Note: This document contains code needed for each part of the Starter Analysis exercise for the MADA Spring 2026 course. Each part is listed under its corresponding part name. As a disclaimer, AI was used for code brevity and assistance in fixing errors in code. Cmd + option + I was used to create chunks for code sections (mac option).
Part 1
Package loading and install
# install dslabs package (run once in the console if not already installed)# install.packages("dslabs")# load required packages# tidyverse added for later steps with data processinglibrary("dslabs")library("tidyverse")
── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
✔ dplyr 1.1.4 ✔ readr 2.1.5
✔ forcats 1.0.0 ✔ stringr 1.5.1
✔ ggplot2 3.5.2 ✔ tibble 3.2.1
✔ lubridate 1.9.4 ✔ tidyr 1.3.1
✔ purrr 1.1.0
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag() masks stats::lag()
ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
Show dataset structure
# only run the next command interactively, not in a script# help(gapminder)# 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 the type of object gapminder isclass(gapminder)
[1] "data.frame"
Data processing
Process Africa subset
# subset gapminder data to rows where continent is "Africa"africadata <- gapminder[gapminder$continent =="Africa", ]# inspect structure (should show 2907 observations; troubleshoot if not)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 ...
# check summary statistics 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
# keep only infant_mortality and life_expectancyafrica_infant_mortality <- africadata[, c("infant_mortality", "life_expectancy")]# keep only population and life_expectancyafrica_population <- africadata[, c("population", "life_expectancy")]# inspect structure + summariesstr(africa_infant_mortality)
'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_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
str(africa_population)
'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_population)
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
How to plot the data
# life expectancy vs infant mortality (points)plot(x = africa_infant_mortality$infant_mortality,y = africa_infant_mortality$life_expectancy,xlab ="Infant Mortality",ylab ="Life Expectancy",main ="Infant Mortality vs Life Expectancy (Africa)")
# life expectancy vs population (points) with log-scaled x-axisplot(x = africa_population$population,y = africa_population$life_expectancy,xlab ="Population (log scale)",ylab ="Life Expectancy",main ="Population vs Life Expectancy (Africa)",log ="x")
The infant mortality plot shows a negative correlation with life expectancy, while the population plot shows a general positive relationship. The plots appear to in a streaking form because individual countries are counted across multiple points. In the population vs life expectancy (Africa) plot, we can see that for individual country populations, as population increases, so does life expectancy.
# count missing infant_mortality values for each yeartapply(africadata$infant_mortality, africadata$year, function(x) sum(is.na(x)))
# subset to year 2000africa_2000 <- africadata[africadata$year ==2000, ]str(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 ...
summary(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
fit1 <-lm(life_expectancy ~ infant_mortality, data = africa_2000)summary(fit1)
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
fit2 <-lm(life_expectancy ~ population, data = africa_2000)summary(fit2)
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
Fit1 shows that infant mortality shows a statistically significant negative relationship with life expectancy(p = 2.83^-08), explaining approximately 47% of the variation in life expectancy among African countries in 2000. In contrast, population size shows no significant association with life expectancy (p = 0.616). The model fit is also highly significant with a prediction error rate of 6.221 years (F= 43.48, p= 2.825^-08).
Fit2 indicates that there is no statistically significant relationship between population size and life expectancy (estimate =2.756^-08; p=0.616). The model is not significant and does not explain the variation in life expectancy (R2= 0.005176; adjusted value of -0.01513; F= 0.2549, p= 0.6159). Predictor error is large for this dataset at 8.524 years.
The following section contributed by Elle Adams
#Need dplyr to pipe data library(dplyr)library(tidyverse)library(dslabs)#New dslabs data set - murders (I like true crime)#overview of structurestr(murders)
state abb region population
Length:51 Length:51 Northeast : 9 Min. : 563626
Class :character Class :character South :17 1st Qu.: 1696962
Mode :character Mode :character North Central:12 Median : 4339367
West :13 Mean : 6075769
3rd Qu.: 6636084
Max. :37253956
total
Min. : 2.0
1st Qu.: 24.5
Median : 97.0
Mean : 184.4
3rd Qu.: 268.0
Max. :1257.0
#create new column total/population * 100000 to get number of murders per 100,000 people for each state (how it's typically expressed)murders <- murders %>%mutate(murder_rate = (total/population)*100000)#check new structure str(murders)
'data.frame': 51 obs. of 6 variables:
$ state : chr "Alabama" "Alaska" "Arizona" "Arkansas" ...
$ abb : chr "AL" "AK" "AZ" "AR" ...
$ region : Factor w/ 4 levels "Northeast","South",..: 2 4 4 2 4 4 1 2 2 2 ...
$ population : num 4779736 710231 6392017 2915918 37253956 ...
$ total : num 135 19 232 93 1257 ...
$ murder_rate: num 2.82 2.68 3.63 3.19 3.37 ...
#Question 1 - what is the relationship between population and number of murders? hypothesis - more people = more murder#Plot population (x) vs total (y)ggplot(murders, (aes(x = population, y = total))) +geom_point()
#Fit with total as outcome and population as predictortotal_vs_pop <-lm(total ~ population, data = murders)#See the fitsummary(total_vs_pop)
Call:
lm(formula = total ~ population, data = murders)
Residuals:
Min 1Q Median 3Q Max
-112.889 -25.656 -3.687 25.505 217.780
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -1.713e+01 1.198e+01 -1.43 0.159
population 3.316e-05 1.315e-06 25.23 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 63.77 on 49 degrees of freedom
Multiple R-squared: 0.9285, Adjusted R-squared: 0.9271
F-statistic: 636.5 on 1 and 49 DF, p-value: < 2.2e-16
What I found: There is a strong, positive correlation between population and total number of murders (R-squared = 0.9271) and this is significant (p-value = 2e-16, much smaller than 0.05). This is confirmed visually by the graph.
#Question 2 - which state has the most murders per 100,000 people? hypothesis - new york #Figure showing the number of murders per 100,000 people for each stateggplot(murders, aes(x = state, y = murder_rate)) +geom_col() +theme(axis.text.x =element_text(angle =90))
#What is murder rate for DC? (Alphabetically row number 9)slice(murders, 9)
state abb region population total murder_rate
1 District of Columbia DC South 601723 99 16.45275
Using this figure, I can see that I was incorrect in my hypothesis - DC actually as the highest murder rate, at 16.45275 murders per 100,000 people.
