Do dollars decide in africa whether a child should live or not

Do dollars decide in
Africa whether a child
should live or not?
Association of health expenditure on health
outcomes in Africa

Health expenditures have a statistically significant effect,
although low, on infant, neonatal and under‐five mortality
in Africa.
Supervisor: professor Whitehead
Author: Soheila Abachi
11/17/2014

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Table of Contents
1. Abstract ................................................................................................................................................ 3
2. Introduction .......................................................................................................................................... 4
3. Methods ................................................................................................................................................ 5
4. Analysis ................................................................................................................................................. 5
4.1. Linear regression .......................................................................................................................... 5
4.1.1. Assumption of the linear regression .................................................................................... 5
4.2. Principal component analysis ...................................................................................................... 6
4.2.1. Assumption of principal component analysis ..................................................................... 6
4.3. Redundancy analysis .................................................................................................................... 7
5. Results................................................................................................................................................... 7
5.1. General linear model .................................................................................................................... 7
5.2. Principal component analysis ...................................................................................................... 8
5.2.1. PCA on all the variables ............................................................................................................ 8
5.2.2. PCA on 2 sets of variables ........................................................................................................ 9
5.3. Redundancy analysis .................................................................................................................. 10
6. Discussion ........................................................................................................................................... 10
7. Acknowledgments .............................................................................................................................. 10
8. References .......................................................................................................................................... 11

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1. Abstract
Health expenditures have a statistically significant effect on infant, neonatal and under‐
five mortality. For African countries, our results imply that total health expenditures (as well as
the government component) are certainly important contributor to health outcomes in terms
of child mortality rates. Per capita government expenditure on health seemed to be more
significant on models especially per capita government expenditure on health for the year
1995. Inter correlation of the two sets of variables, health expenditures and mortality rates, are
strong but not between the variables. Infant, neonatal and under‐five mortalities are negatively
correlated with the health expenditure in the Sub‐Saharan African countries studied. Health
care expenditure seems to be only one of the many factors important in improving the health
status of a member. The analysis presented in this paper finds evidence of a weak statistically
significant relationship between per capita health spending, and health outcomes. Each of the
health outcomes can be an indication of the other health outcome. Neonatal mortality rate
itself is an indication of how high or low the infant mortality is going to be in a specific year in a
country. This may be due to the infection caused death among the under five which accounts
for 73% of under 5 death in Africa. In countries with high infant mortality rate, the absence of a
strong statistical relationship may be due to model misspecification or may reflect the fact that
at high levels of population health, the returns for the increases in health spending are small.
For future studies, other variables should be included.

Abbreviations
PC95TEXH 1995 Per capita total expenditure on health (PPP int. $)
PC05TEXH 2005 Per capita total expenditure on health (PPP int. $)
PC95GEXH 1995 Per capita government expenditure on health (PPP int. $)
PC05GEXH 2005 Per capita government expenditure on health (PPP int. $)
UFD00 2000 Number of under‐five deaths (thousands)
UFD10 2010 Number of under‐five deaths (thousands)
ID00 2000 Number of infant deaths (thousands),
ID10 2010 Number of infant deaths (thousands)
ND00 2000 Number of neonatal deaths (thousands)
ND10 2010 Number of neonatal deaths (thousands)

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2. Introduction
Life expectancy is linked to economic growth and, 10% increase in life expectancy at
birth will increase the economic growth rate by 0.35% a year, according to WHO (world health
organization). There is evidence that empowering health will bring significant benefits for the
economy (1). Low health status is a heavy financial burden and according to Commission on
Macroeconomics and Health (2001) economic growth of wealthy and poor countries is about
50% different due to the life expectancy and health status. Economists consider child health
and mortality as important indicators of the success or failure of a government policy especially
when studying developing countries (2). Health definitely is linked with sustainable economic
growth and development. This could be due to the fact that healthy population is more
productive at work, spend more time in the workplace, stay in labor force longer,  invest in their
own and children’s education leading to the increased productivity and generally earn higher
incomes which could potentially be the funds available for investment in the economy (3).
Two‐thirds of deaths occur in just 10 countries. Child mortality in West and Central
Africa is the highest. In these regions, more than 150 of every 1,000 children born die under age
five in compare to 6 of every 1,000 children born in a wealthy country (North America, Western
Europe and Japan) (UNICEF). Health care expenditure per person per year in high‐income
countries exceeded US$ 2,000 while in Africa it averaged between US$13‐$21 in 2001
(Commission for Africa, 2004). In sub‐ Saharan Africa the expenditure should rise to US$ 38 by
2015 just to deliver basic treatment and care for the major communicable diseases (HIV/AIDS,
TB and malaria), and early childhood and maternal illnesses (Commission for Macroeconomics
and Health, 2001). Total spending on health has shown minimal to no impact on child mortality
in some of earlier studies(4, 5). These studies have recorded empirical evidence that public
spending on health is not the main cause of child mortality outcomes (6). The variation could be
very well explained by other factors such as income, income inequality, female education,
mother literacy, degree of ethnolinguistic fractionalization and findings show that these all play
significant role in child mortality across countries (7‐9). These results mean that reduced
poverty, income inequality, and increased female education would reduce child mortality as
much than just increasing public spending on health. Despite public belief, study has shown
that government health expenditures account for less than one‐seventh of one percent
variation in under‐five mortality across countries and the conclusion was drawn that 95% of the
variation in under‐5 mortality can be enlightened by factors such as a country’s per capita
income, female educational level, resources at hospital, managed care and choice of region (10,
11). The same applies to low‐income countries where no significant relationship between
health expenditure spending and infant mortality was found (12). Enhanced sanitation as a
public health measure have proved to play a bigger role in improving child health in the past
150 years than even the most advanced personal medical care technologies (13, 14). Therefore,
child mortality may be not a good measure of social and economic conditions such as public
health, insurance coverage, or economic crises in all countries but certainly is considered good
indicator for African countries. In 2000, the United Nations (UN) set eight targets, known as
Millennium Development Goals, aiming to promote human development of which four are in
direct or indirect relation to child mortality rate. The key targets to be reached by 2015
throughout the world are in the areas of poverty reduction, health improvements, education
attainment, gender equality, environmental sustainability, and fostering global partnerships

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(figure 1). The fourth goal to reduce child mortality by two‐thirds requires action on the first
goal, halving extreme poverty and hunger, since malnutrition caused by chronic hunger causes
the death of more than 5 million children each year globally (15).
3. Methods
The dataset contains 12 continuous variables with the sample size of 45 (45 African
countries) which is large and good enough for the central limit theorem (CLT) [approximately
normally distributed]. It is hypothesized that child yearly death rate as an indicator of health
outcome, depend upon variance in government and total health expenditure (figure 4, 5, 6). In
this research, the economical consequences of health spending on child death rate will be
studied and results will be reported. The questions to be answered are as below;
1. Neonatal mortality rate 2010 is a response of government and total health expenditure of
1995 and 2005
2. Neonatal mortality rate 2010 is a response of government and total health expenditure
2005
3. Infant mortality rate 2010 is a response of government and total health expenditure of
1995 and 2005
4. Infant mortality rate 2010 is a response of government and total health expenditure 2005
5. Under 5‐mortality rate 2010 is a response of government and total health expenditure of
1995 and 2005
6. Under 5‐mortality rate 2010 is a response of government and total health expenditure
2005
7. Neonatal mortality rate 2000 is a response of government and total health expenditure
1995
8. Infant mortality rate 2000 is a response of government and total health expenditure 1995
9. Under 5‐mortality rate 2000 is a response of government and total health expenditure
1995
4. Analysis
4.1. Linear regression
Performing linear regression about child mortality (response) and explanatory variables
(government and total health expenditures) would tell us if there is any relationship between
the response and the explanatory variables thus there might be some collinearity or
multicollinearity among the independent variables (exact collinearity should be considered
because if there is any then the regression coefficient cannot be calculated). Correlations
whether positive, negative, and associations whether strong or weak can be determined in this
step.
4.1.1. Assumption of the linear regression
To check the normality of each variable, Shapiro‐Wilk normality test was performed
and the p‐values were analyzed on both original dataset and the log10 transformed dataset
(table 3). For the original data, the p‐values for all the variables are less than alpha so the null
hypothesis is rejected in the favor of alternative hypothesis. To make the data of normal
distribution log10 transformation was applied to the dataset. P‐values were improved but still
most of the variables are of non‐normal distribution. PC95TEXH, PC05GEXH, UFD10 have p‐
values above alpha so Ho is accepted and these variables are of normal distribution.

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Transforming improved the normality but not to satisfactory level thus since listwise deletion of
outliers has the risk of losing some influential observation then I decided to keep all the data in
the analysis. The hypothesis for Shapiro‐Wilk normality test is as follows;
Ho: data is normal
Ha: data is non‐normal
The null hypothesis for multiple linear regression is that all the slopes are equal to zero
and the alternative hypothesis is that at least one slope does not equal to zero.
Ho: β1=β2=β3=β4=βi=0
Ha: at least one βi is different
Best fit could be interpreted as “how good is the proposed model (regression
equation)”and if “it could predict the y values reasonably.” In other words how good is the
fitted model for describing the relationship between x and y and so for predicting value of y for
a given x within the acceptable x range. Goodness of fit could be measured by coefficient of
determination (R2
). General rule of thumb is that R2
greater than 60% would make a proposed
model safe enough for making predictions.
4.2. Principal component analysis
Textbooks state that “principal component analysis is performed on a matrix of Pearson
correlation coefficients therefore data should satisfy the assumptions for this statistic”.
To extract the important variables out of the 12 variables in the original dataset and
reduce the dimensionality principal component analysis is to be performed. Components are
orthogonal to each other (uncorrelated). PCA is more sensible when data are highly correlated
(correlation coefficients bigger than 0.3 and smaller than ‐0.3) and even though normality of
the dataset is not essential but would be preferred. If all the variables on the same scale, only
then the predictions and interpretation would be rational and this could be achieved by
standardizing the data and performing transformation.
4.2.1. Assumption of principal component analysis
Linearity is preferred and so the relationship between all observed variables should be
linear. Normal distribution of each observed variable is also desirable but not necessary. For the
latter reason variables that demonstrate skewness may be transformed to better approximate
the normality. One could also assume the normality of the dataset if the sample size is greater
than 25 because the Pearson correlation coefficient is robust against violations of the normality
assumption. According to Dr. Whitehead if dataset does not contain any zero values then it can
be analyzed by principal component analysis. In addition, normality is preferred not essential,
and independence is not required.
The dataset contains no missing values but some unusually large or small values are
present which maybe outliers contributing to the non‐normal distribution of the dataset. I kept
all the units in because these values maybe influential not outliers.
Variables are relatively correlated for example; per capita health expenditure,
government and total, are positively related meaning that increase in one would lead in
increasing the other (table 2).
Normality of the original dataset was tested but the data were non‐linear therefore, two
forms of transformation were performed, square root and log10. Square root transforming of
all the variables did not much help the linearity and normality whereas log10 transforming of

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all the variables induced the normality to some degree keeping its original characteristics
(Figure 9, 10).
4.3. Redundancy analysis
Redundancy analysis is done to show that there is a linear dependence of the child
mortality variables, Y on the health expenditure variables, X. In redundancy analysis linear
regression is applied to represent response variable (child mortality) as linear function of
explanatory variable (health expenditure) and then to use PCA in order to visualize the result.
Among those components of Y which can be linearly explained with X (multivariate linear
regression) one could take those components which represent most of the variance.
5. Results
5.1. General linear model
Several multiple linear models were tested with the null hypothesis that the slopes are
all equal to zero. All the tested models have p‐values smaller than alpha (0.5) leading to the
rejection of null hypothesis in favor of alternative hypothesis meaning that at least one β is
different from zero. There is significant relationship between the independent and the response
variable and so changes in x would affect the changes in y.
All the possible models were tested. The answers for biological questions are as follows;
Biological question 1: Neonatal mortality rate 2010 has association with the government and
total health expenditure of 1995 and 2005 at the significance level of 5%. Stepwise regression
shows that it is more dependent on the 1995 government health expenditure (table 4).
total health expenditure 2005 at the significance level of 5%. Stepwise regression shows that it
is more dependent on the 2005 government health expenditure (table 4).
Biological question 3: Infant mortality rate 2010 has association with the government and total
health expenditure of 1995 and 2005 at the significance level of 5%. Stepwise regression shows
that it is more dependent on the 1995 government health expenditure (table 4).
health expenditure 2005 at the significance level of 5%. Stepwise regression shows that it is
more dependent on the 2005 government health expenditure (table 4).
Biological question 5: Under 5‐mortality rate 2010 has association with the government and
total health expenditure of 1995 and 2005 at the significance level of 5%. Stepwise regression
shows that it is more dependent on the 1995 government health expenditure (table 4).
health expenditure 1995 at the significance level of 5%. Stepwise regression shows that it is
more dependent on the 1995 government health expenditure (table 4).

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Testing the dependence of child mortality rate of 2010, neonatal, infant, and under five,
the conclusion can be made that all these variables are more dependent on the government
expenditure 1995 and 2005. Another interpretation of the models could be that government
expenditure of year 1995 had big influence on the child mortality rates of 2010 (table 4).
Also testing for the dependence of child mortality rate of 2000, neonatal, infant, and
under five, the conclusion can be made that all these variables are more dependent on the
government expenditure of 1995 (table 4).
The overall interpretation could be that child mortality rates are more dependent on the
government expenditure rather than on the total health expenditure (table 4).
Quality of fit of the abovementioned models were assessed one by one (figure 13‐19,
34, 35).
To evaluate the quality of fit a model, few assumptions shall be met;
• Normality of error terms by Normal Q‐Q plot
• Constant variance by plotting residuals vs. fitted values
• Independence of error terms by auto‐correlation analysis (time series)
• Presence of influential observations by Cook’s D
For example, the quality of fit of the model 6 was evaluated. The plots show no evident
pattern to the residuals vs. fitted values plot and give almost an impression of horizontal band
confirming that constant variance assumption is met. The Normal Q‐Q plot passes the pen test
and so the normality assumption is met. The residuals vs. leverage plot checks out the absence
of influential observations as observation 30 (country; Mauritania) that was previously
introduced as influential is out of the Cook’s distance range. Therefore, we conclude that all
assumptions are met and none is violated. It is interesting to know that Mauritania is classified
as low‐income country by World Bank but has relatively high per capita total and government
expenditure with significantly low child death rates.
Bonferonni outlier test was done for the models that initially have adjusted r‐squared
values of above 90%. According to this test observation 4 and 30 are outliers (table 8).
Reduced models for all the tested models were the best models as they were simple
and had lower AIC compare to the full models (table 4).
5.2. Principal component analysis
5.2.1. PCA on all the variables
PCA on correlation matrix (Log10 transformed data) revealed two principal components
with Eigen values more than or equal to 1 (pc1: 2.97, pc2: 1.57). These two principal
components cumulatively account for 94.4% of the variance in the dataset (table 6).
Loadings for the correlation matrix (Log10 transformed data) analysis are summarized
(table 6) and as noted loadings for child death rates are positively loaded on first component.
The per capita health expenditure load negatively on the second component therefore 2nd
component could explain the variance on the expenditure (table 6). On the first component,
decrease in the health expenditure causes increase in the child mortality rate. Below is the
formula for the 1st
principal component:

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1st
pc (Correlation Matrix) = ‐0.27 (PC95TEXH) ‐0.27 (PC05TEXH) ‐0.26 (PC12TEXH) ‐0.29
(PC95GEXH) ‐0.27 (PC05GEXH) ‐0.27 (PC12GEXH) +0.3 (UFD00) +0.3 (UFD10) +0.3 (ID00) +0.29
(ID10) +0.3 (ND00) +0.28 (ND10)
Scree plot can be performed to decide which components to keep for the Varimax
rotation analysis. Looking at the plots for PCA on correlation would reveal that only two
components are important, as drop is obvious after these two components. For further
analysis, only first two components were maintained. This would plot the eigenvalue associated
with a principal component versus the number of the component to expose the relative
magnitude of eigenvalues (Figure 20).
Looking at the biplot, one can say that death rates whether infant, neonatal or under 5
are highly correlated for 2000 and 2010. Moreover per capita government and total health
expenditure are also highly correlated (Figure 21). Both health expenditure and mortality rates
load high on the first component and so most of the variance on the 1st
component in explained
by the two set of variables but in different direction. Their importance on the component are
more or less the same because the size of arrows are almost equal.
Examining the scores plot of correlation matrix analysis, prediction can be made that
countries relatively spending big on the health and have very low mortality rates have negative
scores (Algeria) on the 1st
and 2nd
component and countries with very low spending and high
mortality have positive scores on the 1st
component (Nigeria). Seychelles that spend high and
have almost to none mortality rate have high negative scores on the 1st
and relatively high
negative score on the 2nd
component (Figure 22).
Varimax plot makes the interpretation easy as it reveals the relationship of each original
variable to the factor. This rotation maximizes the high correlations while minimizing the low
correlations. Varimax plot for correlation matrix shows that the countries with relatively big
health expenditure have negative scores on both the components and in converse countries
with low to minimal health expenditure have positive scores on both the components (Figure
23).
5.2.2. PCA on 2 sets of variables
Principal component analysis was done on the independent and dependent variable as
two set. Since the measurements are on the same scale, therefore analysis were done with the
covariance matrix.
PCA of the child mortality rates revealed all the principal components with Eigen values
more than or equal to 1. These two principal components cumulatively account for 99.9% of
the variance in the dataset. Below is the formula for the 1st
1st pc for child mortality rates (covariance matrix) = ‐0.63(UFD00) ‐0.54(UFD10) ‐
0.39(ID00) ‐0.30(ID10) ‐0.17(ND00) ‐0.170(ND10)
PCA of the health expenditure revealed all the principal components with Eigen values
more than or equal to 1. These two principal components cumulatively account for 97.1% of
the variance in the dataset. Scree plots for both set of PCA confirms the importance of the first
2 components (figure 26‐27). Below is the formula for the 1st
1st pc for health expenditures (covariance matrix) = ‐0.45(PC95TEXH) ‐0.69(PC05TEXH) ‐
0.305(PC95GEXH) ‐0.467(PC05GEXH)
Looking at the biplot for the PCA of mortality rates, one can say that death rates of 2000
are highly correlated so are the 2010 death rates. Based on the size of arrows, importance of

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the under five death rate is more significant the neonatal and the infant. Biplot of health
expenditures shows that health expenditures of 1995 are correlated and so are the 2005
expenditure thus importance of total expenditure of 2005 is more significant than the others
(1995 government expenditure has the least importance) (figure 28‐29).
Looking at score plot of PCA of the mortality rates, all the variables load negatively on
the pc1, some high and some low (figure 32). Score plot of PCA of the expenditures shows that
all the variables have loaded negatively and relatively high on pc1 (figure 33).
Varimax plot for PCA of mortality rates shows that the countries with high mortality
rates load highly negative on both the components such as Nigeria (figure 30).
Varimax plot for PCA of expenditures shows that the countries with both high
government and high total health expenditures load negatively high on the first and positively
high on the 2nd
component such as Seychelles. In converse, countries with high total and
relatively lower government health expenditures load highly negative on the first and positively
but relatively lower on the 2nd
component such as south Africa (figure 31).
5.3. Redundancy analysis
For the variable UFD00, a one unit increase in under 5 death leads to a 1.33 decrease (‐
1.33) in the first canonical variate of set 2 when all of the other variables are held constant.
Table 7 presents the standardized canonical coefficients for the first two dimensions
across both sets of variables. For the expenditure variables, the first canonical dimension is
most strongly influenced by PC05TEXH (0.25) and for the second dimension (1.00).
For the mortality variables, the first dimension was most strongly influenced by UFD00 ‐
1.33 and ID00 1.41 and the second dimension the ND00 ‐1.64 was the dominant variable (figure
24‐25).
6. Discussion
The overall picture is that health expenditure has impact on the child mortality rate and
the results are relatively statistically significant. This may be because HIV prevalence has been
high in the sub‐Saharan Africa in the two past decades (figure 3). This is in accordance to UN
report 2000 saying that “trend in HIV infection will have a profound impact on future rates of
infant, child and maternal mortality, life expectancy and economic growth.”
Although all the multiple linear regression models tested were accepted in the favor of
the alternative hypothesis that there is relationship between mortality rates and health
expenditure however the factors of the models usually were not statistically significant except
the health mortality rates e.g. dependence of infant mortality rate on neonatal and under 5
mortality rates with low p‐values and high t values (table 5). Negative loadings of the health
expenditure leads to positive relatively high loading of the health outcome, represented as child
mortality. One could say that health expenditure has some impact even though low on the
mortality rates but other variables have to be included in the analysis to decide its significance.
Variables that can be included in the study could be the female education, income, access to
vaccines, HIV prevalence, number of trained health professionals, hunger, sanitation, etc.
The results of this analysis are confirmatory to the other similar studies that have found
little to no impact of the health expenditure on the health outcomes.
7. Acknowledgments

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I would like to acknowledge the use of data from WHO organization. Data were selected
individually and then they were combined in one dataset.
8. References
1. Acemoglu, D.; Johnson, S. Disease and development: the effect of life expectancy on economic
growth; National Bureau of Economic Research: 2006.
2. Sen, A., Mortality as an indicator of economic success and failure. The Economic Journal 1998,
108, 1‐25.
3. Bloom, D.; Canning, D., The health and poverty of nations: from theory to practice. Journal of
Human Development 2003, 4, 47‐71.
4. Sandiford, P.; Cassel, J.; Montenegro, M.; Sanchez, G., The impact of women's literacy on child
health and its interaction with access to health services. Population studies 1995, 49, 5‐17.
5. Rutherford, M. E.; Mulholland, K.; Hill, P. C., How access to health care relates to under‐five
mortality in sub‐Saharan Africa: systematic review. Tropical Medicine & International Health 2010, 15,
508‐519.
6. Gupta, S.; Verhoeven, M.; Tiongson, E., Does higher government spending buy better results in
education and health care? International Monetary Fund: 1999.
7. Black, R. E.; Morris, S. S.; Bryce, J., Where and why are 10 million children dying every year? The
Lancet 2003, 361, 2226‐2234.
8. Lawn, J. E.; Cousens, S.; Zupan, J., 4 million neonatal deaths: when? Where? Why? The Lancet
2005, 365, 891‐900.
9. Kiros, G.‐E.; Hogan, D. P., War, famine and excess child mortality in Africa: the role of parental
education. International Journal of Epidemiology 2001, 30, 447‐455.
10. Filmer, D.; Pritchett, L., The impact of public spending on health: does money matter? Social
science & medicine 1999, 49, 1309‐1323.
11. Filmer, D.; Pritchett, L., Child mortality and public spending on health: how much does money
matter? World Bank Publications: 1997; Vol. 1864.
12. Burnside, C.; Dollar, D., Aid, the incentive regime, and poverty reduction. World Bank,
Development Research Group, Macroeconomics and Growth: 1998.
13. Preston, S. H., Mortality trends. Annual Review of Sociology 1977, 163‐178.
14. U.N., Common Database. 2005.
15. Human Development Report 2003.

Assignment 2d, Soheila Abachi

Figure 1:
Figure 2:
: adapted fro
: adapted fro
om UN
om world baank

122

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Figure 3: adapted from UNAIDS
Figure 4: bar graph of the health expenditures (total and government) for the year 2005 and
health outcomes (Infant, neonatal, under 5mortality rates) for the year 2010
0
100
200
300
400
500
600
700
800
900 Per capita total & government expenditure 2005 and child mortality rate 2010
PC05TEXH PC05GEXH UFD10 ID10 ND10
0
100
200
300
400
500
600
700
800
900
1000
Comparison of 2000 & 2010 mortality rates for all groups
UFD00 UFD10 ID00 ID10 ND10 ND00

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Figure 5: bar graph of health outcomes (Infant, neonatal, under 5mortality rates) for the
years 2000 and 2010
Figure 6: bar graph of the health expenditures (total and government) for the year 1995 and
health outcomes (Infant, neonatal, under 5mortality rates) for the year 2000
Figure 7: box plot of original dataset
0
100
200
300
400
500
600
700
800
900
1000
Per capita total & government health expenditure 1995 and child mortality rate
2000
PC95TEXH PC95GEXH UFD00 ID00 ND00
PC95TEXH PC12GEXH ID10
04008001200

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Figure 8: scatter plot matrix for original dataset
Figure 9: box plot of log10 transformed dataset
ID00
0 300 0 150 0 400 0 800 0 300 0 400
0
0
ID10
ND00
0
0
ND10
PC05GEXH
0
0
PC05TEXH
PC12GEXH
0
0
PC12TEXH
PC95GEXH
0
0
PC95TEXH
UFD00
0
0 300
0
0 150 0 400 0 600 0 300 0 600
UFD10
PC95TEXH PC12TEXH PC05GEXH UFD00 ID00 ID10 ND00
0.00.51.01.52.02.53.0

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Figure 10: scatter plot matrix for log10 transformed dataset
Figure 11: box plot of square root transformed dataset
ID00
0.0 1.5 0.0 1.5 1.5 2.5 1.5 3.0 1.0 2.5 0.0 2.0
0.0
0.0
ID10
ND00
0.0
0.0
ND10
PC05GEXH
0.5
1.5
PC05TEXH
PC12GEXH
1.0
1.5
PC12TEXH
PC95GEXH
0.0
1.0
PC95TEXH
UFD00
0.0
0.0 1.5
0.0
0.0 1.5 0.5 2.0 1.0 2.5 0.0 2.0 0.0 2.0
UFD10
PC95TEXH PC12TEXH PC05GEXH UFD00 ID00 ID10 ND00
0102030

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Figure 12: aq .plot of log10 transformed dataset
Figure 13: model 1 basic diagnostic plots
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Ordered squared robust distance
Cumulativeprobability
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5%Quantile
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Fitted values
Residuals
Residuals vs Fitted
34
11
40
-2 0 1 2
-22
Theoretical Quantiles
Standardizedresiduals
Normal Q-Q
34
11
40
0.5 1.0 1.5
0.01.5
Fitted values
Scale-Location
341140
0.00 0.10
-22
Leverage
Cook's dist
0.5
0.5
Residuals vs Leverage
4034
25
lm(ID10 ~ PC05GEXH + PC05TEXH)

18
0.0 1.0 2.0
-1.0
Fitted values
Residuals
Residuals vs Fitted
34240
-2 0 1 2
-22
Normal Q-Q
34
25
2
0.0 1.0 2.0
0.01.5
Fitted values
Scale-Location
34 252
0.0 0.2 0.4
-22
Leverage
Cook's dist
10.5
0.51
25
40
15
~ PC05GEXH + PC05TEXH + PC95GEXH + PC
0.5 1.5 2.5
-1.0
Fitted values
Residuals
Residuals vs Fitted
342
36
-2 0 1 2
-22
Normal Q-Q
25
342
0.5 1.5 2.5
0.01.5
Fitted values
Scale-Location
25342
0.0 0.2 0.4
-22
Leverage
Cook's dist
10.5
0.51
25
40
14
~ PC05GEXH + PC05TEXH + PC95GEXH + P

19
0.5 1.0 1.5
-1.0
Fitted values
Residuals
Residuals vs Fitted
34
2511
-2 0 1 2
-22
Normal Q-Q
34
2511
0.5 1.0 1.5
0.01.5
Fitted values
Scale-Location
34 2511
0.00 0.10 0.20
-22
Leverage
Cook's dist
0.5
0.5
1
25
40
15
lm(ND10 ~ PC05TEXH + PC95TEXH)
0.0 1.0 2.0
-1.01.5
Fitted values
Residuals
Residuals vs Fitted
342
25
-2 0 1 2
-22
Normal Q-Q
25
342
0.0 1.0 2.0
0.01.5
Fitted values
Scale-Location
25342
0.0 0.2 0.4
-31
Leverage
Cook's dist
10.5
0.51
25
15
40

20
0.0 1.0 2.0
-1.01.5
Fitted values
Residuals
Residuals vs Fitted
342
25
-2 0 1 2
-22
Normal Q-Q
25
342
0.0 1.0 2.0
0.01.5
Fitted values
Scale-Location
25342
0.0 0.2 0.4
-31
Leverage
Cook's dist
10.5
0.51
25
15
40
0.5 1.5 2.5
-1.0
Fitted values
Residuals
Residuals vs Fitted
3440
11
-2 0 1 2
-21
Normal Q-Q
3440
11
0.5 1.5 2.5
0.01.5
Fitted values
Scale-Location
344011
0.0 0.2 0.4
-22
Leverage
Cook's dist
10.5
0.51
40
25
14

21
0.0 1.0 2.0
-1.01.5
Fitted values
Residuals
Residuals vs Fitted
34
40 2
-2 0 1 2
-12
Normal Q-Q
34
402
0.0 1.0 2.0
0.01.5
Fitted values
Scale-Location
3440 2
0.0 0.2 0.4
-22
Leverage
Cook's dist
10.5
0.51
25
4034
lm(ND00 ~ PC95GEXH + PC95TEXH)
0.0 1.0 2.0
-1.01.5
Fitted values
Residuals
Residuals vs Fitted
34
40 2
-2 0 1 2
-12
Normal Q-Q
34
402
0.0 1.0 2.0
0.01.5
Fitted values
Scale-Location
3440 2
0.0 0.2 0.4
-22
Leverage
Cook's dist
10.5
0.51
25
4034
lm(ND00 ~ PC95GEXH + PC95TEXH)

22
Figure 20: scree plot of PCA on correltaion matrix
Figure 21: plot of PCA on correltaion matrix
Comp.1 Comp.4 Comp.7 Comp.10
Scree plot for PCA1Inertia
02468
-0.4 -0.2 0.0 0.2
-0.4-0.20.00.2
Biplot pca1
Comp.1
Comp.2
1 2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
1718
19
20
21
22
23
24
25
26
27
28
29
30 3132
33
34
35
36
37
38
39
40
41
42
434445
-8 -6 -4 -2 0 2 4 6
-8-6-4-20246
PC95TEXH
PC05TEXHPC12TEXH
PC95GEXH
PC05GEXHPC12GEXH UFD0UFD1ID00ID10ND0ND10

23
Figure 22:
Figure 23:
-5 0 5
-4-202
Scores plot pca1
1st principal component
2ndprincipalcomponent
Algeria
Angola
Benin
Botsw ana
Burkina Faso
Burundi
Cabo Verde
Cameroon
Central African Republic
Chad
Comoros
Congo
Côte d'Ivoire
Democratic Republic of the Congo
Equatorial Guinea
Eritrea
EthiopiaGabon
Gambia
Ghana
Guinea
Guinea-Bissau
Kenya
Lesotho
Liberia
Madagascar
Malaw i
Mali
Mauritania
Mauritius
Mozambique
Namibia
Niger
Nigeria
Rw anda
Sao Tome and Principe
Senegal
Seychelles
Sierra Leone
South Africa
Sw aziland
Togo
UgandaUnited Republic of TanzaniaZambia
-10 -5 0 5 10
-6
-4
-2
0
2
4
Varimax Scores plot(pca1)
1st varimax component
2ndvarimaxcomponent
Algeria
Angola
Benin
Botsw ana
Burkina Faso
Burundi
Cabo Verde
Cameroon
Central African Republic
Chad
Comoros
Congo
Côte d'Ivoire
Equatorial Guinea
Eritrea
Ethiopia
Gabon
Gambia
Ghana
Guinea
Guinea-Bissau
Kenya
Lesotho
Liberia
Madagascar
Malaw iMali
Mauritania
Mauritius
Mozambique
Namibia
Niger
Nigeria
Rw anda
Senegal
Seychelles
Sierra Leone
South Africa
Sw aziland
Togo UgandaUnited Republic of Tanzania
Zambia
CountryPC95TEXHPC05TEXHPC12TEXHPC95GEXHPC05GEXH
PC12GEXHUFD00UFD10ID00ID10ND00
ND10
Child death rates
Health expenditure

24
Figure 24: redundancy analysis plot, child mortality rates vs. health expenditure 2005
Figure 25: redundancy analysis plot, child mortality rates vs. health expenditure 1995

-4 -2 0 2 4
-2.0-1.5-1.0-0.50.00.51.0
RDA1
RDA2
type2log.PC05TEXH
type2log.PC05GEXH
1
2
3
4
5
6
7
8
9
10
1112
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
type2log.UFD00
type2log.UFD10
type2log.ID00type2log.ID10
type2log.ND00
type2log.ND10
-6 -4 -2 0 2 4 6
-3-2-1012
RDA1
RDA2
type2log.PC95TEXH
type2log.PC95GEXH
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16 17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41 42
43
4445
type2log.UFD00
type2log.UFD10
type2log.ID00
type2log.ID10
type2log.ND00
type2log.ND10
-10
Comp.1 Comp.3 Comp.5
Scree plot for PCA MortRate
Inertia
0100003000050000
Scree plot for PCA Expd
Inertia
0200004000060000

25
Figure 26: Scree plot  for covariance
matrix of child mortality rates
Figure 27: Scree plot  for covariance matrix of
health expenditures
Figure 28: Bi plot  for covariance matrix
of child mortality rates
Figure 29: Bi plot  for covariance matrix of health
expenditures
Figure 30: Varimax plot  for covariance
Figure 31: Varimax plot  for covariance matrix of
health expenditures
-0.8 -0.6 -0.4 -0.2 0.0 0.2
-0.8-0.6-0.4-0.20.00.2
Biplot pca MortRate
Comp.1
Comp.2
1
2
345678 9
10
111213
14
1516
17
1819
20
21
2223 24
25
2627
282930
31
32
33
34
35
36
37
3839
404142
43
44
45
-1000 -600 -200 0 200
-1000-600-2000200
FD00
UFD10
ID00
ID10
ND00
ND10
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
-0.6-0.4-0.20.00.20.40.6
Biplot pca Expd
Comp.1
Comp.2
1
2 3
4
567
8
9
10
1112
1314
15
16
17
18
192021
22
232425262728
29
30
31
32
33
34
353637
38
39
40
41
42
43
4445
-1000 -500 0 500 1000
-1000-50005001000
PC95TEXH
05TEXH
PC95GEXH
PC05GEXH
-1000 -600 -200 0 200
-800
-600
-400
-200
0
Varimax Scores plot(pca Mort Rate)
2ndvarimaxcomponent
Algeria
Angola
Benin
Botsw ana
Burkina Faso
Burundi
Cabo Verde
Cameroon
Central African Rep
Chad
ComorosCongo
Côte d'Ivoire
Equatorial GuineEritrea
Ethiopia
GabonGambia
GhanaGuinea
Guinea-Bissau
Kenya
LesothoLiberia
MadagascarMalaw iMali
MauritaniaMauritius
Mozambique
Namibia
Niger
Nigeria
Rw anda
Sao Tome and Prin
Senegal
Seychelles
Sierra Leone
South Africa
Sw azilandTogo
UgandaUnited Republic of Tanzania
ZambiaCountryPC95TEXHPC05TEXHPC12TEXHPC95GEXHPC05GEXHPC12GEXHUFD00UFD10ID00ID10ND00ND10
-800 -600 -400 -200 0 200
0
200
400
600
800
Varimax Scores plot(pca Expd)
2ndvarimaxcomponent
Algeria
Angola
Benin
Botsw ana
Burkina FasoBurundi
Cabo Verde
CameroonCentral African RepublicChadComoros
Congo
Côte d'Ivoire
Democratic Republic of the Co
Equatorial Guinea
EritreaEthiopia
Gabon
GambiaGhana
Guinea
Guinea-Bissau
KenyaLesotho
Liberia
MadagascarMalaw iMali
Mauritania
Mauritius
Mozambique
Namibia
NigerNigeria
Rw anda
Senegal
Seychelles
Sierra Leone
South Africa
Sw aziland
TogoUgandaUnited Republic of Tanzania
Zambia

26
Figure 32: Scores plot  for covariance
Figure 33: Scores plot  for covariance matrix of
health expenditures
Table 2:  Correlation coefficients
PC95
TEXH
PC05
TEXH
PC12
TEXH
PC95
GEXH
PC05
GEXH
PC12
GEXH UFD00 UFD10 ID00 ID10 ND00 ND10
PC95TEXH 1.00 0.89   0.78 0.92 0.87 0.83 ‐0.21 ‐0.18 ‐0.20 ‐0.18 ‐0.21 ‐0.18
PC05TEXH 0.89 1.00 0.91 0.80   0.92 0.87 ‐0.19 ‐0.16 ‐0.19 ‐0.16 ‐0.20 ‐0.17
PC12TEXH 0.78   0.91    1.00   0.74    0.86   0.94 ‐0.20 ‐0.18 ‐0.19 ‐0.17 ‐0.20 ‐0.18
PC95GEXH 0.92   0.80   0.74    1.00   0.90   0.88 ‐0.20 ‐0.18 ‐0.20 ‐0.17 ‐0.20 ‐0.18
PC05GEXH 0.87    0.92    0.86   0.90    1.00 0.93 ‐0.21 ‐0.19 ‐0.21 ‐0.19 ‐0.21 ‐0.19
PC12GEXH 0.83 0.87   0.94    0.88   0.93 1.00 ‐0.22 ‐0.20 ‐0.22 ‐0.19 ‐0.22 ‐0.20
UFD00 ‐0.21   ‐0.19 ‐0.20 ‐0.20 ‐0.21 ‐0.22 1.00 0.98 0.99   0.98 0.99 0.99
UFD10 ‐0.18   ‐0.16 ‐0.18 ‐0.18 ‐0.19 ‐0.20 0.98 1.00 0.98   0.99 0.96 0.99
ID00 ‐0.20 ‐0.19 ‐0.19 ‐0.20 ‐0.21 ‐0.22 0.99 0.98 1.00   0.98 0.99   0.99
ID10 ‐0.18   ‐0.16 ‐0.17 ‐0.17 ‐0.19 ‐0.19 0.98 0.99 0.98   1.00 0.96 0.99
ND00 ‐0.21   ‐0.20 ‐0.20 ‐0.20 ‐0.21 ‐0.22 0.99   0.96 0.99   0.96 1.00   0.98
ND10 ‐0.18 ‐0.17 ‐0.18 ‐0.18 ‐0.19 ‐0.20 0.99 0.99 0.99   0.99 0.98 1.00
Table 3: summary of Shapiro‐Wilk normality test‐p values
Shapiro‐Wilk normality test‐p values
Original data Log10 transformed data
PC95TEXH 2.221e‐09 0.437
PC05TEXH 6.416e‐09 0.01336
PC12TEXH 3.201e‐09 0.03242
PC95GEXH 4.121e‐11 0.08201
PC05GEXH 8.008e‐10 0.1731
PC12GEXH 9.39e‐10 0.01635
UFD00 6.136e‐11 0.03946
UFD10 1.899e‐11 0.06938
ID00 6.361e‐11 0.0312
ID10 1.363e‐11 0.01937
ND00 5.93e‐11 0.005314
ND10 2.557e‐11 0.01495
Original data set including all variables   2.24e‐13
-1000 -500 0
-600-2000200600
Scores plot pca Mort Rate
AlgeriaAngola
BeninBotsw aBurkina FasoBurundiCabo VeCameroonCentral African RChadComoroCongoCôte d'Ivoire
Democratic Republic of the CongoEquatorial GEritrea
Ethiopia
GabonGambiaGhanaGuineaGuinea-BisKenyaLesothLiberiaMadagascarMalaw iMaliMauritanMauritiuMozambiqueNamibiNiger
Nigeria
Rw anda
Sao Tome andSenegalSeychelSierra LeonSouth AfricaSw azilaTogoUgandaUnited Republic of TanzanZambiaCountryPC95TEXHPC05TEXHPC12TEXHPC95GEXHPC05GEXHPC12GEXHUFD00UFD10ID00ID10ND00ND10
-1000 -600 -200 0 200
-4000200400
Scores plot pca Expd
Algeria
AngolaBenin
Botsw ana
Burkina FasoBurundiCabo VerdeCameroon
Central AfricanChadComorosCongo
Côte d'IvoireDemocratic Republic
Equatorial Guinea
EritreaEthiopia
Gabon
GambiaGhanaGuinea
Guinea-Bissau
KenyaLesothoLiberiaMadagascMalaw iMaliMauritania
Mauritius
Mozambiqu
Namibia
Niger
NigeriaRw andaSao Tome and PrincipeSenegal
ychelles
Sierra Leone
South Africa
Sw aziland
TogoUganda
United Republic ofZambiaCountryPC95TEXHPC05TEXHPC12TEXHPC95GEXHPC05GEXHPC12GEXHUFD00UFD10ID00ID10ND00ND10

27
Log10 transformed data  including all variables 1.79e‐13
Table 4: summary of multiple regression models tested
General  linear model and
Reduced model with lowest AIC
Adjusted
R‐
squared
p‐value   AIC
Reg1ID10 ID10=2.27‐0.74PC05GEXH+0.01PC05TEXH 0.2438 0.001065   ‐41.53
Reduced
Reg1ID10
ID10 ~ PC05GEXH ‐43.53

Reg2ID10 ID10=1.77‐0.19PC05GEXH+0.56PC05TEXH‐
0.92PC95GEXH‐0.12PC95TEXH
0.3177   0.0006102 ‐44.35
Reduced
Reg2ID10
ID10 ~ PC95GEXH ‐49.57

Reg31ID10 UFD10=2.55‐0.83PC05GEXH+0.06PC05TEXH 0.2578 0.0007182 ‐38.36
Reduced
Reg31ID10
UFD10 ~ PC05GEXH ‐40.35

Reg3UFD10 FD10=2.03‐0.27PC05GEXH+0.71PC05TEXH ‐
0.3379 0.0003494 ‐41.69
Reduced
Reg3UFD10
UFD10 ~ PC95GEXH ‐46.68

Reg5ND10 ND10=2.15+0.21PC05TEXH‐0.93PC05GEXH 0.2226 0.001903 ‐49.83
Reduced
Reg5ND10
ND10 ~ PC05GEXH   ‐51.65

Reg4ND10 ND10=1.39‐0.14PC05GEXH+0.68PC05TEXH‐
0.2808 0.001613 ‐51.53
Reduced
Reg4ND10
ND10 ~ PC95TEXH

‐56.12

Reg13ID00 ID00=2.33‐0.87PC95GEXH+0.06PC95TEXH 0.3603   3.168e‐05 ‐46.38
Reduced
Reg13ID00
ID00 ~ PC95GEXH

‐48.36

Reg14ND00 ND00=1.94‐0.78PC95GEXH+0.02PC95TEXH 0.3638    2.825e‐05 ‐55.04
Reduced
Reg14ND00
ND00 ~ PC95GEXH

‐57.03

Reg16UFD00

UFD00=2.59‐0.96PC95GEXH +
0.08PC95TEXH
0.3856 1.36e‐05 ‐45.19
Reduced
Reg16UFD00
UFD00 ~ PC95GEXH ‐45.2

Table 5: summary of the selected models coefficients and p‐values

28

Table 6: summary of loading on the first 2 components of PCA
PCA on correlation matrix   Comp 1   Comp 2
PC95TEXH   ‐0.278 ‐0.263
PC05TEXH   ‐0.276 ‐0.343
PC12TEXH   ‐0.268 ‐0.337
PC95GEXH   ‐0.294 ‐0.228
PC05GEXH   ‐0.279 ‐0.310
PC12GEXH   ‐0.276 ‐0.302
UFD00       0.303 ‐0.261
UFD10       0.301 ‐0.272
ID00        0.300 ‐0.280
ID10        0.299 ‐0.281
ND00        0.302 ‐0.270
ND10        0.285 ‐0.296
Table 7: standardized canonical coefficients of the canonical correlation analysis
1 2
First set of variable
PC05TEXH   0.25   1.00
PC05GEXH 0.09 ‐0.84
Second set of Variable
UFD00   ‐1.33 ‐0.06
UFD10    0.34 0.34
ID00     1. 0.53
ID10    ‐0.16 0.36
type2log.ND00    ‐0.56 ‐1.64
type2log.ND10     0.17 0.47
Table 8: Summary of Bonferonni outlier test on the selected models
Outlier     rstudent   unadjusted p‐value Bonferonni p
Reg6ND10 30 12.34386          1.0987e‐14     4.9442e‐13
Reg7 ID10 30 ‐3.909981         0.00037968       0.017086
Reg8 UFD10 4 3.436218           0.0014719       0.066235
Reg9 ND10 30 13.33186          1.0957e‐16     4.9307e‐15
Reg10 UFD10 4 3.651499          0.00073142       0.032914
Reg11 UFD10 4 3.18752           0.0027092       0.12191
Reg12 ID10 30 ‐4.224568         0.00012999      0.0058494

29
> str(type2)
'data.frame':   45 obs. of  13 variables:
$ Country : Factor w/ 45 levels "Algeria","Angola",..: 1 2 3 4 5 6 7 8 9 10 ...
$ PC95TEXH: num  164.7 84.2 43.1 249.4 29.4 ...
$ PC05TEXH: num  219.5 139 60.6 628.5 73.7 ...
$ PC12TEXH: num  439 212.1 69.6 871.8 90.1 ...
$ PC95GEXH: num  119 59.5 19.4 130.6 11.4 ...
$ PC05GEXH: num  159.6 69.5 30.1 457.2 43.9 ...
$ PC12GEXH: num  369.3 131.9 35.8 491.3 49 ...
$ UFD00   : num  24 143 41 4 94 40 1 95 24 76 ...
$ UFD10   : num  26 162 33 3 72 36 1 79 22 85 ...
$ ID00    : num  20 86 26 3 49 25 1 58 16 43 ...
$ ID10    : num  23 72 16 1 41 17 1 37 12 44 ...
$ ND00    : num  12 36 11 1 20 11 1 23 7 18 ...
$ ND10    : num  15 44 10 1 19 13 1 23 7 22 ...
> summary(type2)
         Country      PC95TEXH         PC05TEXH        PC12TEXH
Algeria     : 1   Min.   :  6.50   Min.   : 15.6   Min.   :  16.5
Angola      : 1   1st Qu.: 29.40   1st Qu.: 48.8   1st Qu.:  67.3
Benin       : 1   Median : 45.50   Median : 77.1   Median : 107.8
Botswana    : 1   Mean   : 94.69   Mean   :149.5   Mean   : 241.4
Burkina Faso: 1   3rd Qu.: 94.40   3rd Qu.:135.9   3rd Qu.: 204.9
Burundi     : 1   Max.   :629.30   Max.   :739.9   Max.   :1431.7
(Other)     :39
    PC95GEXH         PC05GEXH         PC12GEXH          UFD00
Min.   :  0.50   Min.   :  3.70   Min.   :   7.8   Min.   :  1.00
1st Qu.: 10.70   1st Qu.: 20.60   1st Qu.:  28.8   1st Qu.:  7.00
Median : 18.10   Median : 30.70   Median :  45.7   Median : 41.00
Mean   : 49.37   Mean   : 81.88   Mean   : 141.1   Mean   : 86.02
3rd Qu.: 48.70   3rd Qu.: 69.50   3rd Qu.: 128.8   3rd Qu.: 94.00
Max.   :535.90   Max.   :640.90   Max.   :1116.2   Max.   :934.00

     UFD10             ID00             ID10            ND00
Min.   :  1.00   Min.   :  1.00   Min.   :  1.0   Min.   :  1.00
1st Qu.:  6.00   1st Qu.:  5.00   1st Qu.:  4.0   1st Qu.:  2.00
Median : 33.00   Median : 26.00   Median : 21.0   Median : 12.00
Mean   : 68.87   Mean   : 53.13   Mean   : 38.4   Mean   : 23.47
3rd Qu.: 79.00   3rd Qu.: 55.00   3rd Qu.: 44.0   3rd Qu.: 23.00
Max.   :830.00   Max.   :567.00   Max.   :470.0   Max.   :245.00

      ND10
Min.   :  1.00
1st Qu.:  3.00
Median : 13.00
Mean   : 22.62
3rd Qu.: 23.00
Max.   :257.00
> cor(type2[,2:13])
           PC95TEXH   PC05TEXH   PC12TEXH   PC95GEXH   PC05GEXH   PC12GEXH
PC95TEXH  1.0000000  0.8963071  0.7825579  0.9256020  0.8738156  0.8307543
PC05TEXH  0.8963071  1.0000000  0.9181442  0.8042933  0.9218915  0.8758135
PC12TEXH  0.7825579  0.9181442  1.0000000  0.7406167  0.8695250  0.9479927
PC95GEXH  0.9256020  0.8042933  0.7406167  1.0000000  0.9084133  0.8809864
PC05GEXH  0.8738156  0.9218915  0.8695250  0.9084133  1.0000000  0.9342122
PC12GEXH  0.8307543  0.8758135  0.9479927  0.8809864  0.9342122  1.0000000
UFD00    ‐0.2130300 ‐0.1960245 ‐0.2030396 ‐0.2039303 ‐0.2186197 ‐0.2243362
UFD10    ‐0.1859243 ‐0.1695941 ‐0.1813526 ‐0.1812701 ‐0.1978687 ‐0.2039448
ID00     ‐0.2090670 ‐0.1923454 ‐0.1988736 ‐0.2006420 ‐0.2159624 ‐0.2204190
ID10     ‐0.1816682 ‐0.1663914 ‐0.1770696 ‐0.1777267 ‐0.1937291 ‐0.1988588
ND00     ‐0.2149649 ‐0.2016752 ‐0.2051136 ‐0.2016774 ‐0.2182470 ‐0.2224618
ND10     ‐0.1897916 ‐0.1719560 ‐0.1805229 ‐0.1815529 ‐0.1974623 ‐0.2023317
              UFD00      UFD10       ID00       ID10       ND00       ND10
PC95TEXH ‐0.2130300 ‐0.1859243 ‐0.2090670 ‐0.1816682 ‐0.2149649 ‐0.1897916
PC05TEXH ‐0.1960245 ‐0.1695941 ‐0.1923454 ‐0.1663914 ‐0.2016752 ‐0.1719560
PC12TEXH ‐0.2030396 ‐0.1813526 ‐0.1988736 ‐0.1770696 ‐0.2051136 ‐0.1805229
PC95GEXH ‐0.2039303 ‐0.1812701 ‐0.2006420 ‐0.1777267 ‐0.2016774 ‐0.1815529

30
PC05GEXH ‐0.2186197 ‐0.1978687 ‐0.2159624 ‐0.1937291 ‐0.2182470 ‐0.1974623
PC12GEXH ‐0.2243362 ‐0.2039448 ‐0.2204190 ‐0.1988588 ‐0.2224618 ‐0.2023317
UFD00     1.0000000  0.9837326  0.9986441  0.9841675  0.9950972  0.9917506
UFD10     0.9837326  1.0000000  0.9813491  0.9984373  0.9679026  0.9948934
ID00      0.9986441  0.9813491  1.0000000  0.9829444  0.9966409  0.9915310
ID10      0.9841675  0.9984373  0.9829444  1.0000000  0.9694700  0.9952155
ND00      0.9950972  0.9679026  0.9966409  0.9694700  1.0000000  0.9846367
ND10      0.9917506  0.9948934  0.9915310  0.9952155  0.9846367  1.0000000
Expenditure 2005
> summary(type2log)
    PC95TEXH         PC05TEXH        PC12TEXH        PC95GEXH
Min.   :0.8129   Min.   :1.193   Min.   :1.217   Min.   :‐0.301
1st Qu.:1.4683   1st Qu.:1.688   1st Qu.:1.828   1st Qu.: 1.029
Median :1.6580   Median :1.887   Median :2.033   Median : 1.258
Mean   :1.7465   Mean   :1.954   Mean   :2.113   Mean   : 1.350
3rd Qu.:1.9750   3rd Qu.:2.133   3rd Qu.:2.312   3rd Qu.: 1.688
Max.   :2.7989   Max.   :2.869   Max.   :3.156   Max.   : 2.729
    PC05GEXH         PC12GEXH          UFD00            UFD10
Min.   :0.5682   Min.   :0.8921   Min.   :0.0000   Min.   :0.0000
1st Qu.:1.3139   1st Qu.:1.4594   1st Qu.:0.8451   1st Qu.:0.7782
Median :1.4871   Median :1.6599   Median :1.6128   Median :1.5185
Mean   :1.5973   Mean   :1.7953   Mean   :1.4376   Mean   :1.3523
3rd Qu.:1.8420   3rd Qu.:2.1099   3rd Qu.:1.9731   3rd Qu.:1.8976
Max.   :2.8068   Max.   :3.0477   Max.   :2.9703   Max.   :2.9191
      ID00            ID10             ND00            ND10
Min.   :0.000   Min.   :0.0000   Min.   :0.000   Min.   :0.0000
1st Qu.:0.699   1st Qu.:0.6021   1st Qu.:0.301   1st Qu.:0.4771
Median :1.415   Median :1.3222   Median :1.079   Median :1.1139
Mean   :1.254   Mean   :1.1161   Mean   :0.938   Mean   :0.9479
3rd Qu.:1.740   3rd Qu.:1.6435   3rd Qu.:1.362   3rd Qu.:1.3617
Max.   :2.754   Max.   :2.6721   Max.   :2.389   Max.   :2.4099
> expend <‐data.frame(type2log$PC05TEXH, type2log$PC05GEXH)
> mort <‐ data.frame (type2log$UFD00, type2log$ UFD10, type2log$ID00, type2log$ID10, type2log$ND00, type2log$ND10)
> OK <‐complete.cases(expend,mort)
> ccca<‐cancor(expend[OK,],mort[OK,])
> ccca
$cor
[1] 0.6317665 0.3706533
$xcoef
                        [,1]       [,2]
type2log.PC05TEXH 0.25222659  1.0012115
type2log.PC05GEXH 0.09470577 ‐0.8434111
$ycoef
                     [,1]        [,2]        [,3]        [,4]       [,5]
type2log.UFD00 ‐1.3302539 ‐0.06290979 ‐1.94885071  1.25602481 ‐1.0760095
type2log.UFD10  0.3484259  0.34575788 ‐0.04634281 ‐1.48775584  1.6856152
type2log.ID00   1.4100238  0.53170842  2.10010546 ‐1.57746324 ‐0.4809551
type2log.ID10  ‐0.1676133  0.36381980  0.04142259  2.01909388 ‐1.0925449
type2log.ND00  ‐0.5656447 ‐1.64824239  0.08531634 ‐0.32304602  0.8547105
type2log.ND10   0.1705373  0.47222108 ‐0.02619021  0.09337854  0.2456990
                     [,6]
type2log.UFD00 ‐1.7878817
type2log.UFD10  1.2030900
type2log.ID00   0.5829623
type2log.ID10   0.3455343
type2log.ND00   0.5902689
type2log.ND10  ‐0.9375137
$xcenter
type2log.PC05TEXH type2log.PC05GEXH
         1.953798          1.597318
$ycenter
type2log.UFD00 type2log.UFD10  type2log.ID00  type2log.ID10  type2log.ND00
     1.4375796      1.3523235      1.2541245      1.1161151      0.9379719
type2log.ND10
     0.9478903
> summary(ccca)

31
        Length Class  Mode
cor      2     ‐none‐ numeric
xcoef    4     ‐none‐ numeric
ycoef   36     ‐none‐ numeric
xcenter  2     ‐none‐ numeric
ycenter  6     ‐none‐ numeric
> rdda<‐rda(expend[OK,],mort[OK,])
> rdda
Call: rda(X = expend[OK, ], Y = mort[OK, ])
              Inertia Proportion Rank
Total          0.4292     1.0000
Constrained    0.1667     0.3885    2
Unconstrained  0.2625     0.6115    2
Inertia is variance
Eigenvalues for constrained axes:
    RDA1     RDA2
0.164933 0.001816
Eigenvalues for unconstrained axes:
    PC1     PC2
0.25120 0.01127
> plot(rdda)
Expenditure 2012
> expend12 <‐data.frame(type2log$PC12TEXH, type2log$PC12GEXH)
> OK <‐complete.cases(expend12,mort)
> ccca12 <‐cancor(expend12[OK,],mort[OK,])
> ccca12
$cor
[1] 0.6541995 0.2365056
$xcoef
                        [,1]       [,2]
type2log.PC12TEXH 0.08656742  1.0774556
type2log.PC12GEXH 0.21318541 ‐0.9196562
$ycoef
                     [,1]       [,2]       [,3]       [,4]       [,5]
type2log.UFD00 ‐1.2053364 ‐0.6583229 ‐1.3734335  0.7705718 ‐1.2113809
type2log.UFD10  0.1090623  0.4883119 ‐0.5411692 ‐1.1762698  1.5199605
type2log.ID00   1.6458202  1.2901258  1.6781640 ‐1.1449367 ‐0.1223899
type2log.ID10  ‐0.2818023 ‐0.2427037  0.1256273  1.8570530 ‐1.3927446
type2log.ND00  ‐0.5694125 ‐1.4389385  0.4872880 ‐0.5387228  1.0715744
type2log.ND10   0.1623827  0.6458826 ‐0.1969300  0.2275852  0.2744305
                      [,6]
type2log.UFD00 ‐2.38111298
type2log.ID00   1.10708377
type2log.ID10   0.09736615
type2log.ND00   0.39563066
type2log.ND10  ‐0.76899942
$xcenter
         2.112754          1.795255
$ycenter
     1.4375796      1.3523235      1.2541245      1.1161151      0.9379719
type2log.ND10
     0.9478903
> rdda12 <‐rda(expend12[OK,],mort[OK,])
> rdda12
Call: rda(X = expend12[OK, ], Y = mort[OK, ])
Total          0.4893     1.0000
Inertia is variance
     RDA1      RDA2

32
0.2040830 0.0006333
    PC1     PC2
0.27391 0.01064
> plot(rdda12)

> expend95 <‐data.frame(type2log$PC95TEXH, type2log$PC95GEXH)
> OK <‐complete.cases(expend95,mort)
> ccca<‐cancor(expend95[OK,],mort[OK,])
> ccca
$cor
[1] 0.6994977 0.3100254
$xcoef
                        [,1]       [,2]
type2log.PC95TEXH 0.06660944  0.8773772
type2log.PC95GEXH 0.22907259 ‐0.6585852
$ycoef
                      [,1]       [,2]        [,3]        [,4]        [,5]
type2log.UFD00 ‐1.20708317 ‐0.1060889 ‐2.16784849  1.73946259 ‐0.68511662
type2log.UFD10  0.38616941  0.4910146  0.11621581 ‐2.03093054  1.26932812
type2log.ID00   0.95348626 ‐0.5139874  2.19106357 ‐1.67922471 ‐0.93209836
type2log.ID10   0.04566393  0.9328908  0.06985725  1.88383771 ‐1.00816905
type2log.ND00  ‐0.34496571 ‐0.9789245 ‐0.02747850  0.07542098  1.42980090
type2log.ND10   0.01333914  0.1955510  0.01406220 ‐0.01910233  0.05312349
                     [,6]
type2log.UFD00 ‐1.3566434
type2log.ID00   0.2796347
type2log.ID10   0.3308526
type2log.ND00   1.0484146
type2log.ND10  ‐1.0765585
$xcenter
         1.746545          1.349832
$ycenter
     1.4375796      1.3523235      1.2541245      1.1161151      0.9379719
type2log.ND10
     0.9478903
> rdda31<‐rda(expend95[OK,],mort[OK,])
> rdda31
Call: rda(X = expend95[OK, ], Y = mort[OK, ])

Total          0.4778     1.0000
Inertia is variance
    RDA1     RDA2
0.223500 0.001813
    PC1     PC2
0.23563 0.01688
> plot(rdda31)

Principal component analysis
> pca1 <‐ princomp(type2log, cor=TRUE,scores=TRUE) ######### correlation matrix
> summary(pca1)
Importance of components:
                          Comp.1    Comp.2     Comp.3     Comp.4      Comp.5
Standard deviation     2.9755211 1.5732152 0.54369657 0.36797783 0.302917671
Proportion of Variance 0.7378105 0.2062505 0.02463383 0.01128397 0.007646593
Cumulative Proportion  0.7378105 0.9440610 0.96869480 0.97997877 0.987625368

33
Standard deviation     0.26580451 0.200503950 0.12978737 0.0978056623
Proportion of Variance 0.00588767 0.003350153 0.00140373 0.0007971623
Cumulative Proportion  0.99351304 0.996863190 0.99826692 0.9990640827
Standard deviation     0.0734262542 0.0655267695 0.0393171153
Proportion of Variance 0.0004492846 0.0003578131 0.0001288196
Cumulative Proportion  0.9995133672 0.9998711804 1.0000000000
> pca2 <‐ princomp(type2log, cor=FALSE,scores=TRUE) ######### covariance matrix
> summary(pca2)
Importance of components:
                          Comp.1    Comp.2     Comp.3     Comp.4      Comp.5
Standard deviation     1.8398147 0.8387488 0.26442295 0.19669923 0.174423322
Proportion of Variance 0.7926782 0.1647451 0.01637371 0.00906054 0.007124557
Cumulative Proportion  0.7926782 0.9574234 0.97379708 0.98285762 0.989982182
Standard deviation     0.132818086 0.096927625 0.084810118 0.066385757
Proportion of Variance 0.004131076 0.002200108 0.001684396 0.001032045
Cumulative Proportion  0.994113258 0.996313366 0.997997761 0.999029806
Standard deviation     0.047964249 0.031864686 0.0287579929
Proportion of Variance 0.000538746 0.000237776 0.0001936716
Cumulative Proportion  0.999568552 0.999806328 1.0000000000

> screeplot(pca1,main="Scree plot for PCA1")
> screeplot(pca2,main="Scree plot for PCA2")
> print(loadings(pca1),cutoff=0.00)
Loadings:
         Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8 Comp.9 Comp.10
PC95TEXH ‐0.278 ‐0.263 ‐0.621  0.355  0.021 ‐0.009 ‐0.526  0.162 ‐0.112 ‐0.111
PC05TEXH ‐0.276 ‐0.343 ‐0.058  0.298 ‐0.211 ‐0.411  0.356 ‐0.139  0.031  0.461
PC12TEXH ‐0.268 ‐0.337  0.378  0.456  0.022  0.256  0.335  0.131  0.113 ‐0.422
PC95GEXH ‐0.294 ‐0.228 ‐0.411 ‐0.455  0.286  0.478  0.404 ‐0.062 ‐0.006  0.071
PC05GEXH ‐0.279 ‐0.310  0.102 ‐0.574 ‐0.161 ‐0.544 ‐0.056  0.084 ‐0.001 ‐0.283
PC12GEXH ‐0.276 ‐0.302  0.514 ‐0.133  0.147  0.284 ‐0.546 ‐0.153 ‐0.040  0.265
UFD00     0.303 ‐0.261  0.042  0.042  0.357 ‐0.146  0.061  0.016 ‐0.452 ‐0.014
UFD10     0.301 ‐0.272 ‐0.076  0.046  0.248 ‐0.130 ‐0.024 ‐0.542  0.001 ‐0.462
ID00      0.300 ‐0.280  0.062  0.021  0.260 ‐0.055  0.070  0.228 ‐0.242  0.408
ID10      0.299 ‐0.281 ‐0.100 ‐0.011  0.045  0.006 ‐0.105 ‐0.176  0.764  0.203
ND00      0.302 ‐0.270  0.002 ‐0.110 ‐0.093  0.069 ‐0.018  0.693  0.196 ‐0.145
ND10      0.285 ‐0.296 ‐0.058 ‐0.081 ‐0.747  0.339 ‐0.005 ‐0.214 ‐0.296  0.007
         Comp.11 Comp.12
PC95TEXH  0.116  ‐0.014
PC05TEXH ‐0.376   0.021
PC12TEXH  0.277  ‐0.001
PC95GEXH ‐0.064   0.015
PC05GEXH  0.271  ‐0.017
PC12GEXH ‐0.236   0.012
UFD00     0.039   0.691
UFD10    ‐0.330  ‐0.363
ID00      0.386  ‐0.571
ID10      0.302   0.246
ND00     ‐0.520  ‐0.025
ND10      0.115   0.034
               Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8 Comp.9
SS loadings     1.000  1.000  1.000  1.000  1.000  1.000  1.000  1.000  1.000
Proportion Var  0.083  0.083  0.083  0.083  0.083  0.083  0.083  0.083  0.083
Cumulative Var  0.083  0.167  0.250  0.333  0.417  0.500  0.583  0.667  0.750
SS loadings      1.000   1.000   1.000
Proportion Var   0.083   0.083   0.083
Cumulative Var   0.833   0.917   1.000
> print(loadings(pca2),cutoff=0.00)
Loadings:
         Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8 Comp.9 Comp.10
PC95TEXH ‐0.163 ‐0.296 ‐0.518 ‐0.152  0.422 ‐0.093 ‐0.434 ‐0.351  0.245 ‐0.006
PC05TEXH ‐0.151 ‐0.347 ‐0.048 ‐0.021  0.339 ‐0.390  0.323  0.126 ‐0.100 ‐0.096

34
PC12TEXH ‐0.162 ‐0.377  0.351 ‐0.061  0.451  0.238  0.364  0.046 ‐0.206  0.162
PC95GEXH ‐0.223 ‐0.354 ‐0.511 ‐0.080 ‐0.424  0.524  0.275  0.139 ‐0.026 ‐0.004
PC05GEXH ‐0.190 ‐0.400  0.063  0.166 ‐0.504 ‐0.625  0.023 ‐0.015  0.002  0.004
PC12GEXH ‐0.196 ‐0.407  0.529  0.029 ‐0.139  0.297 ‐0.547 ‐0.014  0.111 ‐0.030
UFD00     0.400 ‐0.176  0.100 ‐0.381 ‐0.071 ‐0.040  0.145 ‐0.004  0.426 ‐0.022
UFD10     0.383 ‐0.183 ‐0.090 ‐0.269  0.013 ‐0.097 ‐0.206  0.548  0.014  0.502
ID00      0.377 ‐0.192  0.116 ‐0.223 ‐0.060  0.054  0.192 ‐0.238  0.156 ‐0.538
ID10      0.366 ‐0.187 ‐0.134  0.006  0.011  0.003 ‐0.287  0.067 ‐0.729 ‐0.343
ND00      0.344 ‐0.162  0.001  0.198 ‐0.109  0.051  0.126 ‐0.649 ‐0.181  0.540
ND10      0.316 ‐0.190 ‐0.107  0.795  0.173  0.113  0.020  0.235  0.324 ‐0.115
         Comp.11 Comp.12
PC95TEXH  0.183  ‐0.049
PC05TEXH ‐0.659   0.119
PC12TEXH  0.487  ‐0.058
PC95GEXH ‐0.079   0.031
PC05GEXH  0.350  ‐0.068
PC12GEXH ‐0.302   0.053
UFD00     0.120   0.656
UFD10    ‐0.049  ‐0.363
ID00     ‐0.052  ‐0.585
ID10      0.107   0.257
ND00     ‐0.201  ‐0.006
ND10      0.061   0.031
               Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8 Comp.9
SS loadings     1.000  1.000  1.000  1.000  1.000  1.000  1.000  1.000  1.000
Proportion Var  0.083  0.083  0.083  0.083  0.083  0.083  0.083  0.083  0.083
Cumulative Var  0.083  0.167  0.250  0.333  0.417  0.500  0.583  0.667  0.750
SS loadings      1.000   1.000   1.000
Proportion Var   0.083   0.083   0.083
Cumulative Var   0.833   0.917   1.000
> vari1<‐varimax(pca1$loadings[,1:2])
> vari2<‐varimax(pca2$loadings[,1:2])
> vscores1<‐pca1$scores[,1:2]%*%vari1$rotmat
> vscores1
         [,1]         [,2]
1   0.3720739 ‐2.955009293
2   2.4999021 ‐1.327818614
3   0.4105807  0.871136570
4  ‐3.2447201 ‐4.360971822
5   1.5873217  0.733732839
6   0.5429265  2.041756424
7  ‐4.1307077 ‐1.201212581
8   1.7146026  0.586077082
9  ‐0.2334898  2.435015489
10  1.5361068  1.632877897
11 ‐3.8249512  1.084925998
12 ‐1.3626646 ‐0.602673957
13  1.7782585  0.036833366
14  4.0771283  4.664696946
15 ‐3.3567977 ‐3.746702190
16 ‐1.1532265  3.646743265
17  3.8715380  2.858754747
18 ‐3.2885421 ‐3.631301646
19 ‐2.3017920  0.357439459
20  1.4247199  0.051331356
21  0.9978187  2.012574998
22 ‐1.7977978  1.092356120
23  2.3295742  0.864449984
24 ‐1.9668199 ‐0.707810827
25 ‐0.7203986  3.001047761
26  1.2038387  1.876521266
27  1.2986547  0.997999199
28  1.8219064  0.985985871
29 ‐1.1372082 ‐0.302660640
30 ‐3.4512141 ‐3.817948791

35
31  2.2244894  1.635346558
32 ‐3.1002496 ‐3.600526342
33  1.8583462  2.018351870
34  5.3608300 ‐0.006155771
35  0.9581852  1.005744587
36 ‐4.1250968 ‐0.849891763
37  0.7298086  0.346200785
38 ‐4.1852269 ‐5.727464852
39  0.4873818 ‐0.044551489
40  1.3677764 ‐4.611692538
41 ‐3.0836505 ‐3.072763999
42 ‐0.2937982  1.290569526
43  2.5093508  1.129988938
44  2.5854837  1.312551976
45  1.2097482 ‐0.003853761
> vscores2<‐pca2$scores[,1:2]%*%vari2$rotmat
> vscores2
         [,1]        [,2]
1   0.2375530 ‐1.45186294
2   1.7449469 ‐0.66932551
3   0.3057144  0.40091176
4  ‐2.2391976 ‐2.04564423
5   1.1097202  0.33414821
6   0.3780727  0.97078498
7  ‐2.9073978 ‐0.60210840
8   1.1922214  0.32192590
9  ‐0.1393674  1.13741534
10  1.0817394  0.79865695
11 ‐2.6496926  0.49823870
12 ‐0.9124563 ‐0.31943867
13  1.2377169  0.05947280
14  2.8025331  2.26308629
15 ‐2.3479731 ‐1.77521358
16 ‐0.7610612  1.70776094
17  2.6719684  1.31366803
18 ‐2.2608175 ‐1.68149566
19 ‐1.5944909  0.18670145
20  0.9816870 ‐0.00943937
21  0.6992733  1.00629122
22 ‐1.2174828  0.58449939
23  1.6208569  0.39535141
24 ‐1.3651976 ‐0.36977208
25 ‐0.5042434  1.41003043
26  0.8473727  0.87437590
27  0.9084763  0.43657562
28  1.2726480  0.45388477
29 ‐0.7819927 ‐0.17706630
30 ‐2.5399899 ‐1.80113202
31  1.5455099  0.73323205
32 ‐2.1258282 ‐1.70436360
33  1.3104108  0.98380921
34  3.7044953  0.01505979
35  0.6671602  0.44732756
36 ‐2.9044284 ‐0.35850893
37  0.5000609  0.16496364
38 ‐2.9372286 ‐2.74178608
39  0.3441797  0.07836710
40  0.9583286 ‐2.15394289
41 ‐2.1177089 ‐1.46051324
42 ‐0.1986811  0.61900882
43  1.7351108  0.57573466
44  1.7913994  0.58782237
45  0.8560798 ‐0.03749178
plot(vscores1[,1],vscores1[,2],col=type2$Country,asp=1,xlab="1st varimax component",ylab="2nd varimax component",main="Varimax Scores
plot(pca1)", las=1)
text(vscores1[,1]‐0.1,vscores1[,2]‐0.1,type2$Country,cex=0.7)

36
arrows(0,0,vari1$loadings [,1],vari1$loadings[,2],col="green")
text(vari1$loadings[,1],vari1$loadings[,2],names(type2),asp=1,cex=0.7 ,col="blue")

plot(vscores2[,1],vscores2[,2],col=type2$Country,asp=1,xlab="1st varimax component",ylab="2nd varimax component",main="Varimax Scores
plot(pca2)", las=1)
text(vscores2[,1]‐0.1,vscores2[,2]‐0.1,type2$Country,cex=0.7)
arrows(0,0,vari2$loadings [,1],vari2$loadings[,2],col="green")
text(vari2$loadings[,1],vari2$loadings[,2],names(type2),asp=1,cex=0.7 ,col="blue")

plot(pca1$scores[,1],pca1$scores[,2],col=type2$Country,asp=1,xlab="1st principal component",ylab="2nd principal component",main="Scores
plot pca1")
text(pca1$scores[,1]‐0.1,pca1$scores[,2]‐0.1,type2$Country,cex=0.7)
arrows(0,0,pca1$loadings [,1],pca1$loadings[,2],col="red")
text(pca1$loadings[,1]‐0.1,pca1$loadings[,2]‐0.1,names(type2),asp=1,cex=0.7 ,col="blue")

plot(pca2$scores[,1],pca2$scores[,2],col=type2$Country,asp=1,xlab="1st principal component",ylab="2nd principal component",main="Scores
plot pca2")
text(pca2$scores[,1]‐0.1,pca2$scores[,2]‐0.1,type2$Country,cex=0.7)
arrows(0,0,pca2$loadings [,1],pca2$loadings[,2],col="red")
text(pca2$loadings[,1]‐0.1,pca2$loadings[,2]‐0.1,names(type2),asp=1,cex=0.7 ,col="blue")

biplot(pca1,main="Biplot pca1")
biplot(pca2,main="Biplot pca2")

Reg1ID10 <‐ lm(ID10~ PC05GEXH+ PC05TEXH, data=type2log)
Reg2ID10 <‐ lm(ID10~ PC05GEXH+ PC05TEXH+ PC95GEXH+ PC95TEXH, data=type2log)
Reg3UFD10 <‐ lm(UFD10~ PC05GEXH+ PC05TEXH+ PC95GEXH+ PC95TEXH, data=type2log)
Reg4ND10 <‐ lm(ND10~ PC05GEXH+ PC05TEXH+ PC95GEXH+ PC95TEXH, data=type2log)
Reg5ND10 <‐ lm(ND10~ PC05TEXH+ PC95TEXH, data=type2log)
Reg6ND10 <‐ lm(ND10~ PC05GEXH+ PC05TEXH+ PC95GEXH+ PC95TEXH+ ID10+ UFD10, data=type2log)
Reg7ID10 <‐ lm(ID10~ PC05GEXH+ PC05TEXH+ PC95GEXH+ PC95TEXH+ ND10+ UFD10, data=type2log)
Reg8UFD10 <‐ lm(UFD10~ PC05GEXH+ PC05TEXH+ PC95GEXH+ PC95TEXH+ ID10+ ND10, data=type2log)
Reg9ND10 <‐ lm(ND10~ ID10, data=type2log)
Reg10UFD10 <‐ lm(UFD10 ~ PC05GEXH +ID10, data=type2log)
Reg11UFD10 <‐ lm(UFD10 ~ ID10, data=type2log)
Reg12ID10 <‐ lm(ID10~ ND10+ UFD10, data=type2log)
summary(Reg1ID10)
summary(Reg2ID10)
summary(Reg3ID10)
summary(Reg4ND10)
summary(Reg5ND10)
summary(Reg6ND10)
summary(Reg7ID10)
summary(Reg8UFD10)
summary(Reg9ND10)
summary(Reg10UFD10)
summary(Reg11UFD10)
summary(Reg12ID10)

> Reg1ID10 <‐ lm(ID10~ PC05GEXH+ PC05TEXH, data=type2log)
> Reg2ID10 <‐ lm(ID10~ PC05GEXH+ PC05TEXH+ PC95GEXH+ PC95TEXH, data=type2log)
> Reg3UFD10 <‐ lm(UFD10~ PC05GEXH+ PC05TEXH+ PC95GEXH+ PC95TEXH, data=type2log)
> Reg4ND10 <‐ lm(ND10~ PC05GEXH+ PC05TEXH+ PC95GEXH+ PC95TEXH, data=type2log)
> Reg5ND10 <‐ lm(ND10~ PC05TEXH+ PC95TEXH, data=type2log)
> Reg6ND10 <‐ lm(ND10~ PC05GEXH+ PC05TEXH+ PC95GEXH+ PC95TEXH+ ID10+ UFD10, data=type2log)
> Reg7ID10 <‐ lm(ID10~ PC05GEXH+ PC05TEXH+ PC95GEXH+ PC95TEXH+ ND10+ UFD10, data=type2log)
> Reg8UFD10 <‐ lm(UFD10~ PC05GEXH+ PC05TEXH+ PC95GEXH+ PC95TEXH+ ID10+ ND10, data=type2log)
> Reg9ND10 <‐ lm(ND10~ ID10, data=type2log)
> Reg10UFD10 <‐ lm(UFD10 ~ PC05GEXH +ID10, data=type2log)
> Reg11UFD10 <‐ lm(UFD10 ~ ID10, data=type2log)
> Reg12ID10 <‐ lm(ID10~ ND10+ UFD10, data=type2log)
> summary(Reg1ID10)

37
Call:
lm(formula = ID10 ~ PC05GEXH + PC05TEXH, data = type2log)
Residuals:
     Min       1Q   Median       3Q      Max
‐1.25751 ‐0.36580  0.00243  0.44775  1.50333
Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)  2.27288    0.54868   4.142 0.000162 ***
PC05GEXH    ‐0.74391    0.51809  ‐1.436 0.158444
PC05TEXH     0.01612    0.63028   0.026 0.979715
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.6104 on 42 degrees of freedom
Multiple R‐squared:  0.2782,    Adjusted R‐squared:  0.2438
F‐statistic: 8.092 on 2 and 42 DF,  p‐value: 0.001065
> summary(Reg2ID10)
Call:
lm(formula = ID10 ~ PC05GEXH + PC05TEXH + PC95GEXH + PC95TEXH,
    data = type2log)
Residuals:
‐0.94914 ‐0.34997  0.01544  0.42213  1.34457
Coefficients:
(Intercept)   1.7753     0.5616   3.161  0.00299 **
PC05GEXH     ‐0.1923     0.6205  ‐0.310  0.75822
PC05TEXH      0.5677     0.8621   0.659  0.51397
PC95GEXH     ‐0.9201     0.5266  ‐1.747  0.08829 .
PC95TEXH     ‐0.1256     0.7100  ‐0.177  0.86052
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> summary(Reg3ID10)
Call:
lm(formula = UFD10 ~ PC05GEXH + PC05TEXH + PC95GEXH + PC95TEXH,
    data = type2log)
Residuals:
‐1.14798 ‐0.31673 ‐0.03463  0.39619  1.33012
Coefficients:
(Intercept)   2.0306     0.5784   3.510  0.00112 **
PC05GEXH     ‐0.2752     0.6392  ‐0.431  0.66911
PC05TEXH      0.7153     0.8880   0.805  0.42531
PC95GEXH     ‐0.9451     0.5424  ‐1.742  0.08915 .
PC95TEXH     ‐0.2064     0.7314  ‐0.282  0.77925
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> summary(Reg4ND10)

Call:
lm(formula = ND10 ~ PC05GEXH + PC05TEXH + PC95GEXH + PC95TEXH,
    data = type2log)
Residuals:
‐0.96955 ‐0.31210  0.01745  0.38764  1.25601
Coefficients:
(Intercept)   1.3982     0.5185   2.697   0.0102 *
PC05GEXH     ‐0.1416     0.5729  ‐0.247   0.8060
PC05TEXH      0.6849     0.7960   0.860   0.3947
PC95GEXH     ‐0.8242     0.4862  ‐1.695   0.0978 .
PC95TEXH     ‐0.2575     0.6556  ‐0.393   0.6966
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

38
> summary(Reg5ND10)
Call:
lm(formula = ND10 ~ PC05TEXH + PC95TEXH, data = type2log)
Residuals:
‐1.10455 ‐0.32213  0.06968  0.38158  1.44247
Coefficients:
(Intercept)   2.1598     0.4062   5.318 3.77e‐06 ***
PC05TEXH      0.2124     0.5114   0.415   0.6800
PC95TEXH     ‐0.9315     0.4955  ‐1.880   0.0671 .
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> summary(Reg6ND10)
Call:
lm(formula = ND10 ~ PC05GEXH + PC05TEXH + PC95GEXH + PC95TEXH +
    ID10 + UFD10, data = type2log)
Residuals:
‐0.28540 ‐0.06882 ‐0.01318  0.05960  0.87147
Coefficients:
(Intercept) ‐0.03657    0.20549  ‐0.178    0.860
PC05GEXH    ‐0.01190    0.19457  ‐0.061    0.952
PC05TEXH     0.25679    0.27244   0.943    0.352
PC95GEXH    ‐0.03069    0.17001  ‐0.181    0.858
PC95TEXH    ‐0.18526    0.22209  ‐0.834    0.409
ID10         1.34080    0.28712   4.670  3.7e‐05 ***
UFD10       ‐0.46567    0.27874  ‐1.671    0.103
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
F‐statistic: 83.48 on 6 and 38 DF,  p‐value: < 2.2e‐16
> summary(Reg7ID10)
Call:
lm(formula = ID10 ~ PC05GEXH + PC05TEXH + PC95GEXH + PC95TEXH +
    ND10 + UFD10, data = type2log)
Residuals:
‐0.206511 ‐0.043103  0.000377  0.055819  0.130839
Coefficients:
(Intercept) ‐0.096069   0.091262  ‐1.053    0.299
PC05GEXH     0.048276   0.087281   0.553    0.583
PC05TEXH    ‐0.143789   0.121913  ‐1.179    0.246
PC95GEXH    ‐0.001895   0.076598  ‐0.025    0.980
PC95TEXH     0.096026   0.099726   0.963    0.342
ND10         0.271952   0.058235   4.670  3.7e‐05 ***
UFD10        0.734343   0.052201  14.068  < 2e‐16 ***
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> summary(Reg8UFD10)
Call:
lm(formula = UFD10 ~ PC05GEXH + PC05TEXH + PC95GEXH + PC95TEXH +
    ID10 + ND10, data = type2log)
Residuals:
‐0.199873 ‐0.061220  0.004548  0.044997  0.277463
Coefficients:

39
(Intercept)  0.20790    0.11044   1.882   0.0674 .
PC05GEXH    ‐0.07629    0.10860  ‐0.703   0.4866
PC05TEXH     0.16733    0.15242   1.098   0.2792
PC95GEXH    ‐0.01512    0.09551  ‐0.158   0.8751
PC95TEXH    ‐0.10078    0.12483  ‐0.807   0.4245
ID10         1.14240    0.08121  14.068   <2e‐16 ***
ND10        ‐0.14694    0.08795  ‐1.671   0.1030
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> summary(Reg9ND10)
Call:
lm(formula = ND10 ~ ID10, data = type2log)
Residuals:
‐0.24440 ‐0.06061 ‐0.01183  0.02462  1.01541
Coefficients:
(Intercept) ‐0.01541    0.05066  ‐0.304    0.762
ID10         0.86309    0.03854  22.392   <2e‐16 ***
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Call:
lm(formula = UFD10 ~ PC05GEXH + ID10, data = type2log)
Residuals:
‐0.200100 ‐0.035128 ‐0.001316  0.035550  0.303160
Coefficients:
(Intercept)  0.26660    0.07723   3.452  0.00128 **
PC05GEXH    ‐0.03483    0.03549  ‐0.981  0.33205
ID10         1.02261    0.02559  39.966  < 2e‐16 ***
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
F‐statistic:  1136 on 2 and 42 DF,  p‐value: < 2.2e‐16
Call:
lm(formula = UFD10 ~ ID10, data = type2log)
Residuals:
‐0.196194 ‐0.039393  0.002385  0.040477  0.280927
Coefficients:
(Intercept)  0.19619    0.02856   6.869 1.99e‐08 ***
ID10         1.03585    0.02173  47.669  < 2e‐16 ***
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> summary(Reg12ID10)
Call:
lm(formula = ID10 ~ ND10 + UFD10, data = type2log)
Residuals:
‐0.223507 ‐0.046779  0.009083  0.038863  0.139237
Coefficients:
(Intercept) ‐0.12621    0.02625  ‐4.809 1.98e‐05 ***
ND10         0.26492    0.05595   4.735 2.51e‐05 ***
UFD10        0.73296    0.04813  15.230  < 2e‐16 ***

40
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> Reg13ID00 <‐ lm(ID00~ PC95GEXH+ PC95TEXH, data=type2log)
> summary(Reg13ID00)
Call:
lm(formula =
ID00 ~ PC95GEXH + PC95TEXH, data = type2log)
0.3603
3.168e‐05
Residuals:
‐1.16781 ‐0.31009 ‐0.01399  0.41798  1.36909
Coefficients:
(Intercept)  2.33200    0.45444   5.132 ***
PC95GEXH    ‐0.87670    0.40332  ‐2.174   0.0354 *
PC95TEXH     0.06042    0.50895   0.119   0.9061
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
F‐statistic: 13.39 on 2 and 42 DF,  p‐value: 3.168e‐05
> step(Reg13ID00)
Start:  AIC=‐46.38
ID00 ~ PC95GEXH + PC95TEXH

           Df Sum of Sq    RSS     AIC
‐ PC95TEXH  1   0.00471 14.056 ‐48.362
<none>                  14.052 ‐46.377
‐ PC95GEXH  1   1.58081 15.632 ‐43.579
Step:  AIC=‐48.36
ID00 ~ PC95GEXH
           Df Sum of Sq    RSS     AIC
<none>                  14.056 ‐48.362
‐ PC95GEXH  1    8.9567 23.013 ‐28.177
Call:
lm(formula = ID00 ~ PC95GEXH, data = type2log)
Coefficients:
(Intercept)     PC95GEXH
     2.3783      ‐0.8328
> Reg14ND00 <‐ lm(ND00~ PC95GEXH+ PC95TEXH, data=type2log)
> summary(Reg14ND00)
Call:
lm(formula =
ND00 ~ PC95GEXH + PC95TEXH, data = type2log)
0.3638
2.825e‐05
Residuals:
‐0.8634 ‐0.3571  0.0345  0.3797  1.3348
Coefficients:
(Intercept)  1.94348    0.41275   4.709 2.73e‐05 ***
PC95GEXH    ‐0.78351    0.36632  ‐2.139   0.0383 *
PC95TEXH     0.02983    0.46226   0.065   0.9489
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

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