#install and load required packages
library(tidyverse)── Attaching packages ─────────────────────────────────────── tidyverse 1.3.2 ──
✔ ggplot2 3.4.0 ✔ purrr 0.3.5
✔ tibble 3.1.8 ✔ dplyr 1.0.10
✔ tidyr 1.2.1 ✔ stringr 1.5.0
✔ readr 2.1.3 ✔ forcats 0.5.2
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag() masks stats::lag()#install and load required packages
library(dslabs)
#find gapminder data to be used for exercise
#help(gapminder)str(gapminder) #get an overview of the data structure'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) #get a summary of the data 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 class(gapminder) #determine the type of object gapminer is [1] "data.frame"#save all data to "data"
data = gapminder
# subset based on Continent == Africa
africaData = data[ which(data$continent=="Africa"), ]
str(africaData) #get an overview of the data structure'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(gapminder) #get a summary of the data 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 ####this section added by Weifan
##did you mean to do below instead of get a summary of gapminder?
summary(data) 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 #Subset Africa infant mortality and life expectancy
infantM_LifeE = africaData[c("infant_mortality", "life_expectancy")]
str(infantM_LifeE) #get an overview of the data structure'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 ...#####this section is added by Weifan
### using select function to extract a data frame only include infant mortality and life expectancy
infantM_LifeE2=select(africaData, infant_mortality,life_expectancy)
###get an overview of the data structure
str(infantM_LifeE2)'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 ...###get a summary of the data
summary(infantM_LifeE2) 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(infantM_LifeE)#get a summary of the data 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 Plot life expectancy as a function of infant mortality
# Plot life expectancy as a function of infant mortality
ggplot(infantM_LifeE, aes(x=infant_mortality, y=life_expectancy)) + geom_point()+xlab("Infant Mortality")+ ylab("Life Expectancy (Years)")+
theme_bw()Warning: Removed 226 rows containing missing values (`geom_point()`).
#Subset Africa population and life expectancy
pop_LifeE = africaData[c("population", "life_expectancy")]
str(pop_LifeE) #get an overview of the data structure'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(pop_LifeE) #get a summary of the data 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 life expectancy as a function of population
# Plot life expectancy as a function of population
ggplot(pop_LifeE, aes(x=log(population), y=life_expectancy)) + geom_point() +xlab("Population (log)")+ ylab("Life Expectancy (Years)")+
theme_bw()Warning: Removed 51 rows containing missing values (`geom_point()`).
# determine the years with missing values for NA
infantNA = (africaData[is.na(africaData$infant_mortality), ] )
table(infantNA$year)
1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975
10 17 16 16 15 14 13 11 11 7 5 6 6 6 5 5
1976 1977 1978 1979 1980 1981 2016
3 3 2 2 1 1 51 ####this section is added by Weifan
#using filter and count functions
infantNA2=africaData%>%
filter(is.na(infant_mortality))%>%
count(year)
infantNA2 year n
1 1960 10
2 1961 17
3 1962 16
4 1963 16
5 1964 15
6 1965 14
7 1966 13
8 1967 11
9 1968 11
10 1969 7
11 1970 5
12 1971 6
13 1972 6
14 1973 6
15 1974 5
16 1975 5
17 1976 3
18 1977 3
19 1978 2
20 1979 2
21 1980 1
22 1981 1
23 2016 51# subset year 2000
y_2000 = africaData[ which(africaData$year=="2000"), ]
summary(y_2000) #get a summary of the data 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 plot life expectancy as a function of infant mortality
# Plot life expectancy as a function of infant mortality
ggplot(y_2000, aes(x=infant_mortality, y=life_expectancy)) + geom_point() +xlab("Infant Mortality")+ ylab("Life Expectancy (Years)")+
theme_bw()
Plot life expectancy as a function of infant mortality
# Plot life expectancy as a function of infant mortality
ggplot(y_2000, aes(x=log(population), y=life_expectancy)) + geom_point() +xlab("Population (log)")+ ylab("Life Expectancy (Years)")+
theme_bw()
#####This section added by Weifan
###find out if there is any missing value of fertility and gdp in year 2000
summary(y_2000) 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 ###since there is no missing value in year 2000, we still choose this year to plot life expectancy as a function of fertility
y_2000%>%
ggplot(aes(x=fertility,y=life_expectancy,color=region))+
geom_point()+
geom_smooth(method="lm",se=FALSE,color="green")`geom_smooth()` using formula = 'y ~ x'
labs(x="fertility",y="life_expectancy", title="relationship between life expectancy and fertility")+
theme_minimal()NULL###plot life expectancy as a function of gdp
y_2000%>%
ggplot(aes(x=gdp,y=life_expectancy,color=region))+
geom_point()+
geom_smooth(method="lm",se=FALSE,color="red")+
labs(x="gdp",y="life_expectancy", title="relationship between life expectancy and gdp in five different regions")+
scale_x_log10(labels=scales::dollar_format())`geom_smooth()` using formula = 'y ~ x'
linear model to fit outcome = life expectancy and predictor = infant mortality
fit1 = lm(life_expectancy~infant_mortality, data=y_2000)
fit1_table = broom::tidy(fit1)
print(fit1_table)# A tibble: 2 × 5
term estimate std.error statistic p.value
<chr> <dbl> <dbl> <dbl> <dbl>
1 (Intercept) 71.3 2.43 29.4 8.91e-33
2 infant_mortality -0.189 0.0287 -6.59 2.83e- 8linear model to fit outcome = life expectancy and predictor = population
fit2 = lm(life_expectancy~population, data=y_2000)
fit2_table = broom::tidy(fit2)
print(fit2_table)# A tibble: 2 × 5
term estimate std.error statistic p.value
<chr> <dbl> <dbl> <dbl> <dbl>
1 (Intercept) 55.9 1.47 38.1 4.51e-38
2 population 0.0000000276 0.0000000546 0.505 6.16e- 1this section is added by Weifan
###linear model to predict life expectancy using fertility
lm1=lm(life_expectancy~fertility, data=y_2000)
table1=broom::tidy(lm1)%>%
knitr::kable(digits=3)
###linear model to predict life expectancy using gdp
lm2=lm(life_expectancy~gdp,data=y_2000)
table2=broom::tidy(lm2)%>%
knitr::kable(digits=3)
table1| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | 76.075 | 3.348 | 22.720 | 0 |
| fertility | -3.823 | 0.625 | -6.113 | 0 |
table2| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | 55.014 | 1.247 | 44.106 | 0.000 |
| gdp | 0.000 | 0.000 | 2.516 | 0.015 |
Based on the p-values of the linear models, a conclusion can be made that there is a statistical relationship between life expectancy and infant mortality but not life expectancy and population. ###this section is added by Weifan based on the p_values of two models, we can conclude that life expectancy can be predicted by both variables (fertility and GDP)