A                                                          4.04e-07
## ZONINGC4-4                                                          4.90e-06
## ZONINGC4-5                                                          4.38e-07
## ZONINGC4-7                                                          5.62e-06
## ZONINGC44A                                                          2.71e-07
## ZONINGC44D                                                          2.11e-05
## ZONINGC45A                                                          2.80e-05
## ZONINGC46A                                                          4.36e-07
## ZONINGC5-1                                                          3.72e-06
## ZONINGC5-2                                                          1.13e-07
## ZONINGC5-3                                                          1.44e-06
## ZONINGC5-5                                                          1.95e-08
## ZONINGC5-P                                                          2.50e-07
## ZONINGC51A                                                          2.66e-05
## ZONINGC52.5                                                         1.64e-06
## ZONINGC6-1                                                          9.17e-07
## ZONINGC6-2                                                          1.29e-06
## ZONINGC6-2G                                                         0.011546
## ZONINGC6-4                                                          4.65e-08
## ZONINGC6-6                                                          4.12e-06
## ZONINGC6-7                                                          2.16e-05
## ZONINGC62A                                                          5.23e-07
## ZONINGC62G                                                          2.06e-07
## ZONINGC62M                                                          6.33e-06
## ZONINGC63A                                                          1.34e-06
## ZONINGC63X                                                          2.25e-05
## ZONINGC64.5                                                         4.29e-07
## ZONINGC64A                                                          4.05e-07
## ZONINGC64M                                                          2.09e-06
## ZONINGC64X                                                          8.11e-06
## ZONINGC66.5                                                         5.37e-05
## ZONINGC8-4                                                          2.95e-06
## ZONINGM1-5                                                          9.12e-05
## ZONINGM1-6                                                          8.17e-07
## ZONINGM15M                                                          6.44e-06
## ZONINGM15R7D                                                        0.000218
## ZONINGM15R7X                                                        2.82e-05
## ZONINGM15R9A                                                        0.001105
## ZONINGM15R9X                                                        2.05e-05
## ZONINGM16D                                                          3.25e-06
## ZONINGR10                                                           1.70e-07
## ZONINGR10A                                                          1.15e-07
## ZONINGR10H                                                          3.22e-07
## ZONINGR6                                                            4.15e-08
## ZONINGR6A                                                           5.94e-06
## ZONINGR7-2                                                          2.63e-08
## ZONINGR7A                                                           2.11e-07
## ZONINGR7B                                                           1.56e-07
## ZONINGR7D                                                           4.20e-06
## ZONINGR8                                                            3.62e-08
## ZONINGR8A                                                           1.10e-07
## ZONINGR8B                                                           1.23e-07
## ZONINGR9                                                            3.82e-08
## ZONINGR9A                                                           4.62e-08
## ZONINGR9X                                                           4.52e-07
## LOT_IRREGR                                                          0.667920
## LOT_IRREGUnknown                                                    0.195409
## BLD_EXTEG                                                           0.867870
## BLD_EXTG                                                            0.041601
## BLD_EXTN                                                            0.402047
## BLD_STORY                                                           2.21e-14
## CORNERYes                                                           0.180764
## LAND_AREA                                                           0.016744
## NUM_BLDGS                                                           1.96e-06
## YRBUILT                                                             0.459044
## YRALT1                                                              0.063474
## YRALT2                                                              0.455324
## UNITS                                                               3.87e-10
## GROSS_SQFT                                                           < 2e-16
## OFFICE_AREA_GROSS                                                   4.71e-07
## FINTAXFLAGT                                                         0.005276
## schooldist02                                                        3.54e-07
## schooldist03                                                        0.001154
## schooldist04                                                        0.410228
## schooldist05                                                        0.873379
## schooldist06                                                        0.284921
## ltdheightLH-1A                                                      0.401973
## ltdheightNone                                                       0.586977
## easements                                                           0.013098
## histdistCarnegie Hill Historic District                             0.550446
## histdistCentral Harlem West -- 130-132nd Street Historic District   0.129277
## histdistCentral Park West-76th Street Historic District             0.615239
## histdistCentral Park West-West 73rd - 74th Street Historic District 0.073661
## histdistCharlton-King-Vandam Historic District                      0.390482
## histdistChelsea Historic District                                   0.409171
## histdistChelsea Historic District Extension                         0.722421
## histdistDorrance Brooks Square Historic District                    0.175242
## histdistEast Village / Lower East Side Historic District            0.240957
## histdistExpanded Carnegie Hill Historic District                    0.118171
## histdistGansevoort Market Historic District                         0.348849
## histdistGramercy Park Historic District                             0.284305
## histdistGreenwich Village Historic District                         0.081579
## histdistGreenwich Village Historic District Extension               0.218885
## histdistGreenwich Village Historic District Extension II            0.255110
## histdistHamilton Heights / Sugar Hill Historic District             0.386844
## histdistHamilton Heights / Sugar Hill Northeast Historic District   0.909688
## histdistHamilton Heights / Sugar Hill Northwest Historic District   0.706670
## histdistHamilton Heights Historic District Extension                0.842482
## histdistIndividual Landmark                                         0.189045
## histdistLadies' Mile Historic District                              0.409877
## histdistLamartine Place Historic District                           0.654789
## histdistMadison Square North Historic District                      0.529225
## histdistMetropolitan Museum Historic District                       0.085989
## histdistMorningside Heights Historic District                       0.848933
## histdistMount Morris Park Historic District                         0.836678
## histdistMount Morris Park Historic District Extension               0.257621
## histdistMurray Hill Historic District                               0.866362
## histdistMurray Hill Historic District Extension                     0.896315
## histdistNoHo East Historic District                                 0.825351
## histdistNoHo Historic District                                      0.910522
## histdistNone                                                        0.324644
## histdistPark Avenue Historic District                               0.201290
## histdistRiverside-West End Historic District                        0.821569
## histdistRiverside-West End Historic District Extension I            0.523532
## histdistRiverside-West End Historic District Extension II           0.791441
## histdistSoHo-Cast Iron Historic District                            0.714416
## histdistSoHo-Cast Iron Historic District Extension                  0.429633
## histdistSouth Village Historic District                             0.131306
## histdistSt. Mark's Historic District                                0.082110
## histdistStuyvesant Square Historic District                         0.406368
## histdistSullivan-Thompson Historic District                         0.239126
## histdistTribeca East Historic District                              0.700405
## histdistTribeca West Historic District                              0.619566
## histdistTudor City Historic District                                0.485265
## histdistUpper East Side Historic District                           0.182664
## histdistUpper East Side Historic District Extension                 0.315858
## histdistUpper West Side / Central Park West Historic District       0.105390
## histdistWeehawken Street Historic District                          0.958204
## histdistWest End-Collegiate Historic District                       0.194053
## histdistWest End-Collegiate Historic District Extension             0.449373
## landmarkNone                                                        2.89e-07
## builtfar                                                            0.028922
## ASP                                                                 0.007255
##                                                                        
## (Intercept)                                                            
## BLDG_CLASSC4                                                           
## BLDG_CLASSC5                                                           
## BLDG_CLASSC6                                                           
## BLDG_CLASSC7                                                           
## BLDG_CLASSD0                                                        *  
## BLDG_CLASSD1                                                           
## BLDG_CLASSD3                                                        *  
## BLDG_CLASSD4                                                        ***
## BLDG_CLASSD5                                                           
## BLDG_CLASSD6                                                        .  
## BLDG_CLASSD7                                                        ** 
## BLDG_CLASSD8                                                        *  
## BLDG_CLASSD9                                                           
## ZONINGC1-6                                                          ***
## ZONINGC1-7                                                          ***
## ZONINGC1-8                                                          ***
## ZONINGC1-9                                                          ***
## ZONINGC16A                                                          ***
## ZONINGC17A                                                          ***
## ZONINGC18A                                                          ***
## ZONINGC18X                                                          ***
## ZONINGC19A                                                          ***
## ZONINGC2-6                                                          ***
## ZONINGC2-7                                                          ***
## ZONINGC2-8                                                          ***
## ZONINGC26A                                                          ***
## ZONINGC27A                                                          ***
## ZONINGC28A                                                          ***
## ZONINGC4-4                                                          ***
## ZONINGC4-5                                                          ***
## ZONINGC4-7                                                          ***
## ZONINGC44A                                                          ***
## ZONINGC44D                                                          ***
## ZONINGC45A                                                          ***
## ZONINGC46A                                                          ***
## ZONINGC5-1                                                          ***
## ZONINGC5-2                                                          ***
## ZONINGC5-3                                                          ***
## ZONINGC5-5                                                          ***
## ZONINGC5-P                                                          ***
## ZONINGC51A                                                          ***
## ZONINGC52.5                                                         ***
## ZONINGC6-1                                                          ***
## ZONINGC6-2                                                          ***
## ZONINGC6-2G                                                         *  
## ZONINGC6-4                                                          ***
## ZONINGC6-6                                                          ***
## ZONINGC6-7                                                          ***
## ZONINGC62A                                                          ***
## ZONINGC62G                                                          ***
## ZONINGC62M                                                          ***
## ZONINGC63A                                                          ***
## ZONINGC63X                                                          ***
## ZONINGC64.5                                                         ***
## ZONINGC64A                                                          ***
## ZONINGC64M                                                          ***
## ZONINGC64X                                                          ***
## ZONINGC66.5                                                         ***
## ZONINGC8-4                                                          ***
## ZONINGM1-5                                                          ***
## ZONINGM1-6                                                          ***
## ZONINGM15M                                                          ***
## ZONINGM15R7D                                                        ***
## ZONINGM15R7X                                                        ***
## ZONINGM15R9A                                                        ** 
## ZONINGM15R9X                                                        ***
## ZONINGM16D                                                          ***
## ZONINGR10                                                           ***
## ZONINGR10A                                                          ***
## ZONINGR10H                                                          ***
## ZONINGR6                                                            ***
## ZONINGR6A                                                           ***
## ZONINGR7-2                                                          ***
## ZONINGR7A                                                           ***
## ZONINGR7B                                                           ***
## ZONINGR7D                                                           ***
## ZONINGR8                                                            ***
## ZONINGR8A                                                           ***
## ZONINGR8B                                                           ***
## ZONINGR9                                                            ***
## ZONINGR9A                                                           ***
## ZONINGR9X                                                           ***
## LOT_IRREGR                                                             
## LOT_IRREGUnknown                                                       
## BLD_EXTEG                                                              
## BLD_EXTG                                                            *  
## BLD_EXTN                                                               
## BLD_STORY                                                           ***
## CORNERYes                                                              
## LAND_AREA                                                           *  
## NUM_BLDGS                                                           ***
## YRBUILT                                                                
## YRALT1                                                              .  
## YRALT2                                                                 
## UNITS                                                               ***
## GROSS_SQFT                                                          ***
## OFFICE_AREA_GROSS                                                   ***
## FINTAXFLAGT                                                         ** 
## schooldist02                                                        ***
## schooldist03                                                        ** 
## schooldist04                                                           
## schooldist05                                                           
## schooldist06                                                           
## ltdheightLH-1A                                                         
## ltdheightNone                                                          
## easements                                                           *  
## histdistCarnegie Hill Historic District                                
## histdistCentral Harlem West -- 130-132nd Street Historic District      
## histdistCentral Park West-76th Street Historic District                
## histdistCentral Park West-West 73rd - 74th Street Historic District .  
## histdistCharlton-King-Vandam Historic District                         
## histdistChelsea Historic District                                      
## histdistChelsea Historic District Extension                            
## histdistDorrance Brooks Square Historic District                       
## histdistEast Village / Lower East Side Historic District               
## histdistExpanded Carnegie Hill Historic District                       
## histdistGansevoort Market Historic District                            
## histdistGramercy Park Historic District                                
## histdistGreenwich Village Historic District                         .  
## histdistGreenwich Village Historic District Extension                  
## histdistGreenwich Village Historic District Extension II               
## histdistHamilton Heights / Sugar Hill Historic District                
## histdistHamilton Heights / Sugar Hill Northeast Historic District      
## histdistHamilton Heights / Sugar Hill Northwest Historic District      
## histdistHamilton Heights Historic District Extension                   
## histdistIndividual Landmark                                            
## histdistLadies' Mile Historic District                                 
## histdistLamartine Place Historic District                              
## histdistMadison Square North Historic District                         
## histdistMetropolitan Museum Historic District                       .  
## histdistMorningside Heights Historic District                          
## histdistMount Morris Park Historic District                            
## histdistMount Morris Park Historic District Extension                  
## histdistMurray Hill Historic District                                  
## histdistMurray Hill Historic District Extension                        
## histdistNoHo East Historic District                                    
## histdistNoHo Historic District                                         
## histdistNone                                                           
## histdistPark Avenue Historic District                                  
## histdistRiverside-West End Historic District                           
## histdistRiverside-West End Historic District Extension I               
## histdistRiverside-West End Historic District Extension II              
## histdistSoHo-Cast Iron Historic District                               
## histdistSoHo-Cast Iron Historic District Extension                     
## histdistSouth Village Historic District                                
## histdistSt. Mark's Historic District                                .  
## histdistStuyvesant Square Historic District                            
## histdistSullivan-Thompson Historic District                            
## histdistTribeca East Historic District                                 
## histdistTribeca West Historic District                                 
## histdistTudor City Historic District                                   
## histdistUpper East Side Historic District                              
## histdistUpper East Side Historic District Extension                    
## histdistUpper West Side / Central Park West Historic District          
## histdistWeehawken Street Historic District                             
## histdistWest End-Collegiate Historic District                          
## histdistWest End-Collegiate Historic District Extension                
## landmarkNone                                                        ***
## builtfar                                                            *  
## ASP                                                                 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 8133000 on 1762 degrees of freedom
##   (11389 observations deleted due to missingness)
## Multiple R-squared:  0.9593, Adjusted R-squared:  0.9556 
## F-statistic: 259.3 on 160 and 1762 DF,  p-value: < 2.2e-16


Residual Analysis

We check the Q-Q plot and it’s clear that we have heteroscedasticity because residuals don’t have equal variance across low to high values.

This suggests, which is typical of financial modeling, that we should have taken the log of FINMKTTOT which we will do, along with check out the one extreme outlier, record 6230.

plot(lm_model)


Log Transformation

While taking the log of assessed market value lowered the R-squared from 0.956 to 0.884, the residuals are much better behaved as seen in the quartile table below. Since the median is close to zero in the log model we can move forward with establishing confidence in our logged model.

Residuals Before Logged
Min -132838164 -3.9551
1Q -2835402 -0.2127
Median -79981 -.0038
3Q 2736015 0.2372
Max 58882393 1.3260

Note since we’re looking at a logged target value our coefficients are multiplicative instead of additive, also known as elasticities. For example, the coefficients of GROSS_SQFT was 3.548 meaning each additional square foot adds $3.55 in assessed market value, while in the logged model the 3.1e-06 coefficient says that each additional square foot ads 0.0003% to assessed value. T

lm_model_log <- lm(log(FINMKTTOT) ~ ., data = df5)

summary(lm_model_log)
## 
## Call:
## lm(formula = log(FINMKTTOT) ~ ., data = df5)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.9551 -0.2127  0.0038  0.2372  1.3260 
## 
## Coefficients:
##                                                                       Estimate
## (Intercept)                                                          7.524e+00
## BLDG_CLASSC4                                                        -4.712e-02
## BLDG_CLASSC5                                                        -1.270e-01
## BLDG_CLASSC6                                                         1.206e-01
## BLDG_CLASSC7                                                         1.725e-01
## BLDG_CLASSD0                                                         1.103e+00
## BLDG_CLASSD1                                                         5.385e-01
## BLDG_CLASSD3                                                         4.793e-01
## BLDG_CLASSD4                                                         9.821e-01
## BLDG_CLASSD5                                                         3.535e-01
## BLDG_CLASSD6                                                         4.531e-01
## BLDG_CLASSD7                                                         7.493e-01
## BLDG_CLASSD8                                                        -1.600e-01
## BLDG_CLASSD9                                                         8.362e-01
## ZONINGC1-6                                                          -1.218e+00
## ZONINGC1-7                                                          -1.064e+00
## ZONINGC1-8                                                          -1.426e+00
## ZONINGC1-9                                                          -1.355e+00
## ZONINGC16A                                                          -1.303e+00
## ZONINGC17A                                                          -1.376e+00
## ZONINGC18A                                                          -1.353e+00
## ZONINGC18X                                                          -1.277e+00
## ZONINGC19A                                                          -1.295e+00
## ZONINGC2-6                                                          -1.086e+00
## ZONINGC2-7                                                          -1.079e+00
## ZONINGC2-8                                                          -1.427e+00
## ZONINGC26A                                                          -9.905e-01
## ZONINGC27A                                                          -1.318e+00
## ZONINGC28A                                                          -1.231e+00
## ZONINGC4-4                                                          -8.901e-01
## ZONINGC4-5                                                          -1.387e+00
## ZONINGC4-7                                                          -1.071e+00
## ZONINGC44A                                                          -1.216e+00
## ZONINGC44D                                                          -1.106e+00
## ZONINGC45A                                                          -1.333e+00
## ZONINGC46A                                                          -9.349e-01
## ZONINGC5-1                                                          -1.162e+00
## ZONINGC5-2                                                          -1.215e+00
## ZONINGC5-3                                                          -1.160e+00
## ZONINGC5-5                                                          -1.823e+00
## ZONINGC5-P                                                          -1.101e+00
## ZONINGC51A                                                          -1.292e+00
## ZONINGC52.5                                                         -1.244e+00
## ZONINGC6-1                                                          -1.317e+00
## ZONINGC6-2                                                          -1.133e+00
## ZONINGC6-2G                                                         -3.363e-01
## ZONINGC6-4                                                          -1.434e+00
## ZONINGC6-6                                                          -1.262e+00
## ZONINGC6-7                                                          -9.306e-01
## ZONINGC62A                                                          -1.168e+00
## ZONINGC62G                                                          -1.251e+00
## ZONINGC62M                                                          -1.119e+00
## ZONINGC63A                                                          -1.265e+00
## ZONINGC63X                                                          -8.552e-01
## ZONINGC64.5                                                         -1.596e+00
## ZONINGC64A                                                          -1.315e+00
## ZONINGC64M                                                          -1.015e+00
## ZONINGC64X                                                          -1.413e+00
## ZONINGC66.5                                                         -8.247e-01
## ZONINGC8-4                                                          -1.390e+00
## ZONINGM1-5                                                          -1.054e+00
## ZONINGM1-6                                                          -1.176e+00
## ZONINGM15M                                                          -1.401e+00
## ZONINGM15R7D                                                        -1.337e+00
## ZONINGM15R7X                                                        -1.232e+00
## ZONINGM15R9A                                                        -6.085e-01
## ZONINGM15R9X                                                        -1.360e+00
## ZONINGM16D                                                          -1.599e+00
## ZONINGR10                                                           -1.227e+00
## ZONINGR10A                                                          -1.179e+00
## ZONINGR10H                                                          -1.337e+00
## ZONINGR6                                                            -1.322e+00
## ZONINGR6A                                                           -2.132e+00
## ZONINGR7-2                                                          -1.323e+00
## ZONINGR7A                                                           -1.495e+00
## ZONINGR7B                                                           -1.349e+00
## ZONINGR7D                                                           -1.876e+00
## ZONINGR8                                                            -1.328e+00
## ZONINGR8A                                                           -1.361e+00
## ZONINGR8B                                                           -1.326e+00
## ZONINGR9                                                            -1.159e+00
## ZONINGR9A                                                           -1.213e+00
## ZONINGR9X                                                           -1.229e+00
## LOT_IRREGR                                                          -6.537e-02
## LOT_IRREGUnknown                                                     2.084e-02
## BLD_EXTEG                                                            1.481e-01
## BLD_EXTG                                                             3.453e-01
## BLD_EXTN                                                             1.213e-01
## BLD_STORY                                                            1.837e-02
## CORNERYes                                                            1.898e-01
## LAND_AREA                                                           -4.812e-06
## NUM_BLDGS                                                            8.287e-02
## YRBUILT                                                              4.210e-03
## YRALT1                                                              -1.487e-05
## YRALT2                                                               6.059e-05
## UNITS                                                                8.847e-04
## GROSS_SQFT                                                           3.118e-06
## OFFICE_AREA_GROSS                                                    7.833e-06
## FINTAXFLAGT                                                          1.319e-01
## schooldist02                                                        -8.149e-03
## schooldist03                                                        -2.858e-01
## schooldist04                                                        -6.026e-01
## schooldist05                                                        -6.367e-01
## schooldist06                                                        -5.629e-01
## ltdheightLH-1A                                                       5.396e-01
## ltdheightNone                                                        3.770e-01
## easements                                                           -4.129e-01
## histdistCarnegie Hill Historic District                             -5.690e-01
## histdistCentral Harlem West -- 130-132nd Street Historic District   -8.295e-01
## histdistCentral Park West-76th Street Historic District             -2.799e-01
## histdistCentral Park West-West 73rd - 74th Street Historic District -2.074e-01
## histdistCharlton-King-Vandam Historic District                      -4.710e-01
## histdistChelsea Historic District                                   -5.486e-01
## histdistChelsea Historic District Extension                         -6.043e-01
## histdistDorrance Brooks Square Historic District                    -1.372e+00
## histdistEast Village / Lower East Side Historic District            -5.636e-01
## histdistExpanded Carnegie Hill Historic District                    -3.484e-01
## histdistGansevoort Market Historic District                         -9.540e-01
## histdistGramercy Park Historic District                             -2.196e-01
## histdistGreenwich Village Historic District                         -3.731e-01
## histdistGreenwich Village Historic District Extension                1.873e-01
## histdistGreenwich Village Historic District Extension II            -5.290e-01
## histdistHamilton Heights / Sugar Hill Historic District             -9.411e-01
## histdistHamilton Heights / Sugar Hill Northeast Historic District    4.111e-02
## histdistHamilton Heights / Sugar Hill Northwest Historic District    9.396e-02
## histdistHamilton Heights Historic District Extension                 5.134e-02
## histdistIndividual Landmark                                         -5.797e-02
## histdistLadies' Mile Historic District                              -4.513e-01
## histdistLamartine Place Historic District                           -2.060e-01
## histdistMadison Square North Historic District                      -4.658e-01
## histdistMetropolitan Museum Historic District                       -2.644e-01
## histdistMorningside Heights Historic District                       -4.679e-01
## histdistMount Morris Park Historic District                         -2.656e-01
## histdistMount Morris Park Historic District Extension               -5.834e-01
## histdistMurray Hill Historic District                               -4.480e-01
## histdistMurray Hill Historic District Extension                     -3.282e-01
## histdistNoHo East Historic District                                 -7.272e-01
## histdistNoHo Historic District                                      -1.055e+00
## histdistNone                                                        -4.527e-01
## histdistPark Avenue Historic District                               -2.640e-01
## histdistRiverside-West End Historic District                        -3.367e-01
## histdistRiverside-West End Historic District Extension I            -3.964e-01
## histdistRiverside-West End Historic District Extension II           -5.162e-01
## histdistSoHo-Cast Iron Historic District                            -3.876e-01
## histdistSoHo-Cast Iron Historic District Extension                  -3.456e-01
## histdistSouth Village Historic District                             -4.014e-01
## histdistSt. Mark's Historic District                                 2.650e-01
## histdistStuyvesant Square Historic District                         -7.666e-01
## histdistSullivan-Thompson Historic District                         -3.249e-01
## histdistTribeca East Historic District                              -6.999e-01
## histdistTribeca West Historic District                              -7.742e-01
## histdistTudor City Historic District                                -5.684e-01
## histdistUpper East Side Historic District                           -3.748e-01
## histdistUpper East Side Historic District Extension                 -3.482e-01
## histdistUpper West Side / Central Park West Historic District       -1.369e-01
## histdistWeehawken Street Historic District                          -1.525e+00
## histdistWest End-Collegiate Historic District                       -1.750e-01
## histdistWest End-Collegiate Historic District Extension             -2.826e-01
## landmarkNone                                                         5.887e-02
## builtfar                                                             5.182e-02
## ASP                                                                  4.844e-09
##                                                                     Std. Error
## (Intercept)                                                          1.425e+00
## BLDG_CLASSC4                                                         1.053e-01
## BLDG_CLASSC5                                                         1.081e-01
## BLDG_CLASSC6                                                         7.282e-02
## BLDG_CLASSC7                                                         7.898e-02
## BLDG_CLASSD0                                                         1.002e-01
## BLDG_CLASSD1                                                         1.144e-01
## BLDG_CLASSD3                                                         1.496e-01
## BLDG_CLASSD4                                                         7.139e-02
## BLDG_CLASSD5                                                         2.997e-01
## BLDG_CLASSD6                                                         1.257e-01
## BLDG_CLASSD7                                                         1.471e-01
## BLDG_CLASSD8                                                         4.489e-01
## BLDG_CLASSD9                                                         1.452e-01
## ZONINGC1-6                                                           5.570e-01
## ZONINGC1-7                                                           5.550e-01
## ZONINGC1-8                                                           6.136e-01
## ZONINGC1-9                                                           5.441e-01
## ZONINGC16A                                                           5.516e-01
## ZONINGC17A                                                           6.801e-01
## ZONINGC18A                                                           5.531e-01
## ZONINGC18X                                                           5.467e-01
## ZONINGC19A                                                           5.551e-01
## ZONINGC2-6                                                           5.737e-01
## ZONINGC2-7                                                           6.831e-01
## ZONINGC2-8                                                           5.472e-01
## ZONINGC26A                                                           5.942e-01
## ZONINGC27A                                                           5.583e-01
## ZONINGC28A                                                           5.696e-01
## ZONINGC4-4                                                           5.955e-01
## ZONINGC4-5                                                           5.986e-01
## ZONINGC4-7                                                           5.743e-01
## ZONINGC44A                                                           5.589e-01
## ZONINGC44D                                                           6.309e-01
## ZONINGC45A                                                           6.824e-01
## ZONINGC46A                                                           5.514e-01
## ZONINGC5-1                                                           5.471e-01
## ZONINGC5-2                                                           5.272e-01
## ZONINGC5-3                                                           5.586e-01
## ZONINGC5-5                                                           5.794e-01
## ZONINGC5-P                                                           5.719e-01
## ZONINGC51A                                                           6.860e-01
## ZONINGC52.5                                                          5.923e-01
## ZONINGC6-1                                                           5.585e-01
## ZONINGC6-2                                                           5.494e-01
## ZONINGC6-2G                                                          7.813e-01
## ZONINGC6-4                                                           5.588e-01
## ZONINGC6-6                                                           5.894e-01
## ZONINGC6-7                                                           6.811e-01
## ZONINGC62A                                                           5.514e-01
## ZONINGC62G                                                           5.931e-01
## ZONINGC62M                                                           5.714e-01
## ZONINGC63A                                                           5.597e-01
## ZONINGC63X                                                           6.784e-01
## ZONINGC64.5                                                          5.903e-01
## ZONINGC64A                                                           5.665e-01
## ZONINGC64M                                                           5.818e-01
## ZONINGC64X                                                           6.849e-01
## ZONINGC66.5                                                          6.799e-01
## ZONINGC8-4                                                           6.137e-01
## ZONINGM1-5                                                           6.806e-01
## ZONINGM1-6                                                           5.557e-01
## ZONINGM15M                                                           6.417e-01
## ZONINGM15R7D                                                         7.552e-01
## ZONINGM15R7X                                                         6.148e-01
## ZONINGM15R9A                                                         8.016e-01
## ZONINGM15R9X                                                         6.339e-01
## ZONINGM16D                                                           6.801e-01
## ZONINGR10                                                            5.424e-01
## ZONINGR10A                                                           5.421e-01
## ZONINGR10H                                                           5.705e-01
## ZONINGR6                                                             5.521e-01
## ZONINGR6A                                                            5.809e-01
## ZONINGR7-2                                                           5.424e-01
## ZONINGR7A                                                            5.433e-01
## ZONINGR7B                                                            5.471e-01
## ZONINGR7D                                                            5.817e-01
## ZONINGR8                                                             5.411e-01
## ZONINGR8A                                                            5.461e-01
## ZONINGR8B                                                            5.403e-01
## ZONINGR9                                                             5.525e-01
## ZONINGR9A                                                            5.505e-01
## ZONINGR9X                                                            5.731e-01
## LOT_IRREGR                                                           2.476e-02
## LOT_IRREGUnknown                                                     2.468e-01
## BLD_EXTEG                                                            4.206e-01
## BLD_EXTG                                                             1.073e-01
## BLD_EXTN                                                             4.510e-02
## BLD_STORY                                                            4.076e-03
## CORNERYes                                                            2.701e-02
## LAND_AREA                                                            4.292e-07
## NUM_BLDGS                                                            1.360e-02
## YRBUILT                                                              6.274e-04
## YRALT1                                                               1.097e-05
## YRALT2                                                               2.031e-05
## UNITS                                                                2.689e-04
## GROSS_SQFT                                                           1.805e-07
## OFFICE_AREA_GROSS                                                    3.484e-06
## FINTAXFLAGT                                                          2.429e-02
## schooldist02                                                         5.825e-02
## schooldist03                                                         6.913e-02
## schooldist04                                                         1.283e-01
## schooldist05                                                         8.084e-02
## schooldist06                                                         7.102e-02
## ltdheightLH-1A                                                       4.735e-01
## ltdheightNone                                                        4.672e-01
## easements                                                            1.760e-01
## histdistCarnegie Hill Historic District                              3.886e-01
## histdistCentral Harlem West -- 130-132nd Street Historic District    4.927e-01
## histdistCentral Park West-76th Street Historic District              4.866e-01
## histdistCentral Park West-West 73rd - 74th Street Historic District  3.457e-01
## histdistCharlton-King-Vandam Historic District                       4.959e-01
## histdistChelsea Historic District                                    3.146e-01
## histdistChelsea Historic District Extension                          3.956e-01
## histdistDorrance Brooks Square Historic District                     4.934e-01
## histdistEast Village / Lower East Side Historic District             3.001e-01
## histdistExpanded Carnegie Hill Historic District                     2.577e-01
## histdistGansevoort Market Historic District                          4.993e-01
## histdistGramercy Park Historic District                              4.936e-01
## histdistGreenwich Village Historic District                          2.657e-01
## histdistGreenwich Village Historic District Extension                4.945e-01
## histdistGreenwich Village Historic District Extension II             3.156e-01
## histdistHamilton Heights / Sugar Hill Historic District              3.848e-01
## histdistHamilton Heights / Sugar Hill Northeast Historic District    3.174e-01
## histdistHamilton Heights / Sugar Hill Northwest Historic District    4.037e-01
## histdistHamilton Heights Historic District Extension                 4.373e-01
## histdistIndividual Landmark                                          3.043e-01
## histdistLadies' Mile Historic District                               3.446e-01
## histdistLamartine Place Historic District                            4.837e-01
## histdistMadison Square North Historic District                       5.185e-01
## histdistMetropolitan Museum Historic District                        2.811e-01
## histdistMorningside Heights Historic District                        2.662e-01
## histdistMount Morris Park Historic District                          4.903e-01
## histdistMount Morris Park Historic District Extension                3.963e-01
## histdistMurray Hill Historic District                                3.884e-01
## histdistMurray Hill Historic District Extension                      4.832e-01
## histdistNoHo East Historic District                                  4.185e-01
## histdistNoHo Historic District                                       5.698e-01
## histdistNone                                                         2.468e-01
## histdistPark Avenue Historic District                                2.606e-01
## histdistRiverside-West End Historic District                         2.618e-01
## histdistRiverside-West End Historic District Extension I             2.593e-01
## histdistRiverside-West End Historic District Extension II            2.558e-01
## histdistSoHo-Cast Iron Historic District                             3.946e-01
## histdistSoHo-Cast Iron Historic District Extension                   4.128e-01
## histdistSouth Village Historic District                              3.167e-01
## histdistSt. Mark's Historic District                                 4.898e-01
## histdistStuyvesant Square Historic District                          3.566e-01
## histdistSullivan-Thompson Historic District                          2.966e-01
## histdistTribeca East Historic District                               3.963e-01
## histdistTribeca West Historic District                               3.197e-01
## histdistTudor City Historic District                                 2.875e-01
## histdistUpper East Side Historic District                            2.560e-01
## histdistUpper East Side Historic District Extension                  2.787e-01
## histdistUpper West Side / Central Park West Historic District        2.527e-01
## histdistWeehawken Street Historic District                           4.952e-01
## histdistWest End-Collegiate Historic District                        3.023e-01
## histdistWest End-Collegiate Historic District Extension              2.595e-01
## landmarkNone                                                         1.336e-01
## builtfar                                                             6.377e-03
## ASP                                                                  1.402e-09
##                                                                     t value
## (Intercept)                                                           5.278
## BLDG_CLASSC4                                                         -0.447
## BLDG_CLASSC5                                                         -1.175
## BLDG_CLASSC6                                                          1.657
## BLDG_CLASSC7                                                          2.184
## BLDG_CLASSD0                                                         11.012
## BLDG_CLASSD1                                                          4.708
## BLDG_CLASSD3                                                          3.205
## BLDG_CLASSD4                                                         13.756
## BLDG_CLASSD5                                                          1.180
## BLDG_CLASSD6                                                          3.603
## BLDG_CLASSD7                                                          5.094
## BLDG_CLASSD8                                                         -0.356
## BLDG_CLASSD9                                                          5.760
## ZONINGC1-6                                                           -2.187
## ZONINGC1-7                                                           -1.917
## ZONINGC1-8                                                           -2.324
## ZONINGC1-9                                                           -2.490
## ZONINGC16A                                                           -2.362
## ZONINGC17A                                                           -2.023
## ZONINGC18A                                                           -2.446
## ZONINGC18X                                                           -2.336
## ZONINGC19A                                                           -2.332
## ZONINGC2-6                                                           -1.894
## ZONINGC2-7                                                           -1.580
## ZONINGC2-8                                                           -2.608
## ZONINGC26A                                                           -1.667
## ZONINGC27A                                                           -2.361
## ZONINGC28A                                                           -2.161
## ZONINGC4-4                                                           -1.495
## ZONINGC4-5                                                           -2.318
## ZONINGC4-7                                                           -1.864
## ZONINGC44A                                                           -2.176
## ZONINGC44D                                                           -1.753
## ZONINGC45A                                                           -1.954
## ZONINGC46A                                                           -1.695
## ZONINGC5-1                                                           -2.123
## ZONINGC5-2                                                           -2.305
## ZONINGC5-3                                                           -2.076
## ZONINGC5-5                                                           -3.147
## ZONINGC5-P                                                           -1.924
## ZONINGC51A                                                           -1.884
## ZONINGC52.5                                                          -2.100
## ZONINGC6-1                                                           -2.358
## ZONINGC6-2                                                           -2.063
## ZONINGC6-2G                                                          -0.430
## ZONINGC6-4                                                           -2.566
## ZONINGC6-6                                                           -2.141
## ZONINGC6-7                                                           -1.366
## ZONINGC62A                                                           -2.119
## ZONINGC62G                                                           -2.109
## ZONINGC62M                                                           -1.958
## ZONINGC63A                                                           -2.261
## ZONINGC63X                                                           -1.261
## ZONINGC64.5                                                          -2.703
## ZONINGC64A                                                           -2.322
## ZONINGC64M                                                           -1.745
## ZONINGC64X                                                           -2.063
## ZONINGC66.5                                                          -1.213
## ZONINGC8-4                                                           -2.266
## ZONINGM1-5                                                           -1.549
## ZONINGM1-6                                                           -2.116
## ZONINGM15M                                                           -2.183
## ZONINGM15R7D                                                         -1.771
## ZONINGM15R7X                                                         -2.004
## ZONINGM15R9A                                                         -0.759
## ZONINGM15R9X                                                         -2.146
## ZONINGM16D                                                           -2.351
## ZONINGR10                                                            -2.262
## ZONINGR10A                                                           -2.175
## ZONINGR10H                                                           -2.344
## ZONINGR6                                                             -2.395
## ZONINGR6A                                                            -3.670
## ZONINGR7-2                                                           -2.439
## ZONINGR7A                                                            -2.752
## ZONINGR7B                                                            -2.466
## ZONINGR7D                                                            -3.225
## ZONINGR8                                                             -2.454
## ZONINGR8A                                                            -2.492
## ZONINGR8B                                                            -2.454
## ZONINGR9                                                             -2.098
## ZONINGR9A                                                            -2.204
## ZONINGR9X                                                            -2.145
## LOT_IRREGR                                                           -2.640
## LOT_IRREGUnknown                                                      0.084
## BLD_EXTEG                                                             0.352
## BLD_EXTG                                                              3.217
## BLD_EXTN                                                              2.690
## BLD_STORY                                                             4.508
## CORNERYes                                                             7.029
## LAND_AREA                                                           -11.213
## NUM_BLDGS                                                             6.093
## YRBUILT                                                               6.709
## YRALT1                                                               -1.355
## YRALT2                                                                2.984
## UNITS                                                                 3.290
## GROSS_SQFT                                                           17.274
## OFFICE_AREA_GROSS                                                     2.248
## FINTAXFLAGT                                                           5.428
## schooldist02                                                         -0.140
## schooldist03                                                         -4.134
## schooldist04                                                         -4.698
## schooldist05                                                         -7.877
## schooldist06                                                         -7.926
## ltdheightLH-1A                                                        1.140
## ltdheightNone                                                         0.807
## easements                                                            -2.347
## histdistCarnegie Hill Historic District                              -1.464
## histdistCentral Harlem West -- 130-132nd Street Historic District    -1.684
## histdistCentral Park West-76th Street Historic District              -0.575
## histdistCentral Park West-West 73rd - 74th Street Historic District  -0.600
## histdistCharlton-King-Vandam Historic District                       -0.950
## histdistChelsea Historic District                                    -1.744
## histdistChelsea Historic District Extension                          -1.527
## histdistDorrance Brooks Square Historic District                     -2.780
## histdistEast Village / Lower East Side Historic District             -1.878
## histdistExpanded Carnegie Hill Historic District                     -1.352
## histdistGansevoort Market Historic District                          -1.911
## histdistGramercy Park Historic District                              -0.445
## histdistGreenwich Village Historic District                          -1.404
## histdistGreenwich Village Historic District Extension                 0.379
## histdistGreenwich Village Historic District Extension II             -1.676
## histdistHamilton Heights / Sugar Hill Historic District              -2.445
## histdistHamilton Heights / Sugar Hill Northeast Historic District     0.130
## histdistHamilton Heights / Sugar Hill Northwest Historic District     0.233
## histdistHamilton Heights Historic District Extension                  0.117
## histdistIndividual Landmark                                          -0.190
## histdistLadies' Mile Historic District                               -1.309
## histdistLamartine Place Historic District                            -0.426
## histdistMadison Square North Historic District                       -0.898
## histdistMetropolitan Museum Historic District                        -0.940
## histdistMorningside Heights Historic District                        -1.758
## histdistMount Morris Park Historic District                          -0.542
## histdistMount Morris Park Historic District Extension                -1.472
## histdistMurray Hill Historic District                                -1.153
## histdistMurray Hill Historic District Extension                      -0.679
## histdistNoHo East Historic District                                  -1.738
## histdistNoHo Historic District                                       -1.852
## histdistNone                                                         -1.834
## histdistPark Avenue Historic District                                -1.013
## histdistRiverside-West End Historic District                         -1.286
## histdistRiverside-West End Historic District Extension I             -1.529
## histdistRiverside-West End Historic District Extension II            -2.018
## histdistSoHo-Cast Iron Historic District                             -0.982
## histdistSoHo-Cast Iron Historic District Extension                   -0.837
## histdistSouth Village Historic District                              -1.267
## histdistSt. Mark's Historic District                                  0.541
## histdistStuyvesant Square Historic District                          -2.150
## histdistSullivan-Thompson Historic District                          -1.095
## histdistTribeca East Historic District                               -1.766
## histdistTribeca West Historic District                               -2.422
## histdistTudor City Historic District                                 -1.977
## histdistUpper East Side Historic District                            -1.464
## histdistUpper East Side Historic District Extension                  -1.250
## histdistUpper West Side / Central Park West Historic District        -0.542
## histdistWeehawken Street Historic District                           -3.080
## histdistWest End-Collegiate Historic District                        -0.579
## histdistWest End-Collegiate Historic District Extension              -1.089
## landmarkNone                                                          0.441
## builtfar                                                              8.126
## ASP                                                                   3.455
##                                                                     Pr(>|t|)
## (Intercept)                                                         1.47e-07
## BLDG_CLASSC4                                                        0.654586
## BLDG_CLASSC5                                                        0.240237
## BLDG_CLASSC6                                                        0.097742
## BLDG_CLASSC7                                                        0.029077
## BLDG_CLASSD0                                                         < 2e-16
## BLDG_CLASSD1                                                        2.69e-06
## BLDG_CLASSD3                                                        0.001376
## BLDG_CLASSD4                                                         < 2e-16
## BLDG_CLASSD5                                                        0.238284
## BLDG_CLASSD6                                                        0.000323
## BLDG_CLASSD7                                                        3.89e-07
## BLDG_CLASSD8                                                        0.721644
## BLDG_CLASSD9                                                        9.91e-09
## ZONINGC1-6                                                          0.028877
## ZONINGC1-7                                                          0.055413
## ZONINGC1-8                                                          0.020227
## ZONINGC1-9                                                          0.012866
## ZONINGC16A                                                          0.018300
## ZONINGC17A                                                          0.043250
## ZONINGC18A                                                          0.014549
## ZONINGC18X                                                          0.019619
## ZONINGC19A                                                          0.019791
## ZONINGC2-6                                                          0.058436
## ZONINGC2-7                                                          0.114370
## ZONINGC2-8                                                          0.009184
## ZONINGC26A                                                          0.095688
## ZONINGC27A                                                          0.018318
## ZONINGC28A                                                          0.030860
## ZONINGC4-4                                                          0.135156
## ZONINGC4-5                                                          0.020577
## ZONINGC4-7                                                          0.062484
## ZONINGC44A                                                          0.029686
## ZONINGC44D                                                          0.079854
## ZONINGC45A                                                          0.050876
## ZONINGC46A                                                          0.090159
## ZONINGC5-1                                                          0.033885
## ZONINGC5-2                                                          0.021307
## ZONINGC5-3                                                          0.038020
## ZONINGC5-5                                                          0.001679
## ZONINGC5-P                                                          0.054458
## ZONINGC51A                                                          0.059761
## ZONINGC52.5                                                         0.035851
## ZONINGC6-1                                                          0.018497
## ZONINGC6-2                                                          0.039301
## ZONINGC6-2G                                                         0.666944
## ZONINGC6-4                                                          0.010375
## ZONINGC6-6                                                          0.032446
## ZONINGC6-7                                                          0.172001
## ZONINGC62A                                                          0.034241
## ZONINGC62G                                                          0.035069
## ZONINGC62M                                                          0.050357
## ZONINGC63A                                                          0.023909
## ZONINGC63X                                                          0.207585
## ZONINGC64.5                                                         0.006931
## ZONINGC64A                                                          0.020340
## ZONINGC64M                                                          0.081146
## ZONINGC64X                                                          0.039226
## ZONINGC66.5                                                         0.225260
## ZONINGC8-4                                                          0.023601
## ZONINGM1-5                                                          0.121606
## ZONINGM1-6                                                          0.034446
## ZONINGM15M                                                          0.029137
## ZONINGM15R7D                                                        0.076817
## ZONINGM15R7X                                                        0.045223
## ZONINGM15R9A                                                        0.447883
## ZONINGM15R9X                                                        0.032000
## ZONINGM16D                                                          0.018834
## ZONINGR10                                                           0.023841
## ZONINGR10A                                                          0.029751
## ZONINGR10H                                                          0.019172
## ZONINGR6                                                            0.016745
## ZONINGR6A                                                           0.000249
## ZONINGR7-2                                                          0.014815
## ZONINGR7A                                                           0.005989
## ZONINGR7B                                                           0.013776
## ZONINGR7D                                                           0.001282
## ZONINGR8                                                            0.014225
## ZONINGR8A                                                           0.012800
## ZONINGR8B                                                           0.014211
## ZONINGR9                                                            0.036013
## ZONINGR9A                                                           0.027639
## ZONINGR9X                                                           0.032104
## LOT_IRREGR                                                          0.008358
## LOT_IRREGUnknown                                                    0.932705
## BLD_EXTEG                                                           0.724744
## BLD_EXTG                                                            0.001319
## BLD_EXTN                                                            0.007208
## BLD_STORY                                                           6.97e-06
## CORNERYes                                                           2.96e-12
## LAND_AREA                                                            < 2e-16
## NUM_BLDGS                                                           1.36e-09
## YRBUILT                                                             2.63e-11
## YRALT1                                                              0.175446
## YRALT2                                                              0.002884
## UNITS                                                               0.001023
## GROSS_SQFT                                                           < 2e-16
## OFFICE_AREA_GROSS                                                   0.024695
## FINTAXFLAGT                                                         6.50e-08
## schooldist02                                                        0.888747
## schooldist03                                                        3.73e-05
## schooldist04                                                        2.83e-06
## schooldist05                                                        5.83e-15
## schooldist06                                                        3.98e-15
## ltdheightLH-1A                                                      0.254623
## ltdheightNone                                                       0.419918
## easements                                                           0.019056
## histdistCarnegie Hill Historic District                             0.143313
## histdistCentral Harlem West -- 130-132nd Street Historic District   0.092421
## histdistCentral Park West-76th Street Historic District             0.565201
## histdistCentral Park West-West 73rd - 74th Street Historic District 0.548609
## histdistCharlton-King-Vandam Historic District                      0.342311
## histdistChelsea Historic District                                   0.081338
## histdistChelsea Historic District Extension                         0.126837
## histdistDorrance Brooks Square Historic District                    0.005489
## histdistEast Village / Lower East Side Historic District            0.060518
## histdistExpanded Carnegie Hill Historic District                    0.176514
## histdistGansevoort Market Historic District                         0.056224
## histdistGramercy Park Historic District                             0.656481
## histdistGreenwich Village Historic District                         0.160488
## histdistGreenwich Village Historic District Extension               0.704819
## histdistGreenwich Village Historic District Extension II            0.093900
## histdistHamilton Heights / Sugar Hill Historic District             0.014565
## histdistHamilton Heights / Sugar Hill Northeast Historic District   0.896968
## histdistHamilton Heights / Sugar Hill Northwest Historic District   0.815996
## histdistHamilton Heights Historic District Extension                0.906553
## histdistIndividual Landmark                                         0.848944
## histdistLadies' Mile Historic District                              0.190567
## histdistLamartine Place Historic District                           0.670220
## histdistMadison Square North Historic District                      0.369179
## histdistMetropolitan Museum Historic District                       0.347115
## histdistMorningside Heights Historic District                       0.078950
## histdistMount Morris Park Historic District                         0.588021
## histdistMount Morris Park Historic District Extension               0.141157
## histdistMurray Hill Historic District                               0.248911
## histdistMurray Hill Historic District Extension                     0.497114
## histdistNoHo East Historic District                                 0.082413
## histdistNoHo Historic District                                      0.064162
## histdistNone                                                        0.066805
## histdistPark Avenue Historic District                               0.311081
## histdistRiverside-West End Historic District                        0.198612
## histdistRiverside-West End Historic District Extension I            0.126490
## histdistRiverside-West End Historic District Extension II           0.043752
## histdistSoHo-Cast Iron Historic District                            0.326158
## histdistSoHo-Cast Iron Historic District Extension                  0.402564
## histdistSouth Village Historic District                             0.205192
## histdistSt. Mark's Historic District                                0.588567
## histdistStuyvesant Square Historic District                         0.031706
## histdistSullivan-Thompson Historic District                         0.273505
## histdistTribeca East Historic District                              0.077538
## histdistTribeca West Historic District                              0.015546
## histdistTudor City Historic District                                0.048155
## histdistUpper East Side Historic District                           0.143390
## histdistUpper East Side Historic District Extension                 0.211610
## histdistUpper West Side / Central Park West Historic District       0.588214
## histdistWeehawken Street Historic District                          0.002103
## histdistWest End-Collegiate Historic District                       0.562745
## histdistWest End-Collegiate Historic District Extension             0.276360
## landmarkNone                                                        0.659408
## builtfar                                                            8.27e-16
## ASP                                                                 0.000563
##                                                                        
## (Intercept)                                                         ***
## BLDG_CLASSC4                                                           
## BLDG_CLASSC5                                                           
## BLDG_CLASSC6                                                        .  
## BLDG_CLASSC7                                                        *  
## BLDG_CLASSD0                                                        ***
## BLDG_CLASSD1                                                        ***
## BLDG_CLASSD3                                                        ** 
## BLDG_CLASSD4                                                        ***
## BLDG_CLASSD5                                                           
## BLDG_CLASSD6                                                        ***
## BLDG_CLASSD7                                                        ***
## BLDG_CLASSD8                                                           
## BLDG_CLASSD9                                                        ***
## ZONINGC1-6                                                          *  
## ZONINGC1-7                                                          .  
## ZONINGC1-8                                                          *  
## ZONINGC1-9                                                          *  
## ZONINGC16A                                                          *  
## ZONINGC17A                                                          *  
## ZONINGC18A                                                          *  
## ZONINGC18X                                                          *  
## ZONINGC19A                                                          *  
## ZONINGC2-6                                                          .  
## ZONINGC2-7                                                             
## ZONINGC2-8                                                          ** 
## ZONINGC26A                                                          .  
## ZONINGC27A                                                          *  
## ZONINGC28A                                                          *  
## ZONINGC4-4                                                             
## ZONINGC4-5                                                          *  
## ZONINGC4-7                                                          .  
## ZONINGC44A                                                          *  
## ZONINGC44D                                                          .  
## ZONINGC45A                                                          .  
## ZONINGC46A                                                          .  
## ZONINGC5-1                                                          *  
## ZONINGC5-2                                                          *  
## ZONINGC5-3                                                          *  
## ZONINGC5-5                                                          ** 
## ZONINGC5-P                                                          .  
## ZONINGC51A                                                          .  
## ZONINGC52.5                                                         *  
## ZONINGC6-1                                                          *  
## ZONINGC6-2                                                          *  
## ZONINGC6-2G                                                            
## ZONINGC6-4                                                          *  
## ZONINGC6-6                                                          *  
## ZONINGC6-7                                                             
## ZONINGC62A                                                          *  
## ZONINGC62G                                                          *  
## ZONINGC62M                                                          .  
## ZONINGC63A                                                          *  
## ZONINGC63X                                                             
## ZONINGC64.5                                                         ** 
## ZONINGC64A                                                          *  
## ZONINGC64M                                                          .  
## ZONINGC64X                                                          *  
## ZONINGC66.5                                                            
## ZONINGC8-4                                                          *  
## ZONINGM1-5                                                             
## ZONINGM1-6                                                          *  
## ZONINGM15M                                                          *  
## ZONINGM15R7D                                                        .  
## ZONINGM15R7X                                                        *  
## ZONINGM15R9A                                                           
## ZONINGM15R9X                                                        *  
## ZONINGM16D                                                          *  
## ZONINGR10                                                           *  
## ZONINGR10A                                                          *  
## ZONINGR10H                                                          *  
## ZONINGR6                                                            *  
## ZONINGR6A                                                           ***
## ZONINGR7-2                                                          *  
## ZONINGR7A                                                           ** 
## ZONINGR7B                                                           *  
## ZONINGR7D                                                           ** 
## ZONINGR8                                                            *  
## ZONINGR8A                                                           *  
## ZONINGR8B                                                           *  
## ZONINGR9                                                            *  
## ZONINGR9A                                                           *  
## ZONINGR9X                                                           *  
## LOT_IRREGR                                                          ** 
## LOT_IRREGUnknown                                                       
## BLD_EXTEG                                                              
## BLD_EXTG                                                            ** 
## BLD_EXTN                                                            ** 
## BLD_STORY                                                           ***
## CORNERYes                                                           ***
## LAND_AREA                                                           ***
## NUM_BLDGS                                                           ***
## YRBUILT                                                             ***
## YRALT1                                                                 
## YRALT2                                                              ** 
## UNITS                                                               ** 
## GROSS_SQFT                                                          ***
## OFFICE_AREA_GROSS                                                   *  
## FINTAXFLAGT                                                         ***
## schooldist02                                                           
## schooldist03                                                        ***
## schooldist04                                                        ***
## schooldist05                                                        ***
## schooldist06                                                        ***
## ltdheightLH-1A                                                         
## ltdheightNone                                                          
## easements                                                           *  
## histdistCarnegie Hill Historic District                                
## histdistCentral Harlem West -- 130-132nd Street Historic District   .  
## histdistCentral Park West-76th Street Historic District                
## histdistCentral Park West-West 73rd - 74th Street Historic District    
## histdistCharlton-King-Vandam Historic District                         
## histdistChelsea Historic District                                   .  
## histdistChelsea Historic District Extension                            
## histdistDorrance Brooks Square Historic District                    ** 
## histdistEast Village / Lower East Side Historic District            .  
## histdistExpanded Carnegie Hill Historic District                       
## histdistGansevoort Market Historic District                         .  
## histdistGramercy Park Historic District                                
## histdistGreenwich Village Historic District                            
## histdistGreenwich Village Historic District Extension                  
## histdistGreenwich Village Historic District Extension II            .  
## histdistHamilton Heights / Sugar Hill Historic District             *  
## histdistHamilton Heights / Sugar Hill Northeast Historic District      
## histdistHamilton Heights / Sugar Hill Northwest Historic District      
## histdistHamilton Heights Historic District Extension                   
## histdistIndividual Landmark                                            
## histdistLadies' Mile Historic District                                 
## histdistLamartine Place Historic District                              
## histdistMadison Square North Historic District                         
## histdistMetropolitan Museum Historic District                          
## histdistMorningside Heights Historic District                       .  
## histdistMount Morris Park Historic District                            
## histdistMount Morris Park Historic District Extension                  
## histdistMurray Hill Historic District                                  
## histdistMurray Hill Historic District Extension                        
## histdistNoHo East Historic District                                 .  
## histdistNoHo Historic District                                      .  
## histdistNone                                                        .  
## histdistPark Avenue Historic District                                  
## histdistRiverside-West End Historic District                           
## histdistRiverside-West End Historic District Extension I               
## histdistRiverside-West End Historic District Extension II           *  
## histdistSoHo-Cast Iron Historic District                               
## histdistSoHo-Cast Iron Historic District Extension                     
## histdistSouth Village Historic District                                
## histdistSt. Mark's Historic District                                   
## histdistStuyvesant Square Historic District                         *  
## histdistSullivan-Thompson Historic District                            
## histdistTribeca East Historic District                              .  
## histdistTribeca West Historic District                              *  
## histdistTudor City Historic District                                *  
## histdistUpper East Side Historic District                              
## histdistUpper East Side Historic District Extension                    
## histdistUpper West Side / Central Park West Historic District          
## histdistWeehawken Street Historic District                          ** 
## histdistWest End-Collegiate Historic District                          
## histdistWest End-Collegiate Historic District Extension                
## landmarkNone                                                           
## builtfar                                                            ***
## ASP                                                                 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4137 on 1762 degrees of freedom
##   (11389 observations deleted due to missingness)
## Multiple R-squared:  0.8938, Adjusted R-squared:  0.8842 
## F-statistic: 92.68 on 160 and 1762 DF,  p-value: < 2.2e-16


Plot Residuals of Log Model

Here the logged model looks more homoskedastic, however apart from one outlier to the top right, it looks as if you could draw a downward sloping diagonal line with no points above it, this may be some of the systemic biases we’ve discussed being shown as a trade off between being taxed heavily but less heavily than expected based on the taxation burden of similar features at lower levels.

plot(predict(lm_model_log), residuals(lm_model_log))

Outlier

The outliers in the two models are different.

In the first model I noticed (record 6,230) from the residuals graphs, which as block 1373 lot 1 is the Roosevelt Island Lighthouse, but it doesn’t have ~8000 coop units as further listed. A little digging reveals the largest cooperative on Roosevelt Island is Rivercross with 365 units, so this may be a dud record that we can throw away for our final model.

which.max(abs(rstandard())) returned a second major outlier in the first model, record 999. I looked up the block and lot number (398/53) and it corresponds to 170 East 2nd Street, an ordinary six-story walkup in East Village. It looks like it is slightly smaller that comparable buildings but a relatively high tax. It could be that the neighborhood and having commercial tenants on the ground floor could justify their tax assessment but I may write their board a letter (or do it through the CNYC as outreach for membership in the NYC Co-op group lobbying on behalf of Co-ops in NYC.)

Record 63, the largest outlier in the logged model is a unique property, 10 buildings, forming gardened interior parks taking up a whole city block in the Financial District, 80 Gold Street has an enormous tax bill but it is a luxury community taking up a whole block in an expensive part of town. It stays as a valuable piece of data.

Record 7, the second largest outlier in the logged model is the Verdesian, a luxury building in Battery Park City. It also stays as a valuable piece of data.

which.max(abs(rstandard(lm_model_log)))
## 63 
##  7


Next Steps

In the domain dive we learned that the NYC DOF has a different modeling process for Class 2 buildings with fewer than 10 units. I originally thought this meant I should create a field that acts as a flag for whether the building has 10 or more units, however because it’s a different process for calculating the estimated taxable market value we need to model the two sets of data in separate models.

The DOF also said they factored nearby buildings into their statistical modeling. It wasn’t clear if those buildings were comparable (similar zoning and building class) or just nearby. We can generate a field like that by using KNN to derive the average assessed market value, FINMKTTOT, of nearby buildings.

Additionally we may want to include ridge or lasso penalties to improve our results.

Otherwise, it looks like we’ve already reverse-engineered the city’s process for calculating these estimated taxable market values. The discrepancies in the form of residuals could point to tax inequities, even without assessing the relative fairness of differences in capitalization rates between different zoning and building class types.

We expect that the NYC DOF may have tech debt, byproducts of their build process, or legacy structures like doing certain calculations in batch, that might be making their tax assessments less fair than a new, from scratch, model. In a way the city is “billing” buildings for being a part of the city, and billing is often the same as the prior year plus some. If the city is approaching the assessments like a vendor does billing, there may be a lot of historical discrepancies being perpetuated. This too would also show up as discrepancies in the model.