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#help(gapminder)#The str functions is used to look at observations and variables in the dataset str(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 the type of object gapminder is#The class function is a data frame that allows us to look at a class of the datasetclass(gapminder)
[1] "data.frame"
#Using the gapminder dataset, I've created a new dataframe that will only include countries that have Africa as the continentafricadata <- gapminder[gapminder$continent =="Africa", ]#Check the structure and summary of africadatastr(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
#Create a dataframe with infant mortality and life expectancyafrica_mort_life <- africadata[, c("infant_mortality", "life_expectancy")]#Inspect the structure and summarystr(africa_mort_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(africa_mort_life)
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
#Create a dataframe with population and life expectancyafrica_pop_life <- africadata[, c("population", "life_expectancy")]#Inspect the structure and summarystr(africa_pop_life)
'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(africa_pop_life)
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
This analysis looks at African countries using the Gapminder dataset on R. The data is first subset to only include African countries. Then two smaller datasets are created to look at life expectancy with infant mortality and population with infant mortality.
#Plot life expectancy vs infant mortality for African countries#Using the plot function to make the plotplot(#Using the infant_mortality column and makes them the x-axis values africa_mort_life$infant_mortality,#Using the life_expectancy column and makes them the y-axis values africa_mort_life$life_expectancy,#labels the x-axis infant mortality and the y-axis Life expectancyxlab ="Infant Mortality",ylab ="Life Expectancy",#Makes the title of the plot Life expectancy vs infant mortality in Africamain ="Life Expectancy vs Infant Mortality in Africa",pch =16)
#Plot life expectancy vs population size for African countries#Using the plot function to make the plotplot(#Using the population column and makes them the x-axis values africa_pop_life$population,#Using the life expectancy column and makes them the y-axis values africa_pop_life$life_expectancy,#labels the x-axis population size and the y-axis Life expectancyxlab ="Population Size (log scale)",ylab ="Life Expectancy",#Makes the title of the plot Life expectancy vs population size in Africamain ="Life Expectancy vs Population Size in Africa",pch =16,#Setting the scale of the x-axis to be logarithmiclog ="x")
The first plot shows a negative relationship between infant mortality and life expectancy. The second plot shows a positive relationship between population size and life expectancy. The streaks in the plots are most likley due to individual countries obsereved over multiple years. This shows more in the second plot because there is data for the same countries over several years, which is likely to show gradual differences. These gradual differences may form streaks in the plots.
#Identifies which years have missing data for infant mortality #is.na() functions chacks if each value in the dataframe is NA or notmissing_im <-is.na(africadata$infant_mortality)#Lists the years when infant mortality is missingmissing_years <-sort(unique(africadata$year[missing_im]))missing_years
#Extract data for the year 2000 onlyafrica_2000 <- africadata[africadata$year ==2000, ]#Check the structure of the new datasetstr(africa_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 ...
#View summary statistics for the year 2000 datasummary(africa_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
#Plot life expectancy vs infant mortality for Africa in the year 2000#Using the plot function to make the plotplot(#Using the infant mortality column and makes them the x-axis values africa_2000$infant_mortality,#Using the life expectancy column and makes them the y-axis values africa_2000$life_expectancy,#labels the x-axis infant mortality and the y-axis Life expectancyxlab ="Infant Mortality",ylab ="Life Expectancy",#Makes the title of the plot Life expectancy vs infant mortality in Africa in 2000main ="Life Expectancy vs Infant Mortality in Africa in 2000",pch =16)
# Plot life expectancy vs population size for Africa in the year 2000#Using the plot function to make the plotplot(#Using the population column and makes them the x-axis values africa_2000$population,#Using the life expectancy column and makes them the y-axis values africa_2000$life_expectancy,#labels the x-axis population size and the y-axis Life expectancyxlab ="Population Size (log scale)",ylab ="Life Expectancy",#Makes the title of the plot Life expectancy vs population size in Africa in 2000main ="Life Expectancy vs Population Size in Africa in 2000",pch =16,#Setting the scale of the x-axis to be logarithmiclog ="x")
#Models life expectancy as a function of infant mortality#lm is used to fit linear modelslm_infant <-lm(life_expectancy ~ infant_mortality, data = africa_2000)# Models life expectancy as a function of population sizelm_population <-lm(life_expectancy ~ population, data = africa_2000)# prints results for both modelssummary(lm_infant)
Call:
lm(formula = life_expectancy ~ infant_mortality, data = africa_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(lm_population)
Call:
lm(formula = life_expectancy ~ population, data = africa_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
The relationship between life expectancy and infant mortality are highly significant, and negatively correlated. The negative correlation is indicated by the negative slope. The relationship between population size and life expectancy is not significant because the p-value is 0.6159.
Additional contribution
This section contributed by Kexin (Cassie) Cui.
Data overview
Dataset picked from dslabs: admissions
# Load required packageslibrary(dplyr) library(ggplot2) # Load the dataset into the sessiondata("admissions") # Preview the first 6 rowshead(admissions)
major gender admitted applicants
1 A men 62 825
2 B men 63 560
3 C men 37 325
4 D men 33 417
5 E men 28 191
6 F men 6 373
# Get basic summary statistics for each columnsummary(admissions)
major gender admitted applicants
Length:12 Length:12 Min. : 6.00 Min. : 25.0
Class :character Class :character 1st Qu.:27.00 1st Qu.:291.5
Mode :character Mode :character Median :34.50 Median :374.0
Mean :39.92 Mean :377.2
3rd Qu.:62.25 3rd Qu.:452.8
Max. :82.00 Max. :825.0
# Check for missing values in each columncolSums(is.na(admissions))
major gender admitted applicants
0 0 0 0
Descriptive analysis and visualization
# Compute total applicants and mean admission percentage by genderadmissions |>group_by(gender) |>summarize(total_applicants =sum(applicants), mean_admitted_pct =mean(admitted), .groups ="drop" )
# A tibble: 2 × 3
gender total_applicants mean_admitted_pct
<chr> <dbl> <dbl>
1 men 2691 38.2
2 women 1835 41.7
ggplot(admissions, aes(x = major, y = applicants, fill = gender)) +geom_col(position ="dodge") +labs(x ="Major",y ="Number of applicants",fill ="Gender" )
# Plot applicants by major, faceted by genderggplot(admissions, aes(x = major, y = applicants)) +geom_col() +facet_wrap(~ gender) +# separate panels by genderlabs(x ="Major", y ="Number of applicants" )
# Plot admission percentage by major and genderggplot(admissions, aes(x = major, y = admitted, group = gender)) +geom_point(size =2) +geom_line() +facet_wrap(~ gender) +labs(x ="Major", y ="Admission percentage" )
Binomial logistic regression for admission outcome
# Create integer counts for admitted and rejected applicantsadmissions_glm <- admissions |>mutate(admitted_num =round(admitted * applicants /100), rejected_num = applicants - admitted_num )# Fit a binomial logistic regression model# Outcome: number admitted out of total applicants# Predictors: gender and majorglm1 <-glm(cbind(admitted_num, rejected_num) ~ gender + major,family =binomial(link ="logit"),data = admissions_glm)# Display model resultssummary(glm1)
Call:
glm(formula = cbind(admitted_num, rejected_num) ~ gender + major,
family = binomial(link = "logit"), data = admissions_glm)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 0.58205 0.06899 8.436 <2e-16 ***
genderwomen 0.09987 0.08085 1.235 0.217
majorB -0.04340 0.10984 -0.395 0.693
majorC -1.26260 0.10663 -11.841 <2e-16 ***
majorD -1.29461 0.10582 -12.234 <2e-16 ***
majorE -1.73931 0.12611 -13.792 <2e-16 ***
majorF -3.30648 0.16998 -19.452 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 877.056 on 11 degrees of freedom
Residual deviance: 20.204 on 5 degrees of freedom
AIC: 103.14
Number of Fisher Scoring iterations: 4
After fitting a binomial logistic regression model, gender was not a significant predictor of admission probability after adjusting for major (p = 0.217). In contrast, admission rates differed substantially across majors, with several majors showing much lower odds of admission compared to Major A (p < 0.001). The large reduction in deviance indicates that major explains most of the variation in admission outcomes.
