Ellen Cheng’s Coding Exercise

library(dslabs) # load package with required data
help(gapminder) # help on gapminder data
str(gapminder) # gapminder variable data types

## '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 ...

summary(gapminder) # summary statistics of the data

##                 country           year      infant_mortality
##  Albania            :   57   Min.   :1960   Min.   :  1.50  
##  Algeria            :   57   1st Qu.:1974   1st Qu.: 16.00  
##  Angola             :   57   Median :1988   Median : 41.50  
##  Antigua and Barbuda:   57   Mean   :1988   Mean   : 55.31  
##  Argentina          :   57   3rd Qu.:2002   3rd Qu.: 85.10  
##  Armenia            :   57   Max.   :2016   Max.   :276.90  
##  (Other)            :10203                  NA's   :1453    
##  life_expectancy   fertility       population             gdp           
##  Min.   :13.20   Min.   :0.840   Min.   :3.124e+04   Min.   :4.040e+07  
##  1st Qu.:57.50   1st Qu.:2.200   1st Qu.:1.333e+06   1st Qu.:1.846e+09  
##  Median :67.54   Median :3.750   Median :5.009e+06   Median :7.794e+09  
##  Mean   :64.81   Mean   :4.084   Mean   :2.701e+07   Mean   :1.480e+11  
##  3rd Qu.:73.00   3rd Qu.:6.000   3rd Qu.:1.523e+07   3rd Qu.:5.540e+10  
##  Max.   :83.90   Max.   :9.220   Max.   :1.376e+09   Max.   :1.174e+13  
##                  NA's   :187     NA's   :185         NA's   :2972       
##     continent                region    
##  Africa  :2907   Western Asia   :1026  
##  Americas:2052   Eastern Africa : 912  
##  Asia    :2679   Western Africa : 912  
##  Europe  :2223   Caribbean      : 741  
##  Oceania : 684   South America  : 684  
##                  Southern Europe: 684  
##                  (Other)        :5586

class(gapminder) # gapminder is a dataframe

## [1] "data.frame"

# Work with the Africa data ----
africadata <- subset(gapminder, continent == "Africa") # assign only the African countries to a new variable called africadata
str(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(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

# subset with infant mort
subset_inf_life <- africadata[, c("infant_mortality", "life_expectancy")] # infant mortality is per 1000, life expectancy is in years
str(subset_inf_life) 

## '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 ...

summary(subset_inf_life) # there are 226 NA's for infant mortality

##  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

# subset with pop
subset_pop_life <- africadata[, c("population", "life_expectancy")] # population is the country population size
str(subset_pop_life) # large range of country pop sizes

## '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(subset_pop_life) # there are 51 NA's for population size

##    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

# Plots ----
# life expectancy as a function of infant mortality
with(subset_inf_life, plot(life_expectancy ~ infant_mortality, main = "Life expectancy as a function of infant mortality", ylab = "Life expectancy (yrs)", xlab = "Infant deaths per 1000")) # negative correlation. Each streak is a different country.

# life expectancy as a function of population size, using a log-scale on the x-axis
with(subset_pop_life, plot(life_expectancy ~ population, log = "x", main = "Life expectancy as a function of population size", sub = "(Note that x-axis is on log-scale)", ylab = "Life expectancy (yrs)", xlab = "Country population size")) # Each streak is a different country. Positive correlation within country.

# More data processing ----
(missing_inf_mort <- unique(africadata$year[is.na(africadata$infant_mortality)])) # years with missing data for infant mortality

##  [1] 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973
## [15] 1974 1975 1976 1977 1978 1979 1980 1981 2016

# subset of Yr2000 data
subset_yr2000 <- subset(africadata, year == 2000)
str(subset_yr2000)

## '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 ...

summary(subset_yr2000)

##          country        year      infant_mortality life_expectancy
##  Algeria     : 1   Min.   :2000   Min.   : 12.30   Min.   :37.60  
##  Angola      : 1   1st Qu.:2000   1st Qu.: 60.80   1st Qu.:51.75  
##  Benin       : 1   Median :2000   Median : 80.30   Median :54.30  
##  Botswana    : 1   Mean   :2000   Mean   : 78.93   Mean   :56.36  
##  Burkina Faso: 1   3rd Qu.:2000   3rd Qu.:103.30   3rd Qu.:60.00  
##  Burundi     : 1   Max.   :2000   Max.   :143.30   Max.   :75.00  
##  (Other)     :45                                                  
##    fertility       population             gdp               continent 
##  Min.   :1.990   Min.   :    81154   Min.   :2.019e+08   Africa  :51  
##  1st Qu.:4.150   1st Qu.:  2304687   1st Qu.:1.274e+09   Americas: 0  
##  Median :5.550   Median :  8799165   Median :3.238e+09   Asia    : 0  
##  Mean   :5.156   Mean   : 15659800   Mean   :1.155e+10   Europe  : 0  
##  3rd Qu.:5.960   3rd Qu.: 17391242   3rd Qu.:8.654e+09   Oceania : 0  
##  Max.   :7.730   Max.   :122876723   Max.   :1.329e+11                
##                                                                       
##                        region  
##  Eastern Africa           :16  
##  Western Africa           :16  
##  Middle Africa            : 8  
##  Northern Africa          : 6  
##  Southern Africa          : 5  
##  Australia and New Zealand: 0  
##  (Other)                  : 0

# More plotting ----
# For Yr2000 ONLY, life expectancy as a function of infant mortality
with(subset_yr2000, plot(life_expectancy ~ infant_mortality, main = "Yr 2000: Life expectancy as a function of infant mortality", ylab = "Life expectancy (yrs)", xlab = "Infant deaths per 1000")) # negative correlation

# For Yr2000 ONLY, life expectancy as a function of population size, using a log-scale on the x-axis
with(subset_yr2000, plot(life_expectancy ~ population, log = "x", main = "Yr 2000: Life expectancy as a function of population size", sub = "(Note that x-axis is on log-scale)", ylab = "Life expectancy (yrs)", xlab = "Country population size")) # No apparent correlation

# Linear models (using Yr2000 data) ----
#  linear model predicting life expectancy as a function of infant mortality
summary(fit1 <- with(subset_yr2000, lm(life_expectancy ~ infant_mortality))) # p = 2.83E-8, so highly significant

## 
## Call:
## lm(formula = life_expectancy ~ infant_mortality)
## 
## 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

#  linear model predicting life expectancy as a function of population size
summary(fit2 <- with(subset_yr2000, lm(life_expectancy ~ population))) # p = 0.616, so not statistically significant at alpha = 0.05

## 
## Call:
## lm(formula = life_expectancy ~ population)
## 
## 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