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library(dslabs)
Warning: package 'dslabs' was built under R version 4.4.3
library(dplyr)
#get an overview of data structurestr(gapminder)
'data.frame': 10545 obs. of 9 variables:
$ country : Factor w/ 185 levels "Albania","Algeria",..: 1 2 3 4 5 6 7 8 9 10 ...
$ year : int 1960 1960 1960 1960 1960 1960 1960 1960 1960 1960 ...
$ infant_mortality: num 115.4 148.2 208 NA 59.9 ...
$ life_expectancy : num 62.9 47.5 36 63 65.4 ...
$ fertility : num 6.19 7.65 7.32 4.43 3.11 4.55 4.82 3.45 2.7 5.57 ...
$ population : num 1636054 11124892 5270844 54681 20619075 ...
$ gdp : num NA 1.38e+10 NA NA 1.08e+11 ...
$ continent : Factor w/ 5 levels "Africa","Americas",..: 4 1 1 2 2 3 2 5 4 3 ...
$ region : Factor w/ 22 levels "Australia and New Zealand",..: 19 11 10 2 15 21 2 1 22 21 ...
#get a summary of datasummary(gapminder)
country year infant_mortality life_expectancy
Albania : 57 Min. :1960 Min. : 1.50 Min. :13.20
Algeria : 57 1st Qu.:1974 1st Qu.: 16.00 1st Qu.:57.50
Angola : 57 Median :1988 Median : 41.50 Median :67.54
Antigua and Barbuda: 57 Mean :1988 Mean : 55.31 Mean :64.81
Argentina : 57 3rd Qu.:2002 3rd Qu.: 85.10 3rd Qu.:73.00
Armenia : 57 Max. :2016 Max. :276.90 Max. :83.90
(Other) :10203 NA's :1453
fertility population gdp continent
Min. :0.840 Min. :3.124e+04 Min. :4.040e+07 Africa :2907
1st Qu.:2.200 1st Qu.:1.333e+06 1st Qu.:1.846e+09 Americas:2052
Median :3.750 Median :5.009e+06 Median :7.794e+09 Asia :2679
Mean :4.084 Mean :2.701e+07 Mean :1.480e+11 Europe :2223
3rd Qu.:6.000 3rd Qu.:1.523e+07 3rd Qu.:5.540e+10 Oceania : 684
Max. :9.220 Max. :1.376e+09 Max. :1.174e+13
NA's :187 NA's :185 NA's :2972
region
Western Asia :1026
Eastern Africa : 912
Western Africa : 912
Caribbean : 741
South America : 684
Southern Europe: 684
(Other) :5586
#determine what time of object gapminder isclass(gapminder)
[1] "data.frame"
#assign African countries to new object africadata <- gapminder %>%filter(continent =="Africa")#overview of data structurestr(africadata)
'data.frame': 2907 obs. of 9 variables:
$ country : Factor w/ 185 levels "Albania","Algeria",..: 2 3 18 22 26 27 29 31 32 33 ...
$ year : int 1960 1960 1960 1960 1960 1960 1960 1960 1960 1960 ...
$ infant_mortality: num 148 208 187 116 161 ...
$ life_expectancy : num 47.5 36 38.3 50.3 35.2 ...
$ fertility : num 7.65 7.32 6.28 6.62 6.29 6.95 5.65 6.89 5.84 6.25 ...
$ population : num 11124892 5270844 2431620 524029 4829291 ...
$ gdp : num 1.38e+10 NA 6.22e+08 1.24e+08 5.97e+08 ...
$ continent : Factor w/ 5 levels "Africa","Americas",..: 1 1 1 1 1 1 1 1 1 1 ...
$ region : Factor w/ 22 levels "Australia and New Zealand",..: 11 10 20 17 20 5 10 20 10 10 ...
#summary of data summary(africadata)
country year infant_mortality life_expectancy
Algeria : 57 Min. :1960 Min. : 11.40 Min. :13.20
Angola : 57 1st Qu.:1974 1st Qu.: 62.20 1st Qu.:48.23
Benin : 57 Median :1988 Median : 93.40 Median :53.98
Botswana : 57 Mean :1988 Mean : 95.12 Mean :54.38
Burkina Faso: 57 3rd Qu.:2002 3rd Qu.:124.70 3rd Qu.:60.10
Burundi : 57 Max. :2016 Max. :237.40 Max. :77.60
(Other) :2565 NA's :226
fertility population gdp continent
Min. :1.500 Min. : 41538 Min. :4.659e+07 Africa :2907
1st Qu.:5.160 1st Qu.: 1605232 1st Qu.:8.373e+08 Americas: 0
Median :6.160 Median : 5570982 Median :2.448e+09 Asia : 0
Mean :5.851 Mean : 12235961 Mean :9.346e+09 Europe : 0
3rd Qu.:6.860 3rd Qu.: 13888152 3rd Qu.:6.552e+09 Oceania : 0
Max. :8.450 Max. :182201962 Max. :1.935e+11
NA's :51 NA's :51 NA's :637
region
Eastern Africa :912
Western Africa :912
Middle Africa :456
Northern Africa :342
Southern Africa :285
Australia and New Zealand: 0
(Other) : 0
#create new object from africadata that has only infant_mortality and life_expectancy africa_inf_exp <- africadata %>%select("infant_mortality", "life_expectancy")#create new object from africadata that has only population and life_expectancyafrica_pop_exp <- africadata %>%select("population", "life_expectancy")#structure overview of both africa_inf_exp and africa_pop_expstr(africa_inf_exp)
'data.frame': 2907 obs. of 2 variables:
$ infant_mortality: num 148 208 187 116 161 ...
$ life_expectancy : num 47.5 36 38.3 50.3 35.2 ...
str(africa_pop_exp)
'data.frame': 2907 obs. of 2 variables:
$ population : num 11124892 5270844 2431620 524029 4829291 ...
$ life_expectancy: num 47.5 36 38.3 50.3 35.2 ...
#summary of both summary(africa_inf_exp)
infant_mortality life_expectancy
Min. : 11.40 Min. :13.20
1st Qu.: 62.20 1st Qu.:48.23
Median : 93.40 Median :53.98
Mean : 95.12 Mean :54.38
3rd Qu.:124.70 3rd Qu.:60.10
Max. :237.40 Max. :77.60
NA's :226
summary(africa_pop_exp)
population life_expectancy
Min. : 41538 Min. :13.20
1st Qu.: 1605232 1st Qu.:48.23
Median : 5570982 Median :53.98
Mean : 12235961 Mean :54.38
3rd Qu.: 13888152 3rd Qu.:60.10
Max. :182201962 Max. :77.60
NA's :51
#plot infant_mortality (x) vs. life_expectancy (y)ggplot(africa_inf_exp, (aes(x = infant_mortality, y = life_expectancy))) +geom_point()
Warning: Removed 226 rows containing missing values or values outside the scale range
(`geom_point()`).
#plot population (x) vs. life expectancy (y)##population in log scale so log(x) vs. (y)###check structureafrica_pop_exp <- africa_pop_exp %>%mutate(log_population =log10(population))str(africa_pop_exp)
'data.frame': 2907 obs. of 3 variables:
$ population : num 11124892 5270844 2431620 524029 4829291 ...
$ life_expectancy: num 47.5 36 38.3 50.3 35.2 ...
$ log_population : num 7.05 6.72 6.39 5.72 6.68 ...
ggplot(africa_pop_exp, (aes(x = log_population, y = life_expectancy))) +geom_point()
Warning: Removed 51 rows containing missing values or values outside the scale range
(`geom_point()`).
Appearance of streaks - likely represent each country over time as its population and life expextancy both slowly increase.
#identify where the NA values are, to avoid them in the next step missing_inf_years <- africadata %>%filter(is.na(infant_mortality)) %>%pull(year) %>%unique()#new object with only year 2000 data africadata_2000 <- africadata %>%filter(year ==2000)#structure of new africa_data2000str(africadata_2000)
'data.frame': 51 obs. of 9 variables:
$ country : Factor w/ 185 levels "Albania","Algeria",..: 2 3 18 22 26 27 29 31 32 33 ...
$ year : int 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 ...
$ infant_mortality: num 33.9 128.3 89.3 52.4 96.2 ...
$ life_expectancy : num 73.3 52.3 57.2 47.6 52.6 46.7 54.3 68.4 45.3 51.5 ...
$ fertility : num 2.51 6.84 5.98 3.41 6.59 7.06 5.62 3.7 5.45 7.35 ...
$ population : num 31183658 15058638 6949366 1736579 11607944 ...
$ gdp : num 5.48e+10 9.13e+09 2.25e+09 5.63e+09 2.61e+09 ...
$ continent : Factor w/ 5 levels "Africa","Americas",..: 1 1 1 1 1 1 1 1 1 1 ...
$ region : Factor w/ 22 levels "Australia and New Zealand",..: 11 10 20 17 20 5 10 20 10 10 ...
#plot infant_mortality (x) vs. life_expectancy (y)ggplot(africadata_2000, (aes(x = infant_mortality, y = life_expectancy))) +geom_point()
##plot population (x) vs. life expectancy (y)##population in log scale so log(x) vs. (y)###check structureafricadata_2000 <- africadata_2000 %>%mutate(log_population =log10(population))str(africadata_2000)
'data.frame': 51 obs. of 10 variables:
$ country : Factor w/ 185 levels "Albania","Algeria",..: 2 3 18 22 26 27 29 31 32 33 ...
$ year : int 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 ...
$ infant_mortality: num 33.9 128.3 89.3 52.4 96.2 ...
$ life_expectancy : num 73.3 52.3 57.2 47.6 52.6 46.7 54.3 68.4 45.3 51.5 ...
$ fertility : num 2.51 6.84 5.98 3.41 6.59 7.06 5.62 3.7 5.45 7.35 ...
$ population : num 31183658 15058638 6949366 1736579 11607944 ...
$ gdp : num 5.48e+10 9.13e+09 2.25e+09 5.63e+09 2.61e+09 ...
$ continent : Factor w/ 5 levels "Africa","Americas",..: 1 1 1 1 1 1 1 1 1 1 ...
$ region : Factor w/ 22 levels "Australia and New Zealand",..: 11 10 20 17 20 5 10 20 10 10 ...
$ log_population : num 7.49 7.18 6.84 6.24 7.06 ...
ggplot(africadata_2000, (aes(x = log_population, y = life_expectancy))) +geom_point()
#Fit life expectancy as the outcome, and infant mortality as the predictorfit1 <-lm(life_expectancy ~ infant_mortality, data = africadata_2000)#Fit life expectancy as the outcome, and population as the predictorfit2 <-lm(life_expectancy ~ population, data = africadata_2000)#I wasn't sure if you wanted population or the log_population, so I did fit3 to be the log_populationfit3 <-lm(life_expectancy ~ log_population, data = africadata_2000)#summary of the fits summary(fit1)
Call:
lm(formula = life_expectancy ~ infant_mortality, data = africadata_2000)
Residuals:
Min 1Q Median 3Q Max
-22.6651 -3.7087 0.9914 4.0408 8.6817
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 71.29331 2.42611 29.386 < 2e-16 ***
infant_mortality -0.18916 0.02869 -6.594 2.83e-08 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 6.221 on 49 degrees of freedom
Multiple R-squared: 0.4701, Adjusted R-squared: 0.4593
F-statistic: 43.48 on 1 and 49 DF, p-value: 2.826e-08
summary(fit2)
Call:
lm(formula = life_expectancy ~ population, data = africadata_2000)
Residuals:
Min 1Q Median 3Q Max
-18.429 -4.602 -2.568 3.800 18.802
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.593e+01 1.468e+00 38.097 <2e-16 ***
population 2.756e-08 5.459e-08 0.505 0.616
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 8.524 on 49 degrees of freedom
Multiple R-squared: 0.005176, Adjusted R-squared: -0.01513
F-statistic: 0.2549 on 1 and 49 DF, p-value: 0.6159
summary(fit3)
Call:
lm(formula = life_expectancy ~ log_population, data = africadata_2000)
Residuals:
Min 1Q Median 3Q Max
-19.113 -4.809 -1.554 3.907 18.863
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 65.324 12.520 5.217 3.65e-06 ***
log_population -1.315 1.829 -0.719 0.476
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 8.502 on 49 degrees of freedom
Multiple R-squared: 0.01044, Adjusted R-squared: -0.009755
F-statistic: 0.517 on 1 and 49 DF, p-value: 0.4755
What I found here - fit1: p-value = 2.826e-08, R-squared = 0.4593 - p-value indicates significant difference (well below 0.05), but with an R-squared of 0.4593, that is ia fairly weak inverse (negative) correlation between life expectancy and infant mortality, confirmed visually with plot fit2: p-value = 0.6159, R-squared = -0.01513 - p-value indicates no significant difference (above 0.05), no relationship between life_expectancy and population fit3: p-vlaue = 0.4755, R-squared = -0.009755 - p-value indicates no signifiicant difference (above 0.05), no relationhsip between life expectancy and log_population
Additional exploration: dslabs::gapminder (contributed by Alexandra Tejada-Strop)
In this section I explore the gapminder dataset from the dslabs package. I do basic exploration, some light cleaning, a few figures, and then fit a simple regression model to describe how life expectancy relates to economic output and time.
Load packages —-
library(tidyverse) library(dslabs)
Load data —-
data(gapminder) # loads a data frame called gapminder
I create a few helpful variables: - gdp_per_cap: GDP per capita - log_gdp_per_cap: log10 GDP per capita (often more linear for modeling) I also remove rows where GDP or population are missing or zero (to avoid dividing by zero and taking log of non-positive values).
Relationship between life expectancy and GDP per capita (log scale), colored by region
1) Life expectancy over time by region
gap2 %>% group_by(year, region) %>% summarise(mean_life_exp = mean(life_expectancy), .groups = “drop”) %>% ggplot(aes(x = year, y = mean_life_exp, color = region)) + geom_line() + labs( title = “Average life expectancy over time by region”, x = “Year”, y = “Average life expectancy” )
2) Life expectancy vs GDP per cap (log scale)
gap2 %>% ggplot(aes(x = log_gdp_per_cap, y = life_expectancy, color = region)) + geom_point(alpha = 0.4) + geom_smooth(method = “lm”, se = FALSE) + labs( title = “Life expectancy vs log10(GDP per capita)”, x = “log10(GDP per capita)”, y = “Life expectancy” )
Simple statistical model
I fit a linear regression model predicting life expectancy from: - log10(GDP per capita) - year (to capture general time trends) - region (to capture broad geographic differences)
This is not meant to be causal, just a simple descriptive model.
m1 <- lm(life_expectancy ~ log_gdp_per_cap + year + region, data = gap2) summary(m1)
A cleaner coefficient table
broom::tidy(m1) %>% arrange(p.value)
Results (plain-language summary)
The coefficient for log_gdp_per_cap is typically positive: higher GDP per capita is associated with higher life expectancy.
The coefficient for year is typically positive: life expectancy tends to increase over time.
Regional coefficients reflect systematic differences across regions after accounting for GDP per capita and time.
(Exact estimates may vary slightly depending on filtering and package versions.)
