Infant Mortality Rate(s)
Adhislacy
4/20/2021
In this project, we explore the infant mortality data from around the world in 1970. It has: - 101 rows - 4 columns (country, income per capita ($), infant mortality, as well as region)
This data can be found in my github dataset repository.
Load the data.
## country income infmort region
## 1 Australia 3426 26.7 Asia
## 2 Austria 3350 23.7 Europe
## 3 Belgium 3346 17.0 Europe
## 4 Canada 4751 16.8 Americas
## 5 Denmark 5029 13.5 Europe
## 6 Finland 3312 10.1 Europe
## 7 France 3403 12.9 Europe
## 8 West.Germany 5040 20.4 Europe
## 9 Ireland 2009 17.8 Europe
## 10 Italy 2298 25.7 Europe
## 11 Japan 3292 11.7 Europe
## 12 Netherlands 4103 11.6 Europe
## 13 New.Zealand 3723 16.2 Asia
## 14 Norway 4102 11.3 Europe
## 15 Portugal 956 44.8 Europe
## 16 South.Africa 1000 71.5 Africa
## 17 Sweden 5596 9.6 Europe
## 18 Switzerland 2963 12.8 Europe
## 19 Britain 2503 17.5 Europe
## 20 United.States 5523 17.6 Americas
## 21 Algeria 400 86.3 Africa
## 22 Ecuador 250 78.5 Americas
## 23 Indonesia 110 125.0 Asia
## 24 Iraq 560 28.1 Asia
## 25 Libya 3010 300.0 Africa
## 26 Nigeria 220 58.0 Africa
## 27 Saudi.Arabia 1530 650.0 Asia
## 28 Venezuela 1240 51.7 Americas
## 29 Argentina 1191 59.6 Americas
## 30 Brazil 425 170.0 Americas
## 31 Chile 590 78.0 Americas
## 32 Colombia 426 62.8 Americas
## 33 Costa.Rica 725 54.4 Americas
## 34 Dominican.Republic 406 48.8 Americas
## 35 Greece 1760 27.8 Europe
## 36 Guatemala 302 79.1 Americas
## 37 Israel 2526 22.1 Asia
## 38 Jamaica 727 26.2 Americas
## 39 Lebanon 631 13.6 Asia
## 40 Malaysia 295 32.0 Asia
## 41 Mexico 684 60.9 Americas
## 42 Nicaragua 507 46.0 Americas
## 43 Panama 754 34.1 Americas
## 44 Peru 335 65.1 Americas
## 45 Singapore 1268 20.4 Asia
## 46 Spain 1256 15.1 Europe
## 47 Taiwan 261 19.1 Asia
## 48 Trinidad.and.Tobago 732 26.2 Americas
## 49 Tunisia 434 76.3 Africa
## 50 Uruguay 799 40.4 Americas
## 51 Yugoslavia 406 43.3 Europe
## 52 Zambia 310 259.0 Africa
## 53 Bolivia 200 60.4 Americas
## 54 Cameroon 100 137.0 Africa
## 55 Congo 281 180.0 Africa
## 56 Egypt 210 114.0 Africa
## 57 El.Salvador 319 58.2 Americas
## 58 Ghana 217 63.7 Africa
## 59 Honduras 284 39.3 Americas
## 60 Ivory.Coast 387 138.0 Africa
## 61 Jordan 334 21.3 Asia
## 62 South.Korea 344 58.0 Asia
## 63 Liberia 197 159.2 Africa
## 64 Moroco 279 149.0 Africa
## 65 Papua.New.Guinea 477 10.2 Asia
## 66 Paraguay 347 38.6 Americas
## 67 Philippines 230 67.9 Asia
## 68 Syria 334 21.7 Asia
## 69 Thailand 210 27.0 Asia
## 70 Turkey 435 153.0 Asia
## 71 South.Vietnam 130 100.0 Asia
## 72 Afganistan 75 400.0 Asia
## 73 Bangladesh 100 124.3 Asia
## 74 Burma 73 200.0 Asia
## 75 Burundi 68 150.0 Africa
## 76 Cambodia 123 100.0 Asia
## 77 Central.African.Republic 122 190.0 Africa
## 78 Chad 70 160.0 Africa
## 79 Dahomey 81 109.6 Africa
## 80 Ethiopia 79 84.2 Africa
## 81 Guinea 79 216.0 Africa
## 82 India 93 60.6 Asia
## 83 Kenya 169 55.0 Africa
## 84 Madagascar 120 102.0 Africa
## 85 Malawi 130 148.3 Africa
## 86 Mali 50 120.0 Africa
## 87 Mauritania 174 187.0 Africa
## 88 Niger 70 200.0 Africa
## 89 Pakistan 102 124.3 Asia
## 90 Rwanda 61 132.9 Africa
## 91 Sierra.Leone 148 170.0 Africa
## 92 Somalia 85 158.0 Africa
## 93 Sri.Lanka 162 45.1 Asia
## 94 Sudan 125 129.4 Africa
## 95 Tanzania 120 162.5 Africa
## 96 Togo 160 127.0 Africa
## 97 Uganda 134 160.0 Africa
## 98 Upper.Volta 82 180.0 Africa
## 99 Southern.Yemen 96 80.0 Asia
## 100 Yemen 77 50.0 Asia
## 101 Zaire 118 104.0 Africa####Plot the data
plot(mort)
Make a scatter plot to show the association between infant mortality and income.
par(mar = c(4.5, 4.5, 2, 2), cex = 0.7)
plot(infmort ~ income, xlab = "Income (USD) per Capita",
ylab = "Infant Mortality Rate", data = mort)
- Due to highly non-linear association between income and infant mortality as seen in the plot, therefore being skewed.
- This calls for a log transformation of both the income and infant mortality variables. It will help reduce the skewness.
par(mar = c(4.5, 4.5, 2, 2), cex = 0.7)
mod1 <- lm(log(infmort) ~ log(income), data = mort)
plot(log(infmort) ~ log(income), data = mort, residuals(mort))
abline(mod1)
- Taking the log transformation of the variables into account gives a negative linear association. Basically, the more income a family was able to earn the less likely there was an infant mortality.
- However, we also spot some outliers at the top right. Let’s see if we can identify them.
boxplot(mort$infmort,
ylab = "infant mortality")
Fit a simple linear regression model, with log(infmort) as the response variable, while log(income) being the predictor variable
plot(mod1)
summary(mod1)##
## Call:
## lm(formula = log(infmort) ~ log(income), data = mort)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.66694 -0.42779 -0.02649 0.30441 3.08415
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.14582 0.31654 22.575 <2e-16 ***
## log(income) -0.51179 0.05122 -9.992 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6867 on 99 degrees of freedom
## Multiple R-squared: 0.5021, Adjusted R-squared: 0.4971
## F-statistic: 99.84 on 1 and 99 DF, p-value: < 2.2e-16- From above summary, we note that, for every increase in the per capita log(income) by 1, there is a decrease in the log(infant mortality rate) by 0.512, hence the -ve sign.
This can also be interpreted as:
- A 1% increase in income is associated with a 0.512% decrease in infant mortality rate.
Let’s try to obtain a prediction at 95% prediction for log(income), assuming a $300 income.
md <- data.frame(income = 300)
p <- predict(mod1, newdata = md, interval = "prediction")
p## fit lwr upr
## 1 4.22666 2.856942 5.596379exp(p)## fit lwr upr
## 1 68.48813 17.40821 269.4489- The prediction for log(infmort) is approx. 4.23 with a 95% prediction interval of (2.856942, 5.596379), whereas the prediction for the variable infmort (infant mortality) is approx. 68.48, with a prediction interval of (17.40821 269.4489)
Earlier on, we tried to identify the outliers. From previous plot of the residuals, we were able to see the outliers labelled as 25 & 27. Let’s try refit the model and plot again, to see of we could identify the specific countries.
par(mfrow = c(1, 2), mar = c(4.5, 4.5, 2, 2), cex = 0.7)
plot(mod1, c(1:2))
which(abs(rstandard(mod1)) > 3)## 25 27
## 25 27mort[c(25, 27), ]## country income infmort region
## 25 Libya 3010 300 Africa
## 27 Saudi.Arabia 1530 650 AsiaFrom the plot, we have been able to identify outliers: #25 as Libya, and #27 as Saudi Arabia, in African and Asia regions respectively.
Removing / dropping the outliers…
mort2 <- mort[-c(25, 25) ]
mod2 <- lm(log(infmort) ~ log(income), data = mort2)
summary(mod2)##
## Call:
## lm(formula = log(infmort) ~ log(income), data = mort2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.66694 -0.42779 -0.02649 0.30441 3.08415
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.14582 0.31654 22.575 <2e-16 ***
## log(income) -0.51179 0.05122 -9.992 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6867 on 99 degrees of freedom
## Multiple R-squared: 0.5021, Adjusted R-squared: 0.4971
## F-statistic: 99.84 on 1 and 99 DF, p-value: < 2.2e-16- With the outliers removed in second model (mod2), we notice an R2 change to 0.652 from 0.497.
With the outliers out, let’s fit regression model, and also, a partial F-Test.
mod3 <- lm(log(infmort) ~ log(income) + region, data = mort2)
summary(mod3)##
## Call:
## lm(formula = log(infmort) ~ log(income) + region, data = mort2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.5108 -0.3491 -0.0458 0.2804 2.9928
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.40301 0.35829 17.871 < 2e-16 ***
## log(income) -0.29939 0.06741 -4.441 2.39e-05 ***
## regionAmericas -0.60223 0.19023 -3.166 0.00207 **
## regionAsia -0.72334 0.16324 -4.431 2.49e-05 ***
## regionEurope -1.20282 0.25881 -4.647 1.07e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6122 on 96 degrees of freedom
## Multiple R-squared: 0.6163, Adjusted R-squared: 0.6003
## F-statistic: 38.55 on 4 and 96 DF, p-value: < 2.2e-16- In the above summary for mod3, we have a multiple linear regression model with log(infmort) as the response variable, and log(income) and region as the predictor variables.
mod4 <- lm(log(infmort) ~ log(income) * region, data = mort2)
summary(mod4)##
## Call:
## lm(formula = log(infmort) ~ log(income) * region, data = mort2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.46809 -0.26530 -0.02148 0.27478 3.14219
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.9385 0.6362 7.763 1.06e-11 ***
## log(income) -0.0112 0.1235 -0.091 0.9280
## regionAmericas 1.5661 1.1856 1.321 0.1898
## regionAsia 1.2634 0.8561 1.476 0.1434
## regionEurope 2.0882 1.8422 1.134 0.2599
## log(income):regionAmericas -0.3978 0.1979 -2.010 0.0473 *
## log(income):regionAsia -0.3798 0.1580 -2.404 0.0182 *
## log(income):regionEurope -0.5205 0.2516 -2.069 0.0413 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5971 on 93 degrees of freedom
## Multiple R-squared: 0.6464, Adjusted R-squared: 0.6198
## F-statistic: 24.29 on 7 and 93 DF, p-value: < 2.2e-16mod4 below is a multiple regression model, with log(infmort) as the response, and log(income), region and an interaction between log(income) & region as predictor variables.
Using partial F-Test, we compare the reduced models: mod3 & mod4
anova(mod3, mod4)## Analysis of Variance Table
##
## Model 1: log(infmort) ~ log(income) + region
## Model 2: log(infmort) ~ log(income) * region
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 96 35.980
## 2 93 33.152 3 2.8279 2.6444 0.05375 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Comment, corrections and referrals are highly appreciated.