Poland Prediction Price For Apartments
Pythias
2024-02-11
INTRODUCTION
This is a mini project of creating a model that predicts the price of an apartment in Poland based on certain variables that influences the price of an apartment.
The dataset is from Kaggle website. The link to the dataset is provided here:Poland apartment dataset
The dataset fields:
Data Fields
city - the name of the city where the property is located
type - type of the building
square meters - the size of the apartment in square meters
rooms - number of rooms in the apartment
floor / floor count - the floor where the apartment is located and the total number of floors in the building
buildYear - the year when the building was built
latitude, longitude - geo coordinate of the property
centre distance - distance from the city centre in km
poiCount - number of points of interest in 500m range from the apartment (schools, clinics, post offices, kindergartens, restaurants, colleges, pharmacies)
[poiName]Distance - distance to the nearest point of interest (schools, clinics, post offices, kindergartens, restaurants, colleges, pharmacies)
ownership - the type of property ownership
condition - the condition of the apartment
has[features] - whether the property has key features such as assigned parking space, balcony, elevator, security, storage room
price - offer price in Polish Zloty (sale offers: sale price, rent offers: monthly rent)
DATA DESCRIPTION
## 'data.frame': 18905 obs. of 27 variables:
## $ city : chr "szczecin" "szczecin" "szczecin" "szczecin" ...
## $ type : chr "blockOfFlats" "blockOfFlats" "tenement" "tenement" ...
## $ square_meters : num 63 36 73 87.6 66 ...
## $ rooms : num 3 2 3 3 3 3 2 2 2 4 ...
## $ floor : num 4 8 2 2 1 2 2 3 8 2 ...
## $ floor_count : num 10 10 3 3 3 4 10 4 12 3 ...
## $ build_year : num 1980 NA NA NA NA ...
## $ latitude : num 53.4 53.4 53.5 53.4 53.4 ...
## $ longitude : num 14.6 14.6 14.6 14.5 14.5 ...
## $ centre_distance : num 6.53 2.15 3.24 2.27 4.07 4.48 2.99 3.53 4.27 1.3 ...
## $ poi_count : num 9 16 9 32 1 10 18 8 6 22 ...
## $ school_distance : num 0.118 0.273 0.275 0.175 0.218 0.079 0.327 0.572 0.345 0.232 ...
## $ clinic_distance : num 1.389 0.492 0.672 0.259 1.69 ...
## $ post_office_distance : num 0.628 0.652 0.367 0.223 0.504 0.737 0.234 0.305 0.336 0.356 ...
## $ kindergarten_distance: num 0.105 0.291 0.246 0.359 0.704 0.26 0.262 0.435 0.5 0.301 ...
## $ restaurant_distance : num 1.652 0.348 0.3 0.101 0.501 ...
## $ college_distance : num NA 1.4 1.86 0.31 2.14 ...
## $ pharmacy_distance : num 0.413 0.205 0.28 0.087 0.514 0.745 0.277 0.155 0.42 0.199 ...
## $ ownership : chr "condominium" "cooperative" "condominium" "condominium" ...
## $ building_material : chr "concreteSlab" "concreteSlab" "brick" "brick" ...
## $ condition : chr "" "" "" "" ...
## $ has_parking_space : chr "yes" "no" "no" "yes" ...
## $ has_balcony : chr "yes" "yes" "no" "yes" ...
## $ has_elevator : chr "yes" "yes" "no" "no" ...
## $ has_security : chr "no" "no" "no" "no" ...
## $ has_storage_room : chr "yes" "yes" "no" "yes" ...
## $ price : int 415000 395995 565000 640000 759000 499000 370000 629000 399000 325000 ...- 10 categorial variables and 17 mumerical variables.
Missing Values
## city type square_meters
## 0 0 0
## rooms floor floor_count
## 0 3438 262
## build_year latitude longitude
## 3271 0 0
## centre_distance poi_count school_distance
## 0 0 14
## clinic_distance post_office_distance kindergarten_distance
## 88 25 13
## restaurant_distance college_distance pharmacy_distance
## 58 565 27
## ownership building_material condition
## 0 0 0
## has_parking_space has_balcony has_elevator
## 0 0 0
## has_security has_storage_room price
## 0 0 0- Some variables contain missing values
Removing missing values
library(knitr)
apt_c=na.omit(apt)
kable(colSums(is.na(apt_c))) #returns the sum of missing values in each column| x | |
|---|---|
| city | 0 |
| type | 0 |
| square_meters | 0 |
| rooms | 0 |
| floor | 0 |
| floor_count | 0 |
| build_year | 0 |
| latitude | 0 |
| longitude | 0 |
| centre_distance | 0 |
| poi_count | 0 |
| school_distance | 0 |
| clinic_distance | 0 |
| post_office_distance | 0 |
| kindergarten_distance | 0 |
| restaurant_distance | 0 |
| college_distance | 0 |
| pharmacy_distance | 0 |
| ownership | 0 |
| building_material | 0 |
| condition | 0 |
| has_parking_space | 0 |
| has_balcony | 0 |
| has_elevator | 0 |
| has_security | 0 |
| has_storage_room | 0 |
| price | 0 |
- cleaned dataset
Outliers
library(dplyr)
library(tidyverse)
apt_c_numerical= apt_c %>%
select(c(square_meters,rooms,floor,floor_count,build_year,latitude,longitude,centre_distance,school_distance,clinic_distance,post_office_distance,kindergarten_distance,restaurant_distance,college_distance,pharmacy_distance,price,poi_count,centre_distance)) #splitting the data into numerical variables only
apt_c_categorial= apt_c %>%
select(c(city,type,ownership,building_material,condition,has_parking_space,
has_balcony,has_elevator,has_security,has_storage_room)) #splitting the dataset into categorial variables only
apt_c_numeric_long = apt_c_numerical %>%
pivot_longer(everything(),
names_to = "numeric_variables",
values_to = "numeric_values") #Further splitting the numerical dataset into numeric variables and numeric values
#Checking for outliers using boxplot method
apt_c_numeric_long %>%
ggplot(aes(numeric_variables,numeric_values))+
geom_boxplot(aes(fill=numeric_variables),stat = "boxplot",position = "dodge",outlier.colour = "green")+
facet_wrap(~ numeric_variables, scales = "free")+
theme_dark()+labs(title = "Boxplots for each numeric variables",
x="",y="") 
- Dataset has outliers but it is not advisable to remove them as they can cause a bias in the final results.
DATA ANALYSIS (CATEGORICAL VARIABLES)
ggplot(apt_c_categorial,aes(city,fill=city))+
geom_bar()+ theme_bw()+
theme(axis.text.x = element_text(size = 10,hjust=1,angle=45))
- Most apartments are in the city of Warszawa
ggplot(apt_c_categorial,aes(ownership,fill=ownership))+
geom_bar()+theme_test()+
geom_text(stat = "count",aes(label=(..count..)),vjust=2)
- Most apartments are condominium owned.
Type of apartments
ggplot(apt_c_categorial,aes(type,fill=ownership))+
geom_bar(position = "dodge")+theme_linedraw()+
labs(title = "Type of apartments per ownership")
- Block of flats are mostly common and they are condominium owned.
ggplot(apt_c_categorial,aes(condition,fill=has_parking_space))+
geom_bar(color="black")+theme_get()+
labs(title="Apartment condition")
Most apartments’ condition is unknown and they don’t have parking space.
Most premium apartments have parking space.
Most low apartments don’t have parking space.
Building Material on apartments
ggplot(apt_c_categorial,aes(building_material,fill=condition))+
geom_bar(color="black")+theme_get()+
labs(title="Apartment condition")
- Most apartments are build with brick and their condition is unknown.
FEATURE ENGINEERING
1. Variable conversion
apt_c=apt_c %>% mutate(
b_parking=ifelse(grepl("yes",apt_c$has_parking_space),1,0),
b_balcony=ifelse(apt_c$has_balcony=="yes",1,0),
b_elevator=ifelse(apt_c$has_elevator=="yes",1,0),
b_security=ifelse(apt_c$has_security=="yes",1,0),
b_storage=ifelse(apt_c$has_storage_room=="yes",1,0))
apt_c %>% dplyr::select(b_parking,b_balcony,b_elevator,
b_security,b_storage) %>% str()## 'data.frame': 12403 obs. of 5 variables:
## $ b_parking : num 1 0 0 0 1 0 0 0 0 0 ...
## $ b_balcony : num 1 0 1 1 0 0 0 0 1 0 ...
## $ b_elevator: num 0 1 1 1 0 0 1 0 1 0 ...
## $ b_security: num 0 0 0 0 0 0 0 0 0 0 ...
## $ b_storage : num 1 1 0 1 1 0 0 1 0 1 ...
## - attr(*, "na.action")= 'omit' Named int [1:6502] 1 2 3 4 5 12 13 14 18 20 ...
## ..- attr(*, "names")= chr [1:6502] "1" "2" "3" "4" ...- New dummy variable created
2. Type column
## Var1 Freq
## 1 blockOfFlats 6217
## 2 2280
## 3 apartmentBuilding 2118
## 4 tenement 1788apt_c=apt_c %>%
mutate(block_of_flats=ifelse(grepl("blockofflats",apt_c$type,
ignore.case=TRUE),1,0),
apartment_building=ifelse(grepl("apartmentbuilding",apt_c$type,
ignore.case=TRUE),1,0),
tenement=ifelse(grepl("tenement",apt_c$type),1,0),
unknown=ifelse(apt_c$type=="",1,0))
apt_c %>% dplyr::select(block_of_flats,apartment_building,tenement,
unknown) %>% str()## 'data.frame': 12403 obs. of 4 variables:
## $ block_of_flats : num 1 1 0 1 0 0 0 0 1 1 ...
## $ apartment_building: num 0 0 1 0 0 0 0 0 0 0 ...
## $ tenement : num 0 0 0 0 1 1 1 1 0 0 ...
## $ unknown : num 0 0 0 0 0 0 0 0 0 0 ...
## - attr(*, "na.action")= 'omit' Named int [1:6502] 1 2 3 4 5 12 13 14 18 20 ...
## ..- attr(*, "names")= chr [1:6502] "1" "2" "3" "4" ...- new dummy variables created
3. Ownership column
## Var1 Freq
## 1 condominium 10981
## 2 cooperative 1422apt_c=apt_c %>%
mutate(condominium=ifelse(apt_c$ownership=="condominium",1,0),
cooperative=ifelse(apt_c$ownership=="cooperative",1,0))
apt_c %>% dplyr::select(condominium,cooperative) %>%
str()## 'data.frame': 12403 obs. of 2 variables:
## $ condominium: num 0 1 1 1 1 1 1 1 0 1 ...
## $ cooperative: num 1 0 0 0 0 0 0 0 1 0 ...
## - attr(*, "na.action")= 'omit' Named int [1:6502] 1 2 3 4 5 12 13 14 18 20 ...
## ..- attr(*, "names")= chr [1:6502] "1" "2" "3" "4" ...- new dummy variables created
3. Building material column
## Var1 Freq
## 1 4444
## 2 brick 5993
## 3 concreteSlab 1966apt_c=apt_c %>%
mutate(brick=ifelse(grepl("brick",apt_c$building_material,
ignore.case=TRUE),1,0),
concrete_slab=ifelse(grepl("concreteslab",apt_c$building_material,
ignore.case=TRUE),1,0),
unknown_building_material=ifelse(apt_c$building_material=="",1,0))
apt_c %>% dplyr::select(brick,concrete_slab,unknown_building_material) %>%
str()## 'data.frame': 12403 obs. of 3 variables:
## $ brick : num 0 0 1 0 1 1 1 1 0 1 ...
## $ concrete_slab : num 1 1 0 1 0 0 0 0 1 0 ...
## $ unknown_building_material: num 0 0 0 0 0 0 0 0 0 0 ...
## - attr(*, "na.action")= 'omit' Named int [1:6502] 1 2 3 4 5 12 13 14 18 20 ...
## ..- attr(*, "names")= chr [1:6502] "1" "2" "3" "4" ...MULTIPLE LINEAR REGRESSION
It is generally recommended to split your data into training and testing sets before performing any model selection or evaluation tasks. This allows you to assess the performance of your model on unseen data and helps to mitigate the risk of overfitting.
#Splitting the data
apt_c_subset= apt_c %>%
dplyr::select(3:18,27:41)
apt_c_subset$price=log(apt_c_numerical$price)
set.seed(1) #generating the model
sample=sample(c(TRUE,FALSE),nrow(apt_c_subset),
replace=TRUE,prob = c(0.7,0.3))
train_trans=apt_c_subset[sample,]
test_trans=apt_c_subset[!sample,]
#regression model
#Backward approach
library(MASS)
backward_lm= lm(price ~ .,data = train_trans)#full model including all the variables
backward_lm2= stepAIC(backward_lm,direction="backward",
scope=list(lower= ~1),data=train_trans) #keeping significant variables## Start: AIC=-22549.71
## price ~ square_meters + rooms + floor + floor_count + build_year +
## latitude + longitude + centre_distance + poi_count + school_distance +
## clinic_distance + post_office_distance + kindergarten_distance +
## restaurant_distance + college_distance + pharmacy_distance +
## b_parking + b_balcony + b_elevator + b_security + b_storage +
## block_of_flats + apartment_building + tenement + unknown +
## condominium + cooperative + brick + concrete_slab + unknown_building_material
##
##
## Step: AIC=-22549.71
## price ~ square_meters + rooms + floor + floor_count + build_year +
## latitude + longitude + centre_distance + poi_count + school_distance +
## clinic_distance + post_office_distance + kindergarten_distance +
## restaurant_distance + college_distance + pharmacy_distance +
## b_parking + b_balcony + b_elevator + b_security + b_storage +
## block_of_flats + apartment_building + tenement + unknown +
## condominium + cooperative + brick + concrete_slab
##
##
## Step: AIC=-22549.71
## price ~ square_meters + rooms + floor + floor_count + build_year +
## latitude + longitude + centre_distance + poi_count + school_distance +
## clinic_distance + post_office_distance + kindergarten_distance +
## restaurant_distance + college_distance + pharmacy_distance +
## b_parking + b_balcony + b_elevator + b_security + b_storage +
## block_of_flats + apartment_building + tenement + unknown +
## condominium + brick + concrete_slab
##
##
## Step: AIC=-22549.71
## price ~ square_meters + rooms + floor + floor_count + build_year +
## latitude + longitude + centre_distance + poi_count + school_distance +
## clinic_distance + post_office_distance + kindergarten_distance +
## restaurant_distance + college_distance + pharmacy_distance +
## b_parking + b_balcony + b_elevator + b_security + b_storage +
## block_of_flats + apartment_building + tenement + condominium +
## brick + concrete_slab
##
## Df Sum of Sq RSS AIC
## - post_office_distance 1 0.000 635.78 -22552
## - b_storage 1 0.001 635.79 -22552
## - kindergarten_distance 1 0.026 635.81 -22551
## <none> 635.78 -22550
## - college_distance 1 0.308 636.09 -22548
## - b_parking 1 0.318 636.10 -22547
## - b_balcony 1 0.528 636.31 -22545
## - floor 1 0.633 636.42 -22543
## - b_security 1 0.938 636.72 -22539
## - pharmacy_distance 1 1.190 636.97 -22536
## - block_of_flats 1 1.242 637.03 -22535
## - latitude 1 1.662 637.45 -22529
## - school_distance 1 1.864 637.65 -22526
## - brick 1 2.396 638.18 -22519
## - rooms 1 2.471 638.26 -22518
## - floor_count 1 2.658 638.44 -22516
## - condominium 1 2.841 638.63 -22513
## - restaurant_distance 1 5.423 641.21 -22478
## - apartment_building 1 7.241 643.03 -22454
## - tenement 1 11.046 646.83 -22403
## - longitude 1 16.270 652.05 -22333
## - b_elevator 1 16.424 652.21 -22331
## - clinic_distance 1 16.598 652.38 -22329
## - build_year 1 21.698 657.48 -22261
## - concrete_slab 1 24.670 660.45 -22222
## - centre_distance 1 27.631 663.41 -22183
## - poi_count 1 58.563 694.35 -21789
## - square_meters 1 126.947 762.73 -20976
##
## Step: AIC=-22551.71
## price ~ square_meters + rooms + floor + floor_count + build_year +
## latitude + longitude + centre_distance + poi_count + school_distance +
## clinic_distance + kindergarten_distance + restaurant_distance +
## college_distance + pharmacy_distance + b_parking + b_balcony +
## b_elevator + b_security + b_storage + block_of_flats + apartment_building +
## tenement + condominium + brick + concrete_slab
##
## Df Sum of Sq RSS AIC
## - b_storage 1 0.001 635.79 -22554
## - kindergarten_distance 1 0.027 635.81 -22553
## <none> 635.78 -22552
## - college_distance 1 0.309 636.09 -22550
## - b_parking 1 0.318 636.10 -22549
## - b_balcony 1 0.529 636.31 -22547
## - floor 1 0.633 636.42 -22545
## - b_security 1 0.938 636.72 -22541
## - block_of_flats 1 1.244 637.03 -22537
## - pharmacy_distance 1 1.292 637.08 -22536
## - latitude 1 1.662 637.45 -22531
## - school_distance 1 1.936 637.72 -22527
## - brick 1 2.396 638.18 -22521
## - rooms 1 2.471 638.26 -22520
## - floor_count 1 2.660 638.44 -22518
## - condominium 1 2.841 638.63 -22515
## - restaurant_distance 1 5.617 641.40 -22478
## - apartment_building 1 7.243 643.03 -22456
## - tenement 1 11.046 646.83 -22405
## - longitude 1 16.286 652.07 -22335
## - b_elevator 1 16.425 652.21 -22333
## - clinic_distance 1 16.602 652.39 -22331
## - build_year 1 21.720 657.50 -22263
## - concrete_slab 1 24.670 660.45 -22224
## - centre_distance 1 27.631 663.42 -22185
## - poi_count 1 58.864 694.65 -21787
## - square_meters 1 126.978 762.76 -20977
##
## Step: AIC=-22553.7
## price ~ square_meters + rooms + floor + floor_count + build_year +
## latitude + longitude + centre_distance + poi_count + school_distance +
## clinic_distance + kindergarten_distance + restaurant_distance +
## college_distance + pharmacy_distance + b_parking + b_balcony +
## b_elevator + b_security + block_of_flats + apartment_building +
## tenement + condominium + brick + concrete_slab
##
## Df Sum of Sq RSS AIC
## - kindergarten_distance 1 0.027 635.81 -22555
## <none> 635.79 -22554
## - college_distance 1 0.308 636.09 -22552
## - b_parking 1 0.317 636.10 -22551
## - b_balcony 1 0.533 636.32 -22548
## - floor 1 0.633 636.42 -22547
## - b_security 1 0.941 636.73 -22543
## - block_of_flats 1 1.277 637.06 -22538
## - pharmacy_distance 1 1.293 637.08 -22538
## - latitude 1 1.662 637.45 -22533
## - school_distance 1 1.937 637.72 -22529
## - brick 1 2.399 638.18 -22523
## - rooms 1 2.471 638.26 -22522
## - floor_count 1 2.659 638.44 -22520
## - condominium 1 2.855 638.64 -22517
## - restaurant_distance 1 5.630 641.42 -22479
## - apartment_building 1 7.244 643.03 -22458
## - tenement 1 11.081 646.87 -22406
## - longitude 1 16.297 652.08 -22337
## - clinic_distance 1 16.607 652.39 -22333
## - b_elevator 1 16.713 652.50 -22331
## - build_year 1 23.138 658.92 -22246
## - concrete_slab 1 24.899 660.68 -22223
## - centre_distance 1 27.742 663.53 -22186
## - poi_count 1 58.999 694.78 -21788
## - square_meters 1 127.135 762.92 -20978
##
## Step: AIC=-22555.33
## price ~ square_meters + rooms + floor + floor_count + build_year +
## latitude + longitude + centre_distance + poi_count + school_distance +
## clinic_distance + restaurant_distance + college_distance +
## pharmacy_distance + b_parking + b_balcony + b_elevator +
## b_security + block_of_flats + apartment_building + tenement +
## condominium + brick + concrete_slab
##
## Df Sum of Sq RSS AIC
## <none> 635.81 -22555
## - college_distance 1 0.309 636.12 -22553
## - b_parking 1 0.318 636.13 -22553
## - b_balcony 1 0.533 636.35 -22550
## - floor 1 0.632 636.44 -22549
## - b_security 1 0.938 636.75 -22545
## - block_of_flats 1 1.295 637.11 -22540
## - latitude 1 1.734 637.55 -22534
## - pharmacy_distance 1 1.756 637.57 -22534
## - brick 1 2.389 638.20 -22525
## - school_distance 1 2.416 638.23 -22525
## - rooms 1 2.468 638.28 -22524
## - floor_count 1 2.665 638.48 -22521
## - condominium 1 2.852 638.66 -22519
## - restaurant_distance 1 5.624 641.44 -22481
## - apartment_building 1 7.241 643.05 -22459
## - tenement 1 11.068 646.88 -22408
## - longitude 1 16.274 652.09 -22339
## - clinic_distance 1 16.638 652.45 -22334
## - b_elevator 1 16.701 652.51 -22333
## - build_year 1 23.119 658.93 -22248
## - concrete_slab 1 24.893 660.71 -22225
## - centre_distance 1 27.953 663.77 -22185
## - poi_count 1 59.135 694.95 -21787
## - square_meters 1 127.188 763.00 -20979
##
## Call:
## lm(formula = price ~ square_meters + rooms + floor + floor_count +
## build_year + latitude + longitude + centre_distance + poi_count +
## school_distance + clinic_distance + restaurant_distance +
## college_distance + pharmacy_distance + b_parking + b_balcony +
## b_elevator + b_security + block_of_flats + apartment_building +
## tenement + condominium + brick + concrete_slab, data = train_trans)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.05043 -0.17542 0.01516 0.18058 1.03071
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.8151434 0.3352838 17.344 < 2e-16 ***
## square_meters 0.0107702 0.0002592 41.554 < 2e-16 ***
## rooms 0.0343865 0.0059408 5.788 7.36e-09 ***
## floor -0.0045290 0.0015466 -2.928 0.003417 **
## floor_count 0.0080746 0.0013424 6.015 1.87e-09 ***
## build_year 0.0027457 0.0001550 17.716 < 2e-16 ***
## latitude 0.0113598 0.0023416 4.851 1.25e-06 ***
## longitude 0.0263877 0.0017753 14.864 < 2e-16 ***
## centre_distance 0.0273744 0.0014052 19.481 < 2e-16 ***
## poi_count 0.0045720 0.0001614 28.334 < 2e-16 ***
## school_distance 0.0698001 0.0121882 5.727 1.06e-08 ***
## clinic_distance -0.0702893 0.0046768 -15.029 < 2e-16 ***
## restaurant_distance -0.1163189 0.0133118 -8.738 < 2e-16 ***
## college_distance -0.0073854 0.0036051 -2.049 0.040529 *
## pharmacy_distance 0.0674525 0.0138167 4.882 1.07e-06 ***
## b_parking 0.0144993 0.0069786 2.078 0.037768 *
## b_balcony 0.0176914 0.0065744 2.691 0.007138 **
## b_elevator 0.1188408 0.0078922 15.058 < 2e-16 ***
## b_security 0.0353023 0.0098944 3.568 0.000362 ***
## block_of_flats -0.0354522 0.0084557 -4.193 2.78e-05 ***
## apartment_building 0.1311866 0.0132312 9.915 < 2e-16 ***
## tenement 0.1827071 0.0149048 12.258 < 2e-16 ***
## condominium 0.0611773 0.0098314 6.223 5.12e-10 ***
## brick -0.0513479 0.0090157 -5.695 1.27e-08 ***
## concrete_slab -0.1822201 0.0099120 -18.384 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2714 on 8632 degrees of freedom
## Multiple R-squared: 0.6347, Adjusted R-squared: 0.6336
## F-statistic: 624.8 on 24 and 8632 DF, p-value: < 2.2e-16## 9 11 15 25 28 29 32 34
## 12.98175 13.39999 12.86222 12.80266 13.30026 13.99393 13.76087 13.38320
## 44 51 55 57 59 61 65 69
## 13.56236 13.24134 13.46485 13.57361 13.34239 13.63668 13.04876 13.67586
## 75 92 105 109 112 118 120 122
## 13.23211 13.79396 13.50578 12.87633 12.95702 13.28012 12.66611 12.86015
## 123 127 132 136 149 150 151 157
## 13.40821 13.26830 12.90749 12.75418 13.31389 13.02108 12.83895 12.95760
## 163 174 178 181 190 194 203 222
## 12.86843 12.98645 13.25261 13.23965 13.09532 13.07114 13.05236 12.94137
## 226 234 239 245 268 276 277 293
## 13.19596 13.38071 12.81007 12.96876 13.14647 13.55839 12.96727 13.48360
## 297 299 305 307 311 314 317 320
## 13.07996 13.80784 13.91551 13.45539 13.77944 13.01561 13.56741 13.05447
## 321 323 327 331 339 341 356 357
## 13.24891 13.46847 13.28740 13.62891 13.08436 13.43291 13.14563 13.25289
## 360 361 362 370 371 379 384 408
## 12.72906 13.13184 13.08601 12.83290 12.87111 12.73810 13.29459 13.46303
## 421 422 424 438 442 443 448 463
## 12.91447 13.27683 12.99085 13.11952 12.87402 13.00564 13.00103 13.53569
## 466 487 495 505 508 514 515 526
## 12.67337 14.44606 13.19622 13.43031 12.85051 13.02097 12.73133 13.50812
## 533 534 539 540 541 544 546 553
## 14.32176 13.08542 12.94449 13.41911 14.04212 13.17776 14.31463 13.33470
## 568 571 592 601 604 609 611 618
## 13.23013 13.65592 13.23421 13.05607 13.05309 12.83633 12.81870 13.01396
## 624 628 638 645 653 657 661 663
## 12.87496 12.98070 13.08538 13.08358 13.29897 12.91581 13.20549 13.69004
## 667 689 690 691 692 695 701 702
## 13.78803 13.72046 12.90458 13.14445 13.04321 13.42276 13.52933 13.04694
## 704 707 708 714 724 725 727 730
## 13.45647 13.15439 14.10270 13.60515 13.38665 13.26705 13.15123 13.40973
## 736 737 742 757 762 776 790 791
## 12.95392 13.01827 13.39594 13.37744 12.74260 12.68503 12.99747 13.06542
## 801 802 815 821 825 829 835 841
## 13.10088 13.23688 13.80026 12.70508 13.14357 13.30352 12.86752 13.76799
## 855 866 868 870 873 880 881 892
## 13.09196 13.05837 13.01656 13.63455 13.21012 13.48650 13.14154 13.14510
## 893 899 901 902 904 905 929 942
## 13.24377 13.34369 12.93664 13.02976 13.26327 12.94999 12.97711 12.92516
## 946 947 951 953 966 967 973 976
## 13.16230 13.60837 12.98349 13.39939 13.18074 12.99488 13.13074 13.01174
## 982 990 998 1000 1002 1010 1011 1016
## 13.58322 13.23468 12.87465 13.36744 13.19893 13.40921 13.14039 13.12129
## 1018 1027 1031 1033 1034 1035 1042 1044
## 13.70244 13.47430 12.83269 13.15925 13.01461 13.09080 13.28427 12.79226
## 1049 1055 1077 1080 1089 1098 1101 1105
## 13.47705 13.42612 13.51914 13.26952 13.11944 13.10000 13.73640 13.32318
## 1113 1118 1124 1136 1137 1140 1146 1154
## 12.94128 13.82017 13.03295 13.62857 13.13170 13.27412 13.47997 13.36964
## 1157 1169 1170 1183 1195 1203 1205 1210
## 12.79921 13.52490 13.32531 13.01169 13.35060 12.69445 13.07800 13.25732
## 1212 1213 1224 1225 1227 1231 1241 1245
## 12.73244 13.57071 12.98703 13.42396 13.11444 12.91622 13.46232 13.50120
## 1246 1249 1259 1263 1267 1273 1295 1301
## 13.34316 13.12866 13.12378 12.99661 13.20887 13.14279 13.17749 13.10967
## 1309 1312 1315 1331 1332 1333 1335 1338
## 13.14528 12.85989 13.14553 13.12547 13.18098 13.52467 13.17403 12.74077
## 1343 1345 1346 1347 1348 1351 1367 1384
## 13.23084 12.92681 12.96823 12.98876 13.25415 12.76590 12.90071 13.42332
## 1390 1393 1395 1402 1408 1422 1423 1426
## 13.51772 13.15670 13.39883 13.79603 13.90297 13.41304 13.45055 13.65237
## 1430 1431 1433 1439 1441 1442 1443 1447
## 13.39614 13.12882 13.13109 13.70249 14.11914 13.07486 13.43567 13.31687
## 1448 1451 1461 1463 1466 1468 1474 1491
## 13.89001 13.56419 13.04260 13.28463 13.26183 13.57313 13.53291 13.02860
## 1495 1497 1506 1509 1513 1514 1515 1520
## 13.37264 13.82184 13.64385 13.17236 13.14196 13.55314 13.55278 12.97619
## 1521 1546 1548 1562 1568 1569 1570 1574
## 13.22926 13.38593 13.45559 13.26110 13.39026 13.28501 13.62055 13.11650
## 1575 1579 1580 1581 1590 1595 1596 1597
## 13.50973 13.61985 13.34636 13.85799 13.40655 13.25646 13.42890 13.45016
## 1599 1602 1609 1610 1611 1615 1618 1633
## 13.46969 13.49238 14.02208 13.29274 13.69419 13.50805 13.14596 13.43956
## 1634 1636 1637 1640 1649 1652 1662 1672
## 13.03372 13.75164 13.13507 13.01185 12.78147 13.54505 13.20440 14.10372
## 1685 1692 1694 1702 1705 1706 1712 1716
## 13.07445 12.81541 13.21339 13.07710 13.24328 13.62332 13.19806 13.18041
## 1718 1722 1729 1735 1755 1760 1762 1764
## 13.01574 13.50860 13.30518 13.41790 13.18071 13.19982 13.32747 13.08679
## 1772 1773 1776 1781 1792 1797 1813 1816
## 13.29099 14.14763 13.82647 13.32115 13.30560 13.60312 12.92885 12.91034
## 1820 1826 1827 1832 1848 1856 1862 1865
## 12.85602 13.31609 13.07879 13.27506 12.55163 13.91339 13.20303 13.19946
## 1868 1870 1871 1873 1883 1894 1899 1901
## 13.61684 13.28029 12.99464 12.99946 13.57957 13.19315 13.30145 13.17122
## 1908 1910 1912 1914 1916 1932 1935 1939
## 13.01533 13.46483 12.76069 13.09244 13.85675 13.42398 13.59758 13.37942
## 1940 1947 1963 1969 1972 1976 1977 1980
## 13.81309 13.45627 13.26854 13.79633 13.40959 13.08228 13.56280 13.31048
## 1986 1987 1990 1991 1992 1993 1997 2001
## 12.86580 13.53283 13.19239 13.24749 12.86988 12.77808 13.60334 12.98479
## 2002 2015 2022 2035 2041 2046 2047 2050
## 13.39611 13.15765 13.42384 13.13547 12.98469 13.61966 13.05347 13.57542
## 2051 2053 2062 2064 2074 2077 2079 2083
## 13.49769 13.79848 13.23174 13.52540 13.22826 13.31328 13.03840 13.96534
## 2089 2090 2097 2099 2101 2106 2107 2117
## 12.90079 13.37172 13.28194 13.21521 12.94518 13.27928 13.30696 13.36446
## 2118 2132 2133 2134 2148 2151 2157 2166
## 12.79558 13.04044 13.32323 13.17580 13.72485 13.07837 13.53698 13.17994
## 2170 2175 2181 2182 2191 2199 2214 2215
## 13.39188 13.36569 13.34458 13.33196 12.88358 13.58608 13.48257 13.49163
## 2216 2236 2237 2238 2239 2242 2256 2263
## 13.34775 13.16963 13.10480 12.77001 13.43746 12.94921 13.00245 13.39243
## 2265 2267 2273 2276 2279 2285 2305 2307
## 13.39926 13.14805 13.29200 13.84110 13.53555 13.00723 12.95015 13.15555
## 2310 2312 2323 2325 2330 2333 2335 2341
## 13.22000 13.51471 13.22945 13.60277 13.09287 13.07649 13.12490 13.18617
## 2348 2353 2358 2362 2370 2378 2379 2384
## 13.38372 12.99573 13.28782 13.63097 13.11560 13.59084 13.41815 13.04560
## 2389 2397 2399 2401 2403 2406 2412 2413
## 13.06978 13.73616 14.21950 12.78774 13.36226 13.38589 13.34533 13.73332
## 2414 2421 2426 2437 2440 2441 2443 2450
## 12.89113 13.42115 13.24637 13.35025 13.25301 13.54073 12.89869 13.73827
## 2452 2453 2455 2457 2459 2461 2464 2466
## 13.07098 13.47406 13.36441 13.07068 13.36801 13.44898 13.26280 12.80682
## 2481 2482 2484 2496 2503 2506 2507 2508
## 12.74378 13.43656 13.41489 13.06284 13.36810 13.07206 13.31275 13.22111
## 2510 2511 2515 2517 2518 2523 2526 2527
## 13.61725 13.35053 13.16750 13.26977 13.69224 13.08942 13.46171 13.77396
## 2534 2536 2538 2539 2544 2551 2560 2570
## 13.20274 13.68829 14.04893 13.54171 13.32789 13.32332 13.10416 13.23144
## 2571 2585 2586 2588 2590 2601 2613 2615
## 13.03480 13.39558 13.35268 13.20556 13.46669 13.49312 13.52835 13.66661
## 2618 2620 2624 2626 2628 2641 2642 2650
## 13.06030 12.78984 13.89111 13.76932 13.19429 13.01529 13.16192 13.04603
## 2655 2657 2667 2669 2670 2678 2683 2684
## 13.54094 13.38892 13.09458 13.50618 13.82833 13.20819 12.88621 12.76042
## 2688 2691 2699 2702 2703 2704 2707 2709
## 12.88316 13.16306 13.11163 12.85236 13.41901 13.14102 13.35295 13.38451
## 2712 2719 2727 2744 2753 2757 2758 2767
## 13.05905 13.43328 13.37773 13.36217 13.61453 13.33883 13.51283 13.41508
## 2769 2770 2778 2791 2793 2802 2809 2823
## 13.25124 13.26027 13.74254 13.44179 13.20255 13.62370 13.82372 13.32773
## 2826 2834 2837 2841 2853 2862 2863 2869
## 13.22350 13.55458 12.69589 13.23160 13.27871 13.24736 14.31863 13.53510
## 2888 2889 2901 2906 2907 2914 2922 2924
## 13.10901 13.42588 14.11836 13.75533 13.50007 13.14916 13.23766 13.94854
## 2926 2929 2932 2936 2938 2939 2940 2941
## 13.33158 13.61401 13.26009 13.00347 13.57482 13.16906 13.73581 14.18269
## 2958 2961 2963 2964 2970 2973 2985 2988
## 13.35225 13.82599 13.34445 13.32046 12.87437 13.57545 13.61265 13.80274
## 2993 3011 3013 3015 3023 3027 3029 3030
## 13.52930 13.44990 13.85213 13.57493 13.28177 13.35104 13.12785 13.76716
## 3037 3040 3041 3045 3051 3056 3065 3072
## 13.38883 13.73336 13.76835 13.11976 13.45141 13.32772 13.08308 13.30975
## 3074 3077 3080 3085 3087 3094 3095 3102
## 14.14696 13.07237 13.85973 12.95341 13.52683 13.39497 12.91603 13.48938
## 3115 3128 3132 3139 3144 3154 3157 3158
## 13.41744 13.74866 13.05307 13.43701 13.23551 13.05267 13.07501 13.38572
## 3161 3168 3171 3178 3182 3191 3192 3193
## 13.15652 14.07787 13.07649 13.20159 14.19296 13.42144 13.02774 13.58884
## 3205 3214 3217 3222 3233 3240 3244 3247
## 13.33689 13.26857 13.23240 13.54831 13.50271 13.16503 12.68365 13.42257
## 3249 3253 3256 3260 3267 3272 3280 3283
## 13.16517 13.86742 13.22736 13.34258 13.29234 13.45463 12.97164 13.27442
## 3291 3292 3294 3310 3316 3318 3320 3329
## 13.43427 13.21248 13.06370 13.21712 13.18805 13.34671 13.40576 13.28298
## 3342 3343 3345 3350 3351 3357 3359 3362
## 13.17032 13.20287 13.23713 13.68323 13.28164 13.42113 13.15721 13.26491
## 3365 3367 3376 3380 3382 3388 3391 3402
## 13.50319 13.16696 13.46200 13.27299 13.34179 13.28773 13.12575 13.17416
## 3413 3420 3421 3427 3436 3441 3445 3447
## 13.35350 13.45781 13.05062 13.80786 13.10854 13.12649 13.11962 12.95778
## 3448 3451 3462 3463 3464 3465 3474 3479
## 12.98145 12.86931 13.87877 13.56591 13.10325 13.47960 13.33734 13.22978
## 3492 3500 3507 3513 3517 3518 3529 3545
## 13.24050 13.56602 12.95918 13.37592 12.96194 14.04361 13.14704 12.72978
## 3546 3548 3559 3562 3571 3573 3574 3575
## 13.02454 13.37475 13.38961 12.95079 13.99504 13.42993 13.35829 13.94727
## 3581 3584 3587 3588 3592 3599 3600 3603
## 13.28251 14.05460 13.42594 13.62371 13.54297 13.39679 13.36134 13.16182
## 3615 3620 3622 3625 3628 3632 3653 3654
## 13.45628 13.96570 13.21842 13.50258 13.43513 13.42281 13.79085 13.82430
## 3670 3679 3683 3694 3698 3699 3701 3702
## 13.13795 13.10444 13.38135 13.32098 13.27795 13.27342 14.04477 13.05430
## 3703 3705 3706 3708 3712 3716 3719 3726
## 12.95665 13.20692 13.17610 13.94694 13.76315 13.68432 13.25823 14.12994
## 3732 3733 3734 3740 3741 3746 3753 3759
## 13.98276 13.16124 13.51397 13.56085 13.28858 13.36584 13.71534 13.00510
## 3785 3786 3794 3798 3800 3801 3810 3812
## 13.33684 13.63429 13.72590 14.04167 13.52647 13.48402 13.45783 13.45885
## 3813 3819 3821 3823 3828 3832 3834 3838
## 13.65038 13.50082 13.20941 13.53349 13.19839 13.52755 13.30703 12.83535
## 3839 3844 3847 3852 3854 3855 3859 3862
## 13.67428 13.39968 13.39766 13.77361 13.02297 12.92604 13.61268 13.29649
## 3875 3876 3884 3893 3900 3919 3934 3938
## 13.11070 13.09927 13.47617 13.32576 13.09340 13.56003 12.96490 13.71761
## 3940 3948 3953 3957 3967 3968 3974 3977
## 13.75619 13.20024 13.82974 13.94993 13.75841 13.24213 12.91412 13.27414
## 3991 3995 4004 4008 4011 4012 4014 4016
## 13.78563 13.33046 13.81682 13.37122 13.39557 13.05586 13.34077 13.33056
## 4018 4025 4030 4034 4035 4036 4047 4050
## 13.35114 13.68265 13.80655 13.29689 14.09920 13.36925 13.54944 14.03788
## 4052 4054 4068 4069 4070 4073 4077 4083
## 13.43221 14.09465 13.24804 13.54062 13.53834 13.92308 13.59528 13.30937
## 4086 4099 4102 4108 4117 4121 4133 4137
## 13.98317 13.75296 13.98466 13.74089 13.60004 13.06227 14.07122 13.39433
## 4150 4153 4158 4159 4164 4170 4180 4193
## 13.56708 13.33792 13.55889 12.95829 13.41919 13.35806 13.83362 13.38819
## 4195 4198 4200 4204 4226 4227 4229 4232
## 13.26128 13.47898 13.27991 13.33561 13.19355 13.49257 13.06362 12.96601
## 4238 4242 4245 4252 4253 4270 4276 4283
## 14.25101 13.36841 13.34241 13.58827 14.49425 14.15005 13.85612 13.02224
## 4285 4288 4290 4317 4321 4326 4329 4332
## 13.26364 13.10634 14.06065 13.51141 14.03611 13.33138 13.28795 12.82633
## 4335 4336 4340 4359 4361 4363 4374 4380
## 13.24006 13.06926 14.13108 13.54911 13.96195 13.15807 13.30137 13.27276
## 4390 4392 4393 4403 4409 4415 4416 4418
## 12.71069 13.36026 13.49815 13.40417 13.13847 13.02045 13.42539 13.83307
## 4424 4438 4445 4456 4458 4476 4478 4479
## 13.59442 12.70471 13.18498 13.16842 13.41389 13.40136 13.25299 13.21860
## 4480 4484 4491 4497 4500 4505 4528 4530
## 14.14969 13.48849 13.53544 12.92358 13.05968 13.17097 13.73526 13.63070
## 4532 4535 4539 4545 4549 4551 4558 4580
## 13.19479 13.51381 13.17727 13.31239 13.59893 13.59893 12.94564 13.10608
## 4581 4587 4589 4622 4626 4627 4631 4641
## 13.47332 13.17926 13.06303 13.03099 13.05599 13.27579 12.79137 13.13776
## 4642 4645 4658 4661 4666 4677 4683 4684
## 13.14300 13.11832 14.28006 13.39122 13.27805 13.18630 13.35376 13.61685
## 4687 4697 4704 4721 4727 4733 4737 4742
## 13.38442 13.29636 13.01279 12.86253 13.43133 12.70675 13.32461 13.37419
## 4745 4748 4759 4769 4771 4772 4778 4789
## 13.25405 13.39140 13.08013 12.74762 13.54659 13.07341 12.85675 13.65370
## 4794 4795 4806 4810 4816 4819 4823 4826
## 13.82112 13.80513 13.05563 13.63332 13.33613 13.40020 13.12536 13.26278
## 4833 4834 4857 4862 4872 4887 4908 4915
## 13.34020 13.12386 13.09115 13.37529 12.99464 12.99870 13.20898 13.68417
## 4916 4924 4926 4927 4933 4934 4941 4943
## 13.36247 13.89796 13.16484 13.14780 12.83613 13.41232 13.68589 13.59152
## 4944 4945 4946 4953 4959 4965 4970 4973
## 13.21775 12.91563 13.58740 13.16500 13.22783 13.48569 13.07472 13.38631
## 4979 4986 4987 4990 4995 5022 5023 5025
## 13.06209 13.39687 13.39731 13.16505 13.34498 13.96939 12.77363 13.44661
## 5028 5029 5030 5037 5042 5044 5055 5059
## 13.75317 14.12485 14.12485 13.07057 13.20346 12.84244 13.04883 13.12585
## 5066 5067 5090 5100 5101 5102 5108 5111
## 13.15522 13.20010 13.99294 12.98262 13.73550 13.73550 13.74626 13.43196
## 5118 5120 5126 5132 5133 5135 5139 5150
## 12.96028 13.56231 13.33909 13.91636 13.96111 14.10649 13.61367 13.24583
## 5152 5160 5165 5172 5176 5181 5188 5189
## 13.22283 13.75154 13.54849 13.50086 13.24109 13.18887 13.25686 13.15795
## 5192 5199 5217 5223 5237 5244 5246 5250
## 13.19634 13.04039 13.17170 13.06914 13.08001 13.04725 13.31929 13.69109
## 5254 5261 5269 5271 5272 5275 5279 5281
## 13.54677 13.66052 13.55450 13.27670 13.30201 13.24348 13.70311 13.34747
## 5284 5286 5293 5296 5298 5300 5301 5306
## 13.55569 13.20545 13.16764 13.23501 13.03318 13.50415 13.54393 13.01572
## 5308 5310 5311 5314 5316 5327 5334 5336
## 13.02468 13.38982 13.22006 13.25973 13.45888 13.28861 12.93981 13.64727
## 5341 5347 5351 5355 5358 5359 5360 5365
## 13.54175 13.30814 13.24120 13.53428 13.13009 13.58968 13.53428 13.88678
## 5366 5367 5371 5382 5392 5393 5398 5406
## 13.05501 13.56590 13.39254 13.33756 13.42965 13.42289 13.23261 13.60672
## 5410 5412 5419 5420 5425 5435 5451 5452
## 13.47260 13.40373 13.58625 12.95301 12.96801 13.50959 13.24110 13.59016
## 5456 5460 5462 5470 5473 5480 5481 5484
## 14.04835 13.56900 13.57981 13.21736 13.35191 13.58914 13.40326 13.32734
## 5487 5491 5492 5493 5494 5495 5499 5500
## 13.21421 13.85839 13.37881 13.30729 13.86693 12.97416 13.70668 13.24810
## 5505 5513 5515 5516 5519 5528 5531 5532
## 13.21064 13.09364 13.40077 13.14079 13.05316 13.41029 13.48044 13.86806
## 5537 5538 5541 5542 5543 5544 5551 5552
## 12.92151 13.32099 13.37625 13.34954 13.15857 13.62175 13.08324 12.99611
## 5560 5565 5569 5570 5571 5580 5581 5585
## 13.84093 13.86599 13.30746 13.24574 13.91201 13.06617 12.35260 13.43998
## 5586 5590 5592 5593 5595 5596 5597 5598
## 13.60487 12.96334 13.24533 13.74769 13.65525 13.15031 13.03016 13.32316
## 5601 5604 5608 5610 5613 5621 5626 5630
## 12.84341 13.74487 13.31122 13.16548 13.38101 13.24571 13.44040 13.63870
## 5632 5665 5668 5669 5670 5673 5675 5679
## 13.20974 13.62785 13.03585 13.68854 13.59980 13.03585 13.56106 13.22131
## 5681 5686 5687 5691 5694 5695 5704 5709
## 13.05774 13.67318 13.26057 13.17089 13.83876 12.90392 13.95619 12.90840
## 5710 5711 5714 5716 5720 5727 5730 5731
## 13.46714 12.78273 13.89418 13.78634 13.03315 13.95704 13.03070 13.46095
## 5733 5735 5742 5748 5751 5753 5761 5763
## 12.92451 13.29862 13.40087 13.71521 13.55658 13.40294 13.90872 13.41045
## 5766 5768 5770 5771 5773 5778 5779 5781
## 13.72064 13.62532 13.47788 13.23066 13.24962 13.78739 13.78739 13.72671
## 5782 5784 5786 5787 5788 5789 5790 5792
## 13.35398 13.47039 13.71652 14.09938 13.45649 13.56644 13.38222 13.30204
## 5795 5801 5806 5809 5810 5812 5816 5829
## 13.21490 13.18323 13.40917 13.72353 13.49414 13.94679 13.33913 13.43907
## 5835 5838 5839 5843 5849 5851 5854 5855
## 13.17379 13.27750 13.26165 13.40020 12.42095 13.62533 13.51341 13.21417
## 5857 5874 5892 5894 5901 5903 5905 5909
## 13.37555 13.23771 13.42015 13.03047 13.44268 13.46228 13.48201 13.12092
## 5919 5932 5936 5937 5946 5957 5959 5965
## 13.41856 13.22301 12.82586 13.72221 13.50556 13.13126 13.59930 13.55028
## 5968 5969 5970 5973 5977 5983 5991 5994
## 13.17229 13.34675 13.44169 13.50996 13.63794 13.62227 12.59814 13.83504
## 5998 6007 6026 6028 6041 6042 6050 6065
## 13.35218 13.41408 13.39511 13.85955 13.19673 13.11881 13.23690 13.26970
## 6075 6078 6080 6088 6092 6095 6097 6099
## 13.48314 13.64838 13.22871 13.30026 13.69931 13.76481 13.64672 13.07074
## 6112 6137 6144 6156 6159 6161 6163 6164
## 13.62896 13.12186 13.19388 13.40343 13.59670 12.98825 13.15479 12.89341
## 6181 6186 6187 6193 6196 6200 6218 6220
## 13.68531 13.68068 13.05511 12.97561 12.98075 13.67174 13.09595 13.28409
## 6225 6231 6232 6237 6246 6255 6260 6262
## 13.50544 13.58852 13.05877 13.24701 13.27570 13.41638 13.29883 13.82329
## 6263 6264 6270 6271 6276 6282 6286 6298
## 13.67127 13.09978 13.48616 13.46674 13.52759 12.94864 13.65982 13.68477
## 6306 6325 6327 6329 6330 6331 6332 6336
## 13.16574 13.12023 13.25165 12.87456 13.65223 13.29582 13.28492 13.96114
## 6341 6352 6354 6355 6356 6367 6370 6375
## 13.22770 13.71544 13.28092 13.84409 13.05078 13.03047 13.61472 13.45899
## 6378 6383 6389 6391 6392 6398 6399 6412
## 13.25557 13.76310 13.42149 13.37917 13.71329 13.16251 13.47714 13.70675
## 6418 6419 6422 6423 6424 6428 6429 6432
## 13.16855 13.71768 13.37489 13.55757 13.32469 12.99953 13.14824 13.20422
## 6433 6438 6456 6467 6468 6494 6495 6498
## 13.69613 13.60736 12.95567 13.71903 13.13155 13.38087 13.34648 13.70377
## 6500 6503 6507 6512 6518 6519 6521 6522
## 13.18063 13.27719 13.66899 13.40686 13.74050 14.00084 13.46579 13.77219
## 6532 6551 6555 6564 6566 6572 6575 6584
## 13.35724 14.00502 13.40239 12.89426 13.09954 13.10636 13.44546 13.09238
## 6587 6593 6597 6599 6603 6611 6612 6613
## 13.54585 13.27839 13.19712 13.00134 13.15929 13.64100 13.37780 13.64870
## 6615 6618 6622 6631 6635 6636 6639 6642
## 13.89238 13.09323 13.79574 13.37173 13.14847 13.94393 13.30317 13.24637
## 6643 6654 6660 6664 6666 6672 6673 6677
## 13.23535 13.42145 13.25242 13.76491 14.15461 13.62409 13.69530 13.25440
## 6690 6691 6692 6695 6696 6698 6699 6721
## 13.41806 13.29596 13.41863 13.81169 13.19851 13.39692 13.52806 13.09367
## 6726 6729 6731 6746 6749 6756 6760 6762
## 12.55887 12.71170 13.86980 13.83232 13.77911 13.40247 13.81659 13.41442
## 6763 6767 6776 6777 6779 6787 6791 6797
## 13.60420 13.20138 13.21226 13.52867 13.57467 13.40808 13.23519 13.79340
## 6810 6811 6816 6819 6822 6837 6838 6840
## 13.72918 13.54774 13.46098 13.77862 13.52785 13.96042 14.00395 13.52431
## 6845 6857 6858 6860 6862 6873 6876 6878
## 13.17885 13.42821 13.21856 14.23603 13.13217 13.81116 13.29321 13.55539
## 6880 6883 6885 6890 6892 6894 6915 6918
## 13.26079 13.64324 12.86164 13.47456 13.62086 13.19716 13.01189 13.30630
## 6928 6930 6935 6938 6939 6946 6949 6957
## 13.44572 13.06530 13.88609 13.48072 13.07349 13.09978 13.73032 13.09648
## 6969 6970 6973 6985 6987 6997 6998 6999
## 13.62714 13.03049 13.34812 13.56712 13.22499 14.46293 12.82105 12.99332
## 7004 7006 7009 7014 7023 7026 7031 7034
## 13.50105 12.99590 13.19376 14.06054 13.40815 13.30398 13.42175 13.14962
## 7036 7037 7039 7040 7045 7048 7049 7053
## 13.35053 13.44927 13.55934 12.99061 13.16306 13.75733 13.63672 13.91330
## 7058 7063 7064 7069 7093 7095 7102 7103
## 13.73011 13.85944 13.18075 13.46733 13.80971 13.29057 13.37443 13.81359
## 7107 7109 7111 7120 7121 7123 7135 7137
## 13.43763 12.97857 12.93899 13.32092 13.06173 13.45577 14.11130 13.10966
## 7140 7141 7144 7159 7170 7174 7176 7188
## 13.26895 12.76476 13.62118 13.42196 13.44376 13.30733 13.38294 13.60856
## 7190 7192 7194 7195 7196 7198 7214 7217
## 13.77837 13.39970 13.06256 13.29862 13.29522 13.30313 13.89274 14.06487
## 7220 7233 7241 7243 7244 7257 7275 7280
## 13.05666 13.27984 13.86108 13.39024 13.35792 13.35773 14.03450 14.25196
## 7281 7282 7283 7287 7292 7293 7300 7301
## 13.45097 13.58875 13.60997 13.42851 13.07653 13.49928 13.18313 13.18233
## 7303 7305 7307 7311 7313 7315 7331 7341
## 13.49556 13.35353 13.47511 12.78171 13.16636 12.64549 12.97232 13.35802
## 7342 7344 7348 7349 7356 7360 7361 7364
## 12.95555 13.01668 13.64509 13.42805 13.83853 13.56684 13.12833 13.01349
## 7367 7368 7385 7396 7398 7407 7410 7412
## 13.54384 13.65927 13.88702 13.10655 13.20709 13.11847 13.05127 13.71907
## 7413 7415 7417 7419 7420 7430 7435 7436
## 13.28090 13.09672 13.19821 13.03018 13.20364 13.15194 13.77291 12.73121
## 7437 7442 7449 7454 7455 7456 7460 7461
## 12.84779 13.48258 13.13725 13.45691 12.96097 13.23253 13.39053 13.21217
## 7464 7465 7468 7480 7482 7485 7486 7493
## 12.97950 13.78943 13.35255 13.24249 13.32135 12.90900 13.40831 12.89393
## 7496 7498 7502 7510 7518 7526 7531 7532
## 13.11002 13.71611 13.40977 13.04841 13.45692 13.44790 13.60266 13.47529
## 7535 7536 7539 7542 7545 7546 7549 7551
## 13.51380 13.68834 12.98568 13.02989 13.22931 13.35772 13.44255 13.54893
## 7556 7557 7558 7560 7567 7568 7575 7576
## 13.29829 12.88777 13.34295 13.86841 12.94399 13.20515 12.86974 13.95076
## 7577 7589 7590 7593 7594 7597 7598 7603
## 13.30234 13.51065 13.76655 13.63084 13.87992 13.13830 13.30397 12.82791
## 7606 7617 7618 7624 7629 7631 7632 7637
## 13.24621 13.58634 14.32932 13.37528 13.07193 13.07482 13.05005 12.63576
## 7639 7641 7642 7643 7645 7647 7648 7654
## 13.16937 13.36433 13.20179 13.12270 12.80339 13.10737 12.93109 13.12902
## 7656 7660 7668 7671 7672 7673 7675 7694
## 13.46332 13.41199 13.09659 13.51505 13.95728 13.94434 13.55565 12.81890
## 7698 7703 7704 7715 7725 7732 7733 7735
## 12.79672 12.83156 12.86137 13.02343 13.40307 13.22277 13.12316 12.64587
## 7739 7746 7761 7774 7775 7778 7785 7799
## 13.03379 13.01064 12.94783 13.45085 13.51342 12.86415 13.24910 12.80384
## 7808 7815 7816 7817 7821 7822 7828 7829
## 13.41124 13.53198 13.33735 13.15093 13.07030 13.25429 12.86425 12.65670
## 7831 7833 7838 7846 7847 7850 7856 7881
## 13.05854 13.02316 13.36810 12.57639 13.25615 13.32716 13.20928 13.35770
## 7883 7885 7893 7896 7902 7918 7922 7923
## 12.92887 12.68859 13.04126 13.72116 13.58620 13.46356 13.59661 13.29882
## 7924 7928 7930 7935 7942 7946 7947 7956
## 12.74711 12.93843 12.93905 13.28864 12.99086 13.74134 12.92895 13.19569
## 7958 7962 7969 7973 7977 7978 7983 7989
## 12.96684 13.17224 13.60363 13.06657 13.92890 13.18548 13.10783 13.72658
## 7996 7997 7998 8001 8005 8018 8023 8026
## 13.24075 13.09526 13.18115 13.01396 13.70030 13.43799 13.52891 13.45484
## 8027 8030 8035 8036 8037 8038 8039 8043
## 13.40098 13.19915 12.56796 13.27367 13.21220 13.42116 13.23811 13.31249
## 8044 8046 8051 8055 8064 8070 8080 8088
## 13.09070 13.00433 12.77816 13.51207 13.18656 13.70273 13.36258 13.67730
## 8092 8095 8098 8117 8122 8132 8133 8135
## 13.39259 13.16465 12.85581 12.76782 13.58692 13.17492 13.04122 13.13480
## 8136 8138 8139 8142 8143 8150 8159 8163
## 13.24640 13.93445 13.42768 13.45015 13.33102 12.70066 12.95390 13.41756
## 8166 8169 8172 8173 8211 8214 8217 8221
## 13.26962 13.04650 13.55525 13.24912 13.15899 13.30252 13.33094 13.47321
## 8225 8227 8234 8241 8242 8243 8244 8246
## 12.70392 13.37359 13.55637 13.05911 13.36255 13.05857 13.23609 13.71811
## 8252 8261 8262 8266 8277 8278 8282 8289
## 13.31287 13.72107 13.30503 12.82856 13.02703 13.07274 12.66528 13.42903
## 8292 8299 8302 8317 8323 8324 8325 8333
## 13.31275 13.57451 13.61255 13.35065 12.77226 13.27164 13.10728 13.43157
## 8338 8344 8346 8352 8358 8362 8368 8370
## 13.12851 13.41985 13.54429 13.31340 12.88838 13.63266 13.09282 12.97951
## 8375 8379 8383 8384 8390 8394 8399 8410
## 13.44428 12.79600 13.13602 13.11403 13.24275 13.28703 13.32068 13.45810
## 8417 8431 8433 8435 8440 8443 8446 8447
## 13.35279 13.27692 12.88888 13.08615 13.15805 13.32701 13.29369 13.69459
## 8452 8461 8464 8469 8471 8474 8478 8485
## 13.39439 13.60889 13.17687 13.25235 13.28570 13.15710 13.04077 13.12035
## 8488 8490 8505 8509 8513 8526 8528 8529
## 13.44944 13.57646 13.90253 13.29903 13.30404 12.97207 12.69055 13.32420
## 8532 8537 8539 8541 8544 8547 8549 8550
## 13.60893 12.83863 12.96386 13.31835 13.37526 12.81659 13.36809 13.14309
## 8552 8555 8556 8558 8568 8581 8583 8586
## 13.06961 13.71441 13.37705 13.51810 13.65395 13.84859 13.26126 13.67213
## 8589 8596 8598 8601 8602 8603 8608 8614
## 14.01061 12.89380 13.34179 13.23129 13.27817 13.04504 13.34871 13.07124
## 8617 8619 8622 8630 8632 8634 8639 8646
## 12.97788 13.42846 13.21544 13.52998 13.32487 13.58350 13.92571 13.47008
## 8649 8654 8657 8660 8662 8663 8665 8669
## 13.27183 13.58941 13.21879 13.22703 13.05974 13.02122 13.76731 13.89980
## 8671 8673 8677 8682 8692 8698 8703 8705
## 13.16687 13.27383 13.32984 13.45290 12.78799 13.80250 13.87672 13.39711
## 8718 8719 8720 8723 8726 8728 8729 8745
## 13.51913 13.35296 13.27524 13.19908 13.37106 13.14435 13.24334 13.39141
## 8750 8755 8760 8762 8772 8779 8782 8785
## 12.54151 13.72159 13.54355 13.52273 13.56960 13.83662 13.88058 13.04478
## 8789 8790 8808 8809 8811 8813 8817 8831
## 13.18610 12.93760 13.66851 13.01125 13.54625 13.32645 13.41939 13.81956
## 8842 8844 8848 8849 8857 8859 8861 8863
## 13.01295 13.43398 13.21051 13.46211 13.31593 13.25525 12.98452 13.41583
## 8865 8876 8885 8889 8891 8894 8896 8901
## 13.84219 13.24408 13.14925 13.09068 12.94108 13.09842 13.14820 13.45121
## 8906 8907 8910 8911 8920 8921 8926 8931
## 13.33235 13.41961 13.08502 13.78539 13.19880 13.07447 13.30776 13.07432
## 8948 8951 8953 8954 8959 8962 8967 8976
## 13.62866 13.39822 12.96171 13.66715 13.34164 14.06777 13.29159 13.54726
## 8977 8980 8996 8997 9011 9014 9023 9026
## 13.14082 13.11767 13.24634 13.63455 13.23696 13.31689 13.27464 13.58429
## 9029 9034 9043 9048 9057 9060 9066 9072
## 12.81352 13.50009 13.43846 14.17999 13.70653 13.40067 13.17634 13.64922
## 9076 9081 9084 9089 9094 9097 9099 9100
## 12.96602 13.11528 13.25025 12.95795 13.15820 13.18651 13.11848 12.98670
## 9101 9108 9109 9114 9116 9120 9122 9123
## 13.16597 13.51526 13.04121 13.02291 13.11677 13.07096 12.93800 13.69195
## 9129 9133 9138 9139 9144 9147 9149 9150
## 12.82523 13.33783 13.29492 13.24271 13.25885 12.87809 13.22031 12.99094
## 9152 9163 9166 9176 9181 9183 9184 9197
## 13.64688 12.95418 12.94598 12.87396 13.13827 12.83151 12.72036 13.06741
## 9200 9203 9212 9220 9221 9222 9224 9233
## 13.01191 13.56826 12.99786 12.82936 12.72639 12.97023 13.10476 13.07542
## 9234 9243 9246 9248 9249 9259 9261 9266
## 13.01664 13.17762 13.01434 12.94485 13.85490 13.20884 13.03212 13.11652
## 9269 9278 9285 9288 9291 9295 9301 9302
## 13.28662 13.33136 13.26594 13.28657 13.03118 13.66556 12.86240 12.90181
## 9303 9304 9306 9307 9308 9310 9312 9314
## 13.11724 13.16067 12.96940 13.30792 13.09281 13.49655 13.15583 12.84848
## 9328 9329 9332 9334 9345 9346 9347 9351
## 12.88031 12.72342 13.07305 12.85603 13.53824 13.32915 13.50243 13.14962
## 9355 9356 9357 9370 9372 9375 9380 9382
## 12.99758 12.96912 13.09026 13.01461 13.02628 13.00591 13.09487 13.23165
## 9389 9402 9407 9410 9411 9419 9422 9425
## 13.44594 13.19391 13.09059 12.72167 13.13728 12.85096 13.22355 13.06477
## 9427 9429 9430 9435 9436 9440 9441 9442
## 12.89643 13.41676 13.25840 13.34713 13.51925 13.08938 13.09283 12.65682
## 9446 9448 9450 9466 9471 9473 9478 9480
## 13.04420 13.21200 12.97792 13.00469 13.27209 13.25932 12.92691 13.19635
## 9481 9483 9488 9490 9507 9508 9509 9510
## 13.37186 13.49076 12.83723 13.44691 13.06537 13.08995 13.79288 13.54563
## 9515 9519 9528 9531 9537 9543 9547 9553
## 13.18562 13.81938 13.34748 13.41926 13.42044 12.96992 13.53169 13.20445
## 9562 9565 9572 9592 9595 9596 9604 9605
## 13.03525 13.26003 13.83009 13.65194 14.44921 13.19929 13.71737 13.03978
## 9611 9612 9645 9652 9653 9654 9657 9659
## 13.37648 13.87969 13.50570 13.67387 13.23537 12.94200 13.57729 13.20695
## 9661 9668 9673 9682 9690 9692 9693 9697
## 12.84213 13.12114 12.94564 12.65544 14.12532 13.15321 12.72505 13.27529
## 9699 9704 9708 9710 9711 9715 9718 9720
## 12.87077 13.78061 13.26346 13.28125 13.11777 13.83889 13.20866 13.12536
## 9734 9736 9741 9747 9753 9759 9764 9767
## 13.23886 12.71668 13.55430 12.68572 13.16621 13.12089 13.39082 13.84758
## 9771 9773 9782 9785 9786 9787 9810 9819
## 13.05710 13.62094 12.98103 12.97451 12.68216 12.91501 13.01084 13.59862
## 9836 9839 9843 9847 9848 9851 9856 9857
## 13.54629 13.39171 12.95617 12.65568 13.04741 13.01511 12.91959 13.08037
## 9861 9863 9872 9879 9886 9890 9894 9898
## 13.71156 13.63074 12.82161 13.37446 13.35010 13.75315 13.56850 12.98030
## 9901 9906 9908 9917 9918 9940 9941 9964
## 13.36450 13.86859 13.17564 12.97875 13.55279 13.37259 13.28430 13.36889
## 9970 9973 9982 9988 9991 9999 10003 10006
## 13.06117 13.60073 13.63445 12.49495 12.74065 13.17960 13.50278 13.23128
## 10014 10021 10042 10044 10050 10052 10062 10066
## 13.04422 13.25653 12.95938 12.68406 12.72387 12.92615 13.40145 12.48122
## 10070 10088 10103 10104 10105 10109 10118 10121
## 13.26696 12.92639 13.40988 13.36812 13.12519 13.74275 13.51642 12.73430
## 10125 10127 10128 10129 10133 10138 10143 10148
## 13.71325 13.04067 12.83348 13.32041 13.47301 13.14010 13.09364 13.87468
## 10159 10174 10176 10180 10202 10203 10209 10220
## 13.31438 13.03127 12.75910 12.66898 13.00666 13.24434 12.86522 13.50232
## 10226 10227 10232 10236 10242 10246 10247 10255
## 12.92574 13.00169 12.98044 13.05276 12.83680 13.02666 12.74390 12.88583
## 10256 10270 10271 10273 10274 10289 10303 10310
## 12.90886 14.16756 12.80140 12.92159 12.50559 12.82319 12.83715 13.20690
## 10321 10323 10325 10326 10329 10333 10335 10338
## 12.94162 12.79375 12.70178 13.21121 13.22440 13.50440 12.90628 12.99540
## 10339 10343 10345 10350 10361 10390 10391 10401
## 13.47161 12.77829 13.02233 13.31361 12.92460 13.39258 12.49089 13.09240
## 10407 10410 10412 10414 10424 10433 10434 10437
## 13.73707 12.95195 13.25617 14.00737 12.90980 13.00711 12.73636 12.97793
## 10448 10454 10457 10460 10466 10473 10478 10479
## 13.27213 13.75119 13.80370 13.01369 12.95812 12.73945 13.68922 13.72601
## 10483 10491 10493 10497 10499 10500 10501 10505
## 13.81607 13.70322 13.11954 12.81448 12.91544 13.05755 13.07903 13.11851
## 10517 10519 10547 10553 10555 10559 10563 10564
## 12.98491 13.40091 12.73213 12.78855 13.48550 12.69434 13.80369 13.06632
## 10566 10574 10577 10583 10584 10587 10589 10592
## 13.28947 13.32117 12.91445 13.08327 12.99111 12.99462 13.04509 13.64949
## 10601 10608 10618 10621 10627 10630 10644 10647
## 14.04328 12.95036 12.44229 13.05393 13.00626 12.94444 12.60629 13.65646
## 10661 10663 10672 10680 10687 10703 10707 10709
## 12.69802 13.56066 13.08026 13.49445 13.50877 13.02165 12.90537 13.30504
## 10718 10720 10722 10723 10737 10751 10753 10755
## 12.79536 14.04082 14.31825 12.69647 13.85329 13.14675 13.23891 13.00782
## 10758 10760 10762 10763 10769 10771 10772 10774
## 13.10782 13.43407 12.99586 13.53187 13.13510 13.69136 13.74663 13.08387
## 10778 10790 10794 10796 10798 10804 10808 10814
## 13.72153 13.58211 13.92946 13.47136 12.93274 13.79251 13.39761 13.56856
## 10821 10825 10826 10832 10837 10852 10868 10875
## 12.90939 13.38494 12.91600 13.36267 13.52017 12.82640 13.19806 13.20994
## 10880 10894 10896 10901 10905 10906 10907 10912
## 12.87176 13.41546 13.62538 12.84155 13.48579 12.81630 13.08974 12.73451
## 10924 10929 10931 10935 10945 10952 10963 10965
## 12.85104 14.06031 12.75605 13.37044 14.24118 13.22846 13.37021 13.23475
## 10984 10991 10995 11012 11025 11034 11036 11041
## 12.85851 13.81494 13.08254 13.38029 13.43904 12.89609 12.92981 13.10646
## 11046 11047 11055 11075 11082 11087 11091 11100
## 13.61029 12.82452 12.82015 13.09448 12.83770 13.43936 13.40593 12.93991
## 11101 11103 11123 11130 11136 11140 11144 11163
## 13.28107 13.06224 13.18941 12.96293 13.42607 13.07176 14.42866 14.10804
## 11171 11176 11179 11182 11192 11193 11195 11198
## 13.93619 13.76718 14.23825 13.17676 13.21816 12.70116 13.33782 13.36573
## 11212 11228 11234 11236 11243 11284 11294 11317
## 14.59388 13.49991 13.37501 13.29428 13.74399 13.15628 13.30516 13.33303
## 11322 11329 11336 11344 11366 11369 11382 11385
## 12.91752 13.11466 12.94406 13.84815 13.06628 13.45595 13.46123 13.05108
## 11386 11388 11394 11395 11406 11410 11419 11428
## 13.40972 12.73201 13.23284 12.84717 13.04027 13.74906 13.68226 14.13606
## 11432 11435 11446 11450 11453 11459 11479 11481
## 13.16060 12.99307 13.09313 13.34335 13.15826 13.50621 13.65224 12.98281
## 11486 11489 11490 11494 11495 11507 11537 11553
## 13.07334 13.97359 12.65285 12.97635 12.94055 12.90525 13.40467 13.54290
## 11566 11581 11595 11602 11611 11632 11633 11634
## 13.26473 13.60437 14.28472 13.41434 13.56588 13.45683 13.33437 13.28139
## 11635 11639 11640 11644 11649 11652 11655 11656
## 13.47051 13.01720 13.13074 13.12708 12.99645 13.00966 13.18682 13.01099
## 11660 11677 11681 11683 11684 11690 11696 11703
## 13.08009 13.54992 13.15424 14.38733 13.36222 13.07605 13.49890 13.15804
## 11708 11709 11713 11721 11723 11727 11738 11749
## 12.95227 13.64398 13.20847 13.36012 13.20584 13.29895 13.34356 13.49782
## 11755 11758 11773 11774 11779 11794 11811 11813
## 13.21960 12.96154 13.56358 12.73087 13.24690 13.08613 13.22501 13.27637
## 11814 11844 11846 11851 11853 11855 11858 11864
## 13.57911 13.55079 13.05783 13.44630 12.91107 13.14043 13.21187 13.76443
## 11865 11867 11869 11872 11874 11879 11886 11896
## 13.12186 13.57532 12.85198 13.12154 13.19663 13.07342 13.42176 13.20996
## 11897 11898 11899 11900 11902 11904 11905 11913
## 13.28461 13.50636 13.12698 13.05528 13.03552 13.08572 13.00163 12.99910
## 11917 11921 11925 11942 11955 11956 11967 11970
## 12.71560 13.27571 13.11901 13.58182 13.43479 13.49707 13.83263 13.13045
## 11971 11977 11978 11982 11986 11988 11990 11991
## 13.28641 13.06925 13.14273 13.21369 12.91068 13.52814 12.98576 13.27060
## 11999 12002 12006 12008 12009 12010 12013 12014
## 12.98487 13.31134 13.74190 13.51745 13.13972 13.15786 13.49919 13.09528
## 12016 12018 12022 12027 12033 12034 12039 12049
## 13.17672 13.20525 13.08254 13.01236 13.45102 13.48057 13.22692 13.01894
## 12052 12062 12070 12071 12076 12078 12084 12094
## 13.52302 13.23880 13.33355 13.05634 13.73984 13.37299 13.24693 12.91570
## 12095 12098 12106 12108 12113 12118 12119 12120
## 13.12859 13.28686 13.32004 13.27871 13.14542 13.70463 13.66435 13.09710
## 12121 12128 12131 12133 12135 12159 12160 12161
## 13.29390 13.39497 13.63670 13.95263 13.61199 13.39548 13.68636 13.34612
## 12162 12181 12186 12192 12195 12196 12197 12204
## 13.66475 13.28597 12.95336 13.59010 13.20293 12.74176 13.69450 13.69548
## 12205 12209 12216 12226 12228 12230 12235 12237
## 13.45805 13.87707 13.00205 13.65466 13.18025 12.97747 13.30549 13.32958
## 12242 12247 12274 12289 12295 12300 12312 12347
## 12.91026 13.39584 13.13413 12.83211 12.79040 13.13020 13.86826 13.08040
## 12380 12385 12396 12416 12420 12425 12433 12437
## 13.29970 13.11640 13.04772 13.02379 12.83546 13.09813 13.34213 13.31603
## 12450 12454 12460 12478 12497 12502 12509 12510
## 12.81855 13.11190 12.95412 13.12493 13.05116 13.54709 13.62581 13.50045
## 12514 12516 12520 12521 12524 12527 12547 12553
## 13.36490 13.38020 14.88753 14.06697 13.44278 14.40643 13.56445 14.03872
## 12554 12556 12566 12583 12589 12592 12594 12595
## 13.24130 13.61013 13.58668 13.89393 13.67456 13.05929 13.36464 13.55873
## 12598 12603 12605 12608 12610 12617 12622 12626
## 13.74781 13.55584 13.92270 13.82078 14.07847 13.65487 13.61170 13.83911
## 12628 12629 12630 12640 12644 12645 12648 12656
## 14.06394 13.29583 13.79981 13.69756 13.21546 13.42116 14.00764 13.94222
## 12669 12670 12681 12683 12689 12690 12692 12699
## 13.38475 13.33049 14.24517 13.26466 13.29503 13.19060 14.03104 13.25781
## 12703 12711 12712 12717 12720 12724 12733 12734
## 13.15529 13.82051 13.29972 13.46931 13.90284 14.15754 13.22768 13.95400
## 12737 12745 12748 12757 12759 12761 12771 12772
## 13.36332 13.57436 13.37731 13.34258 13.04211 13.70930 13.61899 13.09192
## 12780 12785 12787 12796 12798 12802 12804 12814
## 14.25915 13.73309 14.05275 13.96893 13.53497 13.83444 13.54644 14.00759
## 12817 12820 12825 12826 12837 12842 12846 12860
## 13.17191 13.89362 13.46416 13.60443 13.44000 14.24675 13.08562 13.44116
## 12864 12876 12880 12881 12884 12893 12896 12897
## 13.07157 13.39230 13.36548 13.51991 13.23904 13.33880 13.55126 13.89340
## 12898 12903 12907 12909 12940 12951 12953 12954
## 13.67936 13.04519 13.40903 13.26865 13.31314 13.27871 14.23201 14.12148
## 12957 12958 12969 12975 12976 12979 12983 12986
## 13.25556 13.71741 13.15211 13.97869 14.10614 13.28988 13.48142 14.05155
## 12990 12995 12996 12997 13008 13009 13012 13013
## 13.53386 13.60305 13.67971 13.37923 13.92284 13.61305 13.00761 13.22068
## 13017 13029 13031 13052 13053 13059 13062 13066
## 13.41315 13.67046 12.95735 13.43286 13.34983 14.10053 14.34755 13.79606
## 13073 13080 13083 13087 13090 13093 13095 13098
## 13.93574 14.30457 13.82917 13.49595 13.31200 13.56680 13.62983 13.86835
## 13102 13111 13120 13138 13142 13143 13147 13149
## 13.77405 13.60913 13.02810 14.13077 13.99333 13.16185 13.88498 13.40021
## 13155 13157 13166 13169 13170 13176 13177 13178
## 13.78279 13.37532 13.21877 13.62023 13.90006 13.66624 13.79304 13.98078
## 13179 13180 13182 13183 13184 13187 13189 13196
## 13.90415 14.46952 13.76278 13.42323 13.87286 13.07621 14.20054 13.98603
## 13198 13208 13210 13212 13220 13223 13225 13226
## 12.93946 14.28363 13.10272 13.66286 13.30839 13.10343 13.66288 13.25493
## 13227 13238 13243 13247 13252 13262 13263 13268
## 13.52676 14.19839 14.11510 13.89786 13.88853 13.39532 13.63237 13.14773
## 13280 13281 13283 13291 13306 13308 13311 13318
## 13.37620 13.59997 14.27974 13.43309 14.06410 14.16557 13.45682 13.80114
## 13320 13325 13331 13332 13339 13345 13346 13350
## 13.70726 13.89518 13.69915 13.35483 13.38227 13.44537 13.45641 13.77334
## 13353 13354 13364 13374 13375 13378 13379 13382
## 13.62858 13.40798 13.53174 14.27016 13.99813 13.35540 13.01589 13.44174
## 13387 13390 13393 13396 13398 13402 13403 13408
## 13.83937 13.12851 14.47395 13.28777 13.69478 13.63937 13.88254 13.76598
## 13417 13418 13427 13428 13429 13434 13436 13439
## 14.01005 13.72775 13.40764 13.49106 13.19558 14.11246 13.44116 13.19540
## 13444 13447 13450 13457 13459 13460 13464 13470
## 13.43830 13.04000 13.59534 13.66036 13.64782 13.09735 13.20485 13.75079
## 13472 13475 13477 13491 13499 13503 13505 13506
## 13.03934 13.38561 13.86960 13.37244 13.78837 13.18620 13.64414 13.71226
## 13507 13508 13510 13511 13512 13522 13524 13528
## 13.72490 13.50380 13.17181 13.80774 13.07680 13.09214 13.62547 13.30520
## 13534 13536 13538 13539 13541 13545 13550 13552
## 13.32371 13.66365 13.60307 13.36825 13.35833 13.75003 13.11259 13.59279
## 13555 13558 13564 13568 13569 13572 13576 13579
## 13.51609 13.26756 13.37676 13.33182 13.06390 13.78695 13.59614 14.30207
## 13581 13582 13586 13587 13594 13608 13624 13629
## 13.79710 13.24463 13.43734 13.39821 13.85389 13.03178 13.50188 13.37258
## 13631 13634 13637 13643 13644 13646 13649 13651
## 13.82490 14.34658 13.61356 13.47573 13.84232 13.43897 14.05544 13.25241
## 13657 13658 13659 13677 13681 13685 13692 13694
## 13.52311 13.81120 13.31404 13.69780 13.44269 13.92076 13.72371 13.45180
## 13696 13705 13707 13711 13714 13715 13720 13721
## 13.84834 13.12784 14.09507 14.14898 14.08460 13.30915 13.43157 13.40490
## 13732 13737 13741 13743 13747 13757 13759 13761
## 13.58252 14.42254 13.10820 13.25010 13.85227 13.69269 13.42957 13.65728
## 13766 13773 13781 13786 13789 13795 13803 13804
## 13.87185 14.17970 13.88110 14.12769 13.30266 13.48073 13.07114 13.30884
## 13806 13811 13823 13828 13837 13843 13845 13851
## 13.34499 13.96297 14.04962 14.10236 13.84345 14.57886 14.11327 13.47273
## 13853 13854 13859 13869 13871 13874 13885 13887
## 13.35278 13.57866 13.32635 14.51234 13.63519 13.23103 13.72418 13.08309
## 13889 13891 13893 13894 13898 13910 13915 13920
## 13.43577 13.83631 13.87329 13.75676 13.50953 13.15147 13.12567 13.67117
## 13929 13934 13941 13945 13947 13951 13954 13955
## 13.70706 13.37923 12.98580 13.69516 12.84354 12.99813 14.54501 13.52803
## 13961 13963 13967 13968 13969 13970 13971 13973
## 13.97112 13.66959 13.58526 13.96791 13.19583 13.97086 13.01412 13.31587
## 13977 13980 13991 13994 13999 14002 14007 14020
## 13.76343 13.11115 13.51886 13.24413 13.24055 13.13042 13.34645 13.31473
## 14033 14041 14043 14045 14046 14048 14057 14058
## 13.26236 13.40084 13.11528 13.57162 13.17726 13.27391 13.47680 13.29656
## 14062 14065 14069 14071 14074 14082 14086 14087
## 13.57188 13.51456 13.91325 13.30054 13.12838 13.23801 13.33969 13.72095
## 14088 14089 14098 14100 14103 14108 14118 14122
## 14.25444 13.19664 13.76856 13.72098 13.23611 13.16843 13.69659 13.14484
## 14125 14134 14142 14147 14148 14152 14154 14158
## 13.29774 13.16909 13.47901 13.38235 13.40133 13.59905 13.01418 13.36720
## 14162 14176 14186 14190 14192 14193 14198 14199
## 13.46035 13.37414 13.44846 13.73164 13.70063 13.73774 13.65725 13.48931
## 14204 14209 14211 14216 14218 14225 14231 14235
## 13.87499 14.04252 13.48898 13.42149 13.37258 13.80013 13.62408 13.11703
## 14242 14245 14246 14247 14250 14253 14255 14260
## 13.79685 13.60179 13.13449 13.74376 13.40842 13.61310 13.61089 13.61008
## 14268 14276 14278 14282 14284 14287 14288 14297
## 13.43974 13.90697 13.16559 13.59862 13.77136 13.45003 13.99742 13.49340
## 14301 14303 14304 14306 14311 14313 14314 14321
## 13.85400 13.91870 13.35960 13.55501 13.71378 13.19577 13.08686 13.31230
## 14325 14327 14332 14347 14352 14354 14364 14370
## 13.36027 13.90638 13.42826 13.24131 12.88030 12.99264 14.04828 13.19713
## 14387 14390 14395 14401 14408 14411 14417 14423
## 13.03726 13.56649 13.12012 13.81863 13.73970 13.26630 13.13377 13.98054
## 14424 14426 14430 14431 14440 14446 14450 14454
## 13.66150 13.11034 13.34472 13.49561 13.20263 13.95122 13.67219 13.42438
## 14457 14461 14466 14468 14469 14470 14476 14479
## 13.51305 14.09401 13.54658 13.56563 13.83066 13.18916 13.83348 13.76591
## 14482 14483 14485 14488 14491 14492 14496 14499
## 13.39299 13.21225 13.20960 12.77615 13.74772 13.04948 13.87444 13.47948
## 14500 14503 14506 14507 14508 14510 14513 14520
## 13.60624 13.40511 13.26131 12.86839 13.63710 13.61703 13.89696 13.61774
## 14524 14525 14531 14533 14539 14545 14546 14548
## 13.25098 13.54495 13.80065 13.55959 13.61581 13.93645 13.07316 13.27338
## 14552 14559 14564 14569 14570 14580 14582 14583
## 13.52003 13.38359 14.08085 13.69986 13.02859 13.11292 13.03619 13.33452
## 14585 14589 14592 14595 14596 14599 14600 14601
## 13.61397 13.14986 13.17219 13.33098 13.75831 13.44417 13.44417 14.29940
## 14607 14609 14614 14618 14624 14625 14630 14631
## 13.14631 13.88598 13.86378 13.39774 13.64395 13.87978 13.18604 13.16066
## 14639 14641 14651 14654 14661 14668 14686 14697
## 13.46707 14.47073 14.03408 13.66860 13.62096 13.48220 13.46539 13.51606
## 14699 14701 14708 14716 14717 14721 14724 14728
## 13.70557 13.18746 13.54710 13.50524 12.91763 13.34642 13.84855 13.76026
## 14730 14746 14748 14757 14758 14763 14771 14774
## 13.13048 12.92032 13.53339 13.15234 13.29506 13.59115 13.69204 13.65086
## 14776 14782 14784 14785 14788 14795 14796 14803
## 13.59010 13.30384 13.12194 13.32471 13.57865 13.56654 13.04067 13.52952
## 14805 14807 14815 14819 14821 14822 14830 14832
## 13.63188 13.80652 13.38404 13.81136 13.82577 13.04300 13.56051 13.33301
## 14833 14838 14854 14856 14865 14866 14869 14875
## 13.36753 13.50109 13.93039 13.31832 13.58143 13.77631 13.63737 13.39611
## 14876 14884 14895 14896 14899 14906 14907 14916
## 14.18323 13.54027 13.43191 13.95504 14.31991 13.93077 13.38355 13.02302
## 14919 14924 14926 14928 14929 14937 14941 14945
## 13.26964 13.59160 13.90413 13.25511 12.97030 13.58792 13.35209 13.38130
## 14947 14949 14950 14954 14956 14968 14975 14980
## 13.22749 13.10693 13.76299 14.47909 13.72046 14.35008 14.23104 13.39282
## 14982 14987 14990 14992 15002 15006 15007 15010
## 13.79843 13.34305 13.89933 13.22693 14.31662 13.87078 13.60793 12.99987
## 15021 15030 15032 15034 15036 15037 15044 15045
## 13.44145 13.51439 13.54024 13.20535 13.34089 12.99673 13.16154 13.60088
## 15047 15048 15057 15058 15059 15061 15077 15078
## 13.42739 13.27639 13.05015 12.93309 13.51862 14.22791 13.20238 13.73304
## 15080 15083 15092 15094 15100 15103 15106 15109
## 13.55250 13.16733 13.77680 13.35123 13.18196 14.01985 13.61449 13.58293
## 15110 15115 15121 15122 15143 15145 15158 15160
## 13.21925 12.86611 13.67189 13.14598 13.44878 13.25409 13.72162 13.16256
## 15167 15170 15189 15194 15198 15212 15220 15227
## 13.30884 13.91230 13.31319 13.23090 13.26379 13.35968 13.43201 13.96770
## 15230 15236 15237 15252 15253 15254 15256 15263
## 13.51656 13.29644 14.17402 13.55724 13.02894 13.80919 13.41756 13.54824
## 15265 15266 15268 15270 15283 15289 15290 15291
## 14.18337 13.37701 13.89429 14.06778 13.21982 13.87054 13.56853 13.86294
## 15296 15297 15298 15309 15316 15317 15321 15323
## 12.96096 13.74752 13.71363 13.66902 13.65965 13.83839 12.99812 13.58073
## 15335 15340 15342 15343 15344 15349 15353 15358
## 14.01704 13.44224 13.63872 14.08043 13.73879 13.55346 13.86643 13.43487
## 15364 15377 15382 15395 15396 15398 15399 15400
## 13.55054 13.10943 13.24797 13.97896 13.63229 13.63983 13.45458 13.19151
## 15428 15431 15432 15436 15442 15444 15451 15454
## 13.38398 14.29314 13.43086 13.03076 13.45528 13.80817 14.03890 13.16560
## 15457 15458 15461 15468 15470 15473 15475 15478
## 13.68920 13.81872 13.43378 13.45542 13.72921 13.57430 12.76133 13.31373
## 15479 15483 15488 15496 15497 15501 15505 15506
## 13.54660 13.41190 13.58776 13.29072 13.63830 13.78512 14.27588 13.21663
## 15509 15520 15521 15526 15537 15541 15543 15546
## 13.76990 13.16437 14.00594 13.53544 13.47453 13.35924 13.18949 13.09682
## 15547 15549 15550 15551 15553 15554 15556 15562
## 13.50629 13.84119 13.61664 13.23794 13.48583 13.67285 13.92117 13.17367
## 15564 15565 15566 15567 15572 15573 15584 15587
## 13.56266 13.90343 13.68299 13.91885 13.87917 13.70932 13.93268 13.35475
## 15588 15591 15597 15602 15606 15617 15626 15628
## 13.47107 13.31007 13.41457 14.01421 13.47837 13.07553 13.36041 13.98285
## 15633 15635 15645 15646 15650 15651 15657 15662
## 13.10236 13.51906 13.76792 13.85558 13.89798 13.55493 13.69052 13.17957
## 15665 15672 15684 15686 15698 15706 15708 15719
## 13.50901 13.64466 13.65457 14.47477 13.35559 14.10439 13.59455 13.20596
## 15724 15725 15735 15747 15748 15749 15752 15753
## 13.93789 13.45853 13.51267 13.95845 13.44682 13.22816 13.77096 13.29619
## 15755 15760 15762 15764 15770 15772 15774 15776
## 13.83427 13.53051 13.99245 13.64173 13.52967 13.73062 13.08748 13.06226
## 15779 15781 15786 15787 15788 15789 15794 15804
## 12.86732 13.02834 14.16400 13.35852 13.36758 14.09311 13.61482 13.51728
## 15813 15826 15827 15830 15831 15837 15843 15848
## 13.13402 13.33185 13.80195 13.37309 12.97682 13.71691 13.54308 13.76233
## 15851 15853 15861 15865 15872 15877 15885 15888
## 13.24582 13.32458 13.40983 13.28250 13.86997 13.23807 13.97095 13.53912
## 15893 15905 15906 15915 15921 15929 15936 15937
## 13.25139 13.16616 14.11774 13.55621 13.19746 13.87782 13.50629 13.61583
## 15938 15944 15946 15947 15953 15954 15961 15963
## 13.51509 13.62471 13.19885 13.22816 14.49552 13.20196 14.04947 14.30586
## 15965 15983 15987 15991 15995 15998 16007 16014
## 13.29403 13.49549 13.03267 13.52680 13.25615 13.91789 14.05847 14.21029
## 16015 16021 16023 16028 16030 16033 16034 16036
## 13.60527 13.50246 13.19606 13.63636 13.63636 13.68791 13.96839 13.58718
## 16037 16039 16046 16051 16053 16056 16057 16066
## 13.07796 13.40966 13.17058 13.65270 14.32998 13.88337 13.89038 13.82989
## 16071 16076 16080 16086 16088 16091 16094 16098
## 13.85406 13.47968 13.49808 13.37202 14.18963 13.57228 14.32249 13.60003
## 16103 16109 16110 16118 16119 16123 16132 16136
## 12.98874 13.65525 13.78168 12.99847 13.79874 13.29404 13.26913 13.10364
## 16139 16145 16148 16150 16161 16162 16166 16173
## 13.43694 13.30190 13.30883 13.26315 13.22413 13.62029 13.63852 13.51776
## 16174 16176 16186 16193 16198 16202 16208 16213
## 13.48157 13.16190 13.48157 13.95301 13.78548 13.87275 13.61381 13.50449
## 16223 16237 16246 16248 16250 16252 16261 16273
## 13.56799 13.16655 13.50559 13.44442 14.93487 13.53973 14.06988 13.12261
## 16276 16281 16297 16299 16301 16321 16323 16327
## 13.78288 13.43592 13.52739 13.27235 14.09341 13.92822 14.11445 13.74090
## 16331 16334 16340 16343 16346 16350 16351 16354
## 13.19393 13.31621 13.35787 13.65570 12.97555 14.00043 13.87727 13.65807
## 16360 16374 16384 16400 16402 16403 16406 16413
## 13.02647 13.88060 13.37715 13.30718 13.73908 13.19515 13.62023 13.63905
## 16416 16422 16423 16424 16426 16434 16435 16442
## 13.84640 13.59902 13.66208 13.62506 14.39790 13.55939 13.17923 13.74793
## 16449 16456 16457 16458 16468 16475 16476 16491
## 14.27700 13.55230 13.57403 13.49377 13.45723 14.43307 14.10123 13.72943
## 16498 16504 16507 16509 16510 16511 16513 16515
## 13.31810 13.57273 14.17679 12.99658 13.79693 13.25006 13.67912 13.51656
## 16519 16524 16525 16528 16538 16539 16545 16549
## 13.14626 13.41524 13.47447 13.90592 12.90932 13.73181 13.27166 13.26224
## 16551 16553 16554 16555 16558 16563 16569 16575
## 13.94219 13.22049 13.60701 13.55332 13.75180 13.19744 13.27546 13.14092
## 16578 16579 16596 16603 16608 16638 16645 16653
## 13.07675 14.08428 13.64699 14.20796 13.41746 13.29520 13.46107 14.10034
## 16654 16658 16660 16661 16662 16666 16672 16674
## 14.20323 14.29465 13.78936 13.41780 13.69367 13.38026 13.40051 13.92755
## 16676 16677 16682 16689 16690 16692 16700 16704
## 13.53227 14.04190 13.58496 13.94681 13.57210 13.41043 13.68403 13.31773
## 16722 16732 16733 16746 16756 16757 16759 16762
## 13.32982 13.39833 13.29526 13.31810 13.70441 13.46667 13.34578 13.27125
## 16784 16798 16801 16802 16804 16811 16818 16834
## 13.76395 13.79855 14.04276 12.96806 13.85151 13.55058 13.79685 14.30253
## 16843 16844 16848 16851 16856 16859 16868 16877
## 13.62114 13.41641 13.14743 14.05418 13.83553 13.06258 13.34396 14.02371
## 16886 16888 16891 16898 16909 16919 16922 16923
## 13.76887 13.57053 13.20294 12.89170 13.84865 13.68489 14.04089 12.95954
## 16925 16928 16934 16943 16948 16959 16962 16963
## 13.54555 13.77488 13.61498 14.34742 13.38720 13.20449 13.33506 14.22239
## 16967 16969 16976 16979 16983 16999 17007 17012
## 13.85377 13.54477 13.46627 13.73603 13.67820 13.14890 13.28026 13.68277
## 17017 17020 17021 17031 17046 17049 17052 17054
## 13.54666 13.85270 13.47613 13.26616 13.14718 13.63222 13.48472 13.45309
## 17056 17063 17064 17067 17068 17079 17082 17084
## 13.38422 14.43314 13.74975 14.59786 14.23853 14.12812 14.04214 13.11306
## 17086 17089 17102 17107 17116 17117 17120 17122
## 12.88599 13.39294 14.17991 13.87331 13.24934 13.66082 13.55758 13.98313
## 17127 17129 17130 17134 17140 17141 17146 17148
## 12.98522 13.96076 13.71650 14.03048 13.44148 12.97466 13.54562 13.86378
## 17150 17163 17176 17183 17187 17188 17189 17192
## 13.41682 13.50200 13.63753 13.88617 13.28184 13.69786 13.64695 14.11074
## 17200 17202 17205 17211 17214 17215 17217 17219
## 13.94123 13.01642 13.25693 13.56538 14.06617 13.35003 13.81333 14.00714
## 17220 17221 17225 17232 17237 17243 17246 17247
## 13.58453 13.83427 13.88482 14.24033 13.80074 13.37252 13.70986 13.36637
## 17248 17253 17261 17262 17266 17270 17271 17272
## 13.38577 13.98716 13.43519 13.63983 13.94141 13.41515 13.99251 13.83214
## 17274 17276 17277 17278 17289 17294 17302 17312
## 13.47249 13.53433 13.28459 13.65144 14.15861 13.19988 13.71542 13.31412
## 17315 17322 17325 17327 17335 17337 17339 17341
## 13.38958 13.58373 13.65344 13.05296 13.49036 14.23990 13.37831 13.34635
## 17343 17351 17354 17365 17368 17374 17378 17387
## 13.83843 13.15724 13.34344 13.30012 14.03293 13.97153 13.95604 13.88377
## 17394 17396 17403 17413 17416 17421 17428 17429
## 13.49385 13.52812 13.13219 13.89214 13.42799 13.56693 14.85473 13.14845
## 17436 17443 17444 17446 17453 17456 17463 17465
## 13.57091 13.12466 14.25919 13.22994 13.51742 13.49628 14.63771 13.23627
## 17472 17473 17474 17476 17480 17483 17484 17508
## 13.54397 13.43268 13.56676 14.13799 14.05189 13.22603 12.88710 13.27340
## 17510 17512 17514 17535 17543 17548 17551 17552
## 14.04842 13.65325 14.75934 13.35251 14.44039 14.37804 13.49899 14.16008
## 17555 17565 17566 17569 17571 17572 17575 17577
## 14.09500 14.09347 13.50914 13.48560 13.54137 13.74227 14.02699 14.04229
## 17578 17596 17603 17606 17611 17631 17636 17641
## 13.57963 13.30816 14.47906 14.13144 13.12804 14.28521 13.97980 13.55921
## 17644 17649 17653 17668 17677 17678 17679 17680
## 13.23985 13.64610 14.12187 13.51468 13.45289 13.50508 13.18571 14.55130
## 17683 17688 17690 17691 17693 17705 17708 17719
## 14.00688 13.27297 13.79806 13.62937 13.32601 13.23401 13.78667 14.05819
## 17720 17721 17726 17730 17732 17733 17736 17740
## 13.80918 13.52554 13.72547 13.22479 13.07474 13.38780 13.32740 13.57095
## 17759 17761 17766 17774 17778 17785 17786 17787
## 13.54465 13.74938 13.58788 13.66702 13.38691 13.99116 13.48306 13.61541
## 17792 17803 17816 17820 17821 17823 17826 17832
## 14.13423 13.36274 13.38742 13.68753 13.42480 13.57271 13.46378 13.30474
## 17833 17838 17839 17840 17844 17864 17866 17870
## 13.52585 13.86172 13.78948 13.54634 13.51805 14.22435 13.71183 13.35117
## 17872 17878 17881 17883 17888 17889 17891 17892
## 14.52248 14.00072 14.11160 13.81704 14.01129 14.20875 13.24175 14.39011
## 17893 17894 17895 17898 17900 17905 17907 17908
## 13.67378 13.34448 14.52595 13.75862 13.43592 14.35341 13.32425 13.32874
## 17917 17919 17920 17922 17930 17935 17939 17948
## 14.02641 13.85864 13.79737 13.79685 14.57483 13.85545 12.97296 14.50437
## 17950 17951 17952 17953 17954 17956 17958 17959
## 14.51925 14.32204 13.68484 14.80568 14.02156 14.53801 13.13534 13.86992
## 17960 17962 17966 17970 17973 17977 17988 17995
## 13.64679 13.77920 13.47575 12.97040 13.57890 13.53991 12.86628 13.21845
## 17998 18003 18004 18005 18009 18020 18024 18029
## 13.25753 12.90666 13.63683 12.76559 13.32175 13.12950 12.64400 13.54224
## 18032 18036 18039 18055 18061 18067 18081 18084
## 13.02043 13.25025 13.55036 13.64253 13.55587 13.20777 13.18688 13.19927
## 18086 18090 18096 18097 18099 18100 18105 18119
## 12.89779 12.85848 13.19839 13.03084 12.88639 13.23676 13.14699 13.23754
## 18125 18129 18131 18133 18134 18144 18146 18148
## 13.14079 13.25411 13.26055 13.16625 13.50389 13.19217 12.91288 13.77668
## 18154 18164 18169 18181 18185 18190 18197 18207
## 13.08369 12.99750 12.98883 12.99027 12.82194 13.00364 13.22330 13.11691
## 18210 18220 18224 18240 18249 18250 18251 18253
## 13.61894 13.22047 13.08186 12.88996 13.00387 12.92388 13.28174 13.19582
## 18256 18259 18267 18269 18270 18271 18275 18279
## 13.37673 13.61676 13.10230 12.77738 13.92828 13.37288 12.83774 13.68834
## 18280 18281 18304 18309 18313 18316 18323 18324
## 13.57387 13.48016 13.05576 13.27097 13.02381 12.83471 13.18576 13.14685
## 18338 18342 18349 18372 18374 18387 18394 18405
## 13.38556 13.04659 12.84817 13.10682 12.76523 13.00931 12.96142 12.98276
## 18408 18409 18427 18434 18443 18448 18454 18461
## 12.61164 13.02616 13.05813 13.26725 13.35853 13.20912 13.17339 13.26887
## 18463 18467 18489 18490 18493 18508 18518 18545
## 13.01318 13.58166 13.96807 12.82009 13.38206 13.20272 13.28858 12.97862
## 18551 18557 18562 18563 18564 18565 18585 18590
## 13.66116 13.04801 13.28436 12.95645 13.19673 13.49926 13.72570 13.53749
## 18591 18600 18602 18612 18622 18635 18638 18668
## 13.27166 13.47030 13.83254 12.99237 12.79508 13.49727 13.84633 13.46674
## 18669 18676 18680 18681 18692 18716 18729 18735
## 13.08596 13.16886 13.26902 13.49182 13.47821 13.40600 13.90559 13.19834
## 18737 18751 18773 18774 18776 18789 18792 18808
## 13.18872 13.74204 13.46612 14.18318 12.98600 13.79651 13.18059 13.55793
## 18810 18812 18818 18833 18843 18861 18869 18872
## 12.91307 14.01510 13.37146 13.62206 13.85939 13.31078 13.29729 13.63294
## 18879 18884
## 13.44566 13.21519Backward regression help in selecting a subset of variables that have the most significant impact on the dependent variable. Including all variables in a full model can lead to overfitting, especially when some variables have weak or non-significant relationships with the dependent variable.
- A p-value of 2.2e-16 from the model indicates that the corresponding predictor variable in the regression model is statistically significant. . In this case, the extremely small p-value suggests strong evidence against the null hypothesis, indicating that the predictor variable has a significant effect on the response variable.
The testing dataset is used for the final evaluation of the model’s performance.
test_pre=predict(backward_lm2,newdata = test_trans)
mse=mean((test_trans$price - test_pre)^2)
ssr=sum((test_pre-mean(test_trans$price))^2)
sst=sum((test_trans$price-mean(test_trans$price))^2)
rsquared=1 - (ssr/sst)
rsquared #0.4019333## [1] -98782.08## [1] 116.83711. R-squared (0.41): The R-squared value represents the proportion of the variance in the response variable that can be explained by the model. In this case, the R-squared value of 0.41 indicates that the model explains approximately 41% of the variability in the test data. R-squared values range from 0 to 1, with higher values indicating a better fit of the model to the data. While an R-squared of 0.41 suggests a moderate level of explanatory power which means there is still a significant amount of unexplained variation in the response that the model does not account for.
2. MSE (0.08): The mean squared error is an average of the squared differences between the predicted and actual values. The MSE value of 0.08 indicates the average squared difference between the predicted and actual response values in the test data. Lower MSE values suggest better model performance, as they represent smaller errors between predicted and actual values.
CONCLUSION
I have trained your model using the training data and evaluated its performance on the test data. One can use the trained model to make predictions on new, unseen data. One can have another dataset for which he/she wants to predict the price of the apartment in Poland, one can apply this trained model to that dataset.
Application of the model
The new dataset must have those variable names ( square_meters + floor + build_year + latitude + longitude + centre_distance + school_distance + clinic_distance + post_office_distance + restaurant_distance + pharmacy_distance + poi_count + rooms + b_parking + b_elevator + b_security + b_storage, data )
The new dataset must have the same variable names and structure as the training and test datasets to ensure compatibility with the trained model. If there are any differences in the variable names or types, there is need to preprocess or transform the new dataset accordingly before making predictions.
The accuracy of the predictions on the new dataset will depend on the quality and representativeness of the new data, as well as the generalization capabilities of the model.