About the Data

The data set contains over two decades of data on each player who has been part of an NBA teams’ roster. It captures demographic variables such as age, height, weight and place of birth, biographical details like the team played for, draft year and round. In addition, it has basic box score statistics such as games played, average number of points, rebounds, assists, etc.

The pull initially contained 52 rows of missing data. The gaps have been manually filled using data from Basketball Reference. I am not aware of any other data quality issues.

Data Dictionary

Field Description
unnamed index
player_name Name of the player
team_abbreviation Abbreviated name of the team the player played for (at the end of the season)
age Age of the player
player_height Height of the player (in centimeters)
player_weight Weight of the player (in kilograms)
college Name of the college the player attended
country Name of the country the player was born in (not necessarily the nationality)
draft_year The year the player was drafted
draft_round The draft round the player was picked
draft_number The number at which the player was picked in his draft round
gp Games played throughout the season
pts Average number of points scored
rebs Average number of rebounds grabbed
ast Average number of assists distributed
net_rating Team’s point differential per 100 possessions while the player is on the court
oreb_pct Percentage of available offensive rebounds the player grabbed while he was on the floor
dreb_pct Percentage of available defensive rebounds the player grabbed while he was on the floor
usg_pct Percentage of team plays used by the player while he was on the floor
ts_pct Measure of the player’s shooting efficiency that takes into account free throws, 2 and 3 point shots
ast_pct Percentage of teammate field goals the player assisted while he was on the floor
season NBA season

Problem statement

This analysis’s main goal is to investigate and comprehend the dynamics of NBA players’ physical attributes and on-court performance over the course of several seasons, as well as the relationships between these variables and their draught positions. The study’s specific objectives are to assess the relationship between player height and draught position, track changes in average player height over the course of seasons, analyse the height distribution of NBA players, and identify top scorers and high-impact players. In order to shed light on how draught position and games played may affect a player’s physical characteristics, the study also aims to create a linear model that can predict player height.

Loading the libraries

Loading the necessary libraries to perform the analysis

library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(ggplot2)
## Warning: package 'ggplot2' was built under R version 4.3.2
library(readr)
## Warning: package 'readr' was built under R version 4.3.2

Loading the data

Loading the necessary data to perform analysis

# Reading the data
data <- read.csv('C:/Users/rohan/OneDrive/Desktop/INTRO TO STATISTICS IN R/DATA SETS/Datasets/Data/Nba_all_seasons_1996_2021.csv')

# Print data shape
cat("Number of Rows:", nrow(data), "\nNumber of Columns:", ncol(data), "\n\n")
## Number of Rows: 12305 
## Number of Columns: 22
# Print first 10 rows
head(data, 10)
##    X       player_name team_abbreviation age player_height player_weight
## 1  0     Dennis Rodman               CHI  36        198.12      99.79024
## 2  1 Dwayne Schintzius               LAC  28        215.90     117.93392
## 3  2      Earl Cureton               TOR  39        205.74      95.25432
## 4  3       Ed O'Bannon               DAL  24        203.20     100.69742
## 5  4       Ed Pinckney               MIA  34        205.74     108.86208
## 6  5     Eddie Johnson               HOU  38        200.66      97.52228
## 7  6       Eddie Jones               LAL  25        198.12      86.18248
## 8  7    Elden Campbell               LAL  28        213.36     113.39800
## 9  8 Eldridge Recasner               ATL  29        193.04      86.18248
## 10 9      Elliot Perry               MIL  28        182.88      72.57472
##                        college country draft_year draft_round draft_number gp
## 1  Southeastern Oklahoma State     USA       1986           2           27 55
## 2                      Florida     USA       1990           1           24 15
## 3                Detroit Mercy     USA       1979           3           58  9
## 4                         UCLA     USA       1995           1            9 64
## 5                    Villanova     USA       1985           1           10 27
## 6                     Illinois     USA       1981           2           29 52
## 7                       Temple     USA       1994           1           10 80
## 8                      Clemson     USA       1990           1           27 77
## 9                   Washington     USA       1992   Undrafted    Undrafted 71
## 10                     Memphis     USA       1991           2           37 82
##     pts  reb ast net_rating oreb_pct dreb_pct usg_pct ts_pct ast_pct  season
## 1   5.7 16.1 3.1       16.1    0.186    0.323   0.100  0.479   0.113 1996-97
## 2   2.3  1.5 0.3       12.3    0.078    0.151   0.175  0.430   0.048 1996-97
## 3   0.8  1.0 0.4       -2.1    0.105    0.102   0.103  0.376   0.148 1996-97
## 4   3.7  2.3 0.6       -8.7    0.060    0.149   0.167  0.399   0.077 1996-97
## 5   2.4  2.4 0.2      -11.2    0.109    0.179   0.127  0.611   0.040 1996-97
## 6   8.2  2.7 1.0        4.1    0.034    0.126   0.220  0.541   0.102 1996-97
## 7  17.2  4.1 3.4        4.1    0.035    0.091   0.209  0.559   0.149 1996-97
## 8  14.9  8.0 1.6        3.3    0.095    0.183   0.222  0.520   0.087 1996-97
## 9   5.7  1.6 1.3       -0.3    0.036    0.076   0.172  0.539   0.141 1996-97
## 10  6.9  1.5 3.0       -1.2    0.018    0.081   0.177  0.557   0.262 1996-97
# Check missing values
colSums(is.na(data))
##                 X       player_name team_abbreviation               age 
##                 0                 0                 0                 0 
##     player_height     player_weight           college           country 
##                 0                 0                 0                 0 
##        draft_year       draft_round      draft_number                gp 
##                 0                 0                 0                 0 
##               pts               reb               ast        net_rating 
##                 0                 0                 0                 0 
##          oreb_pct          dreb_pct           usg_pct            ts_pct 
##                 0                 0                 0                 0 
##           ast_pct            season 
##                 0                 0
# Check data types
sapply(data, class)
##                 X       player_name team_abbreviation               age 
##         "integer"       "character"       "character"         "integer" 
##     player_height     player_weight           college           country 
##         "numeric"         "numeric"       "character"       "character" 
##        draft_year       draft_round      draft_number                gp 
##       "character"       "character"       "character"         "integer" 
##               pts               reb               ast        net_rating 
##         "numeric"         "numeric"         "numeric"         "numeric" 
##          oreb_pct          dreb_pct           usg_pct            ts_pct 
##         "numeric"         "numeric"         "numeric"         "numeric" 
##           ast_pct            season 
##         "numeric"       "character"

Summary of the data

colnames(data)
##  [1] "X"                 "player_name"       "team_abbreviation"
##  [4] "age"               "player_height"     "player_weight"    
##  [7] "college"           "country"           "draft_year"       
## [10] "draft_round"       "draft_number"      "gp"               
## [13] "pts"               "reb"               "ast"              
## [16] "net_rating"        "oreb_pct"          "dreb_pct"         
## [19] "usg_pct"           "ts_pct"            "ast_pct"          
## [22] "season"
print("Summary")
## [1] "Summary"
summary(data[,colnames(data)])
##        X         player_name        team_abbreviation       age       
##  Min.   :    0   Length:12305       Length:12305       Min.   :18.00  
##  1st Qu.: 3076   Class :character   Class :character   1st Qu.:24.00  
##  Median : 6152   Mode  :character   Mode  :character   Median :26.00  
##  Mean   : 6152                                         Mean   :27.08  
##  3rd Qu.: 9228                                         3rd Qu.:30.00  
##  Max.   :12304                                         Max.   :44.00  
##  player_height   player_weight      college            country         
##  Min.   :160.0   Min.   : 60.33   Length:12305       Length:12305      
##  1st Qu.:193.0   1st Qu.: 90.72   Class :character   Class :character  
##  Median :200.7   Median : 99.79   Mode  :character   Mode  :character  
##  Mean   :200.6   Mean   :100.37                                        
##  3rd Qu.:208.3   3rd Qu.:108.86                                        
##  Max.   :231.1   Max.   :163.29                                        
##   draft_year        draft_round        draft_number             gp       
##  Length:12305       Length:12305       Length:12305       Min.   : 1.00  
##  Class :character   Class :character   Class :character   1st Qu.:31.00  
##  Mode  :character   Mode  :character   Mode  :character   Median :57.00  
##                                                           Mean   :51.29  
##                                                           3rd Qu.:73.00  
##                                                           Max.   :85.00  
##       pts              reb              ast           net_rating      
##  Min.   : 0.000   Min.   : 0.000   Min.   : 0.000   Min.   :-250.000  
##  1st Qu.: 3.600   1st Qu.: 1.800   1st Qu.: 0.600   1st Qu.:  -6.400  
##  Median : 6.700   Median : 3.000   Median : 1.200   Median :  -1.300  
##  Mean   : 8.173   Mean   : 3.559   Mean   : 1.814   Mean   :  -2.256  
##  3rd Qu.:11.500   3rd Qu.: 4.700   3rd Qu.: 2.400   3rd Qu.:   3.200  
##  Max.   :36.100   Max.   :16.300   Max.   :11.700   Max.   : 300.000  
##     oreb_pct          dreb_pct        usg_pct           ts_pct      
##  Min.   :0.00000   Min.   :0.000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.02100   1st Qu.:0.096   1st Qu.:0.1490   1st Qu.:0.4800  
##  Median :0.04100   Median :0.131   Median :0.1810   Median :0.5240  
##  Mean   :0.05447   Mean   :0.141   Mean   :0.1849   Mean   :0.5111  
##  3rd Qu.:0.08400   3rd Qu.:0.180   3rd Qu.:0.2170   3rd Qu.:0.5610  
##  Max.   :1.00000   Max.   :1.000   Max.   :1.0000   Max.   :1.5000  
##     ast_pct          season         
##  Min.   :0.0000   Length:12305      
##  1st Qu.:0.0660   Class :character  
##  Median :0.1030   Mode  :character  
##  Mean   :0.1314                     
##  3rd Qu.:0.1780                     
##  Max.   :1.0000

Cleaning the data

# Function to replace undrafted numbers
undraft_number <- function(draft_number) {
  undraft_number_dict <- c('Undrafted' = '61', '0' = '61')
  if (draft_number %in% names(undraft_number_dict)) {
    return(as.integer(undraft_number_dict[draft_number]))
  } else {
    return(as.integer(draft_number))
  }
}

# Apply the function
players <- data
players$draft_number <- sapply(players$draft_number, undraft_number)

# Check data types again
sapply(players, class)
##                 X       player_name team_abbreviation               age 
##         "integer"       "character"       "character"         "integer" 
##     player_height     player_weight           college           country 
##         "numeric"         "numeric"       "character"       "character" 
##        draft_year       draft_round      draft_number                gp 
##       "character"       "character"         "integer"         "integer" 
##               pts               reb               ast        net_rating 
##         "numeric"         "numeric"         "numeric"         "numeric" 
##          oreb_pct          dreb_pct           usg_pct            ts_pct 
##         "numeric"         "numeric"         "numeric"         "numeric" 
##           ast_pct            season 
##         "numeric"       "character"
# Dropping unnecessary columns
columns_to_drop <- c('Unnamed: 0', 'age', 'college', 'country', 
                     'player_weight', 'draft_round', 'draft_year', 
                     'oreb_pct', 'dreb_pct', 'ts_pct', 'ast_pct')
players <- players %>% select(-one_of(columns_to_drop))
## Warning: Unknown columns: `Unnamed: 0`
head(players, 10)
##    X       player_name team_abbreviation player_height draft_number gp  pts
## 1  0     Dennis Rodman               CHI        198.12           27 55  5.7
## 2  1 Dwayne Schintzius               LAC        215.90           24 15  2.3
## 3  2      Earl Cureton               TOR        205.74           58  9  0.8
## 4  3       Ed O'Bannon               DAL        203.20            9 64  3.7
## 5  4       Ed Pinckney               MIA        205.74           10 27  2.4
## 6  5     Eddie Johnson               HOU        200.66           29 52  8.2
## 7  6       Eddie Jones               LAL        198.12           10 80 17.2
## 8  7    Elden Campbell               LAL        213.36           27 77 14.9
## 9  8 Eldridge Recasner               ATL        193.04           61 71  5.7
## 10 9      Elliot Perry               MIL        182.88           37 82  6.9
##     reb ast net_rating usg_pct  season
## 1  16.1 3.1       16.1   0.100 1996-97
## 2   1.5 0.3       12.3   0.175 1996-97
## 3   1.0 0.4       -2.1   0.103 1996-97
## 4   2.3 0.6       -8.7   0.167 1996-97
## 5   2.4 0.2      -11.2   0.127 1996-97
## 6   2.7 1.0        4.1   0.220 1996-97
## 7   4.1 3.4        4.1   0.209 1996-97
## 8   8.0 1.6        3.3   0.222 1996-97
## 9   1.6 1.3       -0.3   0.172 1996-97
## 10  1.5 3.0       -1.2   0.177 1996-97

Analysis

# Histogram for player height
ggplot(players, aes(x=player_height)) +
  geom_histogram(bins=10, fill="blue", color="black") +
  xlab("Player Height (cm)") +
  ylab("Number of Players") +
  ggtitle("NBA Player Height Distribution")

Interpretation

NBA Player Height Distribution :

This histogram shows the distribution of player heights in the NBA. The plot likely displays a bell-shaped curve, indicating a normal distribution of heights, with most players clustering around the average height.

Calculating the average height by season

# Calculate average height
average_height <- round(mean(players$player_height, na.rm=TRUE), 2)
cat('The league average height over last 30 years is', average_height, 'cm.\n')
## The league average height over last 30 years is 200.61 cm.
# Calculating the average player height per season
player_height_by_season <- players %>%
  group_by(season) %>%
  summarise(Player_Height = round(mean(player_height, na.rm = TRUE), 2)) %>%
  arrange(season)

# Renaming the index
names(player_height_by_season)[names(player_height_by_season) == "season"] <- "Season"

# View the result
player_height_by_season
## # A tibble: 26 × 2
##    Season  Player_Height
##    <chr>           <dbl>
##  1 1996-97          201.
##  2 1997-98          201.
##  3 1998-99          201.
##  4 1999-00          201.
##  5 2000-01          201.
##  6 2001-02          201.
##  7 2002-03          202.
##  8 2003-04          201.
##  9 2004-05          201.
## 10 2005-06          201.
## # ℹ 16 more rows

Player’s Average Height by Season:

The line plot with points displays the trend of average player height across different NBA seasons. A potential finding could be an increasing, decreasing, or stable trend in player height over the years. The presence of any such trend can indicate changes in the preferred physical attributes for NBA players over time.

ggplot(player_height_by_season, aes(x=Season, y=Player_Height)) +
  geom_line() +
  geom_point() + # Adding points to the line
  theme_minimal() +
  scale_x_discrete(breaks = function(x) x[seq(1, length(x), by = 5)]) + # Set breaks every 5 seasons
  theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust=1)) + # Rotate x-axis labels for readability
  labs(x = "Season", y = "Player Height (cm)", title = "Player's Average Height by Season") +
  theme(plot.title = element_text(hjust = 0.5))
## `geom_line()`: Each group consists of only one observation.
## ℹ Do you need to adjust the group aesthetic?

## Player Height by Draft Position:

This plot examines whether there is a correlation between a player’s height and their draft position. It can reveal if taller players tend to be drafted earlier compared to shorter players, within the first 30 draft positions.

# Player height by draft position
player_height_by_draft_position <- players %>%
  group_by(draft_number) %>%
  summarise(Player_Height_cm = round(mean(player_height, na.rm=TRUE), 2)) %>%
  arrange(draft_number) %>%
  head(30)

# Line plot of player height by draft position
ggplot(player_height_by_draft_position, aes(x=draft_number, y=Player_Height_cm)) +
  geom_line() +
  ylab("Player Height (cm)") +
  ggtitle("Player Height by Draft Position")

# Filter players with more than 60 games played
qualified_player <- filter(players, gp > 60)

# Get top 15 impact players based on net_rating
impact_player <- qualified_player %>%
  select(player_name, net_rating, season, player_height, draft_number) %>%
  arrange(desc(net_rating)) %>%
  head(15)

# View the top 15 impact players
impact_player
##       player_name net_rating  season player_height draft_number
## 1  Draymond Green       18.9 2015-16        200.66           35
## 2    JaVale McGee       18.7 2016-17        213.36           18
## 3   Stephen Curry       18.3 2015-16        190.50            7
## 4   Stephen Curry       17.2 2016-17        190.50            7
## 5   Kevin Garnett       17.0 2007-08        210.82            5
## 6   Stephen Curry       17.0 2014-15        190.50            7
## 7      Tim Duncan       16.7 2004-05        210.82            1
## 8   Manu Ginobili       16.6 2004-05        198.12           57
## 9    Andrew Bogut       16.6 2014-15        213.36            1
## 10 Draymond Green       16.5 2014-15        200.66           35
## 11   Kevin Durant       16.0 2016-17        205.74            2
## 12  Greg Ostertag       15.9 1996-97        218.44           28
## 13 Draymond Green       15.9 2016-17        200.66           35
## 14    Rudy Gobert       15.9 2020-21        215.90           27
## 15  Klay Thompson       15.8 2014-15        200.66           11
# Summary Statistics
summary(impact_player$net_rating)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   15.80   15.95   16.60   16.87   17.10   18.90
# Histogram of net_rating for the impact players
ggplot(impact_player, aes(x = net_rating)) +
  geom_histogram(binwidth = 1, fill = "green", color = "black") +
  xlab("Net Rating") +
  ylab("Count") +
  ggtitle("Distribution of Net Rating among Top 15 Impact Players")

## Distribution of Net Rating among Top 15 Impact Players:

This histogram will show how the net rating is distributed among the top 15 impact players. A higher frequency at higher net ratings would confirm that these players have significantly positive effects on their teams.

# Scatter plot of net_rating versus player height
ggplot(impact_player, aes(x = player_height, y = net_rating)) +
  geom_point() +
  geom_smooth(method = "lm", se = FALSE) + # Add a linear fit line without confidence interval
  xlab("Player Height (cm)") +
  ylab("Net Rating") +
  ggtitle("Net Rating vs. Player Height among Top 15 Impact Players")
## `geom_smooth()` using formula = 'y ~ x'

Net Rating vs. Player Height among Top 15 Impact Players:

The scatter plot might show if taller players tend to have a higher net rating. The linear regression line will help understand the trend. If the slope is positive, it suggests that taller players have higher net ratings, whereas a flat or negative slope would suggest little to no relationship or an inverse relationship, respectively.

# Scatter plot of net_rating versus draft_number
ggplot(impact_player, aes(x = draft_number, y = net_rating)) +
  geom_point() +
  geom_smooth(method = "lm", se = FALSE) +
  xlab("Draft Number") +
  ylab("Net Rating") +
  ggtitle("Net Rating vs. Draft Number among Top 15 Impact Players")
## `geom_smooth()` using formula = 'y ~ x'

Net Rating vs. Draft Number among Top 15 Impact Players:

This scatter plot will explore whether players drafted earlier (lower draft numbers) have higher net ratings. Similar to the height analysis, the slope of the linear regression line will indicate the direction of the relationship.

Key Takeaways:

Players with a higher net_rating are considered to have a greater positive impact on their team’s performance while on the court. Any strong patterns or correlations observed in these plots can provide insights into the characteristics of high-impact players. The EDA could reveal whether player height or draft number correlates with a player’s on-court impact, as measured by net_rating. If the sample of top 15 players is representative, these insights could guide team strategies in player development, drafting, and game strategy. Outliers or exceptions in these patterns could highlight unique players who bring exceptional value beyond what is typical for their height or draft status.

# Get top 15 scorers
top_scorer <- qualified_player %>%
  select(player_name, pts, season, player_height) %>%
  arrange(desc(pts)) %>%
  head(15)

summary(top_scorer$pts)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   30.20   30.90   31.60   32.17   32.55   36.10
# Plotting the distribution of points scored by the top scorers
ggplot(top_scorer, aes(x = pts)) +
  geom_histogram(binwidth = 1, fill = "blue", color = "black") +
  xlab("Points Scored") +
  ylab("Frequency") +
  ggtitle("Distribution of Points Scored by Top Scorers")

Histogram: Distribution of Points Scored by Top Scorers

This histogram shows the frequency distribution of average points scored by the top 15 scorers. The binwidth is set to 1, which means each bar represents a range of 1 point scored. If the distribution is normal, most players’ average points would cluster around the mean, with fewer players as you move away from the mean. If the distribution is skewed, it may suggest that a few players score significantly higher or lower than the rest of the group, which could point to standout performances or anomalies.

# Scatter plot of points scored versus player height
ggplot(top_scorer, aes(x = player_height, y = pts)) +
  geom_point() +
  geom_smooth(method = "lm") + # Adding a linear regression line
  xlab("Player Height (cm)") +
  ylab("Points Scored") +
  ggtitle("Points Scored vs. Player Height Among Top Scorers")
## `geom_smooth()` using formula = 'y ~ x'

Scatter Plot: Points Scored vs. Player Height Among Top Scorers

The scatter plot depicts each of the top 15 scorers’ average points against their height. The addition of a linear regression line (geom_smooth) helps to identify any trend or correlation between height and scoring ability. A positive slope would indicate that taller players tend to score more points on average, while a negative slope would suggest the opposite. A flat line would imply no correlation.

# Boxplot of points scored by player height
ggplot(top_scorer, aes(x = as.factor(player_height), y = pts)) +
  geom_boxplot() +
  xlab("Player Height (cm)") +
  ylab("Points Scored") +
  ggtitle("Boxplot of Points Scored by Player Height")

Boxplot: Points Scored by Player Height

The boxplot provides a visual summary of the distribution of points scored at different player heights. By using player_height as a factor, each unique height is considered a separate category, and the points scored are summarized for players at each height. This plot can show if there’s any noticeable difference in scoring ability across different heights, indicated by the median (the line within the box) and the spread (the size of the box and whiskers). Outliers, if any, will be displayed as individual points, indicating exceptional scorers that deviate from the typical range.

# View the top 15 scorers
top_scorer
##          player_name  pts  season player_height
## 1       James Harden 36.1 2018-19        195.58
## 2        Kobe Bryant 35.4 2005-06        198.12
## 3       James Harden 34.3 2019-20        195.58
## 4      Allen Iverson 33.0 2005-06        182.88
## 5      Tracy McGrady 32.1 2002-03        203.20
## 6       Kevin Durant 32.0 2013-14        205.74
## 7      Stephen Curry 32.0 2020-21        190.50
## 8        Kobe Bryant 31.6 2006-07        198.12
## 9  Russell Westbrook 31.6 2016-17        190.50
## 10      LeBron James 31.4 2005-06        203.20
## 11     Allen Iverson 31.1 2000-01        182.88
## 12     Allen Iverson 30.7 2004-05        182.88
## 13       Joel Embiid 30.6 2021-22        213.36
## 14      James Harden 30.4 2017-18        195.58
## 15       Dwyane Wade 30.2 2008-09        193.04

Interpretation of the top 15 Scorers Table

Reviewing the actual top_scorer data frame will provide the names of the players, the exact points they scored, the seasons in which they scored those points, and their respective heights. It offers a chance to recognize patterns or anomalies within the top performers, such as if certain heights are more prevalent among the top scorers. ## Key Takeaways The distribution and relationship analysis may reveal whether height is a factor in scoring ability among the top scorers. The EDA can inform basketball analysts and enthusiasts if height plays a significant role in a player’s scoring potential. The insights derived could be used by coaches and team managers to strategize player positions and optimize team performance based on player physical attributes. Observations from the boxplot might inform draft picks and player training programs, especially if a certain height range is consistently associated with high scoring.

Creating Linear Model

# Filter players who played more than 60 games
qualified_players <- filter(players, gp > 60)

# Linear Model
model <- lm(player_height ~ draft_number + gp, data = qualified_players)
summary(model)
## 
## Call:
## lm(formula = player_height ~ draft_number + gp, data = qualified_players)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -41.655  -6.296   0.881   6.484  31.131 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  203.192840   1.326515 153.178   <2e-16 ***
## draft_number  -0.087382   0.006190 -14.117   <2e-16 ***
## gp            -0.007701   0.017723  -0.435    0.664    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 8.872 on 5673 degrees of freedom
## Multiple R-squared:  0.03398,    Adjusted R-squared:  0.03364 
## F-statistic: 99.78 on 2 and 5673 DF,  p-value: < 2.2e-16
predictions <- predict(model)
predictions
##        1        2        3        4        5        6        7        8 
## 201.9136 201.7030 200.2406 197.3158 199.3282 201.8057 201.3816 198.9195 
##        9       10       11       12       13       14       15       16 
## 201.4150 201.7646 200.5516 197.3851 199.3487 199.2278 202.3351 200.4796 
##       17       18       19       20       21       22       23       24 
## 201.6541 198.4544 202.0240 202.4455 198.1715 202.3736 201.0836 202.2273 
##       25       26       27       28       29       30       31       32 
## 201.3585 202.1064 198.7370 199.9399 198.3670 202.1707 197.3081 201.5486 
##       33       34       35       36       37       38       39       40 
## 202.3120 200.8265 197.2850 200.8676 198.5418 201.8031 202.0371 202.3866 
##       41       42       43       44       45       46       47       48 
## 201.6002 202.0883 198.4698 200.0092 202.2350 202.4894 199.8087 200.5516 
##       49       50       51       52       53       54       55       56 
## 201.6437 199.5261 200.1532 202.5048 201.5436 202.3146 199.3487 197.2773 
##       57       58       59       60       61       62       63       64 
## 201.3250 202.4224 200.8881 197.2311 201.0759 198.7293 197.3235 200.5027 
##       65       66       67       68       69       70       71       72 
## 200.5643 202.4020 202.4482 200.1659 200.5439 201.0682 201.8416 201.6079 
##       73       74       75       76       77       78       79       80 
## 202.5202 202.5098 200.3176 199.6751 197.9994 201.3277 201.8623 202.0371 
##       81       82       83       84       85       86       87       88 
## 198.6292 202.0910 199.4233 201.4920 201.4485 200.0427 198.5210 201.4408 
##       89       90       91       92       93       94       95       96 
## 201.7749 201.9574 201.7749 202.3866 202.5125 197.3466 197.2311 197.2927 
##       97       98       99      100      101      102      103      104 
## 198.8475 198.3259 198.8964 198.4544 198.6369 202.3608 202.2350 202.0602 
##      105      106      107      108      109      110      111      112 
## 199.9938 201.7903 202.2992 201.5590 197.3620 196.0154 200.6544 202.2812 
##      113      114      115      116      117      118      119      120 
## 201.9728 202.5510 200.3125 198.6342 202.3069 200.6259 197.8427 202.2195 
##      121      122      123      124      125      126      127      128 
## 197.3851 202.1245 200.0400 197.9736 202.3146 202.4559 201.0836 200.1378 
##      129      130      131      132      133      134      135      136 
## 200.6390 201.9085 199.9295 199.0299 202.3659 202.1245 201.6079 201.8365 
##      137      138      139      140      141      142      143      144 
## 201.9932 200.5104 200.9011 201.7826 200.9885 200.5978 200.1120 199.5954 
##      145      146      147      148      149      150      151      152 
## 201.6618 198.5468 198.5314 201.8931 200.1043 198.2050 201.5282 198.6111 
##      153      154      155      156      157      158      159      160 
## 202.0190 200.5670 201.7311 202.3659 200.2971 198.8270 201.3250 202.3274 
##      161      162      163      164      165      166      167      168 
## 198.1923 201.3816 202.2015 201.6310 201.4947 200.4642 201.0347 201.3457 
##      169      170      171      172      173      174      175      176 
## 201.8700 201.6541 202.0448 201.7826 201.1864 197.2103 202.1630 202.0421 
##      177      178      179      180      181      182      183      184 
## 201.6541 201.6591 201.5101 202.0113 202.5202 197.3235 200.4796 199.5311 
##      185      186      187      188      189      190      191      192 
## 200.5670 201.6876 201.8623 202.3866 202.1245 202.2504 199.0018 201.0116 
##      193      194      195      196      197      198      199      200 
## 202.4894 197.2696 201.1633 201.0963 200.0273 199.2871 202.1245 201.4254 
##      201      202      203      204      205      206      207      208 
## 197.2619 201.9882 199.7651 197.2388 200.7187 202.2992 199.5107 202.1322 
##      209      210      211      212      213      214      215      216 
## 200.5951 201.5436 201.3380 201.6437 201.7465 199.3513 201.8623 200.8007 
##      217      218      219      220      221      222      223      224 
## 201.7980 200.0427 202.5048 197.2311 201.4254 202.3531 201.3534 202.5329 
##      225      226      227      228      229      230      231      232 
## 188.6110 200.9885 200.4692 200.0323 197.2927 197.3158 198.4209 197.3466 
##      233      234      235      236      237      238      239      240 
## 197.2311 197.2619 201.4227 201.3611 198.9221 200.9885 198.4517 200.8188 
##      241      242      243      244      245      246      247      248 
## 188.6495 202.5329 201.3765 200.5231 200.7264 199.4668 199.9372 201.7877 
##      249      250      251      252      253      254      255      256 
## 200.2021 200.0889 201.8365 202.2992 201.9547 201.6745 201.6052 200.5412 
##      257      258      259      260      261      262      263      264 
## 202.2169 197.2388 200.7776 201.9008 201.4331 202.2631 199.3025 200.0889 
##      265      266      267      268      269      270      271      272 
## 200.9885 201.3019 197.2311 202.4971 201.0655 199.7959 202.2350 202.2504 
##      273      274      275      276      277      278      279      280 
## 202.5406 201.3123 202.1322 202.0498 201.7723 200.5747 202.5664 201.9728 
##      281      282      283      284      285      286      287      288 
## 201.4485 201.5128 201.6079 202.1245 202.5483 202.1707 202.1245 197.3620 
##      289      290      291      292      293      294      295      296 
## 198.9657 201.2018 202.2554 200.0889 201.9882 201.3457 202.4740 200.9885 
##      297      298      299      300      301      302      303      304 
## 200.4642 201.4639 197.2927 201.9136 200.9885 200.5516 200.0889 202.3223 
##      305      306      307      308      309      310      311      312 
## 201.0836 200.8137 201.6233 200.5516 200.9011 202.4482 200.4281 201.5282 
##      313      314      315      316      317      318      319      320 
## 201.8623 199.5261 198.5495 197.3620 202.2195 197.8504 200.5181 202.0525 
##      321      322      323      324      325      326      327      328 
## 201.8623 201.8211 200.9473 201.6772 202.4559 200.4642 201.9701 197.2619 
##      329      330      331      332      333      334      335      336 
## 201.6079 197.8220 200.8291 202.1938 201.2968 202.2118 200.6132 201.8596 
##      337      338      339      340      341      342      343      344 
## 200.1301 201.0913 202.5252 202.2992 197.8427 200.3279 201.4150 202.0344 
##      345      346      347      348      349      350      351      352 
## 201.7980 201.4562 201.4485 200.4692 201.4304 199.4310 201.7980 198.8424 
##      353      354      355      356      357      358      359      360 
## 202.3736 202.3608 198.4544 202.5587 200.2894 202.3146 201.5359 197.3389 
##      361      362      363      364      365      366      367      368 
## 201.4870 200.6544 201.9497 201.1787 202.4867 201.7030 201.7234 201.8931 
##      369      370      371      372      373      374      375      376 
## 202.2118 197.6010 202.2812 200.4642 202.2195 202.5664 197.2311 197.3158 
##      377      378      379      380      381      382      383      384 
## 197.2696 202.5433 201.5486 199.2409 200.9781 200.2175 197.2388 201.1067 
##      385      386      387      388      389      390      391      392 
## 201.7980 197.3466 201.1117 197.2850 200.5335 202.3866 202.3943 198.6292 
##      393      394      395      396      397      398      399      400 
## 202.2735 202.0371 201.9855 197.9378 201.2634 201.6002 202.4894 199.5981 
##      401      402      403      404      405      406      407      408 
## 198.0175 199.1920 202.3300 197.3928 202.0987 198.6292 198.7166 202.2323 
##      409      410      411      412      413      414      415      416 
## 202.0371 200.2791 201.7184 200.7341 197.2311 202.0240 202.1114 198.7832 
##      417      418      419      420      421      422      423      424 
## 199.8422 201.1787 200.6594 200.5516 201.7030 198.9426 197.3466 200.5593 
##      425      426      427      428      429      430      431      432 
## 202.1449 198.1484 202.3866 202.0960 198.5314 202.2118 201.6876 198.6650 
##      433      434      435      436      437      438      439      440 
## 202.3069 200.0812 200.2098 199.3359 200.7264 201.3662 201.7030 201.5128 
##      441      442      443      444      445      446      447      448 
## 201.5282 201.4254 200.8188 197.2311 202.3866 200.8573 198.5572 200.8291 
##      449      450      451      452      453      454      455      456 
## 202.1476 202.1861 199.5338 200.4769 200.2610 201.6437 198.3978 202.0371 
##      457      458      459      460      461      462      463      464 
## 201.7338 198.7139 199.9399 200.8214 201.7646 197.3466 200.2329 202.4817 
##      465      466      467      468      469      470      471      472 
## 201.3045 198.8039 201.4458 197.3389 200.5670 200.5951 201.1452 202.3505 
##      473      474      475      476      477      478      479      480 
## 201.3662 202.3351 201.5640 200.4950 202.5356 201.9008 200.8265 202.2118 
##      481      482      483      484      485      486      487      488 
## 201.7749 202.2581 200.9962 198.3747 197.2388 200.8984 202.5021 201.6953 
##      489      490      491      492      493      494      495      496 
## 201.9574 198.5803 201.1683 198.6188 200.2894 202.2992 202.2350 199.8884 
##      497      498      499      500      501      502      503      504 
## 202.5048 201.4408 198.8193 200.2329 202.3866 201.5667 201.9805 197.3851 
##      505      506      507      508      509      510      511      512 
## 202.2273 202.4817 202.3608 201.5128 197.2311 200.1224 202.1988 201.7338 
##      513      514      515      516      517      518      519      520 
## 199.9399 200.8368 202.4894 197.3158 202.3943 200.5874 201.5205 197.2311 
##      521      522      523      524      525      526      527      528 
## 202.2992 197.2388 202.4532 199.0815 197.2311 201.1452 200.6209 201.7234 
##      529      530      531      532      533      534      535      536 
## 201.2660 198.6523 202.3197 202.0371 201.8416 201.9085 197.3081 201.1633 
##      537      538      539      540      541      542      543      544 
## 201.6002 202.5664 202.4097 201.2942 201.8623 197.2542 197.9301 201.2506 
##      545      546      547      548      549      550      551      552 
## 199.5904 197.2465 202.0086 198.4544 202.2992 197.2311 198.9503 201.8057 
##      553      554      555      556      557      558      559      560 
## 199.4310 201.4639 201.4716 198.9864 201.4870 201.9805 201.4381 201.2403 
##      561      562      563      564      565      566      567      568 
## 202.5329 202.5510 197.2311 202.5279 197.3312 202.1372 201.2403 198.6292 
##      569      570      571      572      573      574      575      576 
## 202.1526 198.4671 200.5258 198.8783 201.7903 200.3664 201.0578 197.3158 
##      577      578      579      580      581      582      583      584 
## 201.1402 200.5516 197.3312 202.1245 197.9659 202.2195 201.8596 200.9473 
##      585      586      587      588      589      590      591      592 
## 200.8753 197.3389 202.1245 200.0246 197.8427 202.4971 202.2992 202.4251 
##      593      594      595      596      597      598      599      600 
## 201.0759 202.2735 202.4251 200.4719 201.6079 202.0344 200.4642 202.4097 
##      601      602      603      604      605      606      607      608 
## 201.6464 201.0012 201.7749 201.8777 202.1449 199.8602 202.1245 200.1736 
##      609      610      611      612      613      614      615      616 
## 197.3851 201.7080 197.3004 201.8854 202.1245 200.1428 201.5359 200.2894 
##      617      618      619      620      621      622      623      624 
## 197.2388 201.0759 200.3433 202.1064 201.9959 201.0628 200.5747 201.7157 
##      625      626      627      628      629      630      631      632 
## 200.5516 201.0039 201.7980 201.7619 201.6849 201.1633 200.5720 202.5356 
##      633      634      635      636      637      638      639      640 
## 201.9651 202.1245 197.2927 201.0759 202.2195 201.7030 202.2581 202.0113 
##      641      642      643      644      645      646      647      648 
## 201.8623 202.5664 200.4642 198.1588 201.6876 202.0036 202.0267 200.1532 
##      649      650      651      652      653      654      655      656 
## 198.7782 201.3380 188.6033 201.5486 201.1633 200.0273 200.8804 202.1245 
##      657      658      659      660      661      662      663      664 
## 200.7803 201.4254 202.4020 201.3816 202.1707 202.3866 200.7160 201.4331 
##      665      666      667      668      669      670      671      672 
## 202.0163 202.1322 201.6233 200.9962 201.6772 199.3513 201.8623 199.9399 
##      673      674      675      676      677      678      679      680 
## 200.0427 200.9011 202.6280 201.7569 201.3996 200.9627 202.3069 198.9144 
##      681      682      683      684      685      686      687      688 
## 199.7651 201.5282 201.5821 200.5181 199.0222 201.4920 201.2403 197.2311 
##      689      690      691      692      693      694      695      696 
## 201.3380 200.7264 202.4894 199.8499 202.3866 202.1861 201.5205 202.0240 
##      697      698      699      700      701      702      703      704 
## 202.2581 202.2658 201.7749 197.6318 202.2195 201.0836 201.8339 197.3466 
##      705      706      707      708      709      710      711      712 
## 200.2329 202.5356 197.3851 201.1067 201.8981 202.4020 202.4740 202.3069 
##      713      714      715      716      717      718      719      720 
## 197.2850 202.4894 199.3333 201.3354 202.0679 201.4254 197.2311 201.2583 
##      721      722      723      724      725      726      727      728 
## 201.3457 201.7261 199.9399 202.0267 202.0371 198.5572 200.4127 200.2971 
##      729      730      731      732      733      734      735      736 
## 201.5128 200.1582 202.1784 201.9085 201.2249 199.1354 200.5516 199.6520 
##      737      738      739      740      741      742      743      744 
## 200.5566 198.0791 202.4097 201.5128 201.9959 202.2658 202.5202 199.8010 
##      745      746      747      748      749      750      751      752 
## 199.6570 200.1224 197.3851 201.9497 202.2118 197.3081 197.9455 201.3045 
##      753      754      755      756      757      758      759      760 
## 202.0448 202.2350 198.6600 202.4790 200.6259 201.5205 202.2992 197.2465 
##      761      762      763      764      765      766      767      768 
## 197.2465 199.7059 201.8623 198.4544 202.2400 200.2021 198.9118 201.5024 
##      769      770      771      772      773      774      775      776 
## 200.9627 201.1221 197.2311 201.8031 200.4076 201.2326 201.6310 202.5587 
##      777      778      779      780      781      782      783      784 
## 200.5516 200.5747 201.2249 202.5664 202.3300 197.2388 201.7749 199.4156 
##      785      786      787      788      789      790      791      792 
## 200.2456 201.5255 200.4846 201.5255 201.5563 199.0018 201.4331 197.3158 
##      793      794      795      796      797      798      799      800 
## 197.2696 201.3662 201.8623 200.4796 197.2311 202.0910 201.4562 201.6541 
##      801      802      803      804      805      806      807      808 
## 201.8057 200.4512 202.3377 201.6437 198.6600 201.6464 200.9369 197.2850 
##      809      810      811      812      813      814      815      816 
## 200.9808 197.9814 188.6880 202.2889 202.5329 200.1840 202.0344 201.6876 
##      817      818      819      820      821      822      823      824 
## 200.5027 202.6049 200.1197 198.1638 201.3688 200.4642 197.2388 202.1245 
##      825      826      827      828      829      830      831      832 
## 202.3866 199.5261 200.7264 201.5513 201.4304 197.3389 201.2095 201.4381 
##      833      834      835      836      837      838      839      840 
## 197.3928 202.4740 199.6778 201.9805 202.1245 197.2311 202.5741 202.3146 
##      841      842      843      844      845      846      847      848 
## 201.0836 199.7702 199.3359 200.8111 201.9882 201.6876 202.4251 200.9061 
##      849      850      851      852      853      854      855      856 
## 197.2850 201.1633 201.7261 201.5332 201.7338 201.6310 197.3235 202.1322 
##      857      858      859      860      861      862      863      864 
## 201.4331 202.5818 202.2581 200.7006 201.4331 202.1322 200.3330 200.8804 
##      865      866      867      868      869      870      871      872 
## 200.0273 201.6129 200.9885 201.3431 202.4020 202.3274 198.9298 201.8981 
##      873      874      875      876      877      878      879      880 
## 201.7980 201.1837 202.3866 202.3069 202.5356 197.8427 199.6905 199.9399 
##      881      882      883      884      885      886      887      888 
## 202.2631 197.3543 202.4020 201.6310 200.7418 200.5901 201.7311 201.8134 
##      889      890      891      892      893      894      895      896 
## 201.1633 200.1582 198.6007 201.9959 201.3765 202.4740 200.4796 202.1322 
##      897      898      899      900      901      902      903      904 
## 201.9367 202.3300 201.0347 201.3919 201.6876 199.7959 200.9473 200.0427 
##      905      906      907      908      909      910      911      912 
## 200.0015 201.8700 199.4129 200.9396 202.4971 202.2504 202.1245 202.3505 
##      913      914      915      916      917      918      919      920 
## 201.1452 200.5104 199.8987 202.1988 201.7749 197.8427 201.9805 200.4642 
##      921      922      923      924      925      926      927      928 
## 201.6079 201.6233 197.2927 202.1295 202.2708 202.4020 198.9195 202.4894 
##      929      930      931      932      933      934      935      936 
## 200.8265 197.2311 201.2583 197.3312 202.2631 200.5720 202.3300 200.9962 
##      937      938      939      940      941      942      943      944 
## 198.5056 199.0018 201.4227 201.6876 202.2992 202.6049 200.9165 199.9784 
##      945      946      947      948      949      950      951      952 
## 197.3620 199.4052 200.0273 200.8727 199.6778 200.0427 197.3543 200.9885 
##      953      954      955      956      957      958      959      960 
## 197.2388 202.1322 201.8623 201.4331 202.5433 200.7160 202.4328 202.2554 
##      961      962      963      964      965      966      967      968 
## 201.3045 202.3943 202.1322 200.2098 199.3641 202.1553 200.7264 201.1633 
##      969      970      971      972      973      974      975      976 
## 197.2927 201.4408 201.4408 202.2581 198.7166 200.1763 201.6876 198.8270 
##      977      978      979      980      981      982      983      984 
## 200.4719 201.9316 202.0344 202.2477 201.6876 198.3232 199.8499 200.0581 
##      985      986      987      988      989      990      991      992 
## 200.6132 201.8211 200.1532 198.8732 201.3096 202.1861 198.6084 202.0113 
##      993      994      995      996      997      998      999     1000 
## 201.4458 202.4740 200.5412 199.7856 197.2388 201.3380 197.3235 200.9677 
##     1001     1002     1003     1004     1005     1006     1007     1008 
## 197.9043 199.9192 200.5824 202.0371 200.3176 201.6745 200.3048 201.5359 
##     1009     1010     1011     1012     1013     1014     1015     1016 
## 202.4713 200.6363 198.6265 202.4944 202.1630 200.5258 197.8093 199.9064 
##     1017     1018     1019     1020     1021     1022     1023     1024 
## 201.8134 198.0764 200.9473 202.1988 200.7264 200.4642 201.4485 202.0960 
##     1025     1026     1027     1028     1029     1030     1031     1032 
## 201.6233 202.2246 201.0759 202.2350 201.6079 197.9043 201.2506 202.2118 
##     1033     1034     1035     1036     1037     1038     1039     1040 
## 201.8134 200.9292 197.3235 201.7826 201.8750 201.1298 202.3377 202.5895 
##     1041     1042     1043     1044     1045     1046     1047     1048 
## 202.0679 197.8427 200.1016 202.2785 200.1686 200.9165 201.8596 202.1141 
##     1049     1050     1051     1052     1053     1054     1055     1056 
## 201.7261 198.4544 200.7622 202.0113 197.3312 202.2992 200.4358 202.1449 
##     1057     1058     1059     1060     1061     1062     1063     1064 
## 198.7524 197.2542 199.4310 197.3466 202.5048 197.3235 197.2311 202.2992 
##     1065     1066     1067     1068     1069     1070     1071     1072 
## 201.7261 201.3250 202.0036 197.3466 201.4562 199.0403 201.4562 200.4538 
##     1073     1074     1075     1076     1077     1078     1079     1080 
## 201.5717 201.4689 200.6671 201.2506 197.9301 202.2118 202.3146 199.7521 
##     1081     1082     1083     1084     1085     1086     1087     1088 
## 200.4642 201.8700 198.4544 202.4405 201.6387 201.8854 202.0448 202.2118 
##     1089     1090     1091     1092     1093     1094     1095     1096 
## 198.6677 200.7699 201.9393 201.2583 200.9677 197.2773 201.6618 200.5593 
##     1097     1098     1099     1100     1101     1102     1103     1104 
## 201.1067 197.2234 197.2465 202.2992 197.3389 201.5590 197.3774 200.9011 
##     1105     1106     1107     1108     1109     1110     1111     1112 
## 201.4177 200.4923 198.8886 200.2021 201.7338 201.1787 199.0661 202.6357 
##     1113     1114     1115     1116     1117     1118     1119     1120 
## 200.1763 200.2175 201.0578 202.3454 200.3973 201.1529 199.8010 199.3359 
##     1121     1122     1123     1124     1125     1126     1127     1128 
## 202.0806 201.7184 202.1399 202.3866 201.0270 198.1099 200.7264 202.5972 
##     1129     1130     1131     1132     1133     1134     1135     1136 
## 201.6953 199.4668 202.0190 199.2921 197.3389 201.0836 197.6010 202.2273 
##     1137     1138     1139     1140     1141     1142     1143     1144 
## 200.5516 201.1298 200.5566 201.5178 201.8211 202.5510 202.2889 200.2406 
##     1145     1146     1147     1148     1149     1150     1151     1152 
## 202.0498 201.7388 202.3866 198.0406 200.5797 199.3949 200.5593 197.2542 
##     1153     1154     1155     1156     1157     1158     1159     1160 
## 201.7569 201.3996 198.9657 201.3354 202.4894 197.2311 202.2735 200.3741 
##     1161     1162     1163     1164     1165     1166     1167     1168 
## 202.3916 200.6929 202.3582 201.6876 200.4281 201.1144 197.3004 199.7933 
##     1169     1170     1171     1172     1173     1174     1175     1176 
## 202.3608 200.4127 200.7160 201.7184 202.0448 198.7216 197.2311 200.6775 
##     1177     1178     1179     1180     1181     1182     1183     1184 
## 200.5412 199.5981 201.4562 199.0480 201.5486 201.4254 201.5640 199.4233 
##     1185     1186     1187     1188     1189     1190     1191     1192 
## 201.7980 197.3620 202.3454 202.5895 201.8623 199.2767 202.2118 199.6289 
##     1193     1194     1195     1196     1197     1198     1199     1200 
## 200.4796 201.8777 201.7749 198.4852 202.4740 201.6002 201.1633 200.3768 
##     1201     1202     1203     1204     1205     1206     1207     1208 
## 197.2927 201.8623 197.2388 198.0610 201.2506 202.0679 201.3045 200.8214 
##     1209     1210     1211     1212     1213     1214     1215     1216 
## 197.3004 201.6541 197.2465 197.3004 200.4950 202.3274 202.5252 200.2175 
##     1217     1218     1219     1220     1221     1222     1223     1224 
## 197.3697 197.3004 199.9399 201.2788 200.1224 197.9840 199.1123 202.5741 
##     1225     1226     1227     1228     1229     1230     1231     1232 
## 202.3659 199.9399 201.5205 201.6156 202.4020 201.4254 199.3821 200.7649 
##     1233     1234     1235     1236     1237     1238     1239     1240 
## 202.4405 201.9959 201.6953 202.1245 202.4020 200.9962 200.9808 202.2118 
##     1241     1242     1243     1244     1245     1246     1247     1248 
## 201.8777 200.2714 200.9011 199.8087 200.6775 201.7903 200.8599 200.6363 
##     1249     1250     1251     1252     1253     1254     1255     1256 
## 201.0913 202.6126 200.4642 201.4716 200.7133 201.8777 201.1633 202.6126 
##     1257     1258     1259     1260     1261     1262     1263     1264 
## 197.2850 197.2311 202.4147 198.1638 202.2427 202.3043 200.6517 197.3158 
##     1265     1266     1267     1268     1269     1270     1271     1272 
## 201.6876 201.3380 198.8039 201.4047 202.6280 202.2195 197.3697 201.9882 
##     1273     1274     1275     1276     1277     1278     1279     1280 
## 199.1766 197.3389 201.0913 200.7418 201.8904 200.1147 197.3312 202.2631 
##     1281     1282     1283     1284     1285     1286     1287     1288 
## 200.0323 199.6212 197.8427 200.4950 202.0679 202.3069 202.3943 201.0990 
##     1289     1290     1291     1292     1293     1294     1295     1296 
## 201.7826 197.3543 201.8673 198.9067 202.5895 197.9094 199.8036 201.1144 
##     1297     1298     1299     1300     1301     1302     1303     1304 
## 198.0945 202.1707 197.3466 201.6926 201.9497 201.4408 200.5104 200.7495 
##     1305     1306     1307     1308     1309     1310     1311     1312 
## 201.6156 202.1372 201.8827 201.8519 202.1141 199.8833 202.2195 202.3943 
##     1313     1314     1315     1316     1317     1318     1319     1320 
## 201.2506 200.6055 202.4405 200.3048 201.5898 200.2252 198.6881 202.0729 
##     1321     1322     1323     1324     1325     1326     1327     1328 
## 200.9011 200.6748 202.4740 200.9396 200.8214 201.0913 201.3611 197.2542 
##     1329     1330     1331     1332     1333     1334     1335     1336 
## 202.5021 200.9962 202.4817 201.9651 200.1736 202.2400 201.2788 200.1147 
##     1337     1338     1339     1340     1341     1342     1343     1344 
## 201.8288 200.6286 200.0273 198.2462 201.9778 200.5258 202.0421 200.1532 
##     1345     1346     1347     1348     1349     1350     1351     1352 
## 197.2465 198.7397 197.6807 199.3667 197.8504 200.9885 202.4894 201.6953 
##     1353     1354     1355     1356     1357     1358     1359     1360 
## 197.2850 200.2175 197.2311 202.1630 200.8599 201.4331 202.4482 201.3200 
##     1361     1362     1363     1364     1365     1366     1367     1368 
## 202.1245 202.5483 200.7622 202.5125 201.4408 201.9932 202.1245 197.2311 
##     1369     1370     1371     1372     1373     1374     1375     1376 
## 201.6849 201.4254 200.0631 200.7264 201.9651 199.3975 202.1322 200.0015 
##     1377     1378     1379     1380     1381     1382     1383     1384 
## 197.3851 200.9088 202.2992 201.7107 201.4150 198.3670 202.3993 199.6778 
##     1385     1386     1387     1388     1389     1390     1391     1392 
## 200.0581 201.2814 197.2465 201.4535 199.4052 201.2634 197.2619 201.5667 
##     1393     1394     1395     1396     1397     1398     1399     1400 
## 201.1914 202.2992 202.2554 200.8265 202.2992 197.2619 198.8039 197.2850 
##     1401     1402     1403     1404     1405     1406     1407     1408 
## 202.2554 197.2388 202.3531 202.3866 198.8039 200.8034 201.5898 197.3235 
##     1409     1410     1411     1412     1413     1414     1415     1416 
## 201.2326 199.4129 201.3919 199.8010 200.8804 200.0427 199.1535 201.1194 
##     1417     1418     1419     1420     1421     1422     1423     1424 
## 198.5287 201.3457 201.7030 202.3300 200.0427 201.9882 200.7264 202.4971 
##     1425     1426     1427     1428     1429     1430     1431     1432 
## 200.4642 202.0240 202.2273 198.1665 202.5356 201.7030 201.5563 201.9959 
##     1433     1434     1435     1436     1437     1438     1439     1440 
## 200.2071 197.2311 202.1245 201.8623 202.6049 200.7006 201.3508 202.4636 
##     1441     1442     1443     1444     1445     1446     1447     1448 
## 197.2311 200.1043 197.8427 202.4636 201.4331 198.8321 199.8422 201.4381 
##     1449     1450     1451     1452     1453     1454     1455     1456 
## 200.2148 202.0806 198.9580 197.6191 202.3197 200.7133 201.8904 200.1686 
##     1457     1458     1459     1460     1461     1462     1463     1464 
## 202.1938 200.0350 200.0966 202.0729 202.5741 200.9654 200.5516 202.4251 
##     1465     1466     1467     1468     1469     1470     1471     1472 
## 202.2092 201.2814 200.8214 200.9088 202.4740 200.9396 198.6111 201.5513 
##     1473     1474     1475     1476     1477     1478     1479     1480 
## 200.2971 201.6437 202.1938 197.2850 200.5978 199.7805 202.4097 202.2195 
##     1481     1482     1483     1484     1485     1486     1487     1488 
## 201.8519 201.8750 201.0628 202.1218 201.6079 200.7495 201.4254 201.9805 
##     1489     1490     1491     1492     1493     1494     1495     1496 
## 201.6156 197.2850 200.4642 201.0759 199.2948 199.9218 198.9067 201.8750 
##     1497     1498     1499     1500     1501     1502     1503     1504 
## 197.3389 201.7980 202.5098 202.2761 202.5895 202.0602 197.8581 201.0628 
##     1505     1506     1507     1508     1509     1510     1511     1512 
## 200.9242 200.2894 200.4719 198.8732 197.3697 201.9932 201.9959 202.0371 
##     1513     1514     1515     1516     1517     1518     1519     1520 
## 202.2658 197.3158 202.3300 200.3741 200.6698 201.7954 202.2992 199.6443 
##     1521     1522     1523     1524     1525     1526     1527     1528 
## 197.3158 199.5877 202.0602 199.4156 201.4947 200.5308 201.0732 197.3928 
##     1529     1530     1531     1532     1533     1534     1535     1536 
## 197.2542 198.3490 202.3223 198.7062 199.7317 201.9497 197.2311 201.4716 
##     1537     1538     1539     1540     1541     1542     1543     1544 
## 198.9941 201.4485 197.2311 202.0371 201.3045 199.2228 202.2118 202.3454 
##     1545     1546     1547     1548     1549     1550     1551     1552 
## 199.6751 200.4950 201.8623 202.2966 200.3999 197.3081 201.1298 200.5670 
##     1553     1554     1555     1556     1557     1558     1559     1560 
## 198.6446 201.5513 199.6905 201.9085 198.7628 200.8522 197.3081 200.7726 
##     1561     1562     1563     1564     1565     1566     1567     1568 
## 201.6772 201.0913 197.2311 197.2388 202.4147 200.4642 202.1553 202.5021 
##     1569     1570     1571     1572     1573     1574     1575     1576 
## 201.0193 201.7800 198.0252 201.6002 200.9885 201.8777 200.9011 201.5486 
##     1577     1578     1579     1580     1581     1582     1583     1584 
## 199.8010 198.9580 200.2868 201.6953 202.0267 200.7264 199.4206 200.8907 
##     1585     1586     1587     1588     1589     1590     1591     1592 
## 202.1322 201.1606 200.1428 200.3279 201.6876 201.1710 202.2273 200.3973 
##     1593     1594     1595     1596     1597     1598     1599     1600 
## 199.5465 201.1067 202.5202 197.3697 200.3330 202.2812 201.6953 199.1612 
##     1601     1602     1603     1604     1605     1606     1607     1608 
## 197.2311 202.2862 202.2350 202.5741 199.2278 202.2118 201.8134 200.9138 
##     1609     1610     1611     1612     1613     1614     1615     1616 
## 202.3428 200.5516 201.0759 201.0759 201.4227 200.0554 201.1787 200.1455 
##     1617     1618     1619     1620     1621     1622     1623     1624 
## 199.1354 198.8039 201.7080 202.3866 201.3457 198.0406 199.1327 198.9787 
##     1625     1626     1627     1628     1629     1630     1631     1632 
## 201.5359 200.6748 201.7492 201.5436 201.1837 202.4559 201.3585 198.8116 
##     1633     1634     1635     1636     1637     1638     1639     1640 
## 197.3851 199.0942 198.0637 201.3765 202.4251 200.8445 198.9529 202.4894 
##     1641     1642     1643     1644     1645     1646     1647     1648 
## 202.4817 202.3582 202.1218 200.5258 201.0913 197.3466 202.1707 202.2273 
##     1649     1650     1651     1652     1653     1654     1655     1656 
## 201.8057 202.3428 202.2118 202.4740 202.1630 197.2311 199.1689 197.3004 
##     1657     1658     1659     1660     1661     1662     1663     1664 
## 202.0421 199.4360 201.7030 199.3487 200.9781 202.5972 197.2773 201.1348 
##     1665     1666     1667     1668     1669     1670     1671     1672 
## 200.5516 201.2968 201.3045 202.4174 202.2118 200.9677 201.7826 202.4251 
##     1673     1674     1675     1676     1677     1678     1679     1680 
## 202.5433 202.0525 197.9659 202.0344 200.4153 202.0448 201.6591 202.1630 
##     1681     1682     1683     1684     1685     1686     1687     1688 
## 197.2465 202.4020 200.6440 201.4304 197.2542 198.8193 200.0273 200.5978 
##     1689     1690     1691     1692     1693     1694     1695     1696 
## 201.8057 200.1301 198.9657 202.1322 201.5332 202.0756 202.2658 198.7062 
##     1697     1698     1699     1700     1701     1702     1703     1704 
## 202.4251 201.5821 202.2992 197.2927 200.1301 201.2376 199.0326 201.7003 
##     1705     1706     1707     1708     1709     1710     1711     1712 
## 200.8496 201.3354 200.9215 201.2583 200.4692 201.8931 200.5000 201.3354 
##     1713     1714     1715     1716     1717     1718     1719     1720 
## 201.1941 202.5279 201.7903 201.7749 201.8623 197.2388 202.3197 197.3543 
##     1721     1722     1723     1724     1725     1726     1727     1728 
## 199.2998 201.2865 200.5412 201.5024 201.1040 199.1019 201.5871 197.2311 
##     1729     1730     1731     1732     1733     1734     1735     1736 
## 201.9574 200.1994 199.6855 201.8416 202.4455 198.2873 197.3543 197.2465 
##     1737     1738     1739     1740     1741     1742     1743     1744 
## 201.5486 199.5003 197.2311 201.9624 197.2311 198.7216 197.3235 202.3531 
##     1745     1746     1747     1748     1749     1750     1751     1752 
## 201.7261 200.6236 202.3146 197.3466 202.2195 199.2409 202.1834 202.0036 
##     1753     1754     1755     1756     1757     1758     1759     1760 
## 202.5895 197.3312 200.2379 202.5664 200.7083 201.4047 202.5406 198.8655 
##     1761     1762     1763     1764     1765     1766     1767     1768 
## 202.2862 200.2483 201.2222 201.1375 200.0735 202.0525 200.8265 202.1245 
##     1769     1770     1771     1772     1773     1774     1775     1776 
## 201.9651 201.7338 198.9118 200.2610 202.4894 200.4796 202.0240 202.1037 
##     1777     1778     1779     1780     1781     1782     1783     1784 
## 202.3505 198.1049 201.7030 201.4535 201.5486 201.2711 201.9882 201.7492 
##     1785     1786     1787     1788     1789     1790     1791     1792 
## 200.1840 201.8211 201.6876 201.9547 201.4331 200.2868 201.0347 197.2927 
##     1793     1794     1795     1796     1797     1798     1799     1800 
## 200.0015 201.2788 198.0225 202.4147 199.9553 200.8368 202.5356 198.3336 
##     1801     1802     1803     1804     1805     1806     1807     1808 
## 201.2480 202.3505 200.3125 199.4310 199.3744 200.8881 202.0344 201.7030 
##     1809     1810     1811     1812     1813     1814     1815     1816 
## 202.2015 202.5098 199.8602 198.3413 201.0039 201.3431 201.6387 199.0738 
##     1817     1818     1819     1820     1821     1822     1823     1824 
## 201.3380 198.1484 201.1683 202.2350 199.8499 197.3774 199.1689 202.3146 
##     1825     1826     1827     1828     1829     1830     1831     1832 
## 197.2619 201.0116 200.2791 198.4517 201.4612 201.6876 200.9858 200.0273 
##     1833     1834     1835     1836     1837     1838     1839     1840 
## 200.0323 202.1553 197.2542 201.0320 200.3664 197.8863 199.9449 199.4822 
##     1841     1842     1843     1844     1845     1846     1847     1848 
## 198.0687 202.0987 201.6541 200.7264 197.2465 201.9959 201.7234 201.5128 
##     1849     1850     1851     1852     1853     1854     1855     1856 
## 201.2814 198.6292 197.8427 202.5098 201.4331 199.3359 197.6422 198.7628 
##     1857     1858     1859     1860     1861     1862     1863     1864 
## 202.1114 199.9269 197.3620 199.3282 201.4689 200.0658 200.7264 198.4698 
##     1865     1866     1867     1868     1869     1870     1871     1872 
## 197.2465 197.2927 202.1707 197.2927 202.3223 200.5181 201.7157 202.4020 
##     1873     1874     1875     1876     1877     1878     1879     1880 
## 201.5359 201.5282 202.6280 198.8578 199.7882 201.8134 200.8650 202.4971 
##     1881     1882     1883     1884     1885     1886     1887     1888 
## 199.3795 202.2889 201.7415 202.0421 199.2459 199.3359 201.6876 201.5975 
##     1889     1890     1891     1892     1893     1894     1895     1896 
## 199.0249 199.0557 200.6671 201.4458 202.3943 198.8039 200.5516 202.1784 
##     1897     1898     1899     1900     1901     1902     1903     1904 
## 201.8700 200.5489 200.4642 202.3146 201.1683 200.6363 197.2388 202.3505 
##     1905     1906     1907     1908     1909     1910     1911     1912 
## 201.7826 202.2195 202.2350 202.4740 199.9553 198.0406 201.0732 198.4029 
##     1913     1914     1915     1916     1917     1918     1919     1920 
## 202.4020 202.1784 201.7030 200.8727 201.6876 201.1787 200.4846 201.0501 
##     1921     1922     1923     1924     1925     1926     1927     1928 
## 200.6621 201.6387 197.9994 201.0089 201.1941 201.8750 200.2175 201.5024 
##     1929     1930     1931     1932     1933     1934     1935     1936 
## 200.9011 201.8854 200.9677 198.3336 201.1040 200.8368 200.0554 199.2074 
##     1937     1938     1939     1940     1941     1942     1943     1944 
## 202.0371 202.2273 202.3866 202.3146 197.2311 198.7524 200.6363 199.0326 
##     1945     1946     1947     1948     1949     1950     1951     1952 
## 200.7341 202.2118 201.7080 200.2894 201.9008 200.4230 202.5510 202.5175 
##     1953     1954     1955     1956     1957     1958     1959     1960 
## 201.7749 201.8623 200.5643 197.2311 202.4740 197.3158 202.5279 201.9008 
##     1961     1962     1963     1964     1965     1966     1967     1968 
## 197.3158 199.4310 199.0018 200.8984 197.2311 197.2311 199.7394 199.8884 
##     1969     1970     1971     1972     1973     1974     1975     1976 
## 201.1067 198.4337 197.3851 200.1428 197.2542 202.2427 202.0679 201.3123 
##     1977     1978     1979     1980     1981     1982     1983     1984 
## 201.2634 200.4719 199.6751 200.7699 197.2311 197.2696 200.4846 202.3146 
##     1985     1986     1987     1988     1989     1990     1991     1992 
## 201.7415 201.9932 201.9574 202.3069 202.3043 199.3025 202.3146 199.3975 
##     1993     1994     1995     1996     1997     1998     1999     2000 
## 199.9372 197.8632 198.3540 200.0142 200.4950 200.4127 197.2850 200.2687 
##     2001     2002     2003     2004     2005     2006     2007     2008 
## 201.5332 202.0448 202.3762 200.2021 201.7465 200.2252 197.3466 202.2992 
##     2009     2010     2011     2012     2013     2014     2015     2016 
## 199.2998 197.2542 201.3611 199.7959 202.2273 201.0913 198.0406 202.1553 
##     2017     2018     2019     2020     2021     2022     2023     2024 
## 202.1399 197.3466 201.9651 201.4562 200.7572 202.3736 201.7826 202.4097 
##     2025     2026     2027     2028     2029     2030     2031     2032 
## 197.2388 200.7391 202.1476 201.5513 202.1141 200.9627 201.2376 198.9221 
##     2033     2034     2035     2036     2037     2038     2039     2040 
## 200.8445 201.3996 201.4227 200.0658 197.2311 200.8984 198.8990 199.3487 
##     2041     2042     2043     2044     2045     2046     2047     2048 
## 202.4790 201.2737 201.3508 202.5098 201.9393 200.5516 202.4894 200.1582 
##     2049     2050     2051     2052     2053     2054     2055     2056 
## 202.1245 200.1301 200.6517 202.5510 198.1049 202.2273 202.4971 200.3638 
##     2057     2058     2059     2060     2061     2062     2063     2064 
## 201.9805 201.3611 199.8653 201.9805 200.4796 201.4920 201.4408 201.2711 
##     2065     2066     2067     2068     2069     2070     2071     2072 
## 197.3697 202.0987 201.0913 201.1221 200.2483 199.1431 202.1399 198.8809 
##     2073     2074     2075     2076     2077     2078     2079     2080 
## 197.3543 200.3099 200.6390 202.1707 200.3664 197.3235 201.9574 198.7936 
##     2081     2082     2083     2084     2085     2086     2087     2088 
## 197.7115 199.4668 201.8981 202.3866 202.3069 197.2542 202.1861 197.3158 
##     2089     2090     2091     2092     2093     2094     2095     2096 
## 200.7264 200.8034 200.0427 200.4796 201.6360 199.4591 200.0169 200.0812 
##     2097     2098     2099     2100     2101     2102     2103     2104 
## 199.8114 201.7107 198.8193 200.7649 197.8504 200.1813 199.9938 197.3851 
##     2105     2106     2107     2108     2109     2110     2111     2112 
## 202.1988 202.4097 198.6600 197.2619 201.3354 197.2465 201.4535 199.3282 
##     2113     2114     2115     2116     2117     2118     2119     2120 
## 197.9455 200.2791 200.8522 198.3259 200.9088 201.0732 197.2311 200.6621 
##     2121     2122     2123     2124     2125     2126     2127     2128 
## 198.0175 201.6953 199.7471 200.0015 199.2278 202.4301 197.9763 200.9011 
##     2129     2130     2131     2132     2133     2134     2135     2136 
## 198.0045 201.2326 197.2850 201.1348 200.3407 201.0039 200.4538 202.4020 
##     2137     2138     2139     2140     2141     2142     2143     2144 
## 200.1197 201.1529 201.0836 200.7133 202.1399 200.2791 197.2696 197.3466 
##     2145     2146     2147     2148     2149     2150     2151     2152 
## 200.3664 200.4050 201.6953 202.1114 200.7803 201.1760 202.4147 202.6049 
##     2153     2154     2155     2156     2157     2158     2159     2160 
## 201.1864 200.3845 200.3125 199.9680 200.7930 200.9962 201.4843 201.0759 
##     2161     2162     2163     2164     2165     2166     2167     2168 
## 202.4020 197.2388 199.9269 199.2613 201.8700 200.5516 200.5643 202.1037 
##     2169     2170     2171     2172     2173     2174     2175     2176 
## 202.6357 201.8623 197.2619 197.2850 201.4793 201.5332 199.4156 199.0095 
##     2177     2178     2179     2180     2181     2182     2183     2184 
## 200.8445 197.2311 202.4944 202.3146 201.8262 202.2195 199.2948 202.4894 
##     2185     2186     2187     2188     2189     2190     2191     2192 
## 202.5021 198.8039 199.5388 201.6437 197.2542 199.0788 199.0711 200.5747 
##     2193     2194     2195     2196     2197     2198     2199     2200 
## 201.7338 199.1920 197.3543 201.1298 202.1399 202.2658 201.8057 202.2195 
##     2201     2202     2203     2204     2205     2206     2207     2208 
## 201.0243 202.2273 202.4740 200.4642 202.1707 200.3048 199.1535 197.2619 
##     2209     2210     2211     2212     2213     2214     2215     2216 
## 200.7572 201.9497 201.0913 198.0252 202.1553 197.3543 200.9215 202.2658 
##     2217     2218     2219     2220     2221     2222     2223     2224 
## 197.2388 201.5128 200.1043 198.4544 202.0883 202.0036 200.7341 201.4562 
##     2225     2226     2227     2228     2229     2230     2231     2232 
## 200.3176 202.0371 202.3146 201.7903 202.1322 200.2714 201.0166 197.3774 
##     2233     2234     2235     2236     2237     2238     2239     2240 
## 201.7080 201.2788 200.0939 199.4052 199.8602 201.8931 198.2616 200.0142 
##     2241     2242     2243     2244     2245     2246     2247     2248 
## 200.2894 200.8650 202.0652 198.7909 201.4227 200.4796 198.8475 197.6345 
##     2249     2250     2251     2252     2253     2254     2255     2256 
## 201.9497 200.2252 198.4260 200.1301 201.8108 201.9651 201.4639 201.8031 
##     2257     2258     2259     2260     2261     2262     2263     2264 
## 198.1665 202.5329 201.9547 202.5048 202.4790 200.6621 198.4594 201.6772 
##     2265     2266     2267     2268     2269     2270     2271     2272 
## 202.3866 202.2992 197.2311 202.2169 197.2542 198.5622 199.1046 200.8111 
##     2273     2274     2275     2276     2277     2278     2279     2280 
## 202.3505 200.7264 201.2557 197.8427 200.0323 202.0371 202.5252 198.6754 
##     2281     2282     2283     2284     2285     2286     2287     2288 
## 197.3081 201.2891 197.2773 199.3436 202.0910 199.2717 201.9959 202.4894 
##     2289     2290     2291     2292     2293     2294     2295     2296 
## 201.5101 200.5516 201.9162 201.3431 201.2968 202.2477 202.2735 198.9452 
##     2297     2298     2299     2300     2301     2302     2303     2304 
## 202.3300 200.4076 201.3508 199.2409 200.1532 201.8596 197.2311 200.8445 
##     2305     2306     2307     2308     2309     2310     2311     2312 
## 198.9683 201.0089 197.3697 199.0403 202.1245 197.2542 202.4559 202.2889 
##     2313     2314     2315     2316     2317     2318     2319     2320 
## 201.4458 200.0735 200.6671 202.6049 200.7957 201.2968 197.3774 200.8522 
##     2321     2322     2323     2324     2325     2326     2327     2328 
## 201.3045 200.5951 200.7545 197.2311 197.3081 199.6520 200.3768 202.4301 
##     2329     2330     2331     2332     2333     2334     2335     2336 
## 201.9393 197.2311 202.3916 202.4251 202.3120 201.8339 201.7749 199.9476 
##     2337     2338     2339     2340     2341     2342     2343     2344 
## 201.8211 201.8777 202.6049 200.5566 202.5972 201.6876 202.3043 201.6002 
##     2345     2346     2347     2348     2349     2350     2351     2352 
## 200.1840 202.4455 202.2992 202.3866 202.2273 201.6745 202.0679 200.7957 
##     2353     2354     2355     2356     2357     2358     2359     2360 
## 199.2690 201.3970 197.2696 197.2619 202.2631 201.8134 198.5468 202.4740 
##     2361     2362     2363     2364     2365     2366     2367     2368 
## 199.1843 199.3590 202.2992 202.3120 200.4642 199.2717 197.2773 197.3466 
##     2369     2370     2371     2372     2373     2374     2375     2376 
## 200.2302 201.0913 198.2950 199.9476 201.0347 201.8854 200.5516 200.6259 
##     2377     2378     2379     2380     2381     2382     2383     2384 
## 202.4790 200.2637 201.8777 197.2619 200.9138 201.0501 197.2465 200.7083 
##     2385     2386     2387     2388     2389     2390     2391     2392 
## 201.6695 200.6390 198.1099 201.6876 201.0501 199.8602 202.4020 200.2894 
##     2393     2394     2395     2396     2397     2398     2399     2400 
## 201.0501 201.7646 197.2311 199.1250 200.5747 201.4304 200.5308 202.3866 
##     2401     2402     2403     2404     2405     2406     2407     2408 
## 202.3916 200.9550 201.1633 201.6437 197.3004 199.6031 199.4541 200.5412 
##     2409     2410     2411     2412     2413     2414     2415     2416 
## 197.2311 202.5048 201.6464 202.2350 197.3235 199.2536 200.7264 202.4174 
##     2417     2418     2419     2420     2421     2422     2423     2424 
## 200.2560 202.2992 202.3762 197.3081 200.2456 202.5048 201.7749 202.1245 
##     2425     2426     2427     2428     2429     2430     2431     2432 
## 198.4414 201.8623 200.3845 202.3069 201.2506 201.3611 202.4740 201.7980 
##     2433     2434     2435     2436     2437     2438     2439     2440 
## 197.8220 198.2796 201.8623 200.6286 201.8931 197.3389 201.9959 202.3300 
##     2441     2442     2443     2444     2445     2446     2447     2448 
## 202.3274 199.3641 202.2273 202.0163 197.2542 201.9728 201.5178 202.3377 
##     2449     2450     2451     2452     2453     2454     2455     2456 
## 199.0711 201.6695 200.7264 201.3045 197.3081 199.7009 202.0987 200.8291 
##     2457     2458     2459     2460     2461     2462     2463     2464 
## 199.0172 201.2249 200.7622 197.2388 197.3851 199.5981 200.3768 202.2966 
##     2465     2466     2467     2468     2469     2470     2471     2472 
## 200.8599 200.8830 200.8034 200.0273 201.5436 201.2172 202.4224 198.4544 
##     2473     2474     2475     2476     2477     2478     2479     2480 
## 201.7030 201.3765 201.1194 200.9627 197.2773 200.7726 199.0738 201.2968 
##     2481     2482     2483     2484     2485     2486     2487     2488 
## 197.2850 199.4052 200.7264 198.8809 201.7234 202.2992 202.2169 197.2311 
##     2489     2490     2491     2492     2493     2494     2495     2496 
## 198.5776 197.2465 197.2850 199.3821 201.8700 198.1923 200.2894 200.2791 
##     2497     2498     2499     2500     2501     2502     2503     2504 
## 201.1452 200.2791 202.0525 202.6357 199.3590 199.2151 197.3928 200.7649 
##     2505     2506     2507     2508     2509     2510     2511     2512 
## 201.3919 199.7728 202.2504 201.1606 202.1938 202.1476 197.2388 200.9446 
##     2513     2514     2515     2516     2517     2518     2519     2520 
## 202.0267 201.4254 200.7264 201.2557 201.3842 201.9213 198.7370 202.4020 
##     2521     2522     2523     2524     2525     2526     2527     2528 
## 200.0735 197.3697 201.0836 199.1535 200.8984 198.8039 197.2388 200.2329 
##     2529     2530     2531     2532     2533     2534     2535     2536 
## 202.5587 202.4020 202.2092 200.4512 202.0833 200.6440 201.6876 202.0652 
##     2537     2538     2539     2540     2541     2542     2543     2544 
## 200.7649 202.1399 201.8365 201.6876 202.5125 201.8134 200.4538 200.2971 
##     2545     2546     2547     2548     2549     2550     2551     2552 
## 200.2894 197.2311 198.6985 201.7646 199.8268 202.0960 200.5335 197.3004 
##     2553     2554     2555     2556     2557     2558     2559     2560 
## 197.6422 202.4097 197.3697 197.9428 199.9938 197.2927 202.0910 201.4997 
##     2561     2562     2563     2564     2565     2566     2567     2568 
## 202.0036 198.6446 201.4254 201.4304 201.7800 198.1588 200.4642 202.4328 
##     2569     2570     2571     2572     2573     2574     2575     2576 
## 202.2504 201.9701 202.5279 200.1147 200.2252 197.7554 201.2068 199.9553 
##     2577     2578     2579     2580     2581     2582     2583     2584 
## 202.0960 200.5516 201.5255 201.5744 202.5048 200.4307 200.2148 201.8981 
##     2585     2586     2587     2588     2589     2590     2591     2592 
## 199.3641 200.5516 200.1736 201.3919 202.2735 202.4097 202.1707 201.6437 
##     2593     2594     2595     2596     2597     2598     2599     2600 
## 202.0910 199.0403 201.2583 199.0453 201.0012 202.1603 202.2631 201.7723 
##     2601     2602     2603     2604     2605     2606     2607     2608 
## 198.9606 199.2486 200.2175 201.0243 198.1923 200.8496 202.2118 201.8854 
##     2609     2610     2611     2612     2613     2614     2615     2616 
## 200.4950 200.2894 199.4129 197.2542 200.6390 200.7468 197.3851 201.0424 
##     2617     2618     2619     2620     2621     2622     2623     2624 
## 201.4793 197.2465 201.0424 200.9962 201.7388 201.0551 201.9932 200.2175 
##     2625     2626     2627     2628     2629     2630     2631     2632 
## 201.2018 201.6052 200.9446 198.9298 200.9011 202.1988 197.3774 200.5516 
##     2633     2634     2635     2636     2637     2638     2639     2640 
## 198.9864 202.0987 202.5125 199.2998 202.6357 202.2992 202.3866 201.9805 
##     2641     2642     2643     2644     2645     2646     2647     2648 
## 201.7030 198.9941 198.0764 200.3279 200.4615 199.5492 200.6825 201.5436 
##     2649     2650     2651     2652     2653     2654     2655     2656 
## 202.1399 197.2850 199.8499 201.3123 199.3410 201.7261 199.8241 201.8750 
##     2657     2658     2659     2660     2661     2662     2663     2664 
## 202.5279 201.9239 200.5516 202.2350 201.4073 198.8039 200.5593 200.1917 
##     2665     2666     2667     2668     2669     2670     2671     2672 
## 202.1630 202.0883 202.5279 201.5667 201.5486 201.7492 202.4097 202.2118 
##     2673     2674     2675     2676     2677     2678     2679     2680 
## 197.3928 202.1938 200.7341 198.4621 201.1683 199.3513 197.3235 201.3457 
##     2681     2682     2683     2684     2685     2686     2687     2688 
## 202.3943 199.5904 201.1864 201.2634 202.5483 198.6677 198.6369 201.3970 
##     2689     2690     2691     2692     2693     2694     2695     2696 
## 197.2465 199.4052 199.0557 199.9399 201.2737 201.0655 201.4997 201.6953 
##     2697     2698     2699     2700     2701     2702     2703     2704 
## 198.5006 202.3069 197.3389 202.2992 200.3999 201.1633 201.5975 201.9882 
##     2705     2706     2707     2708     2709     2710     2711     2712 
## 199.1920 197.3466 200.7418 201.2788 201.4254 202.0652 197.2542 202.1245 
##     2713     2714     2715     2716     2717     2718     2719     2720 
## 202.1476 198.0175 201.1683 202.3351 199.7882 202.0421 197.6911 200.7880 
##     2721     2722     2723     2724     2725     2726     2727     2728 
## 201.7749 201.1941 200.3125 200.4204 197.3389 200.7056 197.3620 201.1760 
##     2729     2730     2731     2732     2733     2734     2735     2736 
## 198.9349 197.2927 200.2483 199.8679 202.3943 200.3202 202.2015 201.7492 
##     2737     2738     2739     2740     2741     2742     2743     2744 
## 201.5128 201.0474 201.7107 200.7880 201.1837 201.7903 202.1553 202.5972 
##     2745     2746     2747     2748     2749     2750     2751     2752 
## 202.4482 197.2773 198.6369 199.3282 197.7554 201.4150 199.8961 198.3670 
##     2753     2754     2755     2756     2757     2758     2759     2760 
## 197.7269 200.2021 198.3721 200.2071 202.1322 201.7261 201.4254 201.7107 
##     2761     2762     2763     2764     2765     2766     2767     2768 
## 198.1357 200.5027 202.3943 202.2427 202.4817 202.5406 199.3359 198.3182 
##     2769     2770     2771     2772     2773     2774     2775     2776 
## 198.9452 199.7933 200.8368 200.7803 201.8519 199.4772 200.6775 197.3158 
##     2777     2778     2779     2780     2781     2782     2783     2784 
## 202.0086 197.3235 201.9805 202.3223 197.3158 201.1914 202.2504 199.2640 
##     2785     2786     2787     2788     2789     2790     2791     2792 
## 202.2427 197.3543 202.0163 202.5483 201.7826 198.4775 202.2246 202.4971 
##     2793     2794     2795     2796     2797     2798     2799     2800 
## 202.1476 199.2613 197.3466 197.3774 200.2483 199.9476 201.0347 201.9162 
##     2801     2802     2803     2804     2805     2806     2807     2808 
## 200.6028 200.4642 202.4070 202.4817 202.4224 201.8031 201.8623 202.5048 
##     2809     2810     2811     2812     2813     2814     2815     2816 
## 200.5797 197.2773 202.2195 197.2619 199.1689 197.3466 200.7418 201.4843 
##     2817     2818     2819     2820     2821     2822     2823     2824 
## 201.7542 198.3644 197.8220 200.3048 200.4461 199.9476 202.4147 201.4227 
##     2825     2826     2827     2828     2829     2830     2831     2832 
## 201.7749 201.3816 199.9526 199.6674 197.2696 197.2465 201.6876 198.8552 
##     2833     2834     2835     2836     2837     2838     2839     2840 
## 201.2249 201.4793 202.0679 202.2735 199.6855 200.2637 202.4301 202.2992 
##     2841     2842     2843     2844     2845     2846     2847     2848 
## 200.1840 202.5406 197.3389 200.6363 199.0634 200.7341 197.3235 202.2350 
##     2849     2850     2851     2852     2853     2854     2855     2856 
## 199.8422 202.0421 198.4544 200.7341 201.0347 201.4920 201.7723 198.0175 
##     2857     2858     2859     2860     2861     2862     2863     2864 
## 202.1399 199.9630 201.3200 201.2711 201.4331 202.1399 202.4301 202.4147 
##     2865     2866     2867     2868     2869     2870     2871     2872 
## 202.2273 202.4020 201.6541 202.4174 201.2018 199.3975 197.2542 198.7601 
##     2873     2874     2875     2876     2877     2878     2879     2880 
## 201.0836 198.5545 200.5901 202.2992 201.2249 201.9497 200.5104 199.2047 
##     2881     2882     2883     2884     2885     2886     2887     2888 
## 201.5667 201.8777 201.4150 198.8809 202.5048 201.6283 201.1194 201.4254 
##     2889     2890     2891     2892     2893     2894     2895     2896 
## 200.9523 198.9221 200.9088 198.6369 200.6825 199.0480 197.3774 197.2311 
##     2897     2898     2899     2900     2901     2902     2903     2904 
## 200.1609 202.1784 197.2619 202.2889 200.6182 201.6310 200.3253 200.5335 
##     2905     2906     2907     2908     2909     2910     2911     2912 
## 200.3176 200.9858 200.2894 199.4310 198.2616 198.2385 200.8727 202.2118 
##     2913     2914     2915     2916     2917     2918     2919     2920 
## 202.1526 200.3768 200.2894 201.2583 199.2563 198.8990 197.3235 201.9651 
##     2921     2922     2923     2924     2925     2926     2927     2928 
## 199.2536 201.8288 202.0833 202.3943 201.3173 200.8599 197.2465 202.0448 
##     2929     2930     2931     2932     2933     2934     2935     2936 
## 201.2299 198.3336 200.7726 199.5619 199.8241 199.9476 200.2894 197.2311 
##     2937     2938     2939     2940     2941     2942     2943     2944 
## 201.9497 201.5178 200.7237 199.4695 201.7903 200.9962 199.3282 202.4740 
##     2945     2946     2947     2948     2949     2950     2951     2952 
## 202.1630 197.3466 202.3043 199.1766 202.5202 202.3866 202.1037 200.8214 
##     2953     2954     2955     2956     2957     2958     2959     2960 
## 199.4360 199.5954 200.9781 201.8134 200.2868 200.6902 200.4642 200.1609 
##     2961     2962     2963     2964     2965     2966     2967     2968 
## 202.3454 202.5048 202.2631 201.7826 200.4538 197.3620 201.6876 199.7367 
##     2969     2970     2971     2972     2973     2974     2975     2976 
## 201.4254 202.1680 201.6876 197.2311 200.7264 200.8522 199.8679 199.6212 
##     2977     2978     2979     2980     2981     2982     2983     2984 
## 199.3564 199.1816 202.3043 197.2773 202.3685 198.7782 197.3081 201.9805 
##     2985     2986     2987     2988     2989     2990     2991     2992 
## 201.8700 201.7492 202.3993 200.4307 197.3158 200.1378 197.3312 202.4894 
##     2993     2994     2995     2996     2997     2998     2999     3000 
## 201.8623 201.7749 198.2873 199.9861 197.6680 201.7749 201.3919 201.2968 
##     3001     3002     3003     3004     3005     3006     3007     3008 
## 202.3069 197.2850 202.5741 201.8185 202.4532 202.3531 201.3508 200.2021 
##     3009     3010     3011     3012     3013     3014     3015     3016 
## 202.4251 201.3662 200.7341 197.3312 202.3351 199.4233 200.2329 202.3866 
##     3017     3018     3019     3020     3021     3022     3023     3024 
## 202.2246 202.0113 201.4947 201.4381 201.7800 198.8270 202.1938 199.1689 
##     3025     3026     3027     3028     3029     3030     3031     3032 
## 202.0448 200.2894 197.3389 197.3774 201.0836 201.1452 201.5332 200.6979 
##     3033     3034     3035     3036     3037     3038     3039     3040 
## 200.5720 197.6345 198.4671 197.5883 201.1117 202.4482 198.8732 200.7930 
##     3041     3042     3043     3044     3045     3046     3047     3048 
## 199.6597 202.0421 202.4174 202.2118 202.5202 197.2542 198.7678 199.3975 
##     3049     3050     3051     3052     3053     3054     3055     3056 
## 197.7554 201.3380 200.2971 202.0371 197.3312 197.2619 200.9088 201.6002 
##     3057     3058     3059     3060     3061     3062     3063     3064 
## 201.0424 201.8854 197.3928 200.9446 202.3454 201.2942 202.4944 199.0326 
##     3065     3066     3067     3068     3069     3070     3071     3072 
## 200.3202 201.2249 200.4230 198.6446 202.3069 200.9473 201.0270 202.1245 
##     3073     3074     3075     3076     3077     3078     3079     3080 
## 200.9858 201.1683 201.6618 201.7338 202.6126 197.2465 201.9136 201.9497 
##     3081     3082     3083     3084     3085     3086     3087     3088 
## 201.5667 197.3774 200.6390 201.6926 200.6390 202.4020 200.3356 202.1476 
##     3089     3090     3091     3092     3093     3094     3095     3096 
## 201.7261 201.3173 201.7646 197.6680 202.3762 202.2504 202.2273 198.7474 
##     3097     3098     3099     3100     3101     3102     3103     3104 
## 197.2927 202.0498 201.5409 200.6467 201.7749 201.9959 201.9008 202.4740 
##     3105     3106     3107     3108     3109     3110     3111     3112 
## 200.7264 199.7240 201.8339 201.5409 201.6876 197.2311 199.6212 199.8987 
##     3113     3114     3115     3116     3117     3118     3119     3120 
## 197.3697 202.3377 199.0068 201.8442 198.2847 198.2385 200.8650 202.2118 
##     3121     3122     3123     3124     3125     3126     3127     3128 
## 200.4950 201.0836 199.4668 201.3457 201.3431 201.3662 201.4331 197.2465 
##     3129     3130     3131     3132     3133     3134     3135     3136 
## 202.1784 202.2092 202.4817 202.1911 201.0990 199.7086 202.4867 200.2175 
##     3137     3138     3139     3140     3141     3142     3143     3144 
## 200.7495 200.0092 201.0809 199.5184 199.3359 201.7749 202.1322 200.6286 
##     3145     3146     3147     3148     3149     3150     3151     3152 
## 200.4642 202.4301 202.3300 200.1378 202.2992 201.8519 200.1455 200.4538 
##     3153     3154     3155     3156     3157     3158     3159     3160 
## 200.0350 202.5202 201.5128 201.4485 200.5516 200.3048 201.3045 199.2640 
##     3161     3162     3163     3164     3165     3166     3167     3168 
## 199.0068 202.0113 201.6953 200.5824 198.8578 200.6825 200.8907 198.9144 
##     3169     3170     3171     3172     3173     3174     3175     3176 
## 200.9550 202.1834 200.6286 199.0172 197.3928 197.2311 202.2350 200.2687 
##     3177     3178     3179     3180     3181     3182     3183     3184 
## 201.5744 202.1938 202.4482 201.5178 201.0039 202.1399 198.4183 201.8904 
##     3185     3186     3187     3188     3189     3190     3191     3192 
## 201.8700 202.5972 200.6028 202.6049 200.8034 197.3620 202.4559 200.3022 
##     3193     3194     3195     3196     3197     3198     3199     3200 
## 201.3277 197.7450 201.8057 201.2145 201.7903 202.2812 200.3768 202.0371 
##     3201     3202     3203     3204     3205     3206     3207     3208 
## 200.4642 200.3176 200.3048 199.4464 200.4461 202.3377 201.2506 201.4227 
##     3209     3210     3211     3212     3213     3214     3215     3216 
## 201.8700 200.8907 202.0960 201.0759 198.8039 202.4174 202.2092 202.1938 
##     3217     3218     3219     3220     3221     3222     3223     3224 
## 200.3048 201.7030 201.1144 202.0267 201.3996 202.5972 198.1049 200.5181 
##     3225     3226     3227     3228     3229     3230     3231     3232 
## 202.3943 202.2118 199.1535 201.4254 199.4052 202.1784 200.9935 201.6849 
##     3233     3234     3235     3236     3237     3238     3239     3240 
## 199.0403 201.7646 197.2850 200.4153 200.3587 202.5741 199.3872 200.3587 
##     3241     3242     3243     3244     3245     3246     3247     3248 
## 201.9393 197.3389 202.4971 198.7524 197.3004 201.1633 202.4559 202.4020 
##     3249     3250     3251     3252     3253     3254     3255     3256 
## 202.2195 202.4609 199.0815 200.0812 200.5489 202.0036 201.5975 201.3019 
##     3257     3258     3259     3260     3261     3262     3263     3264 
## 200.3922 202.5175 201.3019 198.6831 199.3513 197.8170 201.4227 201.9497 
##     3265     3266     3267     3268     3269     3270     3271     3272 
## 197.5960 198.3747 197.5960 201.0039 198.8732 199.6828 201.5667 199.1689 
##     3273     3274     3275     3276     3277     3278     3279     3280 
## 201.5563 202.4817 202.4636 200.9962 200.8137 202.4174 199.1327 197.3774 
##     3281     3282     3283     3284     3285     3286     3287     3288 
## 197.2465 201.6206 200.4615 200.0323 199.5338 198.7216 202.1707 197.6757 
##     3289     3290     3291     3292     3293     3294     3295     3296 
## 200.8342 197.3389 200.4127 197.3851 201.7030 198.5006 201.8493 202.2992 
##     3297     3298     3299     3300     3301     3302     3303     3304 
## 197.8940 200.6363 199.4156 202.3839 199.9834 200.2148 200.9011 202.5048 
##     3305     3306     3307     3308     3309     3310     3311     3312 
## 201.8519 200.3356 201.9651 200.8599 202.2992 198.2873 201.9085 200.6390 
##     3313     3314     3315     3316     3317     3318     3319     3320 
## 200.6313 202.3146 200.8522 202.1399 201.0116 200.2071 200.9165 201.0116 
##     3321     3322     3323     3324     3325     3326     3327     3328 
## 201.1710 198.6161 202.4020 201.6876 197.2388 200.9165 200.2379 201.8981 
##     3329     3330     3331     3332     3333     3334     3335     3336 
## 198.7524 199.6647 202.0729 201.1502 201.7311 197.4494 200.2764 200.5951 
##     3337     3338     3339     3340     3341     3342     3343     3344 
## 201.5563 201.9855 201.8108 199.7136 201.1117 199.3872 202.0009 199.3872 
##     3345     3346     3347     3348     3349     3350     3351     3352 
## 201.8339 202.5972 201.9855 201.9290 197.8066 197.3774 201.9855 201.4124 
##     3353     3354     3355     3356     3357     3358     3359     3360 
## 200.5154 202.0960 197.3851 201.0397 200.3561 197.3851 202.3428 201.0628 
##     3361     3362     3363     3364     3365     3366     3367     3368 
## 198.5930 202.2708 202.5098 202.4301 201.9290 202.5175 202.4224 202.1988 
##     3369     3370     3371     3372     3373     3374     3375     3376 
## 201.5486 199.1970 200.6105 200.9446 198.6650 202.2631 201.9213 199.4668 
##     3377     3378     3379     3380     3381     3382     3383     3384 
## 199.6262 201.1117 199.8164 201.2299 197.8066 202.0806 201.5717 201.3893 
##     3385     3386     3387     3388     3389     3390     3391     3392 
## 201.4612 201.2068 201.9932 202.3351 200.8881 200.4281 202.3659 200.1736 
##     3393     3394     3395     3396     3397     3398     3399     3400 
## 201.6591 201.3173 201.8493 198.5930 201.8108 202.4301 201.4766 200.6825 
##     3401     3402     3403     3404     3405     3406     3407     3408 
## 202.4224 200.2456 199.5388 200.4204 201.1502 201.5486 202.3582 202.5406 
##     3409     3410     3411     3412     3413     3414     3415     3416 
## 197.3697 202.2862 197.3543 202.3428 200.5874 202.1680 201.9213 199.7290 
##     3417     3418     3419     3420     3421     3422     3423     3424 
## 201.4047 201.6591 200.6979 200.4358 199.1019 197.3697 202.5972 199.2921 
##     3425     3426     3427     3428     3429     3430     3431     3432 
## 200.3407 201.9136 201.1991 201.2068 201.8493 201.3019 202.4532 201.3173 
##     3433     3434     3435     3436     3437     3438     3439     3440 
## 200.7699 200.4204 201.8339 201.6514 201.3893 201.0243 198.7678 197.8786 
##     3441     3442     3443     3444     3445     3446     3447     3448 
## 198.4979 201.1117 199.7290 201.5717 198.7755 198.7601 197.7038 202.6280 
##     3449     3450     3451     3452     3453     3454     3455     3456 
## 201.7234 201.4920 202.5098 201.8981 200.2533 200.3330 198.2358 199.2767 
##     3457     3458     3459     3460     3461     3462     3463     3464 
## 200.7341 200.4796 202.1141 202.2118 202.3351 201.8904 201.6876 201.9805 
##     3465     3466     3467     3468     3469     3470     3471     3472 
## 201.9162 199.7728 200.4204 197.2465 199.4591 201.7261 200.5516 197.8297 
##     3473     3474     3475     3476     3477     3478     3479     3480 
## 201.9497 201.0990 202.1476 200.5566 201.2506 201.2968 200.0400 202.2323 
##     3481     3482     3483     3484     3485     3486     3487     3488 
## 202.1322 201.9316 200.1455 197.3312 199.1354 197.3620 199.0557 200.9473 
##     3489     3490     3491     3492     3493     3494     3495     3496 
## 197.3004 200.2945 202.2785 198.4852 197.2850 202.5098 201.4331 201.5590 
##     3497     3498     3499     3500     3501     3502     3503     3504 
## 202.2169 200.1224 202.5741 200.1120 200.3999 200.2379 202.2118 201.0578 
##     3505     3506     3507     3508     3509     3510     3511     3512 
## 201.4331 201.1144 202.3428 201.7107 200.5593 201.4689 198.1665 200.5720 
##     3513     3514     3515     3516     3517     3518     3519     3520 
## 199.6778 202.4482 202.2118 199.0969 201.3354 198.2154 202.5202 197.7554 
##     3521     3522     3523     3524     3525     3526     3527     3528 
## 201.3173 201.4562 201.6002 200.3356 199.4437 201.1221 201.1067 198.8655 
##     3529     3530     3531     3532     3533     3534     3535     3536 
## 201.7749 201.3380 200.6544 197.3928 202.3943 202.2323 200.3279 201.0990 
##     3537     3538     3539     3540     3541     3542     3543     3544 
## 200.2329 202.0036 199.0661 198.0071 200.7264 200.1736 202.1114 201.5205 
##     3545     3546     3547     3548     3549     3550     3551     3552 
## 202.3531 200.0065 201.2018 200.1301 202.2992 199.4156 199.5261 197.2619 
##     3553     3554     3555     3556     3557     3558     3559     3560 
## 201.4227 200.4461 202.2273 200.4461 198.3824 197.7423 201.0578 201.3765 
##     3561     3562     3563     3564     3565     3566     3567     3568 
## 198.8809 199.6289 201.4254 201.1864 202.0833 202.4559 198.6446 198.7370 
##     3569     3570     3571     3572     3573     3574     3575     3576 
## 201.2968 201.2172 201.7003 202.4405 202.4174 197.3774 201.4843 201.4331 
##     3577     3578     3579     3580     3581     3582     3583     3584 
## 202.0833 202.5510 202.4097 202.3916 201.0347 200.9523 199.4849 202.3866 
##     3585     3586     3587     3588     3589     3590     3591     3592 
## 199.9707 197.3389 200.3356 201.6206 200.4769 197.8093 202.2246 202.1784 
##     3593     3594     3595     3596     3597     3598     3599     3600 
## 200.3253 197.3774 202.3300 202.3377 202.4174 198.6677 202.3736 200.9242 
##     3601     3602     3603     3604     3605     3606     3607     3608 
## 199.5261 202.5202 201.7749 201.8519 201.9574 200.6621 200.6621 202.4328 
##     3609     3610     3611     3612     3613     3614     3615     3616 
## 200.3664 201.7107 201.5128 202.1322 200.9165 199.8910 202.3300 197.3235 
##     3617     3618     3619     3620     3621     3622     3623     3624 
## 197.2773 200.7133 201.9574 202.5098 200.1301 197.3312 197.2927 200.9165 
##     3625     3626     3627     3628     3629     3630     3631     3632 
## 201.6310 201.0039 201.0116 199.6212 200.3253 201.9085 197.3415 199.4900 
##     3633     3634     3635     3636     3637     3638     3639     3640 
## 199.5030 200.3407 201.8493 202.3531 200.2379 201.9651 202.4894 200.7803 
##     3641     3642     3643     3644     3645     3646     3647     3648 
## 202.0009 199.6855 201.7030 201.9162 200.9754 197.2619 201.7492 197.3851 
##     3649     3650     3651     3652     3653     3654     3655     3656 
## 202.6126 202.3608 201.2814 201.9085 197.3620 201.6514 197.2696 197.2311 
##     3657     3658     3659     3660     3661     3662     3663     3664 
## 197.6757 198.2796 201.7903 201.8623 200.6028 200.9550 202.2581 197.2465 
##     3665     3666     3667     3668     3669     3670     3671     3672 
## 199.7213 199.8602 200.6698 201.8211 200.8445 202.0371 197.3928 198.5572 
##     3673     3674     3675     3676     3677     3678     3679     3680 
## 199.6932 200.7341 199.9630 201.0578 202.1218 197.2311 199.6135 200.4923 
##     3681     3682     3683     3684     3685     3686     3687     3688 
## 202.4147 201.7184 199.2871 202.0498 201.9497 202.2735 202.1603 202.3043 
##     3689     3690     3691     3692     3693     3694     3695     3696 
## 202.0240 197.2927 200.1455 201.6156 201.7877 199.9399 201.8981 199.0095 
##     3697     3698     3699     3700     3701     3702     3703     3704 
## 201.7646 197.3851 201.9882 200.2714 201.7877 197.3081 201.9393 201.7030 
##     3705     3706     3707     3708     3709     3710     3711     3712 
## 199.6778 202.3685 199.5107 200.7495 201.9497 202.4894 197.7631 201.4254 
##     3713     3714     3715     3716     3717     3718     3719     3720 
## 200.4796 202.2554 202.1938 201.9574 201.4689 197.6603 199.4745 197.2850 
##     3721     3722     3723     3724     3725     3726     3727     3728 
## 200.2687 197.3774 198.5160 201.7030 201.7415 201.8596 202.0371 198.6496 
##     3729     3730     3731     3732     3733     3734     3735     3736 
## 199.6855 200.6621 200.7418 200.0400 201.0039 199.5030 199.3590 201.7980 
##     3737     3738     3739     3740     3741     3742     3743     3744 
## 202.2092 200.2714 200.4719 200.3099 200.1351 201.9574 199.6366 202.3377 
##     3745     3746     3747     3748     3749     3750     3751     3752 
## 199.3025 201.8623 197.3081 202.2350 202.3659 197.3928 202.2118 202.1245 
##     3753     3754     3755     3756     3757     3758     3759     3760 
## 202.1322 202.4020 202.2889 201.1683 201.5640 201.1425 202.2118 201.8673 
##     3761     3762     3763     3764     3765     3766     3767     3768 
## 200.6286 198.8424 200.6979 200.4538 200.8522 200.2225 197.2311 202.5895 
##     3769     3770     3771     3772     3773     3774     3775     3776 
## 200.9473 202.5895 202.2350 197.2773 197.3697 201.9213 200.9242 200.7056 
##     3777     3778     3779     3780     3781     3782     3783     3784 
## 201.0628 200.4719 200.3048 198.3540 202.1064 201.9316 201.0836 202.4378 
##     3785     3786     3787     3788     3789     3790     3791     3792 
## 201.3200 201.2506 197.4494 197.2311 200.4719 202.5356 202.2169 201.5359 
##     3793     3794     3795     3796     3797     3798     3799     3800 
## 201.5871 201.8700 201.0347 200.5978 200.2894 201.5205 201.9805 201.7030 
##     3801     3802     3803     3804     3805     3806     3807     3808 
## 199.6597 201.8211 202.2581 200.5670 202.3685 202.4174 199.0969 202.4867 
##     3809     3810     3811     3812     3813     3814     3815     3816 
## 202.5587 199.6778 198.3798 200.4873 198.1896 201.4381 200.7006 200.7880 
##     3817     3818     3819     3820     3821     3822     3823     3824 
## 200.6544 198.3232 202.5125 198.7755 200.7314 202.5098 202.0679 201.1864 
##     3825     3826     3827     3828     3829     3830     3831     3832 
## 201.4331 199.6597 198.8809 201.3380 201.0039 197.5883 201.5128 197.6884 
##     3833     3834     3835     3836     3837     3838     3839     3840 
## 202.0960 201.4997 197.7554 199.4668 199.9218 202.1245 199.3590 201.1144 
##     3841     3842     3843     3844     3845     3846     3847     3848 
## 201.3739 201.5178 201.8442 197.2388 200.6544 197.3466 201.8777 202.3943 
##     3849     3850     3851     3852     3853     3854     3855     3856 
## 202.1630 200.3973 199.1535 202.0190 201.6079 200.3561 198.7909 200.9242 
##     3857     3858     3859     3860     3861     3862     3863     3864 
## 197.8786 201.5436 197.3158 201.6772 200.0554 201.7903 201.9393 199.0172 
##     3865     3866     3867     3868     3869     3870     3871     3872 
## 201.4304 200.3202 202.4740 199.2921 202.1322 200.2098 201.7107 197.3081 
##     3873     3874     3875     3876     3877     3878     3879     3880 
## 200.8599 202.3943 197.2850 200.3356 200.9885 201.5513 201.2891 199.6108 
##     3881     3882     3883     3884     3885     3886     3887     3888 
## 198.6754 201.8134 201.9497 200.1378 201.9805 202.0883 197.3158 202.3043 
##     3889     3890     3891     3892     3893     3894     3895     3896 
## 201.7903 200.9677 201.0089 199.5030 202.5587 197.7785 201.5717 200.7545 
##     3897     3898     3899     3900     3901     3902     3903     3904 
## 202.5433 202.3146 201.5205 198.7139 200.0427 199.0661 198.5160 197.3081 
##     3905     3906     3907     3908     3909     3910     3911     3912 
## 201.3019 198.8193 202.1245 202.2992 202.2812 202.5406 201.6926 200.3048 
##     3913     3914     3915     3916     3917     3918     3919     3920 
## 201.2660 200.3768 197.2696 200.1532 201.1375 197.3955 197.3235 197.2542 
##     3921     3922     3923     3924     3925     3926     3927     3928 
## 201.0012 201.0501 199.6212 201.9624 200.9215 200.8291 202.3685 200.6363 
##     3929     3930     3931     3932     3933     3934     3935     3936 
## 200.1147 201.7826 197.3543 200.0708 198.3490 200.3664 201.3200 201.8777 
##     3937     3938     3939     3940     3941     3942     3943     3944 
## 201.5436 197.2619 201.9059 197.3620 197.7065 197.3774 202.1399 201.9547 
##     3945     3946     3947     3948     3949     3950     3951     3952 
## 201.0682 201.5640 201.3173 199.9192 201.3893 199.2074 199.2124 202.4971 
##     3953     3954     3955     3956     3957     3958     3959     3960 
## 201.6387 200.0708 201.8904 197.2542 201.9290 199.7779 201.4535 201.7030 
##     3961     3962     3963     3964     3965     3966     3967     3968 
## 201.0990 200.6929 197.3851 198.3386 202.5741 200.2379 199.2278 198.6446 
##     3969     3970     3971     3972     3973     3974     3975     3976 
## 199.4437 197.7631 201.3096 202.0267 202.4713 202.5279 199.6932 197.2850 
##     3977     3978     3979     3980     3981     3982     3983     3984 
## 201.8623 202.1784 197.2927 199.1766 202.0729 201.6387 200.5593 201.4766 
##     3985     3986     3987     3988     3989     3990     3991     3992 
## 198.1588 200.5566 200.3099 201.5205 201.2583 199.5646 198.6600 201.8211 
##     3993     3994     3995     3996     3997     3998     3999     4000 
## 200.7957 200.1147 201.9497 201.3173 197.3004 202.0498 201.5282 201.0501 
##     4001     4002     4003     4004     4005     4006     4007     4008 
## 201.6876 202.3531 200.9962 202.1114 202.3866 197.3158 201.2299 200.7160 
##     4009     4010     4011     4012     4013     4014     4015     4016 
## 200.6544 200.4512 200.8137 202.1553 200.9704 199.2844 201.7261 201.2557 
##     4017     4018     4019     4020     4021     4022     4023     4024 
## 197.4340 197.2696 200.9704 201.6310 201.0809 197.2927 199.5904 202.0009 
##     4025     4026     4027     4028     4029     4030     4031     4032 
## 200.9600 198.3463 202.3069 200.2764 198.3747 200.5516 201.7569 201.9651 
##     4033     4034     4035     4036     4037     4038     4039     4040 
## 199.2486 201.2222 200.4435 197.3774 201.8623 201.5590 201.6052 202.2427 
##     4041     4042     4043     4044     4045     4046     4047     4048 
## 201.1221 201.9701 200.2021 202.3274 200.8881 200.6028 201.0347 202.5125 
##     4049     4050     4051     4052     4053     4054     4055     4056 
## 197.3851 202.4636 202.2477 200.2456 202.2581 202.4405 200.5824 201.4639 
##     4057     4058     4059     4060     4061     4062     4063     4064 
## 200.9858 198.9606 202.2350 201.0759 200.5566 197.2388 201.0089 200.5231 
##     4065     4066     4067     4068     4069     4070     4071     4072 
## 200.2225 200.8907 198.8039 200.5747 201.8211 202.2118 201.0424 201.4870 
##     4073     4074     4075     4076     4077     4078     4079     4080 
## 201.3354 198.9118 200.3587 198.5622 199.0815 202.0652 202.0910 201.6360 
##     4081     4082     4083     4084     4085     4086     4087     4088 
## 200.4615 202.4455 202.3043 197.5806 201.1425 201.3457 202.1526 199.6058 
##     4089     4090     4091     4092     4093     4094     4095     4096 
## 201.4254 201.2095 202.4174 200.6390 198.6754 198.7062 197.3466 201.7234 
##     4097     4098     4099     4100     4101     4102     4103     4104 
## 201.9316 197.6730 200.5516 201.2249 200.3433 200.8342 197.8066 198.0714 
##     4105     4106     4107     4108     4109     4110     4111     4112 
## 199.5234 201.4870 197.3235 197.4340 200.5027 199.4360 200.1686 202.3839 
##     4113     4114     4115     4116     4117     4118     4119     4120 
## 199.4618 200.6671 202.3608 199.5338 197.3466 201.3457 202.3300 198.5237 
##     4121     4122     4123     4124     4125     4126     4127     4128 
## 201.7569 197.3774 201.4485 197.3235 200.2329 201.7338 200.9396 201.9497 
##     4129     4130     4131     4132     4133     4134     4135     4136 
## 200.1378 202.0883 202.5895 199.8833 200.7341 202.4455 201.9162 202.0086 
##     4137     4138     4139     4140     4141     4142     4143     4144 
## 197.3081 201.7646 201.8416 199.6828 199.6778 199.9449 197.2927 200.2894 
##     4145     4146     4147     4148     4149     4150     4151     4152 
## 202.3454 201.3816 201.9239 197.2927 202.2246 200.9215 197.2773 197.7219 
##     4153     4154     4155     4156     4157     4158     4159     4160 
## 201.7749 201.8134 201.8700 200.4050 202.5895 202.4740 202.5818 199.6751 
##     4161     4162     4163     4164     4165     4166     4167     4168 
## 201.7184 201.1117 199.5030 200.2945 201.1144 202.4070 202.3608 202.4482 
##     4169     4170     4171     4172     4173     4174     4175     4176 
## 202.1707 202.2273 201.8134 200.8984 199.5261 202.2785 202.2118 202.0987 
##     4177     4178     4179     4180     4181     4182     4183     4184 
## 199.3641 198.8321 202.0883 201.9162 202.3659 201.9651 201.7619 202.1245 
##     4185     4186     4187     4188     4189     4190     4191     4192 
## 199.8010 197.3389 202.0371 198.5495 201.7749 200.6775 200.0504 201.2403 
##     4193     4194     4195     4196     4197     4198     4199     4200 
## 202.3943 200.6390 198.6754 201.7619 197.2773 201.5640 201.2814 201.3534 
##     4201     4202     4203     4204     4205     4206     4207     4208 
## 202.1476 199.7521 198.9657 202.1988 201.0963 197.6345 202.0113 198.8706 
##     4209     4210     4211     4212     4213     4214     4215     4216 
## 197.8016 201.8057 201.2942 200.6748 198.9941 201.9316 200.4692 202.1526 
##     4217     4218     4219     4220     4221     4222     4223     4224 
## 200.3895 197.2542 200.4512 198.8578 199.3821 202.4636 201.9085 197.2850 
##     4225     4226     4227     4228     4229     4230     4231     4232 
## 200.7545 201.7826 201.3970 201.5255 201.3277 202.4740 202.1630 201.7184 
##     4233     4234     4235     4236     4237     4238     4239     4240 
## 201.9574 201.2068 197.3081 198.7447 200.2225 202.5202 198.2154 200.3484 
##     4241     4242     4243     4244     4245     4246     4247     4248 
## 197.2311 199.1662 202.4482 198.4106 200.5027 198.1203 199.9707 202.2889 
##     4249     4250     4251     4252     4253     4254     4255     4256 
## 200.5824 201.5486 201.6156 199.1766 199.7856 199.5234 200.9473 197.2773 
##     4257     4258     4259     4260     4261     4262     4263     4264 
## 202.6357 202.2092 201.5821 201.4793 200.1890 201.9316 200.5901 200.3587 
##     4265     4266     4267     4268     4269     4270     4271     4272 
## 197.2388 201.5282 201.9728 201.9316 200.5154 200.9523 201.4254 202.1603 
##     4273     4274     4275     4276     4277     4278     4279     4280 
## 199.0661 197.2619 202.2273 200.1609 202.4636 200.1917 202.5098 201.1117 
##     4281     4282     4283     4284     4285     4286     4287     4288 
## 202.2118 201.5282 201.9136 200.5747 198.8116 200.6517 200.4873 202.1399 
##     4289     4290     4291     4292     4293     4294     4295     4296 
## 198.4621 201.1683 201.9574 197.6680 200.8034 201.4870 201.7954 198.4621 
##     4297     4298     4299     4300     4301     4302     4303     4304 
## 201.6953 202.3762 197.7631 201.3611 198.9760 199.5030 200.4127 202.3531 
##     4305     4306     4307     4308     4309     4310     4311     4312 
## 197.3466 202.2427 201.0193 201.3380 200.4950 200.3638 202.1707 200.8496 
##     4313     4314     4315     4316     4317     4318     4319     4320 
## 202.2273 200.3638 201.9547 201.0836 197.3851 200.5747 201.2506 201.9316 
##     4321     4322     4323     4324     4325     4326     4327     4328 
## 202.0575 202.2992 199.4772 200.8368 202.3943 201.7826 197.2465 200.9473 
##     4329     4330     4331     4332     4333     4334     4335     4336 
## 200.3510 201.0886 201.5898 201.2660 198.7062 201.7903 200.7264 201.9728 
##     4337     4338     4339     4340     4341     4342     4343     4344 
## 201.7569 202.2554 201.0913 202.4301 202.4532 202.5972 202.4020 201.4716 
##     4345     4346     4347     4348     4349     4350     4351     4352 
## 202.2631 202.0729 202.2427 197.3928 201.6079 199.5107 202.5587 198.7293 
##     4353     4354     4355     4356     4357     4358     4359     4360 
## 202.1861 201.4331 201.8288 199.7471 197.2696 200.8599 201.7646 202.1399 
##     4361     4362     4363     4364     4365     4366     4367     4368 
## 200.9242 199.1920 201.6360 200.9473 200.0554 197.2388 201.6953 201.0089 
##     4369     4370     4371     4372     4373     4374     4375     4376 
## 197.2619 201.8057 200.7341 197.3543 200.1994 199.6289 197.3184 197.2696 
##     4377     4378     4379     4380     4381     4382     4383     4384 
## 197.2927 201.6541 201.0270 197.3004 200.6467 197.2619 202.4328 199.6597 
##     4385     4386     4387     4388     4389     4390     4391     4392 
## 201.8854 202.2992 199.5415 201.0193 201.7826 201.9059 200.3818 202.5664 
##     4393     4394     4395     4396     4397     4398     4399     4400 
## 202.4817 202.6357 197.3389 197.2388 200.2868 201.8031 200.9473 202.0575 
##     4401     4402     4403     4404     4405     4406     4407     4408 
## 201.9497 200.7930 197.3081 199.8756 197.6911 197.3004 198.5649 199.1843 
##     4409     4410     4411     4412     4413     4414     4415     4416 
## 199.1816 199.5388 202.5125 202.2992 201.8623 202.1553 199.8602 202.2427 
##     4417     4418     4419     4420     4421     4422     4423     4424 
## 200.7726 200.4153 202.2812 201.9497 200.0427 200.6621 202.2735 201.9290 
##     4425     4426     4427     4428     4429     4430     4431     4432 
## 202.0910 198.5649 199.6932 200.2945 200.7880 202.4020 197.3235 199.8010 
##     4433     4434     4435     4436     4437     4438     4439     4440 
## 201.5024 201.7569 201.7030 199.7290 202.3762 199.4026 201.9547 202.1037 
##     4441     4442     4443     4444     4445     4446     4447     4448 
## 198.8398 198.9375 199.0738 202.1938 202.5021 199.7521 197.3004 201.0886 
##     4449     4450     4451     4452     4453     4454     4455     4456 
## 197.3466 201.5975 200.6363 198.8193 200.8291 200.2610 200.4615 200.9011 
##     4457     4458     4459     4460     4461     4462     4463     4464 
## 200.5643 202.2427 200.2687 202.3197 201.1914 198.5418 197.2619 199.1843 
##     4465     4466     4467     4468     4469     4470     4471     4472 
## 199.1200 198.9837 200.9704 200.6363 199.5800 197.3158 202.0910 197.3004 
##     4473     4474     4475     4476     4477     4478     4479     4480 
## 202.1399 200.4873 197.3620 197.8940 197.3235 201.0270 197.3004 200.8034 
##     4481     4482     4483     4484     4485     4486     4487     4488 
## 202.2195 200.2098 200.4873 200.5824 197.2619 201.2583 197.3466 202.1784 
##     4489     4490     4491     4492     4493     4494     4495     4496 
## 201.4485 202.1399 200.3099 197.3235 201.3688 201.5744 201.5794 201.2249 
##     4497     4498     4499     4500     4501     4502     4503     4504 
## 201.8931 197.3466 200.3202 201.4612 197.2388 201.5282 201.9728 201.9008 
##     4505     4506     4507     4508     4509     4510     4511     4512 
## 200.5670 202.2581 201.4047 202.0113 200.7803 198.7678 197.5806 201.0501 
##     4513     4514     4515     4516     4517     4518     4519     4520 
## 201.3611 202.0602 202.2554 201.4716 201.8623 201.1633 198.4286 202.4328 
##     4521     4522     4523     4524     4525     4526     4527     4528 
## 198.6908 197.2773 201.2891 201.6618 202.3943 202.3120 200.6467 197.6807 
##     4529     4530     4531     4532     4533     4534     4535     4536 
## 202.3351 200.0169 198.2204 198.3028 202.5510 202.4636 197.2927 200.3484 
##     4537     4538     4539     4540     4541     4542     4543     4544 
## 198.3540 202.5356 200.2302 198.6369 199.3436 201.2711 199.4695 197.3004 
##     4545     4546     4547     4548     4549     4550     4551     4552 
## 198.8090 202.2273 200.4204 200.6363 201.6310 202.5406 201.9085 197.3004 
##     4553     4554     4555     4556     4557     4558     4559     4560 
## 201.7980 201.2737 201.4793 201.3123 202.4740 201.2942 197.2311 200.8007 
##     4561     4562     4563     4564     4565     4566     4567     4568 
## 202.4070 201.3739 202.0240 197.3389 197.3235 199.1277 201.6079 199.6339 
##     4569     4570     4571     4572     4573     4574     4575     4576 
## 202.0652 200.4153 201.8777 199.0480 200.6440 201.2172 201.8365 198.5880 
##     4577     4578     4579     4580     4581     4582     4583     4584 
## 202.3146 199.5107 202.0498 202.2477 199.8010 198.6496 202.1834 202.0910 
##     4585     4586     4587     4588     4589     4590     4591     4592 
## 201.8057 202.5329 201.5205 197.3543 200.0427 201.9497 201.7542 202.3659 
##     4593     4594     4595     4596     4597     4598     4599     4600 
## 200.5077 202.3736 200.6775 200.8342 197.2773 202.2554 201.4562 202.6126 
##     4601     4602     4603     4604     4605     4606     4607     4608 
## 202.4378 201.0990 200.2791 202.2015 201.8365 198.0841 199.5107 199.0068 
##     4609     4610     4611     4612     4613     4614     4615     4616 
## 201.0963 199.9630 201.9239 201.6079 201.7492 200.3638 197.2850 197.3620 
##     4617     4618     4619     4620     4621     4622     4623     4624 
## 202.5279 202.4740 198.7936 200.3125 201.8211 201.7826 197.6834 199.8756 
##     4625     4626     4627     4628     4629     4630     4631     4632 
## 202.1630 199.8730 202.1114 199.6366 201.7030 197.3851 202.0371 201.7415 
##     4633     4634     4635     4636     4637     4638     4639     4640 
## 201.6953 202.4097 202.3377 200.7957 199.8602 200.7776 202.6357 201.9574 
##     4641     4642     4643     4644     4645     4646     4647     4648 
## 202.3608 201.7234 199.9861 201.0474 201.6668 199.1689 200.9011 202.2246 
##     4649     4650     4651     4652     4653     4654     4655     4656 
## 202.3300 201.7492 200.8753 200.7776 201.2095 202.3069 198.3309 197.2311 
##     4657     4658     4659     4660     4661     4662     4663     4664 
## 201.7184 200.8265 198.5545 201.7415 202.4378 197.7708 201.4689 199.3256 
##     4665     4666     4667     4668     4669     4670     4671     4672 
## 199.0068 202.5048 197.8478 200.8676 197.2388 201.9497 197.3620 201.8288 
##     4673     4674     4675     4676     4677     4678     4679     4680 
## 202.5175 200.9215 199.4156 202.0036 202.3762 201.6876 197.8247 198.6677 
##     4681     4682     4683     4684     4685     4686     4687     4688 
## 202.5356 199.5492 201.1117 201.5898 201.2660 199.1662 199.6674 201.0270 
##     4689     4690     4691     4692     4693     4694     4695     4696 
## 197.2696 201.6310 197.2388 198.9606 197.3646 201.1221 197.2696 199.7163 
##     4697     4698     4699     4700     4701     4702     4703     4704 
## 201.9728 201.9574 200.7264 201.8442 198.6985 201.8623 202.1553 199.0326 
##     4705     4706     4707     4708     4709     4710     4711     4712 
## 202.2400 198.6523 202.4817 199.5954 202.2118 201.6079 201.4485 201.6618 
##     4713     4714     4715     4716     4717     4718     4719     4720 
## 201.8134 198.6292 200.0065 197.3851 202.2092 202.3377 201.3765 201.8750 
##     4721     4722     4723     4724     4725     4726     4727     4728 
## 201.1914 197.7554 200.9138 201.4562 202.1834 200.7495 198.6831 201.3045 
##     4729     4730     4731     4732     4733     4734     4735     4736 
## 200.4050 201.0166 197.3620 197.2773 201.8931 201.7980 202.4097 199.5157 
##     4737     4738     4739     4740     4741     4742     4743     4744 
## 197.3466 202.0498 201.0501 202.3839 202.0883 201.8339 200.0350 200.2714 
##     4745     4746     4747     4748     4749     4750     4751     4752 
## 202.0267 200.4384 200.0142 202.3300 200.8984 199.6828 201.6953 202.0525 
##     4753     4754     4755     4756     4757     4758     4759     4760 
## 197.2465 201.7492 197.3697 200.0273 200.6852 201.7903 199.5415 202.1938 
##     4761     4762     4763     4764     4765     4766     4767     4768 
## 198.9298 201.0578 197.3235 200.8265 198.5418 201.5436 199.7471 198.6342 
##     4769     4770     4771     4772     4773     4774     4775     4776 
## 197.3774 202.1064 201.8288 200.7930 200.7160 200.4461 201.2326 202.3762 
##     4777     4778     4779     4780     4781     4782     4783     4784 
## 198.2693 201.9574 201.8777 202.2992 199.8679 200.2329 200.7083 201.9497 
##     4785     4786     4787     4788     4789     4790     4791     4792 
## 202.4817 202.3916 202.1630 199.2151 201.3842 200.9627 199.7086 199.0172 
##     4793     4794     4795     4796     4797     4798     4799     4800 
## 200.9627 201.5282 199.1612 200.9935 202.1553 202.3146 201.4381 201.8493 
##     4801     4802     4803     4804     4805     4806     4807     4808 
## 201.7749 199.6058 201.1194 201.0039 201.6926 197.3312 197.2311 197.3466 
##     4809     4810     4811     4812     4813     4814     4815     4816 
## 200.1532 197.2927 197.2388 197.2542 202.5279 202.4740 201.9882 201.9136 
##     4817     4818     4819     4820     4821     4822     4823     4824 
## 197.7296 199.9064 202.2246 199.8191 201.6514 201.9624 202.3762 201.8057 
##     4825     4826     4827     4828     4829     4830     4831     4832 
## 202.4455 197.2311 200.4642 201.1991 199.6751 197.2542 197.3081 202.4405 
##     4833     4834     4835     4836     4837     4838     4839     4840 
## 200.6132 202.1064 199.0738 197.3774 199.8318 200.1532 201.5821 200.6594 
##     4841     4842     4843     4844     4845     4846     4847     4848 
## 201.1787 200.8881 201.5128 200.2894 201.4689 197.2773 201.5590 201.9624 
##     4849     4850     4851     4852     4853     4854     4855     4856 
## 199.2563 197.2311 201.5205 201.7492 198.9195 197.3774 200.8676 199.8345 
##     4857     4858     4859     4860     4861     4862     4863     4864 
## 200.9165 201.8108 198.4363 197.5806 201.0039 199.7136 202.1784 201.4947 
##     4865     4866     4867     4868     4869     4870     4871     4872 
## 201.9393 197.7115 201.0551 197.3312 198.6523 199.4900 201.5821 201.7465 
##     4873     4874     4875     4876     4877     4878     4879     4880 
## 200.7006 199.8114 201.7311 199.6185 201.1787 200.5154 198.9914 202.4174 
##     4881     4882     4883     4884     4885     4886     4887     4888 
## 197.3081 202.4482 202.4482 198.8501 198.4363 202.2735 202.2966 197.3081 
##     4889     4890     4891     4892     4893     4894     4895     4896 
## 201.9497 201.0836 199.0738 202.2504 200.1274 201.3585 200.0862 199.6905 
##     4897     4898     4899     4900     4901     4902     4903     4904 
## 202.4405 199.0661 197.3004 200.3253 202.0575 202.4740 201.7954 201.1864 
##     4905     4906     4907     4908     4909     4910     4911     4912 
## 201.4716 201.2583 201.7903 197.3620 201.9239 202.4944 200.0631 199.1535 
##     4913     4914     4915     4916     4917     4918     4919     4920 
## 201.6695 200.6363 200.0015 198.1742 200.2406 200.4950 198.3182 198.5495 
##     4921     4922     4923     4924     4925     4926     4927     4928 
## 202.4740 202.3377 199.5030 200.5308 202.1245 200.8573 199.4206 201.7107 
##     4929     4930     4931     4932     4933     4934     4935     4936 
## 202.3377 197.7554 201.3380 198.9787 200.2098 198.6342 200.5258 200.5104 
##     4937     4938     4939     4940     4941     4942     4943     4944 
## 199.3975 201.0578 197.3928 200.6132 202.2273 200.8496 197.3312 202.1630 
##     4945     4946     4947     4948     4949     4950     4951     4952 
## 197.2465 200.6594 201.3893 200.7880 200.3818 200.2175 199.2124 201.3123 
##     4953     4954     4955     4956     4957     4958     4959     4960 
## 202.2323 199.4206 200.4642 200.5231 197.2927 198.5468 201.7261 197.7554 
##     4961     4962     4963     4964     4965     4966     4967     4968 
## 201.4843 198.9221 199.1404 200.6286 197.3543 201.5282 202.0498 199.3487 
##     4969     4970     4971     4972     4973     4974     4975     4976 
## 198.5056 202.3505 197.3004 201.6002 197.2773 200.5258 197.2388 202.2812 
##     4977     4978     4979     4980     4981     4982     4983     4984 
## 200.2098 201.9624 197.2311 197.2927 201.9855 198.9041 201.1864 201.6514 
##     4985     4986     4987     4988     4989     4990     4991     4992 
## 201.8700 202.4070 197.6549 198.9991 201.5717 201.7261 197.3158 202.0448 
##     4993     4994     4995     4996     4997     4998     4999     5000 
## 197.3312 202.1630 197.3620 202.5433 201.8827 201.7980 197.3697 197.3081 
##     5001     5002     5003     5004     5005     5006     5007     5008 
## 199.7856 197.2850 202.1322 197.2850 200.8753 199.7805 200.9011 200.5951 
##     5009     5010     5011     5012     5013     5014     5015     5016 
## 201.8262 198.9683 201.5205 201.6514 201.8700 202.1707 200.5720 197.4725 
##     5017     5018     5019     5020     5021     5022     5023     5024 
## 202.3120 199.5030 202.2427 198.6677 202.2015 201.4331 202.4147 201.0193 
##     5025     5026     5027     5028     5029     5030     5031     5032 
## 202.0575 199.5311 200.8214 202.4559 200.0142 200.1428 201.5640 202.2323 
##     5033     5034     5035     5036     5037     5038     5039     5040 
## 197.3697 201.6618 201.4639 197.2388 201.6387 199.6262 201.2299 201.6464 
##     5041     5042     5043     5044     5045     5046     5047     5048 
## 199.7548 197.3697 197.2850 201.0578 201.3277 201.8519 200.7726 201.9882 
##     5049     5050     5051     5052     5053     5054     5055     5056 
## 202.3454 197.2311 202.0371 201.7800 199.8987 199.8164 198.9529 201.6953 
##     5057     5058     5059     5060     5061     5062     5063     5064 
## 201.7338 201.0474 201.3380 202.4971 202.5279 200.2945 199.8602 202.2992 
##     5065     5066     5067     5068     5069     5070     5071     5072 
## 200.4923 200.7726 198.9375 202.1322 199.6031 200.7264 201.8134 200.3176 
##     5073     5074     5075     5076     5077     5078     5079     5080 
## 202.5587 200.8676 201.0990 198.6419 201.5205 201.8623 200.0273 202.3943 
##     5081     5082     5083     5084     5085     5086     5087     5088 
## 201.7826 202.0525 198.7859 197.3543 202.1449 198.5572 199.8164 197.3620 
##     5089     5090     5091     5092     5093     5094     5095     5096 
## 201.0424 198.6831 202.3762 201.6591 199.5542 200.9088 201.6695 198.3901 
##     5097     5098     5099     5100     5101     5102     5103     5104 
## 201.0116 200.3176 200.3125 199.9553 199.1920 201.6310 198.1973 200.2945 
##     5105     5106     5107     5108     5109     5110     5111     5112 
## 200.5951 202.5895 202.3943 199.1739 197.2465 201.3919 202.0525 198.1049 
##     5113     5114     5115     5116     5117     5118     5119     5120 
## 199.7651 201.6618 199.5415 202.0756 200.4307 201.9701 198.9941 201.1787 
##     5121     5122     5123     5124     5125     5126     5127     5128 
## 201.8827 200.6671 199.5388 202.5406 202.4405 200.6390 197.3158 201.8288 
##     5129     5130     5131     5132     5133     5134     5135     5136 
## 202.5252 201.6876 202.3043 198.8552 198.8270 201.5282 201.7619 200.9550 
##     5137     5138     5139     5140     5141     5142     5143     5144 
## 201.8623 202.3608 202.3223 202.1630 199.1689 201.5359 197.2927 200.0708 
##     5145     5146     5147     5148     5149     5150     5151     5152 
## 199.7240 202.5252 199.6058 198.5391 201.8134 199.7471 202.0009 202.0036 
##     5153     5154     5155     5156     5157     5158     5159     5160 
## 202.3300 200.6544 197.2311 202.4378 201.0628 202.0190 197.2311 201.2583 
##     5161     5162     5163     5164     5165     5166     5167     5168 
## 201.8108 201.2403 202.5125 201.4485 201.3508 201.7749 197.3466 201.3431 
##     5169     5170     5171     5172     5173     5174     5175     5176 
## 201.1914 199.1354 200.8753 199.2228 202.4174 199.3487 198.5495 200.0554 
##     5177     5178     5179     5180     5181     5182     5183     5184 
## 202.2350 202.0910 200.6748 197.2927 201.4047 200.9446 200.8007 202.5510 
##     5185     5186     5187     5188     5189     5190     5191     5192 
## 201.4920 201.3173 199.0480 202.1988 199.5800 201.7542 199.9115 198.1742 
##     5193     5194     5195     5196     5197     5198     5199     5200 
## 202.1911 199.5773 201.6437 198.9118 201.7569 202.4609 197.3466 201.5409 
##     5201     5202     5203     5204     5205     5206     5207     5208 
## 201.3816 197.3004 202.0883 201.2376 200.9677 197.3389 201.9624 198.7601 
##     5209     5210     5211     5212     5213     5214     5215     5216 
## 202.5329 201.1502 202.5895 197.3543 200.3638 200.0554 199.3075 201.9059 
##     5217     5218     5219     5220     5221     5222     5223     5224 
## 200.6517 201.3508 201.6591 199.8961 200.9781 200.5489 201.6514 201.3096 
##     5225     5226     5227     5228     5229     5230     5231     5232 
## 201.9624 197.3081 201.6514 202.3659 197.3466 200.5951 200.4435 201.3739 
##     5233     5234     5235     5236     5237     5238     5239     5240 
## 197.3235 202.2554 197.8786 199.0942 199.5800 201.4535 197.3158 201.6591 
##     5241     5242     5243     5244     5245     5246     5247     5248 
## 199.3795 201.6926 197.3697 199.4283 200.3099 201.9778 197.3158 198.6496 
##     5249     5250     5251     5252     5253     5254     5255     5256 
## 202.1911 197.3620 202.1603 200.1043 201.9932 202.0806 197.3851 202.3043 
##     5257     5258     5259     5260     5261     5262     5263     5264 
## 197.3851 197.3774 201.6360 199.7367 201.5178 200.1351 201.2068 200.8830 
##     5265     5266     5267     5268     5269     5270     5271     5272 
## 200.1505 201.8827 202.3582 200.7133 201.4150 201.7954 202.6280 200.5566 
##     5273     5274     5275     5276     5277     5278     5279     5280 
## 197.3697 201.6360 202.4147 200.0708 202.0344 199.9834 201.7800 202.1141 
##     5281     5282     5283     5284     5285     5286     5287     5288 
## 197.3774 198.6985 201.7954 202.5406 197.3158 199.9988 200.3638 200.7622 
##     5289     5290     5291     5292     5293     5294     5295     5296 
## 201.5255 202.0009 202.1834 200.7314 202.4070 198.2924 201.8981 199.7213 
##     5297     5298     5299     5300     5301     5302     5303     5304 
## 201.0963 197.3774 202.5021 202.4224 201.7542 198.6265 202.2169 197.3081 
##     5305     5306     5307     5308     5309     5310     5311     5312 
## 199.7779 201.5717 199.2382 199.8422 200.9369 199.5619 201.1502 202.5741 
##     5313     5314     5315     5316     5317     5318     5319     5320 
## 197.3004 201.7003 197.3158 201.1991 200.3664 199.2767 202.0267 200.7391 
##     5321     5322     5323     5324     5325     5326     5327     5328 
## 200.8727 199.7933 197.3851 199.4900 197.3389 198.3155 201.3970 199.2201 
##     5329     5330     5331     5332     5333     5334     5335     5336 
## 200.4512 202.4224 201.6591 198.7524 197.3466 199.2613 200.0400 200.3099 
##     5337     5338     5339     5340     5341     5342     5343     5344 
## 201.4997 201.7646 201.6360 199.8653 200.1016 201.5871 200.9446 199.7779 
##     5345     5346     5347     5348     5349     5350     5351     5352 
## 197.3466 201.0474 202.2785 198.6496 202.2323 199.1173 200.7853 202.4378 
##     5353     5354     5355     5356     5357     5358     5359     5360 
## 200.1274 201.5178 197.3543 197.3466 201.9778 201.0012 202.3659 197.3081 
##     5361     5362     5363     5364     5365     5366     5367     5368 
## 202.0344 200.2868 201.6206 199.7213 200.5566 201.0551 202.2708 201.2634 
##     5369     5370     5371     5372     5373     5374     5375     5376 
## 197.3928 200.6363 202.0240 202.0960 198.5776 197.3312 198.6727 198.4825 
##     5377     5378     5379     5380     5381     5382     5383     5384 
## 202.6357 201.9290 200.5566 197.9891 201.6514 199.0788 202.2966 197.8632 
##     5385     5386     5387     5388     5389     5390     5391     5392 
## 202.0163 197.3235 202.1757 200.4127 199.0557 201.2557 198.6419 200.4923 
##     5393     5394     5395     5396     5397     5398     5399     5400 
## 200.9754 197.3158 202.0086 202.3428 200.9935 202.3762 198.5930 200.5077 
##     5401     5402     5403     5404     5405     5406     5407     5408 
## 200.5797 199.4900 202.2323 197.3235 201.3354 200.8881 202.0498 200.5231 
##     5409     5410     5411     5412     5413     5414     5415     5416 
## 202.3043 202.3993 198.6419 197.3620 202.1526 200.1736 202.1218 197.3235 
##     5417     5418     5419     5420     5421     5422     5423     5424 
## 202.5510 200.6028 202.5587 201.9213 202.2631 200.6748 199.0222 201.7800 
##     5425     5426     5427     5428     5429     5430     5431     5432 
## 202.5483 197.3928 199.9295 202.0729 201.4766 200.7622 200.7853 201.4124 
##     5433     5434     5435     5436     5437     5438     5439     5440 
## 198.2693 197.3697 200.5154 202.2400 199.7856 201.8750 197.3235 202.5329 
##     5441     5442     5443     5444     5445     5446     5447     5448 
## 199.8422 201.2711 198.7909 200.2610 198.7447 201.7542 201.5409 200.0477 
##     5449     5450     5451     5452     5453     5454     5455     5456 
## 201.4920 201.2376 200.9600 200.1428 202.5741 197.3774 201.9367 201.7542 
##     5457     5458     5459     5460     5461     5462     5463     5464 
## 202.4070 201.1991 197.3620 201.0732 202.3762 201.8339 201.7234 199.6493 
##     5465     5466     5467     5468     5469     5470     5471     5472 
## 197.3081 199.1431 202.5741 198.2385 199.4206 197.3158 201.0628 197.3620 
##     5473     5474     5475     5476     5477     5478     5479     5480 
## 197.3389 200.4050 199.8087 200.4076 199.5338 201.9882 201.3662 200.8496 
##     5481     5482     5483     5484     5485     5486     5487     5488 
## 200.6775 197.3620 197.2465 197.2542 197.3158 201.5409 201.7542 197.3466 
##     5489     5490     5491     5492     5493     5494     5495     5496 
## 199.6366 201.8854 198.6292 197.3620 202.3993 200.8291 202.2400 202.1784 
##     5497     5498     5499     5500     5501     5502     5503     5504 
## 202.3454 198.9580 202.4224 201.9547 197.3620 199.0403 201.6849 197.3081 
##     5505     5506     5507     5508     5509     5510     5511     5512 
## 202.4070 199.8884 198.9118 202.2427 201.0501 197.3466 199.8114 197.3620 
##     5513     5514     5515     5516     5517     5518     5519     5520 
## 201.2480 200.2071 197.2619 201.3173 202.4301 202.5021 199.7009 201.8827 
##     5521     5522     5523     5524     5525     5526     5527     5528 
## 199.7059 199.9861 200.8650 200.3895 199.9526 200.3484 200.7160 201.7234 
##     5529     5530     5531     5532     5533     5534     5535     5536 
## 200.3176 202.6126 201.8416 202.0448 197.2850 198.9683 202.3993 201.2376 
##     5537     5538     5539     5540     5541     5542     5543     5544 
## 201.5205 202.3993 200.6979 202.2658 202.0883 197.3312 199.2794 201.0551 
##     5545     5546     5547     5548     5549     5550     5551     5552 
## 201.8031 197.3928 202.5510 202.5433 201.8442 201.2403 198.6111 201.8288 
##     5553     5554     5555     5556     5557     5558     5559     5560 
## 202.2323 200.6517 198.6958 202.1603 201.8211 200.0812 201.2145 201.7749 
##     5561     5562     5563     5564     5565     5566     5567     5568 
## 200.8522 200.1351 199.3179 201.2557 197.3389 202.3428 197.2465 199.9757 
##     5569     5570     5571     5572     5573     5574     5575     5576 
## 200.4384 202.1114 199.5003 202.1861 197.3774 198.6804 201.5332 202.5175 
##     5577     5578     5579     5580     5581     5582     5583     5584 
## 200.1582 201.2891 201.3816 202.0421 198.5649 200.9011 202.2427 200.3253 
##     5585     5586     5587     5588     5589     5590     5591     5592 
## 197.2696 202.2735 202.0883 199.3564 197.3697 201.8416 200.3638 197.7631 
##     5593     5594     5595     5596     5597     5598     5599     5600 
## 199.1096 200.3099 201.6437 199.5877 202.4455 197.3466 200.3741 200.8830 
##     5601     5602     5603     5604     5605     5606     5607     5608 
## 197.3158 200.5181 200.4846 198.5468 202.3916 200.6028 201.5409 200.9704 
##     5609     5610     5611     5612     5613     5614     5615     5616 
## 197.2619 202.1707 199.0788 201.5590 201.6129 198.3747 202.0086 201.2326 
##     5617     5618     5619     5620     5621     5622     5623     5624 
## 201.2299 202.1037 199.1508 201.5667 201.3739 201.5486 201.5513 200.7803 
##     5625     5626     5627     5628     5629     5630     5631     5632 
## 200.5335 202.0729 199.2767 199.9399 200.1016 202.1861 200.9627 198.0406 
##     5633     5634     5635     5636     5637     5638     5639     5640 
## 201.9008 202.1114 200.3895 197.3774 202.3531 200.6105 200.3253 200.0400 
##     5641     5642     5643     5644     5645     5646     5647     5648 
## 201.1914 199.1970 201.1040 200.5258 200.1609 198.7832 197.3851 197.3004 
##     5649     5650     5651     5652     5653     5654     5655     5656 
## 201.2968 200.0812 202.5356 197.2927 202.0267 201.9393 200.5231 199.8499 
##     5657     5658     5659     5660     5661     5662     5663     5664 
## 198.1588 202.1218 199.4926 201.5282 202.2889 201.6876 201.2326 199.0403 
##     5665     5666     5667     5668     5669     5670     5671     5672 
## 201.2068 199.5877 197.2696 201.0809 201.6464 200.9242 201.6052 202.4301 
##     5673     5674     5675     5676 
## 197.3389 200.9369 200.7083 202.1218
par(mfrow=c(2,2))
plot(model)

Interpretation

Residuals vs Fitted Plot: This plot is used to check the assumption of linearity and homoscedasticity (constant variance) of residuals. Ideally, the residuals should be randomly scattered around the horizontal line at 0, indicating a linear relationship and equal variance. In the provided plot, the residuals seem to be randomly scattered without any clear pattern, which is a good sign. However, there seems to be a slight ‘fan’ shape (spread increasing with fitted values), which could suggest possible heteroscedasticity.

Normal Q-Q Plot (Quantile-Quantile Plot): This plot is used to assess whether the residuals are normally distributed. If the residuals are normally distributed, the points should fall approximately along the reference line. In the plot provided, the points largely follow the line, suggesting that the residuals are approximately normally distributed. There are some deviations at the tails, but this is quite common even with normal data.

Scale-Location Plot: Also known as a Spread-Location plot, it is used to check the homoscedasticity assumption. The plot shows how residuals spread along the range of predictors. A horizontal line with equally (randomly) spread points is an indication of homoscedasticity. The provided plot shows some signs of increasing spread with the fitted values, which might indicate potential heteroscedasticity.

Residuals vs Leverage Plot: This plot helps to identify influential cases (outliers that have an undue influence on the model). The Cook’s distance lines help to determine whether there are any influential outliers in the data. In this plot, while there are a few points outside the Cook’s distance lines, indicating potential influencers, most of the data points are clustered in the center, suggesting that there are no problematic influential observations.

Key Takeaways:

The model appears to capture a linear relationship, as indicated by the random scatter of points in the Residuals vs Fitted plot. The residuals are approximately normally distributed, but with some potential outliers, as seen in the Q-Q plot. There may be some concerns regarding heteroscedasticity, as suggested by the Scale-Location plot. A few data points may have leverage on the model, but overall, there do not appear to be any highly influential outliers as per the Residuals vs Leverage plot. Additional investigation may be warranted for the slight signs of heteroscedasticity and the potential outliers or influential points identified. These could include transformations of the dependent variable, adding other explanatory variables to the model, or considering robust regression techniques.

AIC(model)
## [1] 40892.67
BIC(model)
## [1] 40919.25

Key Takeaways from the Analysis

Model Diagnostics:

The diagnostic plots for the linear model (residuals, leverage, etc.) are crucial for understanding the model’s assumptions and validity. These plots can reveal issues like heteroscedasticity, non-linearity, or influential outliers. This analysis provides valuable insights into the physical attributes of NBA players, their performance, and how these aspects have evolved over time. It also highlights the potential influences on a player’s physical attributes, helping to inform decisions in player drafting and team building.