Condo price
Spatial prices
- Spatial statistics: rent of 4 1/2
Plexes Longitudinal price model: Plateau, Ahuntsic, Rosemont, Villeray

Condo price

Neighborhood map

plateau<-mtl_p%>%filter(nom_arr=='Le Plateau-Mont-Royal')%>%st_buffer(dist=0)

# near the border between two
neighbourhood<-mtl_p%>%filter(nom_qr %in% c("Saint-Louis", "Milton-Parc"))%>%summarize()


if(file.exists("osm_neighbourhood.RDS")){
  osm_neighbourhood<-readRDS(file="osm_neighbourhood.RDS")
} else {
  # osm understands information in 4326 projection
  osm_neighbourhood<-read_osm(st_bbox(neighbourhood%>%st_transform(4326)), type="esri") # ext=1.5,
  # save to file to speedup runs
  saveRDS(osm_neighbourhood, file = "osm_neighbourhood.RDS")
}

# my region of interest
ROI_p<-mtl_p %>% filter( nom_arr %in% 
  c('Le Plateau-Mont-Royal',
    'Villeray–Saint-Michel–Parc-Extension',
    'Rosemont–La Petite-Patrie',
    "Ahuntsic-Cartierville",
    "Outremont",
    "Ville-Marie",
    "Le Sud-Ouest",
    "Côte-des-Neiges–Notre-Dame-de-Grâce","Verdun","Westmount","Hampstead","Côte-Saint-Luc","Saint-Laurent","Mont-Royal"
    ) ) %>% st_intersection(st_geometry(mtl_land)%>%st_buffer(0)) %>%
   mutate( arr=factor(nom_arr, 
    levels=c('Le Plateau-Mont-Royal',
    'Villeray–Saint-Michel–Parc-Extension',
    'Rosemont–La Petite-Patrie',
    "Ahuntsic-Cartierville","Outremont", "Ville-Marie","Le Sud-Ouest",
    "Côte-des-Neiges–Notre-Dame-de-Grâce","Verdun","Westmount","Hampstead","Côte-Saint-Luc","Saint-Laurent","Mont-Royal"),
    labels=c('Plateau','Villeray','Rosemont','Ahuntsic',"Outremont",
    "Ville-Marie","Sud-Ouest","CdN-NdG","Verdun","Westmount","Hampstead","Côte-Saint-Luc","Saint-Laurent","TMR"
    )),
     qr=as.factor(nom_qr))
#
if(file.exists("osm_roi.RDS")){
  osm_roi<-readRDS(file="osm_roi.RDS")
} else {
  osm_roi<-read_osm(st_bbox(ROI_p%>%st_transform(4326)), type="esri") # ext=1.5,
  # save to file to speedup runs
  saveRDS(osm_roi, file = "osm_roi.RDS")
}

# create subset of data
neighbors<-prop_geo_p %>% 
  filter(type=='Apartment', mprice>0, bedrooms %in% c(1,2,3,4), area_interior<10000, area_interior>0) %>% 
  st_join(neighbourhood, left=F) %>% 
  mutate(bedrooms=droplevels(bedrooms), parking=as.factor(parking>0))

tm_shape(osm_neighbourhood) + tm_rgb(alpha=0.7)+
  tm_shape(neighbourhood) + tm_borders(col='red',alpha=0.8)  + 
  tm_shape(neighbors) + tm_symbols(shape=3,size=0.2,alpha=0.8) +
  tm_shape(ref_home) + tm_symbols(col='red',shape=4,size=0.5,alpha=0.8)+
  tm_compass(position=c("right", "bottom"))+
  tm_scale_bar(position=c("left", "bottom"))+
  tm_layout(scale=1.5)

neighbourhood prices,

simple linear model

# convert spatial object into a simple data frame with x and y 
neighbors_<-bind_cols(as.data.frame(neighbors),as.data.frame(st_coordinates(neighbors)))%>%rename(x=X,y=Y) 
  
ggplot(neighbors_, aes(y=price, x=area_interior, col=parking))+
  geom_point(alpha=0.7,size=2)+
  scale_y_continuous( labels = scales::dollar)+
  geom_smooth(method='lm')+
  geom_vline(data=ref_home, aes(xintercept=area_interior),col='black',lty=2)+
  coord_cartesian(xlim=c(400,2000),ylim=c(2e5,1e6))+
  ylab('Price')+xlab('Surface sqft')

# simple regression model
model_price_lm <- lm(mprice ~ parking:area_interior , data=neighbors_)

print(summary(model_price_lm))

## 
## Call:
## lm(formula = mprice ~ parking:area_interior, data = neighbors_)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -369729  -64800   -9132   55880  690669 
## 
## Coefficients:
##                            Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                40564.16   22427.94   1.809   0.0715 .  
## parkingFALSE:area_interior   438.79      23.57  18.616   <2e-16 ***
## parkingTRUE:area_interior    513.52      19.41  26.459   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 129400 on 311 degrees of freedom
## Multiple R-squared:  0.6989, Adjusted R-squared:  0.6969 
## F-statistic: 360.9 on 2 and 311 DF,  p-value: < 2.2e-16

# predict price
print(predict(model_price_lm, ref_home, se.fit=T))

## $fit
##        1 
## 443160.1 
## 
## $se.fit
## [1] 10814.63
## 
## $df
## [1] 311
## 
## $residual.scale
## [1] 129405.7

neighbors_$pred<- predict(model_price_lm)
neighbors_$res <- neighbors_$mprice-neighbors_$pred

ggplot(neighbors_, aes(x=pred, y=res) ) +
  geom_point(alpha=0.7,size=2)+
  scale_y_continuous(labels = scales::dollar )+
  scale_x_continuous(labels = scales::dollar )+
  xlab('predicted')+ylab('residuals')

glm model

ggplot(neighbors_, aes(y=price, x=area_interior, col=parking))+
  geom_point(alpha=0.7,size=2)+
  scale_y_continuous( labels = scales::dollar)+
  geom_smooth(method='glm',method.args=list(family = inverse.gaussian(link="log")))+
  geom_vline(data=ref_home, aes(xintercept=area_interior),col='black',lty=2)+
  coord_cartesian(xlim=c(400,2000),ylim=c(2e5,1e6))+
  ylab('Price')+xlab('Surface sqft')

fam=inverse.gaussian(link="log")
ilink <- fam$linkinv

model_price_glm <- glm(mprice ~ parking:area_interior , data=neighbors_, family=fam)

print(summary(model_price_glm))

## 
## Call:
## glm(formula = mprice ~ parking:area_interior, family = fam, data = neighbors_)
## 
## Deviance Residuals: 
##        Min          1Q      Median          3Q         Max  
## -1.158e-03  -2.304e-04  -3.213e-05   1.643e-04   7.957e-04  
## 
## Coefficients:
##                             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                1.230e+01  3.984e-02  308.73   <2e-16 ***
## parkingFALSE:area_interior 7.482e-04  4.486e-05   16.68   <2e-16 ***
## parkingTRUE:area_interior  8.749e-04  3.836e-05   22.81   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for inverse.gaussian family taken to be 8.466078e-08)
## 
##     Null deviance: 8.4965e-05  on 313  degrees of freedom
## Residual deviance: 2.6885e-05  on 311  degrees of freedom
## AIC: 8169
## 
## Number of Fisher Scoring iterations: 4

# predict price
predict_home<-predict(model_price_glm, ref_home, se.fit=T)

print("prediction and 95% confidence intervals:")

## [1] "prediction and 95% confidence intervals:"

print(ilink(predict_home$fit))

##        1 
## 436702.2

print(c(ilink(predict_home$fit-2*predict_home$se.fit), ilink(predict_home$fit+2*predict_home$se.fit)))

##        1        1 
## 421749.4 452185.2

neighbors_$pred<- ilink(predict(model_price_glm))
neighbors_$res <- neighbors_$mprice-neighbors_$pred

ggplot(neighbors_, aes(x=pred, y=res) ) +
  geom_point(alpha=0.7,size=2)+
  scale_y_continuous(labels = scales::dollar )+
  scale_x_continuous(labels = scales::dollar )+
  ggtitle('GLM Residuals')

price per square foot

ggplot(neighbors_, aes(y=price_sqft,x=parking, col=parking))+
  geom_point(alpha=0.7,size=2,pos='jitter')+
  geom_boxplot(alpha=0.5,size=0.5)+
  facet_wrap(~bedrooms,labeller = label_both)+
  scale_y_continuous( labels = scales::dollar)+
  ylab('Price/sqft')+xlab('')

model_psqft <- glm(price_sqft ~ parking + bedrooms, data=neighbors_, family=fam)

print(summary(model_psqft))

## 
## Call:
## glm(formula = price_sqft ~ parking + bedrooms, family = fam, 
##     data = neighbors_)
## 
## Deviance Residuals: 
##       Min         1Q     Median         3Q        Max  
## -0.026625  -0.006673  -0.000958   0.004938   0.031624  
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  6.22330    0.02782 223.695  < 2e-16 ***
## parkingTRUE  0.11456    0.02400   4.772 2.81e-06 ***
## bedrooms2   -0.02917    0.02934  -0.994  0.32080    
## bedrooms3   -0.02281    0.03862  -0.591  0.55521    
## bedrooms4   -0.18546    0.06694  -2.771  0.00593 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for inverse.gaussian family taken to be 8.650397e-05)
## 
##     Null deviance: 0.028868  on 313  degrees of freedom
## Residual deviance: 0.026257  on 309  degrees of freedom
## AIC: 3830.3
## 
## Number of Fisher Scoring iterations: 4

print("Understanding factors")

## [1] "Understanding factors"

print(ilink(model_psqft$coeff))

## (Intercept) parkingTRUE   bedrooms2   bedrooms3   bedrooms4 
## 504.3627105   1.1213758   0.9712496   0.9774513   0.8307217

# predict price
predict_home<-predict(model_psqft, ref_home, se.fit=T)

print("prediction and 95% confidence intervals:")

## [1] "prediction and 95% confidence intervals:"

print(c(ilink(predict_home$fit-2*predict_home$se.fit), 
        ilink(predict_home$fit),
        ilink(predict_home$fit+2*predict_home$se.fit))*ref_home$area_interior)

##        1        1        1 
## 413724.7 430666.5 448302.0

Longitudinal condo price model: Loess smoothihg

Longitudinal condo price model:GAM model

## 
## Family: inverse.gaussian 
## Link function: log 
## 
## Formula:
## price_sqft ~ bedrooms + parking + s(start_date, k = 24)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  6.22248    0.02732 227.797  < 2e-16 ***
## bedrooms2   -0.03438    0.02879  -1.194  0.23335    
## bedrooms3   -0.03203    0.03797  -0.844  0.39953    
## bedrooms4   -0.18025    0.06643  -2.713  0.00704 ** 
## parkingTRUE  0.12210    0.02360   5.173 4.17e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                 edf Ref.df     F p-value   
## s(start_date) 1.971  2.454 5.154 0.00532 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.109   Deviance explained =   13%
## -REML = 1920.4  Scale est. = 8.3199e-05  n = 314

## Analysis of Deviance Table
## 
## Model 1: price_sqft ~ parking + bedrooms
## Model 2: price_sqft ~ bedrooms + parking + s(start_date, k = 24)
##   Resid. Df Resid. Dev     Df  Deviance
## 1    309.00   0.026257                 
## 2    307.03   0.025128 1.9712 0.0011288

## 
## Family: poisson 
## Link function: log 
## 
## Formula:
## n ~ s(start_date, k = 24)
## 
## Parametric coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  0.37645    0.05988   6.287 3.23e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                 edf Ref.df Chi.sq p-value    
## s(start_date) 8.955     23  160.6  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.349   Deviance explained = 47.8%
## -REML = 304.87  Scale est. = 1         n = 197

Longitudinal condo price model: prediction

## [1] "prediction and 95% confidence intervals:"

##        1        1        1 
## 527.7101 549.3195 571.8138

Longitudinal condo price model: relative price change

Condo price (sqft) relative to start

survival analysis

survdiff(Surv(time_on_market, !active) ~ parking, neighbors)

## Call:
## survdiff(formula = Surv(time_on_market, !active) ~ parking, data = neighbors)
## 
##                 N Observed Expected (O-E)^2/E (O-E)^2/V
## parking=FALSE 146      117      105     1.491      2.57
## parking=TRUE  168      144      156     0.996      2.57
## 
##  Chisq= 2.6  on 1 degrees of freedom, p= 0.1

surv_type<-survfit(Surv(time_on_market, !active) ~ 1, neighbors_)

p<-ggsurvplot( surv_type, data=neighbors_, conf.int = TRUE,
    conf.int.style ='step', censor=F, surv.scale='percent',
    break.time.by=30,surv.median.line='hv',
    xlim=c(0.0,365.0))
p$plot <- p$plot + theme(legend.text = element_text(size = 5, color = "black", face = "bold"))
p

Plex price estimate

selected_mls=17758383
max_distance=2000 # 2km

plex_pe<-prop_geo_p %>% filter(type!='Apartment', type!='House') %>% 
  mutate(parking=as.factor(parking>0), stories=as.factor(stories),type=as.factor(type))

selected<-plex_pe%>%filter(mls==selected_mls) %>% rename(mls_ref=mls)

# selected
print(selected%>%as.data.frame()%>%dplyr::select(mls_ref,area_interior,area_land,type,bedrooms,parking,first_ts))

##    mls_ref area_interior area_land    type bedrooms parking   first_ts
## 1 17758383       1765.28      1750 Triplex        3    TRUE 2020-02-05

# create a cicrcle around reference
search_roi <- st_buffer(selected, max_distance)
# remove some noise entries
result <- st_intersection(plex_pe %>% filter(mls!=selected_mls), search_roi) %>% 
  filter(area_interior<10000, area_interior>100,area_land>0,price<1e7,price>100 ) 

if(file.exists("osm_result.RDS")){
  osm_result<-readRDS(file="osm_result.RDS")
} else {
  # osm understands information in 4326 projection
  osm_result <- read_osm(st_bbox(st_transform(search_roi, 4326 )), ext=1.5, type="esri")
  # save to file to speedup runs
  saveRDS(osm_result, file = "osm_result.RDS")
}

# 
ggplot(result%>%as.data.frame(), aes(x=area_interior, y=price, col=type))+
   geom_point(alpha=0.7)+
   geom_point(data=selected%>%as.data.frame(), aes(x=area_interior, y=price) , size=10, shape='+', alpha=0.9, col='black') +
   scale_y_continuous(labels = scales::dollar )+xlim(c(0,5000))+
   geom_smooth(method='glm',method.args=list(family = inverse.gaussian(link="log")))

ggplot(result%>%as.data.frame(), aes(y=price_sqft, x=parking, col=parking))+
  geom_point(alpha=0.7,size=2,pos='jitter')+
  geom_boxplot(alpha=0.5,size=0.5)+
  facet_grid(type~bedrooms,labeller = label_both)+
  scale_y_continuous(labels = scales::dollar)+
  ylab('Price/sqft')+xlab('')

per sqft price regression model

m_plex <- glm(price_sqft ~ type+bedrooms+parking, data=result%>%as.data.frame(), family=fam)
print(summary(m_plex))

## 
## Call:
## glm(formula = price_sqft ~ type + bedrooms + parking, family = fam, 
##     data = result %>% as.data.frame())
## 
## Deviance Residuals: 
##       Min         1Q     Median         3Q        Max  
## -0.098291  -0.012601  -0.005437   0.003621   0.093939  
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   5.7965411  0.0905453  64.018   <2e-16 ***
## typeTriplex  -0.1066840  0.0465888  -2.290   0.0226 *  
## typeFourplex  0.0343763  0.0734954   0.468   0.6402    
## bedrooms2    -0.0005084  0.0913386  -0.006   0.9956    
## bedrooms3    -0.0442496  0.0871485  -0.508   0.6119    
## bedrooms4    -0.0801371  0.1065306  -0.752   0.4524    
## bedrooms5    -0.1019773  0.1764383  -0.578   0.5636    
## parkingTRUE   0.1319670  0.0443394   2.976   0.0031 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for inverse.gaussian family taken to be 0.00053711)
## 
##     Null deviance: 0.14560  on 402  degrees of freedom
## Residual deviance: 0.13659  on 395  degrees of freedom
## AIC: 4904.7
## 
## Number of Fisher Scoring iterations: 7

# # predict price
predict_selected<-predict(m_plex, selected%>%as.data.frame(), se.fit=T)

print("prediction and 95% confidence intervals:")

## [1] "prediction and 95% confidence intervals:"

print(ilink(predict_selected$fit))

##        1 
## 322.9749

print(ilink(predict_selected$se.fit))

## [1] 1.043278

print(c(ilink(predict_selected$fit-2*predict_selected$se.fit),
        ilink(predict_selected$fit),
        ilink(predict_selected$fit+2*predict_selected$se.fit))*selected$area_interior)

##        1        1        1 
## 523820.3 570140.9 620557.6

Spatial prices

Spatial statistics: rent of 4 1/2

Simple median over quartier

# summarize by neighorhoods and bedrooms
# only keeping 2 bedroom
rent_by_quartier<-aggregate(filter(kijiji_geo_p,bedrooms==2)%>%dplyr::select(price),mtl_p,median,join = st_contains) 

# extract borders of districts
mtl_arr<-mtl_p%>%group_by(nom_arr)%>%summarize()

if(file.exists("osm_mtl.RDS")){
  osm_mtl<-readRDS(file="osm_mtl.RDS")
} else {
  osm_mtl<-read_osm(st_bbox(mtl_p%>%st_transform(4326)), type="esri",ext=1.5) # ext=1.5,
  # save to file to speedup runs
  saveRDS(osm_mtl, file = "osm_mtl.RDS")
}


# whole island
tm_shape(osm_mtl)+tm_rgb(alpha=0.6)+
  tm_shape(mtl_arr) + tm_borders(alpha=0.7,col='black')+
  tm_shape(rent_by_quartier) + tm_fill(col='price',alpha=0.8,breaks=seq(400,2000,by=200),title='$')+
  tm_shape(ref_home) + tm_symbols(col='red',shape=4,size=0.5,alpha=0.8)+
  tm_legend(position = c("left", "top"), 
            frame = TRUE, outside = FALSE,
            bg.color="white")+
  tm_compass(position=c("right", "bottom"))+
  tm_scale_bar(position=c("left", "bottom"))+
  tm_layout(scale=1.5)

Rental prices spatial model, whole island

## 
## Family: inverse.gaussian 
## Link function: log 
## 
## Formula:
## price ~ bedrooms + s(x, y, k = 100)
## 
## Parametric coefficients:
##              Estimate Std. Error  t value Pr(>|t|)    
## (Intercept) 6.9242917  0.0021694 3191.743   <2e-16 ***
## bedrooms1   0.0005471  0.0025870    0.211    0.833    
## bedrooms2   0.2449609  0.0027388   89.439   <2e-16 ***
## bedrooms3   0.4586584  0.0034735  132.047   <2e-16 ***
## bedrooms4   0.6946183  0.0059213  117.308   <2e-16 ***
## bedrooms5   0.8458260  0.0110996   76.204   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##          edf Ref.df     F p-value    
## s(x,y) 98.12  98.98 812.7  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.547   Deviance explained = 54.6%
## -REML = 7.5656e+05  Scale est. = 6.9015e-05  n = 104895

Rental price map for 4 1/2

Rental prices spatial model, central part

## 
## Family: inverse.gaussian 
## Link function: log 
## 
## Formula:
## price ~ bedrooms + s(x, y, k = 100)
## 
## Parametric coefficients:
##             Estimate Std. Error  t value Pr(>|t|)    
## (Intercept) 6.960093   0.002313 3009.122  < 2e-16 ***
## bedrooms1   0.022683   0.002777    8.169 3.15e-16 ***
## bedrooms2   0.281851   0.003004   93.816  < 2e-16 ***
## bedrooms3   0.494016   0.003988  123.878  < 2e-16 ***
## bedrooms4   0.726634   0.006484  112.059  < 2e-16 ***
## bedrooms5   0.843509   0.012560   67.160  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##          edf Ref.df     F p-value    
## s(x,y) 97.68  98.97 600.1  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.529   Deviance explained = 52.3%
## -REML = 6.442e+05  Scale est. = 6.8437e-05  n = 88393

Rental price map for 4 1/2

Plex price spatial model

## 
## Family: inverse.gaussian 
## Link function: log 
## 
## Formula:
## price_sqft ~ type + bedrooms + parking + s(x, y, k = 100)
## 
## Parametric coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   5.71963    0.02517 227.269  < 2e-16 ***
## typeTriplex  -0.06820    0.01244  -5.485 4.63e-08 ***
## typeFourplex -0.03992    0.01826  -2.187   0.0289 *  
## bedrooms2    -0.02285    0.02502  -0.913   0.3611    
## bedrooms3    -0.04356    0.02483  -1.755   0.0795 .  
## bedrooms4    -0.04786    0.02965  -1.614   0.1066    
## bedrooms5     0.06915    0.05271   1.312   0.1897    
## bedrooms6    -0.06575    0.08221  -0.800   0.4239    
## parkingTRUE   0.06414    0.01214   5.284 1.39e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##         edf Ref.df     F p-value    
## s(x,y) 62.2  78.88 13.13  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.322   Deviance explained = 37.4%
## -REML =  12939  Scale est. = 0.0002071  n = 2252

## 
## Family: inverse.gaussian 
## Link function: log 
## 
## Formula:
## area_interior ~ type + bedrooms + parking + s(x, y, k = 100)
## 
## Parametric coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   7.52380    0.03298 228.121  < 2e-16 ***
## typeTriplex   0.24187    0.01733  13.954  < 2e-16 ***
## typeFourplex  0.39287    0.02749  14.294  < 2e-16 ***
## bedrooms2     0.04943    0.03272   1.511  0.13097    
## bedrooms3     0.17813    0.03280   5.430 6.25e-08 ***
## bedrooms4     0.23820    0.04056   5.873 4.94e-09 ***
## bedrooms5     0.53905    0.07990   6.746 1.94e-11 ***
## bedrooms6     0.40691    0.12476   3.262  0.00112 ** 
## parkingTRUE  -0.01280    0.01630  -0.785  0.43230    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##         edf Ref.df    F  p-value    
## s(x,y) 65.7  82.16 1.92 2.05e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.139   Deviance explained = 44.4%
## -REML =  17426  Scale est. = 4.7884e-05  n = 2252

Price per sqft for a triplex with 3br and parking in ROI

area for a triplex with 3br and parking in ROI

Triplex Profitability (rent per year/triplex total price)

Plexes Longitudinal price model: Plateau, Ahuntsic, Rosemont, Villeray

## 
## Family: inverse.gaussian 
## Link function: log 
## 
## Formula:
## price_sqft ~ type + arr + parking + s(start_date, by = type, 
##     k = 6) + s(start_date, by = arr, k = 6)
## 
## Parametric coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   6.17259    0.01175 525.224  < 2e-16 ***
## typeDuplex   -0.18065    0.01704 -10.602  < 2e-16 ***
## typeTriplex  -0.22729    0.01787 -12.722  < 2e-16 ***
## typeFourplex -0.19927    0.02389  -8.340  < 2e-16 ***
## arrVilleray  -0.29194    0.01839 -15.878  < 2e-16 ***
## arrRosemont  -0.14782    0.01701  -8.691  < 2e-16 ***
## arrAhuntsic  -0.32195    0.01866 -17.252  < 2e-16 ***
## parkingTRUE   0.05441    0.01164   4.675 3.04e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                               edf Ref.df     F p-value  
## s(start_date):typeApartment 1.004  1.007 0.842  0.3592  
## s(start_date):typeDuplex    2.090  2.566 0.954  0.3281  
## s(start_date):typeTriplex   3.513  4.112 2.338  0.0505 .
## s(start_date):typeFourplex  2.040  2.516 0.814  0.5513  
## s(start_date):arrPlateau    1.104  1.593 1.273  0.4057  
## s(start_date):arrVilleray   2.682  3.236 2.810  0.0360 *
## s(start_date):arrRosemont   1.828  2.267 0.885  0.4134  
## s(start_date):arrAhuntsic   1.029  1.054 2.254  0.1346  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Rank: 47/48
## R-sq.(adj) =   0.28   Deviance explained = 29.4%
## -REML =  24666  Scale est. = 0.00031759  n = 3996

Montreal real estate statistics, HABR version

Condo price

Neighborhood map

neighbourhood prices,

simple linear model

glm model

price per square foot

Longitudinal condo price model: Loess smoothihg

Longitudinal condo price model:GAM model

Longitudinal condo price model: prediction

Longitudinal condo price model: relative price change

Condo price (sqft) relative to start

survival analysis

Plex price estimate

per sqft price regression model

Spatial prices

Spatial statistics: rent of 4 1/2

Simple median over quartier

Rental prices spatial model, whole island

Rental price map for 4 1/2

Rental prices spatial model, central part

Rental price map for 4 1/2

Plex price spatial model

Price per sqft for a triplex with 3br and parking in ROI

area for a triplex with 3br and parking in ROI

Triplex Profitability (rent per year/triplex total price)

Plexes Longitudinal price model: Plateau, Ahuntsic, Rosemont, Villeray