February 22, 2022
Add labels, make notes, and work with models
The gss_sm data and summary
- The
socvizpackage includes thegss_smdata frame.gss_smis a dataset containing an extract from the 2016 General Social Survey.
- Summarize the relative frequencies of educational degrees by race.
- The sum of the relative frequencies of educational degrees is one for each race.
library(tidyverse) library(socviz) library(gapminder) library(skimr) library(ggrepel) library(ggthemes) theme_set(theme_minimal()) view(gss_sm)
The gss_sm data and summary
## # A tibble: 18 × 4 ## # Groups: race [3] ## race degree N pct ## <fct> <fct> <int> <dbl> ## 1 White Lt High School 197 9 ## 2 White High School 1057 50 ## 3 White Junior College 166 8 ## 4 White Bachelor 426 20 ## 5 White Graduate 250 12 ## 6 White <NA> 4 0 ## 7 Black Lt High School 60 12 ## 8 Black High School 292 60 ## 9 Black Junior College 33 7 ## 10 Black Bachelor 71 14 ## 11 Black Graduate 31 6 ## 12 Black <NA> 3 1 ## 13 Other Lt High School 71 26 ## 14 Other High School 112 40 ## 15 Other Junior College 17 6 ## 16 Other Bachelor 39 14 ## 17 Other Graduate 37 13 ## 18 Other <NA> 1 0
The organdata data
- The
socvizpackage includes theorgandatadata frame.organdatacontains a little more than a decade’s worth of information on the donation of organs for transplants in seventeen OECD countries.
library(tidyverse) library(socviz) library(skimr) library(ggrepel) theme_set(theme_minimal()) ?organdata glimpse(organdata)
## Rows: 238 ## Columns: 21 ## $ country <chr> "Australia", "Australia", "Australia", "Australia", "… ## $ year <date> NA, 1991-01-01, 1992-01-01, 1993-01-01, 1994-01-01, … ## $ donors <dbl> NA, 12.09, 12.35, 12.51, 10.25, 10.18, 10.59, 10.26, … ## $ pop <int> 17065, 17284, 17495, 17667, 17855, 18072, 18311, 1851… ## $ pop_dens <dbl> 0.2204433, 0.2232723, 0.2259980, 0.2282198, 0.2306484… ## $ gdp <int> 16774, 17171, 17914, 18883, 19849, 21079, 21923, 2296… ## $ gdp_lag <int> 16591, 16774, 17171, 17914, 18883, 19849, 21079, 2192… ## $ health <dbl> 1300, 1379, 1455, 1540, 1626, 1737, 1846, 1948, 2077,… ## $ health_lag <dbl> 1224, 1300, 1379, 1455, 1540, 1626, 1737, 1846, 1948,… ## $ pubhealth <dbl> 4.8, 5.4, 5.4, 5.4, 5.4, 5.5, 5.6, 5.7, 5.9, 6.1, 6.2… ## $ roads <dbl> 136.59537, 122.25179, 112.83224, 110.54508, 107.98096… ## $ cerebvas <int> 682, 647, 630, 611, 631, 592, 576, 525, 516, 493, 474… ## $ assault <int> 21, 19, 17, 18, 17, 16, 17, 17, 16, 15, 16, 15, 14, N… ## $ external <int> 444, 425, 406, 376, 387, 371, 395, 385, 410, 409, 393… ## $ txp_pop <dbl> 0.9375916, 0.9257116, 0.9145470, 0.9056433, 0.8961075… ## $ world <chr> "Liberal", "Liberal", "Liberal", "Liberal", "Liberal"… ## $ opt <chr> "In", "In", "In", "In", "In", "In", "In", "In", "In",… ## $ consent_law <chr> "Informed", "Informed", "Informed", "Informed", "Info… ## $ consent_practice <chr> "Informed", "Informed", "Informed", "Informed", "Info… ## $ consistent <chr> "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes… ## $ ccode <chr> "Oz", "Oz", "Oz", "Oz", "Oz", "Oz", "Oz", "Oz", "Oz",…
skim(organdata)
| Name | organdata |
| Number of rows | 238 |
| Number of columns | 21 |
| _______________________ | |
| Column type frequency: | |
| character | 7 |
| Date | 1 |
| numeric | 13 |
| ________________________ | |
| Group variables | None |
Variable type: character
| skim_variable | n_missing | complete_rate | min | max | empty | n_unique | whitespace |
|---|---|---|---|---|---|---|---|
| country | 0 | 1.00 | 5 | 14 | 0 | 17 | 0 |
| world | 14 | 0.94 | 6 | 11 | 0 | 3 | 0 |
| opt | 28 | 0.88 | 2 | 3 | 0 | 2 | 0 |
| consent_law | 0 | 1.00 | 8 | 8 | 0 | 2 | 0 |
| consent_practice | 0 | 1.00 | 8 | 8 | 0 | 2 | 0 |
| consistent | 0 | 1.00 | 2 | 3 | 0 | 2 | 0 |
| ccode | 0 | 1.00 | 2 | 4 | 0 | 17 | 0 |
Variable type: Date
| skim_variable | n_missing | complete_rate | min | max | median | n_unique |
|---|---|---|---|---|---|---|
| year | 34 | 0.86 | 1991-01-01 | 2002-01-01 | 1996-07-02 | 12 |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| donors | 34 | 0.86 | 16.48 | 5.11 | 5.20 | 13.00 | 15.10 | 19.60 | 33.90 | ▁▇▅▂▁ |
| pop | 17 | 0.93 | 39921.29 | 62219.22 | 3514.00 | 6938.00 | 15531.00 | 57301.00 | 288369.00 | ▇▁▁▁▁ |
| pop_dens | 17 | 0.93 | 12.00 | 11.09 | 0.22 | 1.94 | 9.49 | 19.11 | 38.89 | ▇▃▃▂▁ |
| gdp | 17 | 0.93 | 22986.18 | 4665.92 | 12917.00 | 19546.00 | 22756.00 | 26180.00 | 36554.00 | ▂▇▇▃▁ |
| gdp_lag | 0 | 1.00 | 22574.92 | 4790.71 | 11434.00 | 19034.25 | 22158.00 | 25886.50 | 36554.00 | ▂▇▇▃▁ |
| health | 0 | 1.00 | 2073.75 | 733.59 | 791.00 | 1581.00 | 1956.00 | 2407.50 | 5665.00 | ▆▇▂▁▁ |
| health_lag | 0 | 1.00 | 1972.99 | 699.24 | 727.00 | 1542.00 | 1850.50 | 2290.25 | 5267.00 | ▆▇▂▁▁ |
| pubhealth | 21 | 0.91 | 6.19 | 0.92 | 4.30 | 5.50 | 6.00 | 6.90 | 8.80 | ▂▇▅▃▁ |
| roads | 17 | 0.93 | 113.04 | 36.33 | 58.21 | 83.46 | 111.22 | 139.57 | 232.48 | ▇▇▆▂▁ |
| cerebvas | 17 | 0.93 | 610.80 | 144.45 | 300.00 | 500.00 | 604.00 | 698.00 | 957.00 | ▂▅▇▃▂ |
| assault | 17 | 0.93 | 16.53 | 17.33 | 4.00 | 9.00 | 11.00 | 16.00 | 103.00 | ▇▁▁▁▁ |
| external | 17 | 0.93 | 450.06 | 118.19 | 258.00 | 367.00 | 421.00 | 534.00 | 853.00 | ▆▇▅▁▁ |
| txp_pop | 17 | 0.93 | 0.72 | 0.20 | 0.22 | 0.63 | 0.71 | 0.83 | 1.12 | ▁▂▇▃▃ |
view(organdata)
Continuous variables by group or category
What we would like to do is apply the
mean()andsd()functions to every numerical variable inorgandata, but only the numerical ones.summarize_if()examines each column in our data and applies a test to it.summarize_if()only summarizes if the test is passed, that is, if it returns a value ofTRUE.
Continuous variables by group or category
by_country <- organdata %>% group_by(consent_law, country) %>%
summarize_if(is.numeric, funs(mean, sd), na.rm = TRUE) %>%
ungroup()
by_country
## # A tibble: 17 × 28 ## consent_law country donors_mean pop_mean pop_dens_mean gdp_mean gdp_lag_mean ## <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> ## 1 Informed Austral… 10.6 18318. 0.237 22179. 21779. ## 2 Informed Canada 14.0 29608. 0.297 23711. 23353. ## 3 Informed Denmark 13.1 5257. 12.2 23722. 23275 ## 4 Informed Germany 13.0 80255. 22.5 22163. 21938. ## 5 Informed Ireland 19.8 3674. 5.23 20824. 20154. ## 6 Informed Netherl… 13.7 15548. 37.4 23013. 22554. ## 7 Informed United … 13.5 58187. 24.0 21359. 20962. ## 8 Informed United … 20.0 269330. 2.80 29212. 28699. ## 9 Presumed Austria 23.5 7927. 9.45 23876. 23415. ## 10 Presumed Belgium 21.9 10153. 30.7 22500. 22096. ## 11 Presumed Finland 18.4 5112. 1.51 21019. 20763 ## 12 Presumed France 16.8 58056. 10.5 22603. 22211. ## 13 Presumed Italy 11.1 57360. 19.0 21554. 21195. ## 14 Presumed Norway 15.4 4386. 1.35 26448. 25769. ## 15 Presumed Spain 28.1 39666. 7.84 16933 16584. ## 16 Presumed Sweden 13.1 8789. 1.95 22415. 22094 ## 17 Presumed Switzer… 14.2 7037. 17.0 27233 26931. ## # … with 21 more variables: health_mean <dbl>, health_lag_mean <dbl>, ## # pubhealth_mean <dbl>, roads_mean <dbl>, cerebvas_mean <dbl>, ## # assault_mean <dbl>, external_mean <dbl>, txp_pop_mean <dbl>, ## # donors_sd <dbl>, pop_sd <dbl>, pop_dens_sd <dbl>, gdp_sd <dbl>, ## # gdp_lag_sd <dbl>, health_sd <dbl>, health_lag_sd <dbl>, pubhealth_sd <dbl>, ## # roads_sd <dbl>, cerebvas_sd <dbl>, assault_sd <dbl>, external_sd <dbl>, ## # txp_pop_sd <dbl>
Cleveland dotplot
p <- ggplot(data = by_country,
mapping = aes(x = donors_mean, y = reorder(country, donors_mean),
color = consent_law))
p + geom_point(size=3) +
labs(x = "Donor Procurement Rate",
y = "", color = "Consent Law") +
theme(legend.position="top")
- Cleveland dotplot is a simple and extremely effective method of presenting data that is usually better than either a bar chart or a table.
Cleveland dotplot
Plot text directly
p_title <- "Presidential Elections: Popular & Electoral College Margins"
p_subtitle <- "1824-2016"
p_caption <- "Data for 2016 are provisional."
x_label <- "Winner's share of Popular Vote"
y_label <- "Winner's share of Electoral College Votes"
p <- ggplot(elections_historic, aes(x = popular_pct, y = ec_pct, label = winner_label))
p + geom_hline(yintercept = 0.5, size = 1.4, color = "gray80") +
geom_vline(xintercept = 0.5, size = 1.4, color = "gray80") +
geom_point() + geom_text_repel() +
scale_x_continuous(labels = scales::percent) +
scale_y_continuous(labels = scales::percent) +
labs(x = x_label, y = y_label, title = p_title, subtitle = p_subtitle,
caption = p_caption)
geom_hline()andgeom_vline()to make the lines.geom_text_repel()makes sure the labels do not overlap with each other, or obscure other points.
Plot text directly
Label outliers
p <- ggplot(data = by_country,
mapping = aes(x = gdp_mean, y = health_mean))
p + geom_point() +
geom_text_repel(data = subset(by_country, gdp_mean > 25000),
mapping = aes(label = country))
- Sometimes we want to pick out some points of interest in the data without labeling every single item.
- We do this using the
subset()function.
- We do this using the
Label outliers
Label outliers
p + geom_point() +
geom_text_repel(data = subset(by_country,
gdp_mean > 25000 | health_mean < 1500 |
country %in% "Belgium"),
mapping = aes(label = country))
Label outliers
Label outliers
organdata$ind <- organdata$ccode %in% c("Ita", "Spa") &
organdata$year > 1998
p <- ggplot(data = organdata,
mapping = aes(x = roads,
y = donors, color = ind))
p + geom_point() +
geom_text_repel(data = subset(organdata, ind),
mapping = aes(label = ccode)) +
guides(label = FALSE, color = FALSE)
Label outliers
Write and draw in the plot area
p <- ggplot(data = organdata, mapping = aes(x = roads, y = donors))
p + geom_point() + annotate(geom = "text", x = 91, y = 33,
label = "A surprisingly high \n recovery rate.",
hjust = 0)
- Sometimes we want to annotate the figure directly.
- We use
annotate()to point out something important that is not mapped to a variable.
- We use
Write and draw in the plot area
Write and draw in the plot area
p <- ggplot(data = organdata,
mapping = aes(x = roads, y = donors))
p + geom_point() +
annotate(geom = "rect", xmin = 125, xmax = 155,
ymin = 30, ymax = 35, fill = "red", alpha = 0.2) +
annotate(geom = "text", x = 157, y = 33,
label = "A surprisingly high \n recovery rate.", hjust = 0)
- We can use
annotate()to draw rectangles, line segments, and arrows.
Write and draw in the plot area
Understanding scales, guides, and themes
If you want to adjust how that scale is marked or graduated, then you use a
scale_function.- \(\color{green}{\text{scale}}\)_\(\color{orange}{\text{<MAPPING>}}\)_\(\color{orange}{\text{<KIND>}}\)()
The
guides()function allows for adjustments to a legend or key to help the reader interpret the graph.- Making the legend disappear
- Adjusting the arrangement of the key in legends and colorbars.
The
theme()function allows for adjustments to cosmetic features:- Background color
- Typeface used for labels
- Placement of the legend
Understanding scales, guides, and themes
p <- ggplot(data = organdata,
mapping = aes(x = roads,
y = donors,
color = world))
p + geom_point()
- The
xandyscales are both continuous. - The
colormapping also has a scale:- The
worldmeasure is an unordered categorical variable, so its scale is discrete.
- The
- Mappings like
color,fill,shape, andsizehave scales that we might want to customize or adjust.- If we want to adjust them, we use one of the
scale_functions.
- If we want to adjust them, we use one of the
Understanding scales, guides, and themes
Understanding scales, guides, and themes
p <- ggplot(data = organdata,
mapping = aes(x = roads,
y = donors,
color = world))
p + geom_point() +
scale_x_log10() +
scale_y_continuous(breaks = c(5, 15, 25),
labels = c("Five", "Fifteen", "Twenty Five"))
- We may end up with a lot of individual
scale_functions:scale_x_continuous()controlsxscales for continuous variables.scale_y_discrete()adjustsyscales for discrete variables.scale_x_log10()transforms anxmapping to a base 10 log scale.
- If you want to adjust the labels or tick marks on a scale, you need to know which mapping it is for and what sort of scale it is.
Understanding scales, guides, and themes
Understanding scales, guides, and themes
p <- ggplot(data = organdata,
mapping = aes(x = roads,
y = donors,
color = world))
p + geom_point() +
scale_color_discrete(labels =
c("Corporatist", "Liberal",
"Social Democratic", "Unclassified")) +
labs(x = "Road Deaths",
y = "Donor Procurement",
color = "Welfare State")
When working with a scale that produces a legend, we can also use appropriate
scale_functions to specify the labels in the key.To change the title of the legend, however, we use the
labs()function, which lets us label all the mappings.
Understanding scales, guides, and themes
Understanding scales, guides, and themes
p <- ggplot(data = organdata,
mapping = aes(x = roads,
y = donors,
color = world))
p + geom_point() +
scale_color_discrete(labels =
c("Corporatist", "Liberal",
"Social Democratic", "Unclassified")) +
labs(x = "Road Deaths",
y = "Donor Procurement",
color = "Welfare State") +
theme(legend.position = "top")
Adding
+ theme(legend.position = "top")will move the legend as instructedAdding
+ guides(color = "none")make the legend disappear altogether here.
Understanding scales, guides, and themes
gapminder data
- The
gapminderpackage include thegapminderdata frame.
gapminder
## # A tibble: 1,704 × 6 ## country continent year lifeExp pop gdpPercap ## <fct> <fct> <int> <dbl> <int> <dbl> ## 1 Afghanistan Asia 1952 28.8 8425333 779. ## 2 Afghanistan Asia 1957 30.3 9240934 821. ## 3 Afghanistan Asia 1962 32.0 10267083 853. ## 4 Afghanistan Asia 1967 34.0 11537966 836. ## 5 Afghanistan Asia 1972 36.1 13079460 740. ## 6 Afghanistan Asia 1977 38.4 14880372 786. ## 7 Afghanistan Asia 1982 39.9 12881816 978. ## 8 Afghanistan Asia 1987 40.8 13867957 852. ## 9 Afghanistan Asia 1992 41.7 16317921 649. ## 10 Afghanistan Asia 1997 41.8 22227415 635. ## # … with 1,694 more rows
skim(gapminder)
| Name | gapminder |
| Number of rows | 1704 |
| Number of columns | 6 |
| _______________________ | |
| Column type frequency: | |
| factor | 2 |
| numeric | 4 |
| ________________________ | |
| Group variables | None |
Variable type: factor
| skim_variable | n_missing | complete_rate | ordered | n_unique | top_counts |
|---|---|---|---|---|---|
| country | 0 | 1 | FALSE | 142 | Afg: 12, Alb: 12, Alg: 12, Ang: 12 |
| continent | 0 | 1 | FALSE | 5 | Afr: 624, Asi: 396, Eur: 360, Ame: 300 |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| year | 0 | 1 | 1979.50 | 17.27 | 1952.00 | 1965.75 | 1979.50 | 1993.25 | 2007.0 | ▇▅▅▅▇ |
| lifeExp | 0 | 1 | 59.47 | 12.92 | 23.60 | 48.20 | 60.71 | 70.85 | 82.6 | ▁▆▇▇▇ |
| pop | 0 | 1 | 29601212.32 | 106157896.74 | 60011.00 | 2793664.00 | 7023595.50 | 19585221.75 | 1318683096.0 | ▇▁▁▁▁ |
| gdpPercap | 0 | 1 | 7215.33 | 9857.45 | 241.17 | 1202.06 | 3531.85 | 9325.46 | 113523.1 | ▇▁▁▁▁ |
str(gapminder)
## tibble [1,704 × 6] (S3: tbl_df/tbl/data.frame) ## $ country : Factor w/ 142 levels "Afghanistan",..: 1 1 1 1 1 1 1 1 1 1 ... ## $ continent: Factor w/ 5 levels "Africa","Americas",..: 3 3 3 3 3 3 3 3 3 3 ... ## $ year : int [1:1704] 1952 1957 1962 1967 1972 1977 1982 1987 1992 1997 ... ## $ lifeExp : num [1:1704] 28.8 30.3 32 34 36.1 ... ## $ pop : int [1:1704] 8425333 9240934 10267083 11537966 13079460 14880372 12881816 13867957 16317921 22227415 ... ## $ gdpPercap: num [1:1704] 779 821 853 836 740 ...
- We can use the
str()function to learn more about the internal structure of any object.
Work with models
- Let us consider the linear regression of
lifeExpongdpPercap,pop, andcontinent.
out <- lm(formula = lifeExp ~ gdpPercap + pop + continent,
data = gapminder)
summary(out)
## ## Call: ## lm(formula = lifeExp ~ gdpPercap + pop + continent, data = gapminder) ## ## Residuals: ## Min 1Q Median 3Q Max ## -49.161 -4.486 0.297 5.110 25.175 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 4.781e+01 3.395e-01 140.819 < 2e-16 *** ## gdpPercap 4.495e-04 2.346e-05 19.158 < 2e-16 *** ## pop 6.570e-09 1.975e-09 3.326 0.000901 *** ## continentAmericas 1.348e+01 6.000e-01 22.458 < 2e-16 *** ## continentAsia 8.193e+00 5.712e-01 14.342 < 2e-16 *** ## continentEurope 1.747e+01 6.246e-01 27.973 < 2e-16 *** ## continentOceania 1.808e+01 1.782e+00 10.146 < 2e-16 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 8.365 on 1697 degrees of freedom ## Multiple R-squared: 0.5821, Adjusted R-squared: 0.5806 ## F-statistic: 393.9 on 6 and 1697 DF, p-value: < 2.2e-16
str(out)
## List of 13 ## $ coefficients : Named num [1:7] 4.78e+01 4.50e-04 6.57e-09 1.35e+01 8.19 ... ## ..- attr(*, "names")= chr [1:7] "(Intercept)" "gdpPercap" "pop" "continentAmericas" ... ## $ residuals : Named num [1:1704] -27.6 -26.1 -24.5 -22.4 -20.3 ... ## ..- attr(*, "names")= chr [1:1704] "1" "2" "3" "4" ... ## $ effects : Named num [1:1704] -2455.1 311.1 42.6 101.1 -17.2 ... ## ..- attr(*, "names")= chr [1:1704] "(Intercept)" "gdpPercap" "pop" "continentAmericas" ... ## $ rank : int 7 ## $ fitted.values: Named num [1:1704] 56.4 56.4 56.5 56.5 56.4 ... ## ..- attr(*, "names")= chr [1:1704] "1" "2" "3" "4" ... ## $ assign : int [1:7] 0 1 2 3 3 3 3 ## $ qr :List of 5 ## ..$ qr : num [1:1704, 1:7] -41.2795 0.0242 0.0242 0.0242 0.0242 ... ## .. ..- attr(*, "dimnames")=List of 2 ## .. .. ..$ : chr [1:1704] "1" "2" "3" "4" ... ## .. .. ..$ : chr [1:7] "(Intercept)" "gdpPercap" "pop" "continentAmericas" ... ## .. ..- attr(*, "assign")= int [1:7] 0 1 2 3 3 3 3 ## .. ..- attr(*, "contrasts")=List of 1 ## .. .. ..$ continent: chr "contr.treatment" ## ..$ qraux: num [1:7] 1.02 1.02 1 1.01 1.04 ... ## ..$ pivot: int [1:7] 1 2 3 4 5 6 7 ## ..$ tol : num 1e-07 ## ..$ rank : int 7 ## ..- attr(*, "class")= chr "qr" ## $ df.residual : int 1697 ## $ contrasts :List of 1 ## ..$ continent: chr "contr.treatment" ## $ xlevels :List of 1 ## ..$ continent: chr [1:5] "Africa" "Americas" "Asia" "Europe" ... ## $ call : language lm(formula = lifeExp ~ gdpPercap + pop + continent, data = gapminder) ## $ terms :Classes 'terms', 'formula' language lifeExp ~ gdpPercap + pop + continent ## .. ..- attr(*, "variables")= language list(lifeExp, gdpPercap, pop, continent) ## .. ..- attr(*, "factors")= int [1:4, 1:3] 0 1 0 0 0 0 1 0 0 0 ... ## .. .. ..- attr(*, "dimnames")=List of 2 ## .. .. .. ..$ : chr [1:4] "lifeExp" "gdpPercap" "pop" "continent" ## .. .. .. ..$ : chr [1:3] "gdpPercap" "pop" "continent" ## .. ..- attr(*, "term.labels")= chr [1:3] "gdpPercap" "pop" "continent" ## .. ..- attr(*, "order")= int [1:3] 1 1 1 ## .. ..- attr(*, "intercept")= int 1 ## .. ..- attr(*, "response")= int 1 ## .. ..- attr(*, ".Environment")=<environment: R_GlobalEnv> ## .. ..- attr(*, "predvars")= language list(lifeExp, gdpPercap, pop, continent) ## .. ..- attr(*, "dataClasses")= Named chr [1:4] "numeric" "numeric" "numeric" "factor" ## .. .. ..- attr(*, "names")= chr [1:4] "lifeExp" "gdpPercap" "pop" "continent" ## $ model :'data.frame': 1704 obs. of 4 variables: ## ..$ lifeExp : num [1:1704] 28.8 30.3 32 34 36.1 ... ## ..$ gdpPercap: num [1:1704] 779 821 853 836 740 ... ## ..$ pop : int [1:1704] 8425333 9240934 10267083 11537966 13079460 14880372 12881816 13867957 16317921 22227415 ... ## ..$ continent: Factor w/ 5 levels "Africa","Americas",..: 3 3 3 3 3 3 3 3 3 3 ... ## ..- attr(*, "terms")=Classes 'terms', 'formula' language lifeExp ~ gdpPercap + pop + continent ## .. .. ..- attr(*, "variables")= language list(lifeExp, gdpPercap, pop, continent) ## .. .. ..- attr(*, "factors")= int [1:4, 1:3] 0 1 0 0 0 0 1 0 0 0 ... ## .. .. .. ..- attr(*, "dimnames")=List of 2 ## .. .. .. .. ..$ : chr [1:4] "lifeExp" "gdpPercap" "pop" "continent" ## .. .. .. .. ..$ : chr [1:3] "gdpPercap" "pop" "continent" ## .. .. ..- attr(*, "term.labels")= chr [1:3] "gdpPercap" "pop" "continent" ## .. .. ..- attr(*, "order")= int [1:3] 1 1 1 ## .. .. ..- attr(*, "intercept")= int 1 ## .. .. ..- attr(*, "response")= int 1 ## .. .. ..- attr(*, ".Environment")=<environment: R_GlobalEnv> ## .. .. ..- attr(*, "predvars")= language list(lifeExp, gdpPercap, pop, continent) ## .. .. ..- attr(*, "dataClasses")= Named chr [1:4] "numeric" "numeric" "numeric" "factor" ## .. .. .. ..- attr(*, "names")= chr [1:4] "lifeExp" "gdpPercap" "pop" "continent" ## - attr(*, "class")= chr "lm"
out$coefficients
## (Intercept) gdpPercap pop continentAmericas ## 4.781408e+01 4.495058e-04 6.569823e-09 1.347594e+01 ## continentAsia continentEurope continentOceania ## 8.192632e+00 1.747269e+01 1.808330e+01
out$residuals
## 1 2 3 4 5 ## -27.611428453 -26.104399813 -24.460636949 -22.438388173 -20.337265855 ## 6 7 8 9 10 ## -18.019834243 -16.676963374 -15.658977259 -14.731798900 -14.675330131 ## 11 12 13 14 15 ## -14.370390444 -12.826300978 -10.784882304 -6.889539586 -1.517781716 ## 16 17 18 19 20 ## -0.320530593 0.898955244 2.038639144 3.482862209 5.012352638 ## 21 22 23 24 25 ## 5.149761523 6.205410711 8.271558758 8.443844996 -5.898886545 ## 26 27 28 29 30 ## -3.551355709 -0.729959584 2.049545857 4.726814372 7.879970085 ## 31 32 33 34 35 ## 10.839820771 15.278337257 17.499181113 18.990511833 20.597365990 ## 36 37 38 39 40 ## 21.470488738 -19.409417128 -17.565727037 -15.764848964 -14.346073141 ## 41 42 43 44 45 ## -12.385081065 -9.723970419 -9.157441377 -9.052203353 -8.405704088 ## 46 47 48 49 50 ## -7.939543527 -8.129075435 -7.321061828 -1.579640398 -0.102055919 ## 51 52 53 54 55 ## 0.505748307 0.573455646 1.367479116 2.483118673 4.414603867 ## 56 57 58 59 60 ## 5.167899447 6.170686118 6.817271471 8.843559356 8.020796946 ## 61 62 63 64 65 ## -1.347338534 -0.553123157 -0.530017605 -1.404958094 -1.600538922 ## 66 67 68 69 70 ## -0.741174435 -0.012168063 0.476628366 1.018196209 0.674918980 ## 71 72 73 74 75 ## 0.549875877 -0.275527560 -1.290936705 -1.827334439 -0.626124222 ## 76 77 78 79 80 ## -0.964464482 -2.195831930 -2.043973498 -1.864548517 -1.044377465 ## 81 82 83 84 85 ## -1.454314242 -0.908572714 -0.932205462 -1.750708775 -9.503813054 ## 86 87 88 89 90 ## -7.405980108 -4.817510033 -2.739824233 -0.920093752 0.890848581 ## 91 92 93 94 95 ## 4.407285193 6.413647504 8.034208596 8.792978877 8.263942653 ## 96 97 98 99 100 ## 6.230139238 -19.138320419 -17.293582240 -15.472648910 -13.290616320 ## 101 102 103 104 105 ## -11.502880053 -9.908728717 -6.913499990 -4.207442142 -1.112329826 ## 106 107 108 109 110 ## 2.157864275 4.604234480 6.441494069 -1.094402253 -0.472758846 ## 111 112 113 114 115 ## -0.037945218 -0.320125471 -1.404782817 -1.144938312 -0.852086905 ## 116 117 118 119 120 ## -0.126986978 -0.389135444 -0.212698569 -0.738099284 -1.059066245 ## 121 122 123 124 125 ## -10.080212084 -7.900072686 -5.637021295 -3.410637768 -1.306292334 ## 126 127 128 129 130 ## 0.892492709 2.491574547 3.944011300 5.536738162 6.368839005 ## 131 132 133 134 135 ## 5.928644717 8.212982628 -22.098438291 -20.377529620 -18.865992937 ## 136 137 138 139 140 ## -17.447388444 -15.945694881 -12.895285052 -8.886959849 -5.317268249 ## 141 142 143 144 145 ## -2.709611632 -0.785685212 1.003213919 2.485994347 -11.922716414 ## 146 147 148 149 150 ## -7.465605967 -4.147286255 -1.496808996 0.852475818 2.960311785 ## 151 152 153 154 155 ## 3.520878517 3.885503012 5.718474566 5.791026973 6.070298679 ## 156 157 158 159 160 ## 6.188167433 -0.577622109 1.388052465 3.260394676 4.934266083 ## 161 162 163 164 165 ## 7.188346318 10.054690344 11.617781971 13.010777986 11.346681869 ## 166 167 168 169 170 ## 0.844886562 -6.136973336 -2.747067946 -11.692873259 -9.553766754 ## 171 172 173 174 175 ## -7.624401693 -5.778237362 -4.689629176 -3.545805938 -1.961686726 ## 176 177 178 179 180 ## -0.533434217 1.618051382 3.413497847 4.878946637 5.776512167 ## 181 182 183 184 185 ## -6.833286986 -0.079453457 2.258235754 2.571737165 2.591272916 ## 186 187 188 189 190 ## 2.043687969 2.037987746 2.290422392 3.013278374 2.296512059 ## 191 192 193 194 195 ## 3.343146187 2.869041010 -16.112641761 -13.216472261 -10.357172856 ## 196 197 198 199 200 ## -7.508047171 -4.642986843 -2.049928643 -0.098506965 1.283101638 ## 201 202 203 204 205 ## 1.968764453 2.016540188 2.289005792 3.839737612 -8.951661421 ## 206 207 208 209 210 ## -7.469220038 -5.948203585 -4.473598210 -3.988885194 -2.179241479 ## 211 212 213 214 215 ## -0.624715789 0.083733365 -3.400196816 -2.736469252 -0.700866621 ## 216 217 218 219 220 ## 1.517478183 -16.786177087 -14.870781200 -12.855044195 -10.872722597 ## 221 222 223 224 225 ## -15.928181940 -25.068536581 -5.378194612 -2.455126533 -0.577093877 ## 226 227 228 229 230 ## 0.119812263 0.257504719 2.853092459 -9.851107976 -8.011514856 ## 231 232 233 234 235 ## -5.838273176 -3.734759958 -1.568238902 0.686963322 4.021723130 ## 236 237 238 239 240 ## 5.930181952 5.611977245 3.530043169 1.067915086 1.581726488 ## 241 242 243 244 245 ## 2.253235162 2.943920040 3.833779773 3.476677146 2.916192172 ## 246 247 248 249 250 ## 2.833660964 4.011267296 3.426779595 4.631305728 4.105468317 ## 251 252 253 254 255 ## 3.288824302 2.817905691 -12.841124971 -10.894516870 -8.885378684 ## 256 257 258 259 260 ## -6.858132114 -4.850717315 -1.551988890 0.034582331 2.272486429 ## 261 262 263 264 265 ## 1.224282443 -2.105225727 -4.864718841 -3.419140736 -10.269518851 ## 266 267 268 269 270 ## -8.540273410 -6.743507133 -4.774019554 -2.766995716 -0.969641286 ## 271 272 273 274 275 ## 1.312228621 2.772691360 3.392075443 3.257504581 2.133161925 ## 276 277 278 279 280 ## 2.003667965 -8.357964791 -7.202225984 -5.449684788 -3.120693783 ## 281 282 283 284 285 ## -0.382459839 3.554146693 6.908978809 8.626659065 9.332303670 ## 286 287 288 289 290 ## 9.881936091 11.623039952 11.235262841 -15.841267356 -9.904317718 ## 291 292 293 294 295 ## -16.098553851 -2.858265216 1.144514429 1.429126550 2.514006333 ## 296 297 298 299 300 ## 3.525546014 4.285358153 5.308890400 6.207153249 6.061624122 ## 301 302 303 304 305 ## -11.691956278 -7.311756216 -4.659099925 -2.660972463 -1.282608100 ## 306 307 308 309 310 ## 0.666884730 3.203833809 4.070523359 4.458871460 6.025783581 ## 311 312 313 314 315 ## 7.535538901 8.158912771 -7.595890538 -5.899619641 -3.980634291 ## 316 317 318 319 320 ## -2.186792688 0.257326619 2.595827669 4.547062266 6.517784790 ## 321 322 323 324 325 ## 9.561444011 12.314904669 14.672301700 16.889971540 -9.114571240 ## 326 327 328 329 330 ## -7.671612078 -6.209859799 -4.276378878 -2.382990741 -0.541750545 ## 331 332 333 334 335 ## -0.534274009 -0.937602718 -2.745604452 -5.681439814 -3.320319720 ## 336 337 338 339 340 ## -1.901294577 -6.664173936 -3.807888327 -0.493897322 3.014421472 ## 341 342 343 344 345 ## 5.639784373 6.335805560 6.675895159 7.753899526 6.797771602 ## 346 347 348 349 350 ## 3.563367902 3.567946066 5.850096596 -5.270963435 -2.615356498 ## 351 352 353 354 355 ## -0.012570572 2.252819977 4.246287389 6.781960683 9.778420959 ## 356 357 358 359 360 ## 10.912904580 11.632988123 12.945494542 13.336049377 13.129308675 ## 361 362 363 364 365 ## -7.980818244 -6.041420205 -3.686393433 -1.417659887 0.878016512 ## 366 367 368 369 370 ## 3.379176418 4.939689465 5.800658890 3.405189216 -0.722105031 ## 371 372 373 374 375 ## -1.830001428 -0.298797411 -5.504391590 -2.493053098 -0.645896612 ## 376 377 378 379 380 ## 0.057109943 0.176157943 0.243020119 -0.799051324 -0.009563421 ## 381 382 383 384 385 ## 3.413371451 3.924887467 4.332761469 3.860283720 -4.419673318 ## 386 387 388 389 390 ## -1.747117823 1.579538634 4.388695986 6.990129608 8.428246076 ## 391 392 393 394 395 ## 9.073667909 9.430611213 10.539512708 12.347110811 12.944061605 ## 396 397 398 399 400 ## 12.885746831 -1.567586719 -0.030549081 -0.006554931 -0.095502276 ## 401 402 403 404 405 ## -0.953889234 -1.296290627 -1.306617511 -1.106154813 0.618863076 ## 406 407 408 409 410 ## 1.441655398 2.246248926 0.868324109 1.107972173 1.504383721 ## 411 412 413 414 415 ## 0.926921833 0.477570505 -0.330033888 0.189586959 -0.439293387 ## 416 417 418 419 420 ## -1.810320482 -1.860727942 -2.608708907 -2.601108951 -2.848548106 ## 421 422 423 424 425 ## -14.202462172 -11.774370568 -9.479621106 -7.098446940 -5.109823145 ## 426 427 428 429 430 ## -2.681850227 -0.298426207 0.929255509 2.718852342 4.488354946 ## 431 432 433 434 435 ## 4.698207882 6.037573029 -16.006671420 -12.175444670 -8.600850580 ## 436 437 438 439 440 ## -5.308982001 -2.674072816 -0.742429725 1.111689688 3.408758308 ## 441 442 443 444 445 ## 5.750290411 6.989910480 7.448689063 8.175309282 -14.539545538 ## 446 447 448 449 450 ## -11.660062170 -8.517511602 -6.706032099 -4.909240359 -3.030371781 ## 451 452 453 454 455 ## -0.245624667 2.964672117 5.059207931 7.604136460 10.203071223 ## 456 457 458 459 460 ## 10.524034821 -6.704850498 -4.190178821 -1.768336304 0.454982431 ## 461 462 463 464 465 ## 2.184439680 3.998023047 6.316853508 9.889504112 13.763895327 ## 466 467 468 469 470 ## 17.092561730 19.373048966 20.487824728 -17.411672779 -14.273493420 ## 471 472 473 474 475 ## -10.698768604 -7.415475293 -5.139803978 -6.932132836 -6.557650238 ## 476 477 478 479 480 ## -0.028986730 3.475616942 5.889858280 6.996674704 7.967457784 ## 481 482 483 484 485 ## -13.502357593 -12.024141476 -10.592706584 -9.240351365 -7.602155414 ## 486 487 488 489 490 ## -6.222225571 -4.571016836 -2.586946027 -0.780491712 -0.837094261 ## 491 492 493 494 495 ## -1.932100356 -1.702033018 -12.043391504 -9.931915862 -7.838287642 ## 496 497 498 499 500 ## -5.847763643 -3.918119152 -3.522925293 -4.177339722 -1.614488559 ## 501 502 503 504 505 ## 1.890822311 5.126648752 7.052887455 9.905386880 -14.035917964 ## 506 507 508 509 510 ## -11.467292585 -8.108827154 -6.114113959 -4.755764249 -3.781799825 ## 511 512 513 514 515 ## -3.408217664 -1.670477766 -0.254691865 0.962748146 2.226261009 ## 516 517 518 519 520 ## 4.319730912 -1.651503423 -1.216886821 -0.778976419 -0.396368543 ## 521 522 523 524 525 ## -0.901650346 0.187367612 0.900755631 0.007821479 1.099090508 ## 526 527 528 529 530 ## 1.145444444 0.370985602 -0.934962574 -1.315663522 -0.541879945 ## 531 532 533 534 535 ## 0.166633361 0.094031362 -0.486916735 -0.028700816 0.123386130 ## 536 537 538 539 540 ## 0.768756072 0.691791975 1.330475874 0.907113834 1.272470335 ## 541 542 543 544 545 ## -12.743784755 -11.054765359 -10.308951130 -6.976602722 -4.252854277 ## 546 547 548 549 550 ## -4.803479479 1.951425576 7.037017639 7.467157808 6.021520547 ## 551 552 553 554 555 ## 3.309802898 2.974972551 -18.034060338 -15.985361025 -14.190081927 ## 556 557 558 559 560 ## -12.290255628 -9.849341078 -6.373777261 -2.614480522 1.170403513 ## 561 562 563 564 565 ## 4.523982972 7.744947324 9.920407274 11.284464014 -1.452368482 ## 566 567 568 569 570 ## -1.232840707 -1.270955564 -1.616742078 -2.902305338 -2.520949877 ## 571 572 573 574 575 ## -1.904720879 -2.025822504 -1.660570647 -0.976832880 -0.659066471 ## 576 577 578 579 580 ## -0.882899694 -5.111378739 -3.546154981 -1.945331442 -0.303864982 ## 581 582 583 584 585 ## 1.469848316 3.426228275 5.461241681 7.441105526 9.164153274 ## 586 587 588 589 590 ## 10.169052894 10.004063299 11.460879935 -1.064642854 0.310132920 ## 591 592 593 594 595 ## 1.462963474 1.829277156 1.274947895 1.951103812 3.025690229 ## 596 597 598 599 600 ## 4.071427811 3.790388932 4.086031797 2.779276122 1.747215672 ## 601 602 603 604 605 ## -20.379199839 -18.348368401 -15.599977920 -12.762375781 -9.397994876 ## 606 607 608 609 610 ## -7.492077173 -5.361880130 -2.464974897 0.031661723 2.861942439 ## 611 612 613 614 615 ## 5.430681266 6.555216942 -14.451918336 -13.534013357 -12.390236613 ## 616 617 618 619 620 ## -10.958345131 -9.330501810 -7.473025575 -5.339364534 -2.661309117 ## 621 622 623 624 625 ## 0.358930538 3.197219478 5.379010498 7.703837696 -15.452677663 ## 626 627 628 629 630 ## -14.523119815 -13.564860553 -12.647686397 -11.700882616 -10.697723169 ## 631 632 633 634 635 ## -8.869246567 -6.906195057 -4.890107371 -3.307026146 -2.577615036 ## 636 637 638 639 640 ## -1.696117483 -24.559310561 -21.393312837 -18.533090698 -15.728099494 ## 641 642 643 644 645 ## -14.022576746 -12.241778308 -10.767202174 -8.511295238 -6.897206512 ## 646 647 648 649 650 ## -5.267556566 -3.774039090 -0.970026621 -20.374623179 -17.634774962 ## 651 652 653 654 655 ## -14.292641998 -11.523417589 -8.562680999 -5.347954635 -1.808378888 ## 656 657 658 659 660 ## 1.814354214 3.690381448 4.909784070 5.837763443 7.263816043 ## 661 662 663 664 665 ## 3.566342951 7.094021890 9.512202665 11.182811557 12.228192668 ## 666 667 668 669 670 ## 12.534940681 12.863660552 11.149191606 10.427304539 11.194703627 ## 671 672 673 674 675 ## 11.864735203 8.298823037 -3.685262538 -1.656507432 -0.786813614 ## 676 677 678 679 680 ## -0.046317796 -0.165928049 -0.654562187 -1.606599744 -1.613992581 ## 681 682 683 684 685 ## -0.920585957 0.420962391 0.564548687 -0.109305306 3.935388876 ## 686 687 688 689 690 ## 4.026912156 3.739576615 2.454553702 2.070533317 1.986752649 ## 691 692 693 694 695 ## 1.241868923 -0.160514915 2.178978152 1.047821256 1.203297796 ## 696 697 698 699 700 ## 0.204772132 -21.323369047 -18.710004321 -15.680340937 -12.453041335 ## 701 702 703 704 705 ## -9.406256919 -6.329578096 -4.446797864 -3.069679136 -2.036003783 ## 706 707 708 709 710 ## -1.197917680 -0.707224113 0.293899330 -19.414763705 -17.066889715 ## 711 712 713 714 715 ## -14.521067445 -11.103792002 -8.099961051 -4.824501965 -1.536989894 ## 716 717 718 719 720 ## 2.232279734 4.388845648 7.322909107 9.902822381 11.583082118 ## 721 722 723 724 725 ## -12.615580843 -10.434730038 -8.714217331 -6.367170260 -5.295305712 ## 726 727 728 729 730 ## -3.881804050 -0.089680902 3.706370112 6.086017892 7.904704570 ## 731 732 733 734 735 ## 8.850941369 9.284156515 -12.578815400 -10.410884117 -8.346936735 ## 736 737 738 739 740 ## -5.618423114 -3.427296677 -2.274225206 -0.587709344 3.694750891 ## 741 742 743 744 745 ## 1.653253046 1.285009462 -1.092050740 1.347853831 -0.738217401 ## 746 747 748 749 750 ## 1.077501612 2.003694977 2.332953283 1.689221694 1.709302737 ## 751 752 753 754 755 ## 2.118357656 2.814038876 2.264066230 -0.211620702 -2.847086450 ## 756 757 758 759 760 ## -4.712861693 7.535725317 9.399801622 10.174085523 10.952558204 ## 761 762 763 764 765 ## 9.855150551 11.048920169 11.510372440 11.869022470 12.776594117 ## 766 767 768 769 770 ## 12.832803297 13.802985623 13.223207556 -1.876623008 -0.608695250 ## 771 772 773 774 775 ## -0.086339807 0.922088128 1.030947413 1.416782213 1.888105590 ## 776 777 778 779 780 ## 2.126762020 1.884534359 2.064033278 2.000837500 2.034954977 ## 781 782 783 784 785 ## -4.072297325 -0.828192803 1.950883059 3.454661658 4.355278175 ## 786 787 788 789 790 ## 5.816507110 7.177254691 7.609774983 7.131795267 7.754001771 ## 791 792 793 794 795 ## 7.595280285 7.967935393 5.009228746 6.950908399 9.137450163 ## 796 797 798 799 800 ## 10.334247733 10.065932118 11.158707567 11.611794331 11.803056566 ## 801 802 803 804 805 ## 10.478523592 10.902556915 12.300560848 11.529262822 -13.548048199 ## 806 807 808 809 810 ## -11.190419191 -8.942287297 -5.618409054 -0.438153154 3.832411174 ## 811 812 813 814 815 ## 5.846289648 7.844055249 10.440360363 12.096933989 13.493108104 ## 816 817 818 819 820 ## 14.456997436 -5.970217627 -3.601585470 -0.325286564 2.297956017 ## 821 822 823 824 825 ## 5.116331619 7.675857046 10.229853698 10.773455461 10.703339513 ## 826 827 828 829 830 ## 5.795687374 2.392970282 5.404230026 -6.498142154 -2.693775529 ## 831 832 833 834 835 ## -0.151396961 2.888864291 6.215279341 9.199229140 11.131441823 ## 836 837 838 839 840 ## 12.669127262 12.160332587 10.818474407 9.769111363 10.421109334 ## 841 842 843 844 845 ## -9.154589325 -4.142946106 -1.578882740 0.599184578 5.022771225 ## 846 847 848 849 850 ## 6.426463919 8.330379783 9.694167939 10.508552639 11.147752976 ## 851 852 853 854 855 ## 12.077352430 11.798950866 -49.161252920 -49.004410306 -38.448034718 ## 856 857 858 859 860 ## -27.749203615 -37.452737251 -13.311375357 1.198631868 5.515466810 ## 861 862 863 864 865 ## 3.471424613 2.022331033 5.101222506 0.300064400 -2.261440054 ## 866 867 868 869 870 ## 0.734072170 3.506165509 5.148748694 6.031509559 6.179235914 ## 871 872 873 874 875 ## 7.521551923 9.481959649 10.166677520 10.300345970 10.810458178 ## 876 877 878 879 880 ## 11.258221464 -5.815330659 -2.923454556 -0.258052975 0.447234416 ## 881 882 883 884 885 ## 1.722368244 4.050651379 6.896271891 9.007500703 11.419689191 ## 886 887 888 889 890 ## 7.197714422 -3.807728167 -5.940724695 -9.598473587 -8.613619835 ## 891 892 893 894 895 ## -7.604463680 -6.607252850 -5.570774608 -4.349099515 -3.232141754 ## 896 897 898 899 900 ## -2.029489172 -7.310811999 -5.881364003 -4.318474574 -2.343385502 ## 901 902 903 904 905 ## -6.170994465 -4.082996268 -3.052875457 -6.037096149 -4.500215040 ## 906 907 908 909 910 ## -0.257156086 6.513609874 13.104009400 16.578949830 19.453979888 ## 911 912 913 914 915 ## 20.601758518 20.678344790 -11.813011992 -9.697476929 -7.742260226 ## 916 917 918 919 920 ## -5.709209003 -3.795597869 -1.679823734 0.509015130 0.947109653 ## 921 922 923 924 925 ## 3.851911495 6.627513592 8.961549219 11.033363285 -11.743189703 ## 926 927 928 929 930 ## -10.815402020 -9.620261745 -8.577061890 -6.341951186 -4.382237001 ## 931 932 933 934 935 ## -2.499249847 -0.694154349 1.286968075 -0.698717892 -3.181874795 ## 936 937 938 939 940 ## 0.060032860 -8.411150774 -4.769191286 -1.243815230 2.273715581 ## 941 942 943 944 945 ## 5.647436767 7.444224991 9.686680497 11.026176203 11.294470070 ## 946 947 948 949 950 ## 11.241964151 12.300306590 12.474127244 -14.357622593 -12.755376475 ## 951 952 953 954 955 ## -11.131926569 -9.606308164 -8.136697055 -6.451266042 -4.221856615 ## 956 957 958 959 960 ## -1.807771568 0.186437309 1.672038370 3.506747523 6.105228392 ## 961 962 963 964 965 ## -7.611831322 -5.863489086 -4.048243768 -2.171975818 -0.099133608 ## 966 967 968 969 970 ## 2.355220013 5.108478887 7.679805958 9.893053505 11.933181823 ## 971 972 973 974 975 ## 13.704558099 15.517910844 2.283920470 9.356603406 11.290485626 ## 976 977 978 979 980 ## 12.625034992 13.966633503 15.441814956 17.232609852 18.768821613 ## 981 982 983 984 985 ## 19.200499744 19.576470200 20.076678260 20.053472926 -12.262502097 ## 986 987 988 989 990 ## -8.187221774 -5.320642495 -4.082130159 -2.357696233 -0.126838398 ## 991 992 993 994 995 ## 1.324043969 3.776211444 5.328213030 7.359507568 8.109914330 ## 996 997 998 999 1000 ## 8.806843661 -14.121536893 -11.174752909 -8.237184894 -5.312374905 ## 1001 1002 1003 1004 1005 ## -2.900467001 -1.266315014 0.571470206 3.151102395 4.446546469 ## 1006 1007 1008 1009 1010 ## 6.746825969 8.046445760 9.385839692 -7.315595045 -5.496877591 ## 1011 1012 1013 1014 1015 ## -3.651907995 -0.767675972 1.849320118 3.462123436 3.765915171 ## 1016 1017 1018 1019 1020 ## 4.300656554 6.996103593 7.247347730 5.742000384 5.092050581 ## 1021 1022 1023 1024 1025 ## -5.765234551 -3.204105625 -0.679942922 1.654758863 4.070830161 ## 1026 1027 1028 1029 1030 ## 6.729449595 10.488376078 13.473488955 16.084267491 18.318015841 ## 1031 1032 1033 1034 1035 ## 20.131442224 21.410952143 -16.781034739 -14.304086211 -11.954484137 ## 1036 1037 1038 1039 1040 ## -10.012831515 -7.876380468 -5.617982169 -5.309540953 -5.213027866 ## 1041 1042 1043 1044 1045 ## -3.801242595 -1.791481681 -4.194262815 -6.233408712 -19.968504186 ## 1046 1047 1048 1049 1050 ## -14.401811738 -11.228392649 -6.954550966 -3.284203055 -0.321610943 ## 1051 1052 1053 1054 1055 ## 1.630854836 1.909388899 2.890927566 3.850613920 3.327070302 ## 1056 1057 1058 1059 1060 ## 5.324168451 -7.181773514 -3.770035210 -0.858539540 1.634991443 ## 1061 1062 1063 1064 1065 ## 4.363637660 6.873999932 9.262777466 11.352170631 12.464548674 ## 1066 1067 1068 1069 1070 ## 9.330403072 1.821431459 2.915820704 -20.155407772 -18.653097432 ## 1071 1072 1073 1074 1075 ## -16.974846281 -14.912762335 -12.420580039 -9.662256534 -6.839402181 ## 1076 1077 1078 1079 1080 ## -3.936074305 -0.816789408 2.813774570 4.688082268 7.097837498 ## 1081 1082 1083 1084 1085 ## 2.755732899 2.562073500 2.116106954 1.544599936 -0.072692527 ## 1086 1087 1088 1089 1090 ## 0.328622873 1.050031295 0.815474369 -0.009149404 -0.955099627 ## 1091 1092 1093 1094 1095 ## -2.022168124 -2.174520072 -1.265729745 -1.157304280 -0.596275211 ## 1096 1097 1098 1099 1100 ## -0.896921052 -1.239412562 -0.995325156 -0.004346144 -0.143017857 ## 1101 1102 1103 1104 1105 ## 2.155612057 2.166183174 2.762992931 2.958770784 -20.382706361 ## 1106 1107 1108 1109 1110 ## -17.421077446 -14.302139478 -11.505509877 -8.260912797 -6.302960457 ## 1111 1112 1113 1114 1115 ## -3.571533076 -0.632725617 3.551085342 6.092947300 8.399840363 ## 1116 1117 1118 1119 1120 ## 10.335856498 -10.734750103 -9.615908006 -8.802358694 -8.199818494 ## 1121 1122 1123 1124 1125 ## -7.730246002 -6.924012622 -5.667294955 -3.607657274 -0.739462742 ## 1126 1127 1128 1129 1130 ## 3.174565470 6.338542987 8.689656255 -12.191909433 -10.751023396 ## 1131 1132 1133 1134 1135 ## -9.246514332 -7.540780533 -6.109576849 -4.599680446 -3.176792999 ## 1136 1137 1138 1139 1140 ## -2.086436263 -1.683596109 -1.778265616 -2.719889140 -2.747503702 ## 1141 1142 1143 1144 1145 ## 2.823415987 2.891759368 2.113288792 1.413597620 0.502487994 ## 1146 1147 1148 1149 1150 ## -0.421920120 -1.165192615 -3.602123209 -3.262692040 -5.552735712 ## 1151 1152 1153 1154 1155 ## -6.352273338 -7.307516965 -19.253846767 -16.938529921 -14.160478940 ## 1156 1157 1158 1159 1160 ## -11.145497203 -8.642026499 -3.972208736 0.889488878 3.573921073 ## 1161 1162 1163 1164 1165 ## 6.809390172 7.621099095 9.279559702 9.580976913 -13.150080297 ## 1166 1167 1168 1169 1170 ## -11.092207677 -9.046679558 -7.028734843 -5.005123011 -3.005743027 ## 1171 1172 1173 1174 1175 ## -1.098430118 0.780964005 3.156135104 3.999457799 5.654769326 ## 1176 1177 1178 1179 1180 ## 7.192823181 -7.220143215 -3.427355419 -1.070704137 0.784475358 ## 1181 1182 1183 1184 1185 ## 2.504097727 4.973175827 6.017743756 7.055998450 8.180489096 ## 1186 1187 1188 1189 1190 ## 9.232367186 10.095749970 9.816392279 0.471182353 0.974585351 ## 1191 1192 1193 1194 1195 ## 2.092223500 2.612363638 3.373549036 3.583208084 3.647639392 ## 1196 1197 1198 1199 1200 ## 4.264926844 5.019208523 6.166885641 7.725534766 8.542461298 ## 1201 1202 1203 1204 1205 ## -19.130227166 -16.995377398 -14.491330468 -12.526509493 -8.602789270 ## 1206 1207 1208 1209 1210 ## -5.771550334 -2.895446304 -0.147986158 3.021940280 4.309016520 ## 1211 1212 1213 1214 1215 ## 5.783969186 6.612244405 -8.974295916 -5.539810172 -2.190425160 ## 1216 1217 1218 1219 1220 ## -0.661457682 0.895676351 2.678718126 4.553901554 6.765729860 ## 1221 1222 1223 1224 1225 ## 8.985321780 10.924280531 12.559422315 13.648788394 -5.957023325 ## 1226 1227 1228 1229 1230 ## -1.830346475 -0.245831301 1.166926510 1.747193793 0.881808912 ## 1231 1232 1233 1234 1235 ## 1.996209419 1.362709819 1.972468379 2.642481166 3.734387359 ## 1236 1237 1238 1239 1240 ## 3.105310984 -6.902013344 -5.531393388 -3.081272689 -1.606115315 ## 1241 1242 1243 1244 1245 ## -0.141257674 0.487156286 2.135032544 2.846842708 2.222746006 ## 1246 1247 1248 1249 1250 ## 2.686757670 2.957642049 3.522102474 1.589988523 5.478841186 ## 1251 1252 1253 1254 1255 ## 6.017664640 6.677824762 6.750413258 7.737830501 7.794596643 ## 1256 1257 1258 1259 1260 ## 7.796814763 6.015946535 5.960936285 7.986917754 8.741710769 ## 1261 1262 1263 1264 1265 ## 3.686073937 6.029008921 8.422956752 10.917659866 14.187937146 ## 1266 1267 1268 1269 1270 ## 17.304911801 19.699874235 21.711330394 23.054284277 24.224049878 ## 1271 1272 1273 1274 1275 ## 25.085881136 25.174913998 -5.759549149 -3.076474402 -0.737908965 ## 1276 1277 1278 1279 1280 ## -1.522160836 0.186301910 -0.174818826 -0.091294950 -0.264347362 ## 1281 1282 1283 1284 1285 ## 0.957433071 0.982681967 2.343521464 2.184406993 -8.052484375 ## 1286 1287 1288 1289 1290 ## -6.575482206 -5.102692137 -3.966432541 -3.505775368 -3.145879658 ## 1291 1292 1293 1294 1295 ## -2.028533240 -4.216969570 -24.594290352 -12.039647277 -4.805823207 ## 1296 1297 1298 1299 1300 ## -2.018254160 -1.738850577 0.743612482 3.596823868 5.987962694 ## 1301 1302 1303 1304 1305 ## 7.976332658 9.954307369 11.686609907 13.231506632 14.284850505 ## 1306 1307 1308 1309 1310 ## 14.889042565 15.913579438 16.994104598 -19.061634009 -16.834630884 ## 1311 1312 1313 1314 1315 ## -15.351327767 -13.740638661 -13.327802337 -12.728719124 -8.213927744 ## 1316 1317 1318 1319 1320 ## 0.663500027 1.483508207 5.132978164 6.911173235 6.854984123 ## 1321 1322 1323 1324 1325 ## -11.206125975 -9.209815314 -7.126541478 -5.001918468 -2.747406118 ## 1326 1327 1328 1329 1330 ## 0.328334475 3.841966229 7.259745325 9.712461363 11.684398655 ## 1331 1332 1333 1334 1335 ## 13.031422550 14.397560227 -8.945727851 -5.888570358 -3.633031936 ## 1336 1337 1338 1339 1340 ## -2.017459104 -1.371117990 -0.878724834 -2.008103861 -1.263467108 ## 1341 1342 1343 1344 1345 ## 2.115999204 3.319786615 4.607140110 4.249439611 -17.892628849 ## 1346 1347 1348 1349 1350 ## -16.710682166 -15.565228117 -14.260692028 -13.041515842 -11.652775508 ## 1351 1352 1353 1354 1355 ## -10.050370508 -8.415358184 -9.989456814 -8.205464129 -7.151711371 ## 1356 1357 1358 1359 1360 ## -5.674164152 3.341217503 5.884798358 8.127976357 9.688918888 ## 1361 1362 1363 1364 1365 ## 9.635407868 9.734013102 8.917242114 9.056563286 8.625821938 ## 1366 1367 1368 1369 1370 ## 6.059111507 6.543117804 2.744246616 -3.231236068 -0.600984262 ## 1371 1372 1373 1374 1375 ## 1.652588951 1.882395972 0.684456668 0.221710575 0.378827313 ## 1376 1377 1378 1379 1380 ## 0.348249081 1.788773792 1.937052845 2.346976279 0.944429812 ## 1381 1382 1383 1384 1385 ## -1.621242655 -0.081970346 0.525450978 -0.345412799 -1.044352212 ## 1386 1387 1388 1389 1390 ## -1.195361198 -2.267193615 -1.445664232 1.950497264 2.115996280 ## 1391 1392 1393 1394 1395 ## 2.073215950 1.043048262 -15.363206426 -13.420889770 -11.468907381 ## 1396 1397 1398 1399 1400 ## -9.437100256 -7.430246800 -6.520910733 -5.426354755 -3.849973718 ## 1401 1402 1403 1404 1405 ## -8.612827021 -4.480967897 -2.325517163 -0.131292899 -5.022844070 ## 1406 1407 1408 1409 1410 ## -2.401676180 -0.576755632 0.776974087 2.233822627 3.925757681 ## 1411 1412 1413 1414 1415 ## 6.290852100 9.266092962 10.563653894 8.778564996 1.792885720 ## 1416 1417 1418 1419 1420 ## -2.930900919 -2.257759546 -0.874730348 1.639110190 2.344278455 ## 1421 1422 1423 1424 1425 ## 2.764303426 2.913758699 4.503791553 4.271338748 3.661211352 ## 1426 1427 1428 1429 1430 ## 4.031105976 3.065746351 2.433257265 1.046793191 4.907200847 ## 1431 1432 1433 1434 1435 ## 5.633838043 7.671756809 8.404343742 9.243262116 11.908226332 ## 1436 1437 1438 1439 1440 ## 12.052300929 13.288627599 13.129744931 13.324243507 14.470827488 ## 1441 1442 1443 1444 1445 ## -9.961349904 -9.049933197 -7.898398933 -5.798385806 -3.573001741 ## 1446 1447 1448 1449 1450 ## -1.116711141 1.538055660 3.089702992 4.885720146 6.613943131 ## 1451 1452 1453 1454 1455 ## 7.415200852 9.294272972 -6.925187179 -4.951728636 -3.658873854 ## 1456 1457 1458 1459 1460 ## -2.358446528 0.222253935 3.019532968 5.991654299 8.067592960 ## 1461 1462 1463 1464 1465 ## 9.056495121 4.725364047 -5.808116424 -10.237358000 2.693105638 ## 1466 1467 1468 1469 1470 ## 2.699403551 2.491395337 1.962845517 1.364269003 1.623259866 ## 1471 1472 1473 1474 1475 ## 1.788426431 1.245441151 2.081742320 2.687293088 1.505169417 ## 1476 1477 1478 1479 1480 ## 0.317744329 -2.321527383 -2.810866885 -3.187889637 -2.880018150 ## 1481 1482 1483 1484 1485 ## -3.773187157 -2.066963932 -1.884202091 -1.532260700 -1.629166413 ## 1486 1487 1488 1489 1490 ## -0.409045643 -0.214525644 -0.494755283 -10.886522204 -8.701683781 ## 1491 1492 1493 1494 1495 ## -6.719255768 -3.234967784 0.089394691 3.699785798 6.830496665 ## 1496 1497 1498 1499 1500 ## 9.492418154 11.653849550 13.616786520 15.094684504 16.128416728 ## 1501 1502 1503 1504 1505 ## 1.894585250 5.648720227 8.295589721 10.215190463 11.457129393 ## 1506 1507 1508 1509 1510 ## 11.957346009 12.693549577 12.294395275 11.277854460 10.018111212 ## 1511 1512 1513 1514 1515 ## 10.391312774 9.332007914 -6.975896910 -5.216177603 -3.963997582 ## 1516 1517 1518 1519 1520 ## -2.521185411 -0.702438704 1.559737529 2.270570403 3.195639890 ## 1521 1522 1523 1524 1525 ## 2.079979298 0.095570382 1.205507523 3.954531260 -5.639212258 ## 1526 1527 1528 1529 1530 ## -2.897948933 -0.588459991 1.472439326 3.455044153 5.315661461 ## 1531 1532 1533 1534 1535 ## 7.193737775 8.388958019 8.843675284 8.487887882 9.486648591 ## 1536 1537 1538 1539 1540 ## 10.829211339 -9.612576728 -7.031197724 -4.381980806 -1.720668936 ## 1541 1542 1543 1544 1545 ## 1.189879957 4.368762511 7.035150401 8.565802181 9.757377498 ## 1546 1547 1548 1549 1550 ## 10.105990459 9.315859825 10.171563131 -3.553354758 -1.338197510 ## 1551 1552 1553 1554 1555 ## 1.357731688 1.576832651 1.628044835 3.452256994 3.435362516 ## 1556 1557 1558 1559 1560 ## 4.962934068 5.250898838 4.215188834 2.527133576 0.427107905 ## 1561 1562 1563 1564 1565 ## -3.898131653 -1.367199836 0.990443831 3.338864900 6.515460565 ## 1566 1567 1568 1569 1570 ## 10.580617291 14.589334433 17.316364438 20.183343809 21.906122090 ## 1571 1572 1573 1574 1575 ## 22.591256084 22.853099305 -22.732977954 -18.373767603 -14.428621117 ## 1576 1577 1578 1579 1580 ## -12.440741173 -10.079201220 -7.977353321 -6.468227142 -4.813746667 ## 1581 1582 1583 1584 1585 ## -2.075448185 0.166636100 2.190598990 2.220685089 -8.204622238 ## 1586 1587 1588 1589 1590 ## -5.635019546 -2.865485532 -0.230115897 2.707611952 2.081383222 ## 1591 1592 1593 1594 1595 ## 1.643229402 3.316843955 0.601449426 -3.742474058 -0.580630928 ## 1596 1597 1598 1599 1600 ## 3.061428265 -0.923933950 -0.276510700 -0.485453187 -0.645135050 ## 1601 1602 1603 1604 1605 ## -0.790146689 -0.730180104 0.187507085 -0.392577180 0.546987281 ## 1606 1607 1608 1609 1610 ## -0.175783089 -0.460365141 -1.186117444 -0.173919396 0.396204609 ## 1611 1612 1613 1614 1615 ## 0.424534346 -0.614536263 -1.130940095 -0.177739809 0.592604374 ## 1616 1617 1618 1619 1620 ## -1.298385617 -1.273722968 -2.350670844 -3.444370441 -4.333473307 ## 1621 1622 1623 1624 1625 ## 2.196457045 2.973238779 4.427165175 4.712532648 4.800673570 ## 1626 1627 1628 1629 1630 ## 5.248361549 6.384890853 7.258075836 7.783657609 8.762495591 ## 1631 1632 1633 1634 1635 ## 10.521551434 10.301415055 -9.694368069 -7.833322283 -4.359697718 ## 1636 1637 1638 1639 1640 ## -2.163759421 -0.375852276 0.168980559 2.151279979 4.339583268 ## 1641 1642 1643 1644 1645 ## 4.901875360 6.139533752 7.448393957 7.154136203 -16.039128313 ## 1646 1647 1648 1649 1650 ## -13.614219852 -11.212785556 -8.714371848 -6.360515913 -0.895445594 ## 1651 1652 1653 1654 1655 ## 2.122538889 6.031576635 10.751219833 13.542692615 15.685603994 ## 1656 1657 1658 1659 1660 ## 16.584628397 -13.534748585 -11.164020410 -8.875598357 -5.574279411 ## 1661 1662 1663 1664 1665 ## -0.890354148 3.094550554 6.440850522 8.732464083 10.992491179 ## 1666 1667 1668 1669 1670 ## 11.874437009 14.311283070 16.028977774 -23.842708378 -22.434607750 ## 1671 1672 1673 1674 1675 ## -21.238040580 -19.454668824 -16.776019444 -12.709413056 -7.846082450 ## 1676 1677 1678 1679 1680 ## -4.044728599 -1.340380298 0.957490882 3.173860874 5.520143226 ## 1681 1682 1683 1684 1685 ## -6.309390882 -4.346625136 -2.466562390 -0.870507224 1.466117003 ## 1686 1687 1688 1689 1690 ## 2.823525223 3.333633850 2.413751019 -2.313440803 -8.119531348 ## 1691 1692 1693 1694 1695 ## -9.172387670 -6.078664733 0.433783803 2.397778235 4.278805719 ## 1696 1697 1698 1699 1700 ## 5.891976299 7.423097049 9.508108491 12.144156074 14.158949558 ## 1701 1702 1703 1704 ## 12.180899313 -1.436217742 -8.205519071 -4.619097498
out$fitted.values
## 1 2 3 4 5 6 7 8 ## 56.41243 56.43640 56.45764 56.45839 56.42527 56.45783 56.53096 56.48098 ## 9 10 11 12 13 14 15 16 ## 56.40580 56.43833 56.49939 56.65430 66.01488 66.16954 66.33778 66.54053 ## 17 18 19 20 21 22 23 24 ## 66.79104 66.89136 66.93714 66.98765 66.43124 66.74459 67.37944 67.97916 ## 25 26 27 28 29 30 31 32 ## 48.97589 49.23636 49.03296 49.35745 49.79119 50.13403 50.52818 50.52066 ## 33 34 35 36 37 38 39 40 ## 50.24482 50.16149 50.39663 50.83051 49.42442 49.56473 49.76485 50.33107 ## 41 42 43 44 45 46 47 48 ## 50.31308 49.20697 49.09944 48.95820 49.05270 48.90254 49.13208 50.05206 ## 49 50 51 52 53 54 55 56 ## 64.06464 64.50106 64.63625 65.06054 65.69752 65.99788 65.52740 65.60610 ## 57 58 59 60 61 62 63 64 ## 65.69731 66.45773 65.49644 67.29920 70.46734 70.88312 71.46002 72.50496 ## 65 66 67 68 69 70 71 72 ## 73.53054 74.23117 74.75217 75.84337 76.54180 78.15508 79.82012 81.51053 ## 73 74 75 76 77 78 79 80 ## 68.09094 69.30733 70.16612 71.10446 72.82583 74.21397 75.04455 75.98438 ## 81 82 83 84 85 86 87 88 ## 77.49431 78.41857 79.91221 81.57971 60.44281 61.23798 61.74051 62.66282 ## 89 90 91 92 93 94 95 96 ## 64.22009 64.70215 64.64471 64.33635 64.56679 65.13202 66.53106 69.40486 ## 97 98 99 100 101 102 103 104 ## 56.62232 56.64158 56.68865 56.74362 56.75488 56.83173 56.92250 57.02644 ## 105 106 107 108 109 110 111 112 ## 57.13033 57.25414 57.40877 57.62051 69.09440 69.71276 70.28795 71.26013 ## 113 114 115 116 117 118 119 120 ## 72.84478 73.94494 74.78209 75.47699 76.84914 77.74270 79.05810 80.50007 ## 121 122 123 124 125 126 127 128 ## 48.30321 48.25807 48.25502 48.29564 48.32029 48.29751 48.41243 48.39299 ## 129 130 131 132 133 134 135 136 ## 48.38226 48.40816 48.47736 48.51502 62.51244 62.26753 62.29399 62.47939 ## 137 138 139 140 141 142 143 144 ## 62.65969 62.91829 62.74596 62.56827 62.66661 62.83569 62.87979 63.06801 ## 145 146 147 148 149 150 151 152 ## 65.74272 65.91561 66.07729 66.28681 66.59752 66.89969 67.16912 67.25450 ## 153 154 155 156 157 158 159 160 ## 66.45953 67.45297 68.01970 68.66383 48.19962 48.22995 48.25961 48.36373 ## 161 162 163 164 165 166 167 168 ## 48.83565 49.26431 49.86622 50.61122 51.39832 51.71111 52.77097 53.47507 ## 169 170 171 172 173 174 175 176 ## 62.60987 62.83877 63.28940 63.41024 64.19363 65.03481 65.29769 65.73843 ## 177 178 179 180 181 182 183 184 ## 65.43895 65.97450 66.12705 66.61349 66.43329 66.68945 67.25176 67.84826 ## 185 186 187 188 189 190 191 192 ## 68.30873 68.76631 69.04201 69.04958 68.17672 68.02349 68.79685 70.13596 ## 193 194 195 196 197 198 199 200 ## 48.08764 48.12247 48.17117 48.20505 48.23399 48.18693 48.22051 48.27390 ## 201 202 203 204 205 206 207 208 ## 48.29124 48.30746 48.36099 48.45526 47.98266 48.00222 47.99320 48.02160 ## 209 210 211 212 213 214 215 216 ## 48.04589 48.08924 48.09572 48.12727 48.13620 48.06247 48.06087 48.06252 ## 217 218 219 220 221 222 223 224 ## 56.20318 56.23678 56.27004 56.28772 56.24518 56.28854 56.33519 56.36913 ## 225 226 227 228 229 230 231 232 ## 56.38009 56.41419 56.49450 56.86991 48.37411 48.43951 48.48127 48.53376 ## 233 234 235 236 237 238 239 240 ## 48.61724 48.66804 48.93928 49.05482 48.70202 48.66896 48.78808 48.84827 ## 241 242 243 244 245 246 247 248 ## 66.49676 67.01608 67.46622 68.65332 69.96381 71.37634 71.74873 73.43322 ## 249 250 251 252 253 254 255 256 ## 73.31869 74.50453 76.48118 77.83509 48.30412 48.35852 48.36038 48.33613 ## 257 258 259 260 261 262 263 264 ## 48.30772 48.32699 48.26042 48.21251 48.17172 48.17123 48.17272 48.16014 ## 265 266 267 268 269 270 271 272 ## 48.36152 48.42127 48.45951 48.37502 48.33600 48.35264 48.20477 48.27831 ## 273 274 275 276 277 278 279 280 ## 48.33192 48.31550 48.39184 48.64733 63.10296 63.27623 63.37368 63.64369 ## 281 282 283 284 285 286 287 288 ## 63.82346 63.49785 63.65602 63.86534 64.79370 65.93406 66.23696 67.31774 ## 289 290 291 292 293 294 295 296 ## 59.84127 60.45328 60.59991 61.23939 61.97437 62.53823 63.01099 63.74845 ## 297 298 299 300 301 302 303 304 ## 64.40464 65.11711 65.82085 66.89938 62.33496 62.42976 62.52210 62.62397 ## 305 306 307 308 309 310 311 312 ## 62.90561 63.17012 63.44917 63.69748 63.96213 64.28722 64.14646 64.73009 ## 313 314 315 316 317 318 319 320 ## 48.31089 48.35962 48.44763 48.65879 48.68667 48.34317 48.38594 48.40822 ## 321 322 323 324 325 326 327 328 ## 48.37756 48.34510 48.30170 48.26203 48.25757 48.32361 48.33186 48.33238 ## 329 330 331 332 333 334 335 336 ## 48.37199 48.34575 48.31827 48.34960 48.29360 48.26844 48.28632 48.36329 ## 337 338 339 340 341 342 343 344 ## 48.77517 48.86089 48.92890 49.02558 49.26722 49.28919 50.01910 49.71610 ## 345 346 347 348 349 350 351 352 ## 49.63523 49.39863 49.40205 49.47190 62.47696 62.64136 62.85457 63.17118 ## 353 354 355 356 357 358 359 360 ## 63.60271 63.96804 63.67158 63.83910 64.08001 64.31451 64.78695 65.65269 ## 361 362 363 364 365 366 367 368 ## 48.45782 48.51042 48.61639 48.76766 48.92298 48.99482 49.04331 48.85434 ## 369 370 371 372 373 374 375 376 ## 48.63881 48.71311 48.66200 48.62680 66.71439 67.26305 67.77590 68.44289 ## 377 378 379 380 381 382 383 384 ## 69.43384 70.39698 71.25905 71.52956 69.11363 69.75511 70.54324 71.88772 ## 385 386 387 388 389 390 391 392 ## 63.84067 64.07212 63.66646 63.90130 63.73287 64.22075 64.64333 64.74339 ## 393 394 395 396 397 398 399 400 ## 63.87449 63.80389 64.21394 65.38725 68.43759 69.06055 69.90655 70.47550 ## 401 402 403 404 405 406 407 408 ## 71.24389 72.00629 72.26662 72.68615 71.78114 72.56834 73.26375 75.61768 ## 409 410 411 412 413 414 415 416 ## 69.67203 70.30562 71.42308 72.48243 73.80003 74.50041 75.06929 76.61032 ## 417 418 419 420 421 422 423 424 ## 77.19073 78.71871 79.78111 81.18055 49.01446 49.10237 49.17262 49.17245 ## 425 426 427 428 429 430 431 432 ## 49.47582 49.20085 49.11043 49.11074 48.88515 48.66865 48.67479 48.75343 ## 433 434 435 436 437 438 439 440 ## 61.93467 62.00344 62.05985 62.05998 62.30507 62.53043 62.61531 62.63724 ## 441 442 443 444 445 446 447 448 ## 62.70671 62.96709 63.39831 64.05969 62.89655 63.01606 63.15751 63.38403 ## 449 450 451 452 453 454 455 456 ## 63.70524 64.34037 64.58762 64.26633 64.55379 64.70786 63.96993 64.46997 ## 457 458 459 460 461 462 463 464 ## 48.59785 48.63418 48.76034 48.83802 48.95256 49.32098 49.68915 49.90750 ## 465 466 467 468 469 470 471 472 ## 49.91010 50.12444 50.43295 50.85018 62.67367 62.84349 63.00577 63.27048 ## 473 474 475 476 477 478 479 480 ## 63.34680 63.62813 63.16165 63.18299 63.32238 63.64514 63.73733 63.91054 ## 481 482 483 484 485 486 487 488 ## 47.98436 48.00714 48.07771 48.22735 48.11816 48.24623 48.23302 48.25095 ## 489 490 491 492 493 494 495 496 ## 48.32549 49.08209 51.28010 53.28103 47.97139 47.97892 47.99629 48.03676 ## 497 498 499 500 501 502 503 504 ## 48.06012 48.05793 48.06734 48.06749 48.10018 48.25135 48.18711 48.13461 ## 505 506 507 508 509 510 511 512 ## 48.11392 48.13429 48.16783 48.22911 48.27076 48.29180 48.32422 48.35448 ## 513 514 515 516 517 518 519 520 ## 48.34569 48.43925 48.49874 48.62727 68.20150 68.70689 69.52898 70.22637 ## 521 522 523 524 525 526 527 528 ## 71.77165 72.33263 73.64924 74.82218 74.60091 75.98456 77.99901 80.24796 ## 529 530 531 532 533 534 535 536 ## 68.72566 69.47188 70.34337 71.45597 72.86692 73.85870 74.76661 75.57124 ## 537 538 539 540 541 542 543 544 ## 76.76821 77.30952 78.68289 79.38453 49.74678 50.05377 50.79795 51.57460 ## 545 546 547 548 549 550 551 552 ## 52.94285 57.59348 54.61257 53.15298 53.89884 54.43948 53.45120 53.76003 ## 553 554 555 556 557 558 559 560 ## 48.03406 48.05036 48.08608 48.14726 48.15734 48.21578 48.19448 48.09460 ## 561 562 563 564 565 566 567 568 ## 48.12002 48.11605 48.12059 48.16354 68.95237 70.33284 71.57096 72.41674 ## 569 570 571 572 573 574 575 576 ## 73.90231 75.02095 75.70472 76.87282 77.73057 78.31683 79.32907 80.28890 ## 577 578 579 580 581 582 583 584 ## 48.26038 48.32515 48.39733 48.37586 48.40515 48.32977 48.28276 48.28789 ## 585 586 587 588 589 590 591 592 ## 48.33685 48.38695 48.44894 48.56112 66.92464 67.54987 68.04704 69.17072 ## 593 594 595 596 597 598 599 600 ## 71.06505 71.72890 72.21431 72.59857 73.23961 73.78297 75.47672 77.73578 ## 601 602 603 604 605 606 607 608 ## 62.40220 62.49037 62.55398 62.77838 63.13599 63.52108 63.49888 63.24697 ## 609 610 611 612 613 614 615 616 ## 63.34134 63.46006 63.54732 63.70378 48.06092 48.09201 48.14324 48.15535 ## 617 618 619 620 621 622 623 624 ## 48.17250 48.23503 48.23036 48.21331 48.21707 48.25778 48.29699 48.30316 ## 625 626 627 628 629 630 631 632 ## 47.95268 48.01212 48.05286 48.13969 48.18688 48.16272 48.19625 48.15120 ## 633 634 635 636 637 638 639 640 ## 48.15611 48.18003 48.08162 48.08412 62.13831 62.08931 62.12309 61.97110 ## 641 642 643 644 645 646 647 648 ## 62.06458 62.16478 62.22820 62.14730 61.98621 61.93856 61.91104 61.88603 ## 649 650 651 652 653 654 655 656 ## 62.28662 62.29977 62.33364 62.44742 62.44668 62.74995 62.71738 62.67765 ## 657 658 659 660 661 662 663 664 ## 62.70862 62.74922 62.72724 62.93418 57.39366 57.65598 58.13780 58.81719 ## 665 666 667 668 669 670 671 672 ## 59.77181 61.06506 62.58634 65.05081 67.17370 68.80530 69.63026 73.90918 ## 673 674 675 676 677 678 679 680 ## 67.71526 68.06651 68.74681 69.54632 69.92593 70.60456 70.99660 71.19399 ## 681 682 683 684 685 686 687 688 ## 70.09059 70.61904 72.02545 73.44731 68.55461 69.44309 69.94042 71.27545 ## 689 690 691 692 693 694 695 696 ## 72.38947 74.12325 75.74813 77.39051 76.59102 77.90218 79.29670 81.55223 ## 697 698 699 700 701 702 703 704 ## 58.69637 58.95900 59.28534 59.64604 60.05726 60.53758 61.04280 61.62268 ## 705 706 707 708 709 710 711 712 ## 62.25900 62.96292 63.58622 64.40410 56.88276 56.98489 57.03907 57.06779 ## 713 714 715 716 717 718 719 720 ## 57.30296 57.52650 57.69599 57.90472 58.29215 58.71809 58.68518 59.06692 ## 721 722 723 724 725 726 727 728 ## 57.48458 57.61573 58.03922 58.83617 60.52931 61.58380 59.70968 59.33363 ## 729 730 731 732 733 734 735 736 ## 59.65598 60.13730 60.60006 61.67984 57.89882 58.84788 59.80394 60.07742 ## 737 738 739 740 741 742 743 744 ## 60.37730 62.68723 62.62571 61.34925 57.80775 57.52599 58.13805 58.19715 ## 745 746 747 748 749 750 751 752 ## 67.64822 67.82250 68.28631 68.74705 69.59078 70.32070 70.98164 71.54596 ## 753 754 755 756 757 758 759 760 ## 73.20293 76.33362 80.63009 83.59786 57.85427 58.44020 59.21591 59.79744 ## 761 762 763 764 765 766 767 768 ## 61.77485 62.01108 62.93963 63.73098 64.15341 65.43620 65.89301 67.52179 ## 769 770 771 772 773 774 775 776 ## 67.81662 68.41870 69.32634 70.13791 71.15905 72.06322 73.09189 74.29324 ## 777 778 779 780 781 782 783 784 ## 75.55547 76.75597 78.23916 78.51105 62.60230 63.43819 63.65912 64.05534 ## 785 786 787 788 789 790 791 792 ## 64.64472 64.29349 64.03275 64.16023 64.63420 64.50800 64.45172 64.59906 ## 793 794 795 796 797 798 799 800 ## 58.02077 58.54909 59.59255 61.09575 63.35407 64.22129 65.49821 66.86694 ## 801 802 803 804 805 806 807 808 ## 68.88148 69.78744 69.69944 71.07374 56.70605 56.85942 57.06829 57.24741 ## 809 810 811 812 813 814 815 816 ## 56.96615 57.30159 57.89271 58.02494 57.57464 57.67507 57.76989 58.07800 ## 817 818 819 820 821 822 823 824 ## 48.24022 48.28759 48.27429 48.35604 48.44267 48.47914 48.53615 48.56554 ## 825 826 827 828 829 830 831 832 ## 48.58166 48.61131 48.59903 48.70577 56.55414 56.77478 56.80740 57.05314 ## 833 834 835 836 837 838 839 840 ## 57.76772 57.95977 57.96856 57.97787 57.81767 56.90853 56.89289 56.87589 ## 841 842 843 844 845 846 847 848 ## 56.60759 56.82395 56.87088 57.11682 57.58923 58.33954 58.79262 60.11583 ## 849 850 851 852 853 854 855 856 ## 61.73545 63.49925 64.96765 66.82405 104.72625 107.03741 98.91803 92.37320 ## 857 858 859 860 861 862 863 864 ## 105.16474 82.65438 70.11037 68.65853 71.71858 74.13367 71.80278 77.28794 ## 865 866 867 868 869 870 871 872 ## 58.18944 58.75493 58.58783 58.72125 59.38949 59.91976 59.46145 58.44404 ## 873 874 875 876 877 878 879 880 ## 59.12532 59.96465 60.21754 60.73478 47.95333 47.97045 48.00505 48.04477 ## 881 882 883 884 885 886 887 888 ## 48.04463 48.15735 48.18173 48.17250 48.26531 48.36029 48.40073 48.53272 ## 889 890 891 892 893 894 895 896 ## 48.07847 48.09962 48.10646 48.14325 48.18477 48.11310 48.08414 48.05649 ## 897 898 899 900 901 902 903 904 ## 48.11281 48.10236 48.07147 48.02139 48.89399 49.37200 50.86088 56.26410 ## 905 906 907 908 909 910 911 912 ## 57.27322 57.69916 55.64139 53.12999 52.17605 52.10102 52.13524 53.27366 ## 913 914 915 916 917 918 919 920 ## 48.49401 48.56248 48.59026 48.59021 48.64660 48.56082 48.45998 48.40289 ## 921 922 923 924 925 926 927 928 ## 48.36209 48.35049 48.32445 48.40964 47.99919 48.02240 48.03026 48.06406 ## 929 930 931 932 933 934 935 936 ## 48.10795 48.14924 48.14125 48.15115 48.13303 48.19372 48.19087 48.24297 ## 937 938 939 940 941 942 943 944 ## 56.87415 56.87119 56.98082 57.09728 57.36256 57.81178 58.31332 58.47382 ## 945 946 947 948 949 950 951 952 ## 59.39853 60.69604 60.74369 61.76687 48.04262 48.06238 48.06793 48.09331 ## 953 954 955 956 957 958 959 960 ## 48.11370 48.16527 48.13786 48.17177 48.20156 48.23096 48.31125 48.36177 ## 961 962 963 964 965 966 967 968 ## 48.15483 48.20149 48.29624 48.46098 48.53613 48.49678 48.49052 48.46519 ## 969 970 971 972 973 974 975 976 ## 48.43995 48.49682 48.54244 48.64609 48.70208 48.73240 48.95551 48.93197 ## 977 978 979 980 981 982 983 984 ## 48.97737 49.48819 49.47839 49.97118 50.54450 51.15953 51.87732 52.74753 ## 985 986 987 988 989 990 991 992 ## 63.05150 63.37722 63.61964 64.19213 64.71870 65.15884 66.08096 65.72179 ## 993 994 995 996 997 998 999 1000 ## 66.12679 66.31049 66.79209 67.38816 56.36554 56.42275 56.48818 56.56537 ## 1001 1002 1003 1004 1005 1006 1007 1008 ## 56.65447 56.75732 56.91753 57.07090 56.82445 56.87817 56.98655 57.41716 ## 1009 1010 1011 1012 1013 1014 1015 1016 ## 66.47960 66.94488 67.37991 67.94568 68.78668 69.60388 70.33508 70.56434 ## 1017 1018 1019 1020 1021 1022 1023 1024 ## 68.43890 68.19765 68.23900 69.45095 48.63823 48.62711 48.60394 48.68024 ## 1025 1026 1027 1028 1029 1030 1031 1032 ## 48.79117 49.00055 49.16162 49.20351 49.30873 49.34198 49.48356 49.75305 ## 1033 1034 1035 1036 1037 1038 1039 1040 ## 48.06703 48.08309 48.11548 48.12583 48.20438 48.11298 48.10454 48.07403 ## 1041 1042 1043 1044 1045 1046 1047 1048 ## 48.08524 48.13548 48.22026 48.31541 56.28750 56.30681 56.33639 56.33355 ## 1049 1050 1051 1052 1053 1054 1055 1056 ## 56.35420 56.38061 56.42515 56.42961 56.42907 56.47739 56.58093 56.74483 ## 1057 1058 1059 1060 1061 1062 1063 1064 ## 48.90677 48.99604 49.24454 49.52401 49.50336 49.56300 49.70522 49.48283 ## 1065 1066 1067 1068 1069 1070 1071 1072 ## 49.53445 49.57860 49.65757 49.99018 56.31241 56.33910 56.36785 56.38476 ## 1073 1074 1075 1076 1077 1078 1079 1080 ## 56.39158 56.41026 56.43340 56.47307 56.54379 56.61223 56.65192 56.68716 ## 1081 1082 1083 1084 1085 1086 1087 1088 ## 69.37427 70.42793 71.11389 72.27540 73.82269 74.91138 74.99997 76.01453 ## 1089 1090 1091 1092 1093 1094 1095 1096 ## 77.42915 78.98510 80.55217 81.93652 70.65573 71.41730 71.83628 72.41692 ## 1097 1098 1099 1100 1101 1102 1103 1104 ## 73.12941 73.21533 73.84435 74.46302 74.17439 75.38382 76.34701 77.24523 ## 1105 1106 1107 1108 1109 1110 1111 1112 ## 62.69671 62.85308 62.93414 63.38951 63.41191 63.77296 62.86953 62.64073 ## 1113 1114 1115 1116 1117 1118 1119 1120 ## 62.29191 62.33305 62.43616 62.56314 48.17875 48.21391 48.28936 48.31782 ## 1121 1122 1123 1124 1125 1126 1127 1128 ## 48.27625 48.21501 48.26529 48.16266 48.13046 48.13843 48.15746 48.17734 ## 1129 1130 1131 1132 1133 1134 1135 1136 ## 48.51591 48.55302 48.60651 48.58078 48.93058 49.11368 49.00279 48.97244 ## 1137 1138 1139 1140 1141 1142 1143 1144 ## 49.15560 49.24227 49.32789 49.60650 69.84658 70.54824 71.35671 72.66640 ## 1145 1146 1147 1148 1149 1150 1151 1152 ## 73.83751 75.79192 77.13519 79.49212 80.58269 83.87274 85.40227 87.50352 ## 1153 1154 1155 1156 1157 1158 1159 1160 ## 56.83185 57.01853 57.32548 58.13350 60.78503 61.33921 61.83851 64.16008 ## 1161 1162 1163 1164 1165 1166 1167 1168 ## 64.38761 64.87790 64.91344 66.05902 56.58608 56.64921 56.71668 56.82873 ## 1169 1170 1171 1172 1173 1174 1175 1176 ## 56.93412 57.04874 57.25643 57.46404 57.68186 57.81854 57.95523 58.29018 ## 1177 1178 1179 1180 1181 1182 1183 1184 ## 62.41114 62.62836 62.88770 63.28652 63.71190 63.70782 64.45426 64.46700 ## 1185 1186 1187 1188 1189 1190 1191 1192 ## 64.28151 64.50563 64.61625 65.72061 62.17782 62.22141 62.26878 62.33864 ## 1193 1194 1195 1196 1197 1198 1199 1200 ## 62.44145 62.76979 63.22636 63.11307 63.20579 63.23311 63.02947 63.20954 ## 1201 1202 1203 1204 1205 1206 1207 1208 ## 63.03223 63.25838 63.58733 63.97151 64.05079 64.21855 64.30145 64.28199 ## 1209 1210 1211 1212 1213 1214 1215 1216 ## 63.43606 64.07698 64.12203 64.80876 56.72630 56.87381 56.94743 57.05446 ## 1217 1218 1219 1220 1221 1222 1223 1224 ## 57.16932 57.38128 57.52810 57.38527 57.47268 57.63972 57.74358 58.03921 ## 1225 1226 1227 1228 1229 1230 1231 1232 ## 67.26702 67.60035 67.88583 68.44307 69.10281 69.78819 69.32379 69.61729 ## 1233 1234 1235 1236 1237 1238 1239 1240 ## 69.01753 70.10752 70.93561 72.45769 66.72201 67.04139 67.47127 68.20612 ## 1241 1242 1243 1244 1245 1246 1247 1248 ## 69.40126 69.92284 70.63497 71.21316 72.63725 73.28324 74.33236 74.57590 ## 1249 1250 1251 1252 1253 1254 1255 1256 ## 62.69001 63.06116 63.60234 64.42218 65.40959 65.70217 65.95540 66.83319 ## 1257 1258 1259 1260 1261 1262 1263 1264 ## 67.89505 68.95606 69.79108 70.00429 49.03793 49.06099 49.24304 49.62434 ## 1265 1266 1267 1268 1269 1270 1271 1272 ## 50.08606 49.75909 50.18513 50.20167 50.56072 50.54795 50.65812 51.26709 ## 1273 1274 1275 1276 1277 1278 1279 1280 ## 66.80955 67.17647 67.53791 68.32216 69.02370 69.63482 69.75129 69.79435 ## 1281 1282 1283 1284 1285 1286 1287 1288 ## 68.40257 68.73732 68.97848 70.29159 48.05248 48.07548 48.10269 48.06643 ## 1289 1290 1291 1292 1293 1294 1295 1296 ## 48.10578 48.14588 48.24653 48.23697 48.19329 48.12665 48.21882 48.26025 ## 1297 1298 1299 1300 1301 1302 1303 1304 ## 48.20985 48.20139 48.29618 48.43704 48.50367 48.59569 48.66439 48.49649 ## 1305 1306 1307 1308 1309 1310 1311 1312 ## 48.45715 48.41696 48.42342 48.53390 58.93663 59.70263 61.26533 63.64164 ## 1313 1314 1315 1316 1317 1318 1319 1320 ## 67.21380 71.41872 71.22593 65.63150 67.28449 65.40002 64.71483 65.92202 ## 1321 1322 1323 1324 1325 1326 1327 1328 ## 48.48413 48.53882 48.58054 48.56492 48.56241 48.55067 48.53703 48.50925 ## 1329 1330 1331 1332 1333 1334 1335 1336 ## 48.48354 48.50260 48.56858 48.66444 66.94173 67.57357 68.16403 68.93146 ## 1337 1338 1339 1340 1341 1342 1343 1344 ## 70.07112 71.17872 72.17010 72.48147 69.54300 68.91221 68.60586 69.75256 ## 1345 1346 1347 1348 1349 1350 1351 1352 ## 48.22363 48.28068 48.33223 48.37369 48.44152 48.44078 48.49537 48.42136 ## 1353 1354 1355 1356 1357 1358 1359 1360 ## 48.32246 48.10246 48.16371 48.24216 57.05478 57.29420 57.67002 58.25708 ## 1361 1362 1363 1364 1365 1366 1367 1368 ## 59.88559 61.06099 62.84276 64.50344 67.16218 71.09889 72.22688 77.22775 ## 1369 1370 1371 1372 1373 1374 1375 1376 ## 67.59124 68.05098 68.67741 69.09760 69.66554 70.22829 70.42117 70.73175 ## 1377 1378 1379 1380 1381 1382 1383 1384 ## 69.59123 70.77295 71.45302 73.71857 67.19124 67.93197 68.62455 69.52541 ## 1385 1386 1387 1388 1389 1390 1391 1392 ## 70.86435 72.16536 73.33019 73.69566 71.68950 73.01400 74.58678 76.88295 ## 1393 1394 1395 1396 1397 1398 1399 1400 ## 48.34121 48.39789 48.44991 48.41410 48.40325 48.49491 48.38135 48.35097 ## 1401 1402 1403 1404 1405 1406 1407 1408 ## 48.27083 48.27597 48.26152 48.29029 50.03184 50.38668 50.52776 51.15003 ## 1409 1410 1411 1412 1413 1414 1415 1416 ## 51.46218 51.60124 51.87015 51.56791 51.32435 51.45744 51.57211 52.26990 ## 1417 1418 1419 1420 1421 1422 1423 1424 ## 67.19776 67.53473 68.05089 69.09572 70.29570 71.47624 71.79621 72.62866 ## 1425 1426 1427 1428 1429 1430 1431 1432 ## 73.90879 74.73889 76.71425 78.50774 56.54621 56.54880 56.55816 56.59424 ## 1433 1434 1435 1436 1437 1438 1439 1440 ## 56.63766 56.70574 56.84877 56.95870 57.09037 57.32726 57.49076 57.92517 ## 1441 1442 1443 1444 1445 1446 1447 1448 ## 48.59635 48.67393 48.76840 48.65639 48.65600 48.91671 48.79994 48.65430 ## 1449 1450 1451 1452 1453 1454 1455 1456 ## 48.67028 48.75906 48.95380 49.26173 48.33219 48.37573 48.65087 48.99145 ## 1457 1458 1459 1460 1461 1462 1463 1464 ## 49.32975 49.51747 49.56935 49.61041 49.41750 49.56364 49.67712 49.85036 ## 1465 1466 1467 1468 1469 1470 1471 1472 ## 69.16689 69.79060 70.87860 72.19715 73.35573 73.81674 74.63157 75.94456 ## 1473 1474 1475 1476 1477 1478 1479 1480 ## 76.07826 76.70271 78.53483 80.56626 71.94153 73.37087 74.50789 75.65002 ## 1481 1482 1483 1484 1485 1486 1487 1488 ## 77.55319 77.45696 78.09420 78.94226 79.65917 79.77905 80.83453 82.19576 ## 1489 1490 1491 1492 1493 1494 1495 1496 ## 56.76952 56.98568 57.02426 56.88997 57.20661 57.49521 57.75950 57.48158 ## 1497 1498 1499 1500 1501 1502 1503 1504 ## 57.59515 57.91021 57.95832 58.01458 56.60541 56.75128 56.90441 57.28481 ## 1505 1506 1507 1508 1509 1510 1511 1512 ## 57.93287 58.63265 59.46645 61.10560 62.98215 65.23189 66.59869 69.06799 ## 1513 1514 1515 1516 1517 1518 1519 1520 ## 48.19090 48.19018 48.21000 48.27819 48.32244 48.35926 48.33743 48.33936 ## 1521 1522 1523 1524 1525 1526 1527 1528 ## 48.36002 48.37043 48.44549 48.56247 56.48721 56.52795 56.64946 56.81256 ## 1529 1530 1531 1532 1533 1534 1535 1536 ## 56.94996 57.17834 57.40326 57.69504 58.45432 59.03311 59.07735 59.78679 ## 1537 1538 1539 1540 1541 1542 1543 1544 ## 48.20858 48.23920 48.30398 48.48967 48.56912 48.51824 48.43585 48.37520 ## 1545 1546 1547 1548 1549 1550 1551 1552 ## 48.30362 48.28401 48.24514 48.24844 62.65335 63.13820 63.54227 63.82317 ## 1553 1554 1555 1556 1557 1558 1559 1560 ## 64.27196 64.84774 65.39664 64.61907 64.61110 65.24981 66.44887 69.39189 ## 1561 1562 1563 1564 1565 1566 1567 1568 ## 48.49813 48.46720 48.58856 48.71414 49.08654 49.25638 49.45867 49.57764 ## 1569 1570 1571 1572 1573 1574 1575 1576 ## 49.81766 50.06688 50.45074 51.06990 66.31798 66.45277 66.52662 66.77674 ## 1577 1578 1579 1580 1581 1582 1583 1584 ## 67.08420 67.48435 67.50423 67.92175 68.22145 68.66836 68.65440 69.55631 ## 1585 1586 1587 1588 1589 1590 1591 1592 ## 48.18262 48.20602 48.20949 48.28112 48.30839 48.26862 48.20577 48.19216 ## 1593 1594 1595 1596 1597 1598 1599 1600 ## 48.22355 48.32047 48.39363 48.48057 70.10393 70.69651 71.24545 72.00514 ## 1601 1602 1603 1604 1605 1606 1607 1608 ## 72.80015 73.49018 73.85249 75.39958 75.87301 77.39378 78.93137 80.61112 ## 1609 1610 1611 1612 1613 1614 1615 1616 ## 68.61392 69.09380 69.78547 71.37454 72.47094 73.55774 74.05740 76.31839 ## 1617 1618 1619 1620 1621 1622 1623 1624 ## 77.36372 79.16067 80.75437 82.57547 63.87454 64.07076 63.82583 63.75547 ## 1625 1626 1627 1628 1629 1630 1631 1632 ## 63.87233 64.23264 64.42011 64.65992 64.96834 65.46050 64.78545 66.08258 ## 1633 1634 1635 1636 1637 1638 1639 1640 ## 64.78237 65.74032 65.12970 65.64276 66.08785 67.28702 66.40572 65.85042 ## 1641 1642 1643 1644 1645 1646 1647 1648 ## 66.24812 66.00647 65.31761 66.59286 56.45113 56.50122 56.57579 56.55237 ## 1649 1650 1651 1652 1653 1654 1655 1656 ## 56.61452 56.65945 56.69346 56.78842 56.91078 57.12931 57.33140 57.66437 ## 1657 1658 1659 1660 1661 1662 1663 1664 ## 56.69475 56.83502 57.00260 57.20528 57.42235 57.67045 57.96515 58.31354 ## 1665 1666 1667 1668 1669 1670 1671 1672 ## 58.72551 59.22156 58.05872 57.39302 56.39071 56.40461 56.41804 56.43867 ## 1673 1674 1675 1676 1677 1678 1679 1680 ## 56.62402 56.88441 56.95908 56.96673 56.93938 57.06251 57.13414 57.17786 ## 1681 1682 1683 1684 1685 1686 1687 1688 ## 48.34739 48.42363 48.48956 48.63851 48.64088 48.56247 48.48737 48.40725 ## 1689 1690 1691 1692 1693 1694 1695 1696 ## 48.41344 48.35753 48.36539 48.46266 48.01722 48.07122 48.07919 48.10302 ## 1697 1698 1699 1700 1701 1702 1703 1704 ## 48.21190 48.16589 48.21884 48.19205 48.19610 48.24522 48.19452 48.10610
Generate predictions to graph
- Having fitted a model, then, we might want to get a picture of the predictions the model produces over the range of some particular variable.
min_gdp <- min(gapminder$gdpPercap)
max_gdp <- max(gapminder$gdpPercap)
med_pop <- median(gapminder$pop)
pred_df <- expand.grid(gdpPercap = (seq(from = min_gdp,
to = max_gdp,
length.out = 100)),
pop = med_pop,
continent = c("Africa", "Americas",
"Asia", "Europe", "Oceania"))
dim(pred_df)
## [1] 500 3
head(pred_df)
## gdpPercap pop continent ## 1 241.1659 7023596 Africa ## 2 1385.4282 7023596 Africa ## 3 2529.6905 7023596 Africa ## 4 3673.9528 7023596 Africa ## 5 4818.2150 7023596 Africa ## 6 5962.4773 7023596 Africa
Generate predictions to graph
- Now we can use
predict()- It needs some new data to fit the model to.
- If we specify
interval = 'predict'as an argument, it will calculate 95% prediction intervals in addition to the point estimate.
pred_out <- predict(object = out,
newdata = pred_df,
interval = "predict")
head(pred_out)
## fit lwr upr ## 1 47.96863 31.54775 64.38951 ## 2 48.48298 32.06231 64.90365 ## 3 48.99733 32.57670 65.41797 ## 4 49.51169 33.09092 65.93245 ## 5 50.02604 33.60497 66.44711 ## 6 50.54039 34.11885 66.96193
Generate predictions to graph
- We can bind the two data frames,
pred_dfandpred_out, together by column. - This is because
pred_dfandpred_outcorrespond row for row.
pred_df <- cbind(pred_df, pred_out) head(pred_df)
## gdpPercap pop continent fit lwr upr ## 1 241.1659 7023596 Africa 47.96863 31.54775 64.38951 ## 2 1385.4282 7023596 Africa 48.48298 32.06231 64.90365 ## 3 2529.6905 7023596 Africa 48.99733 32.57670 65.41797 ## 4 3673.9528 7023596 Africa 49.51169 33.09092 65.93245 ## 5 4818.2150 7023596 Africa 50.02604 33.60497 66.44711 ## 6 5962.4773 7023596 Africa 50.54039 34.11885 66.96193
Generate predictions to graph
p <- ggplot(data = subset(pred_df, continent %in% c("Europe", "Africa")),
aes(x = gdpPercap,
y = fit, ymin = lwr, ymax = upr,
color = continent, fill = continent, group = continent))
p + geom_point(data = subset(gapminder,
continent %in% c("Europe", "Africa")),
aes(x = gdpPercap, y = lifeExp,
color = continent),
alpha = 0.5,
inherit.aes = FALSE) +
geom_line() +
geom_ribbon(alpha = 0.2, color = FALSE) +
scale_x_log10(labels = scales::dollar)
geom_ribbon()draws the area covered by the prediction intervals:- It takes an
xargument like a line, but ayminandymaxargument as specified in theggplot()aesthetic mapping.
- It takes an
Generate predictions to graph
Tidy model objects with broom
The
broompackage to help us do a lot of things with our model output.broomcan tidily extract three kinds of information.- We can see component-level information about aspects of the model itself, such as coefficients and t-statistics.
- We can obtain observation-level information about the model’s connection to the underlying data, such as fitted values and residuals.
- We can get model-level information that summarizes the fit as a whole, such as F-statistic, model deviance, or r-squared.
library(broom)
Get component-level statistics with tidy()
- The
tidy()function takes a model object and returns a data frame of component-level information.
out_comp <- tidy(out) out_comp %>% round_df()
## # A tibble: 7 × 5 ## term estimate std.error statistic p.value ## <chr> <dbl> <dbl> <dbl> <dbl> ## 1 (Intercept) 47.8 0.34 141. 0 ## 2 gdpPercap 0 0 19.2 0 ## 3 pop 0 0 3.33 0 ## 4 continentAmericas 13.5 0.6 22.5 0 ## 5 continentAsia 8.19 0.57 14.3 0 ## 6 continentEurope 17.5 0.62 28.0 0 ## 7 continentOceania 18.1 1.78 10.2 0
Get component-level statistics with tidy()
- We can work with
tidy()to make plots in a familiar way, and much more easily.
p <- ggplot(out_comp, mapping = aes(x = term,
y = estimate))
p + geom_point() + coord_flip()
Get component-level statistics with tidy()
Get component-level statistics with tidy()
- We can tell
tidy()to calculate confidence intervals for the estimates, using R’sconf.int = TRUEoption.
out_conf <- tidy(out, conf.int = TRUE) out_conf %>% round_df()
## # A tibble: 7 × 7 ## term estimate std.error statistic p.value conf.low conf.high ## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> ## 1 (Intercept) 47.8 0.34 141. 0 47.2 48.5 ## 2 gdpPercap 0 0 19.2 0 0 0 ## 3 pop 0 0 3.33 0 0 0 ## 4 continentAmericas 13.5 0.6 22.5 0 12.3 14.6 ## 5 continentAsia 8.19 0.57 14.3 0 7.07 9.31 ## 6 continentEurope 17.5 0.62 28.0 0 16.2 18.7 ## 7 continentOceania 18.1 1.78 10.2 0 14.6 21.6
Get component-level statistics with tidy()
- We can tell
tidy()to calculate confidence intervals for the estimates, using R’sconf.int = TRUEoption.
out_conf <- subset(out_conf, term != "(Intercept)") out_conf$nicelabs <- prefix_strip(out_conf$term, "continent")
Get component-level statistics with tidy()
- We can use
geom_pointrange()to make a figure that displays some information about our confidence in the variable estimates
p <- ggplot(out_conf, mapping = aes(x = reorder(nicelabs, estimate),
y = estimate, ymin = conf.low, ymax = conf.high))
p + geom_pointrange() + coord_flip() + labs(x="", y="OLS Estimate")
Get component-level statistics with tidy()
Get observation-level statistics with augment()
The values returned by
augment()are all statistics calculated at the level of the original observations.Working from a call to
augment()will return a data frame with all the original observations used in the estimation of the model, together with columns like the following:.fitted— The fitted values of the model..se.fit— The standard errors of the fitted values..resid— The residuals..hat— The diagonal of the hat matrix..sigma— An estimate of residual standard deviation when the corresponding observation is dropped from the model..cooksd— Cook’s distance, a common regression diagnostic on how the observation is influential in the estimation;.std.resid— The standardized residuals.
Get observation-level statistics with augment()
out_aug <- augment(out) head(out_aug)
## # A tibble: 6 × 10 ## lifeExp gdpPercap pop continent .fitted .resid .hat .sigma .cooksd ## <dbl> <dbl> <int> <fct> <dbl> <dbl> <dbl> <dbl> <dbl> ## 1 28.8 779. 8425333 Asia 56.4 -27.6 0.00322 8.34 0.00505 ## 2 30.3 821. 9240934 Asia 56.4 -26.1 0.00321 8.34 0.00450 ## 3 32.0 853. 10267083 Asia 56.5 -24.5 0.00320 8.35 0.00393 ## 4 34.0 836. 11537966 Asia 56.5 -22.4 0.00319 8.35 0.00330 ## 5 36.1 740. 13079460 Asia 56.4 -20.3 0.00319 8.35 0.00271 ## 6 38.4 786. 14880372 Asia 56.5 -18.0 0.00317 8.36 0.00212 ## # … with 1 more variable: .std.resid <dbl>
head(out_aug) %>% round_df()
## # A tibble: 6 × 10 ## lifeExp gdpPercap pop continent .fitted .resid .hat .sigma .cooksd ## <dbl> <dbl> <dbl> <fct> <dbl> <dbl> <dbl> <dbl> <dbl> ## 1 28.8 779. 8425333 Asia 56.4 -27.6 0 8.34 0.01 ## 2 30.3 821. 9240934 Asia 56.4 -26.1 0 8.34 0 ## 3 32 853. 10267083 Asia 56.5 -24.5 0 8.35 0 ## 4 34.0 836. 11537966 Asia 56.5 -22.4 0 8.35 0 ## 5 36.1 740. 13079460 Asia 56.4 -20.3 0 8.35 0 ## 6 38.4 786. 14880372 Asia 56.5 -18.0 0 8.36 0 ## # … with 1 more variable: .std.resid <dbl>
Get observation-level statistics with augment()
- The new columns created by
augment()can be used to create some standard regression plots.- We can draw the residual plot (the residuals versus the fitted values).
p <- ggplot(data = out_aug,
mapping = aes(x = .fitted, y = .resid))
p + geom_point()
Get observation-level statistics with augment()
Get model-level statistics with glance()
glance()returns the information typically presented at the bottom of a model’ssummary()output.
glance(out) %>% round_df()
## # A tibble: 1 × 12 ## r.squared adj.r.squared sigma statistic p.value df logLik AIC BIC ## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> ## 1 0.58 0.58 8.37 394. 0 6 -6034. 12084. 12127. ## # … with 3 more variables: deviance <dbl>, df.residual <dbl>, nobs <dbl>
Grouped analysis and list columns
- Consider the linear regression model for the relationship between life expectancy and GDP by continent, for each year in the data.
eu77 <- gapminder %>% filter(continent == "Europe", year == 1977) fit <- lm(lifeExp ~ log(gdpPercap), data = eu77) summary(fit)
## ## Call: ## lm(formula = lifeExp ~ log(gdpPercap), data = eu77) ## ## Residuals: ## Min 1Q Median 3Q Max ## -7.4956 -1.0306 0.0935 1.1755 3.7125 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 29.489 7.161 4.118 0.000306 *** ## log(gdpPercap) 4.488 0.756 5.936 2.17e-06 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 2.114 on 28 degrees of freedom ## Multiple R-squared: 0.5572, Adjusted R-squared: 0.5414 ## F-statistic: 35.24 on 1 and 28 DF, p-value: 2.173e-06
Grouped analysis and list columns
- With
dplyrandbroomwe can do the grouped analysis for every continent-year slice of the data in a compact and tidy way.
out_le <- gapminder %>%
group_by(continent, year) %>%
nest()
out_le
## # A tibble: 60 × 3 ## # Groups: continent, year [60] ## continent year data ## <fct> <int> <list> ## 1 Asia 1952 <tibble [33 × 4]> ## 2 Asia 1957 <tibble [33 × 4]> ## 3 Asia 1962 <tibble [33 × 4]> ## 4 Asia 1967 <tibble [33 × 4]> ## 5 Asia 1972 <tibble [33 × 4]> ## 6 Asia 1977 <tibble [33 × 4]> ## 7 Asia 1982 <tibble [33 × 4]> ## 8 Asia 1987 <tibble [33 × 4]> ## 9 Asia 1992 <tibble [33 × 4]> ## 10 Asia 1997 <tibble [33 × 4]> ## # … with 50 more rows
nest()creates a list-column of data frames.- The list column,
data, contains a small table of data corresponding to each continent-year group.
- The list column,
Grouped analysis and list columns
- We can look at specific group, for example, “Europe 1977”, if we like, by filtering the data and then unnesting the list column.
out_le %>% filter(continent == "Europe" & year == 1977) %>% unnest()
## # A tibble: 30 × 6 ## # Groups: continent, year [1] ## continent year country lifeExp pop gdpPercap ## <fct> <int> <fct> <dbl> <int> <dbl> ## 1 Europe 1977 Albania 68.9 2509048 3533. ## 2 Europe 1977 Austria 72.2 7568430 19749. ## 3 Europe 1977 Belgium 72.8 9821800 19118. ## 4 Europe 1977 Bosnia and Herzegovina 69.9 4086000 3528. ## 5 Europe 1977 Bulgaria 70.8 8797022 7612. ## 6 Europe 1977 Croatia 70.6 4318673 11305. ## 7 Europe 1977 Czech Republic 70.7 10161915 14800. ## 8 Europe 1977 Denmark 74.7 5088419 20423. ## 9 Europe 1977 Finland 72.5 4738902 15605. ## 10 Europe 1977 France 73.8 53165019 18293. ## # … with 20 more rows
Grouped analysis and list columns
- List columns are useful because we can act on them in a compact and tidy way.
fit_ols <- function(df) {
lm(lifeExp ~ log(gdpPercap), data = df)
}
out_le <- gapminder %>%
group_by(continent, year) %>%
nest() %>%
mutate(model = map(data, fit_ols))
out_le
## # A tibble: 60 × 4 ## # Groups: continent, year [60] ## continent year data model ## <fct> <int> <list> <list> ## 1 Asia 1952 <tibble [33 × 4]> <lm> ## 2 Asia 1957 <tibble [33 × 4]> <lm> ## 3 Asia 1962 <tibble [33 × 4]> <lm> ## 4 Asia 1967 <tibble [33 × 4]> <lm> ## 5 Asia 1972 <tibble [33 × 4]> <lm> ## 6 Asia 1977 <tibble [33 × 4]> <lm> ## 7 Asia 1982 <tibble [33 × 4]> <lm> ## 8 Asia 1987 <tibble [33 × 4]> <lm> ## 9 Asia 1992 <tibble [33 × 4]> <lm> ## 10 Asia 1997 <tibble [33 × 4]> <lm> ## # … with 50 more rows
map()function applies a function to each element of a vector.
Grouped analysis and list columns
- List columns are useful because we can act on them in a compact and tidy way.
fit_ols <- function(df) {
lm(lifeExp ~ log(gdpPercap), data = df)
}
out_tidy <- gapminder %>%
group_by(continent, year) %>%
nest() %>%
mutate(model = map(data, fit_ols),
tidied = map(model, tidy)) %>%
unnest(tidied, .drop = TRUE) %>%
filter(term != "(Intercept)" &
continent != "Oceania")
Grouped analysis and list columns
- We now have tidy regression output with an estimate of the association between log GDP per capita and life expectancy for each year, within continents.
p <- ggplot(data = out_tidy,
mapping = aes(x = year, y = estimate,
ymin = estimate - 2*std.error,
ymax = estimate + 2*std.error,
group = continent, color = continent))
p + geom_pointrange(position = position_dodge(width = 1)) +
scale_x_continuous(breaks = unique(gapminder$year)) +
theme(legend.position = "top") +
labs(x = "Year", y = "Estimate", color = "Continent")
Grouped analysis and list columns
