Preliminary Analysis Using R

Author

Ahmed MUSTAFA
(& Google Gemini)

Published

October 8, 2026

Code

knitr::opts_chunk$set(
  echo = TRUE,
  message = FALSE,
  warning = FALSE
)

Code

#| label: load-full-data

# Load the dataset
data <- read.csv("Final_Project_Data.csv",
                 stringsAsFactors = FALSE)

# Clean column names by replacing spaces or dots with underscores
names(data) <- gsub("[\\. ]+", "_", names(data))

# Inspect the structure and dimensions of the dataset
str(data)

'data.frame':   155 obs. of  8 variables:
 $ Country_Code: chr  "EGY" "EGY" "EGY" "EGY" ...
 $ Year        : int  1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 ...
 $ FDI_GDP     : num  1 0.9 1.1 1.3 1.2 1.2 0.5 0.8 0.3 1.6 ...
 $ GDP_USD     : num  1.36e+11 1.43e+11 1.51e+11 1.59e+11 1.69e+11 ...
 $ IND_VA_GDP  : num  30.2 29.5 29 28.6 28.4 30.8 30.9 32.6 33.4 34.7 ...
 $ NODA_RCV    : num  3.4 3.2 2.5 2.3 1.8 1.4 1.3 1.5 1.3 1.9 ...
 $ REN_ERG_CONS: num  9.4 9 8.6 8.5 8.8 8.3 7.8 7.3 7.4 7.6 ...
 $ Trade_GDP   : num  50.2 46.9 43.7 41.9 38.4 ...

Code

dim(data)

[1] 155   8

Code

# Display the first 10 observations
head(data, 10)

   Country_Code Year FDI_GDP      GDP_USD IND_VA_GDP NODA_RCV REN_ERG_CONS
1           EGY 1995     1.0 136218680413       30.2      3.4          9.4
2           EGY 1996     0.9 143014263359       29.5      3.2          9.0
3           EGY 1997     1.1 150869114035       29.0      2.5          8.6
4           EGY 1998     1.3 159280817658       28.6      2.3          8.5
5           EGY 1999     1.2 168922784450       28.4      1.8          8.8
6           EGY 2000     1.2 179683172290       30.8      1.4          8.3
7           EGY 2001     0.5 186035425185       30.9      1.3          7.8
8           EGY 2002     0.8 190482051409       32.6      1.5          7.3
9           EGY 2003     0.3 196565009504       33.4      1.3          7.4
10          EGY 2004     1.6 204608590453       34.7      1.9          7.6
   Trade_GDP
1   50.24510
2   46.94856
3   43.73825
4   41.92763
5   38.36151
6   39.01794
7   39.81043
8   40.98707
9   46.17964
10  57.81991

The dataset contains 155 observations covering five countries over the period 1995–2025. Each observation represents a country-year combination. The variables contain information on foreign direct investment, real GDP, industrial value added, net official development assistance, renewable energy consumption, and trade trade openness. The first ten observations are displayed to inspect the structure of the data without printing the entire dataset.

Scalars (Single-Value Computations)

A scalar is a single numerical value. It may represent one particular observation, such as a country’s GDP, FDI share, or renewable-energy consumption in a given year. The following example uses Sudan in 2021 to demonstrate basic scalar operations.

Macroeconomic Scalars for Sudan (Year 2021)

The 2021 observation for Sudan is first extracted from the dataset. Individual variables from this observation are then stored as scalars. This allows basic scalar operations to be demonstrated using values from the empirical dataset rather than manually entered numbers.

Code

# Extract the observation for Sudan in 2021
sdn_2021 <- data[
  data$Country_Code == "SDN" & data$Year == 2021,
]
# Display the selected observation
sdn_2021

    Country_Code Year FDI_GDP     GDP_USD IND_VA_GDP NODA_RCV REN_ERG_CONS
120          SDN 2021 1.52754 48525909156       22.5 11.62119           61
    Trade_GDP
120  4.127549

Code

# Store individual values as scalars
gdp_sdn    <- sdn_2021$GDP_USD
ind_va_pct <- sdn_2021$IND_VA_GDP
fdi_pct    <- sdn_2021$FDI_GDP
trade_pct  <- sdn_2021$Trade_GDP
ren_share  <- sdn_2021$REN_ERG_CONS

# 1. Approximate real industrial value added
real_ind_va <- gdp_sdn * (ind_va_pct / 100)

# 2. FDI-to-trade ratio
fdi_trade_ratio <- fdi_pct / trade_pct

# 3. Natural logarithm of real GDP
ln_real_gdp <- log(gdp_sdn)

# 4. Modulo and integer division
mod_share    <- round(ren_share) %% 10
decade_share <- round(ren_share) %/% 10

# 5. Rounding operations
real_ind_va_bil <- round(real_ind_va / 1e9, 2)
ceil_ratio      <- ceiling(fdi_trade_ratio * 100)
floor_ratio     <- floor(fdi_trade_ratio * 100)

# Display results
real_ind_va

[1] 10918329560

Code

fdi_trade_ratio

[1] 0.3700841

Code

ln_real_gdp

[1] 24.60536

Code

mod_share

[1] 1

Code

decade_share

[1] 6

Code

real_ind_va_bil

[1] 10.92

Code

ceil_ratio

[1] 38

Code

floor_ratio

[1] 37

The extracted observations for Sudan in 2021 are stored as scalars. Real GDP is measured in constant 2015 US$, while industrial value added, FDI, trade, and renewable energy consumption are expressed as percentage indicators.

Multiplying real GDP by industry’s share of GDP gives an approximate real industrial value added of about 10.92 billion constant 2015 US$. The FDI-to-trade ratio is approximately 0.37, while the natural logarithm of real GDP is approximately 24.61.

Creating and Manipulating Character Variables

Character variables contain textual information rather than numerical values. String operations are useful for constructing observation identifiers, variable labels, model formulas, and data headers.

Code

# Define panel identifiers
country_code <- "SDN"
sample_year  <- "2021"

# 1. Combine strings with spaces
panel_desc <- paste("Country:", country_code,
                    "Year:", sample_year)

# 2. Construct a unique country-year identifier
panel_id <- paste0(country_code, "_", sample_year)

# 3. Construct a regression formula from separate strings
dependent_var <- "REN_ERG_CONS"
independent_vars <- "FDI_GDP + GDP_USD + IND_VA_GDP + NODA_RCV + Trade_GDP"

reg_formula <- paste(dependent_var, "~", independent_vars)

# 4. Construct a comma-separated variable header
csv_header <- paste(
  "Country_Code", "Year", "FDI_GDP", "GDP_USD",
  "IND_VA_GDP", "NODA_RCV", "REN_ERG_CONS", "Trade_GDP",
  sep = ","
)

# Display results
panel_desc

[1] "Country: SDN Year: 2021"

Code

panel_id

[1] "SDN_2021"

Code

reg_formula

[1] "REN_ERG_CONS ~ FDI_GDP + GDP_USD + IND_VA_GDP + NODA_RCV + Trade_GDP"

Code

csv_header

[1] "Country_Code,Year,FDI_GDP,GDP_USD,IND_VA_GDP,NODA_RCV,REN_ERG_CONS,Trade_GDP"

Code

# Create an observation-variable key
obs_key <- "SDN_2021_REN_ERG_CONS"

# Count characters
nchar(obs_key)

[1] 21

Code

# Extract selected parts of the string
iso_code <- substr(obs_key, 1, 3)
year_val <- substr(obs_key, 5, 8)
dep_var  <- substr(obs_key, 10, 21)

iso_code

[1] "SDN"

Code

year_val

[1] "2021"

Code

dep_var

[1] "REN_ERG_CONS"

The paste0() function creates the country-year identifier SDN_2021, while paste() constructs a model formula from separate dependent- and independent-variable strings. The functions nchar() and substr() are then used to inspect and extract information from a composite observation key.

Logical (Boolean) Values and Variables

Basic Logical Operators

The following examples use illustrative thresholds to demonstrate comparisons and the logical operators NOT (!), AND (&), OR (|), and exclusive OR (xor). These thresholds are chosen for demonstration and are not intended to represent formal economic classifications.

Code

# Create logical values using illustrative thresholds
high_renew <- ren_share > 50
high_fdi   <- fdi_pct > 5

# Basic logical operators
!high_renew

[1] FALSE

Code

high_renew & high_fdi

[1] FALSE

Code

high_renew | high_fdi

[1] TRUE

Code

xor(high_renew, high_fdi)

[1] TRUE

Code

# Numerical comparisons
fdi_pct > 2

[1] FALSE

Code

ren_share >= 50

[1] TRUE

Code

trade_pct == 20.3

[1] FALSE

Code

trade_pct != 0

[1] TRUE

Code

# Combined conditions
(ren_share > 50) & (fdi_pct > 3)

[1] FALSE

Code

(trade_pct < 15) | (ren_share < 50)

[1] TRUE

Code

# Store several logical checks in a vector
regime_checks <- c(
  FDI_above_3 = fdi_pct > 3,
  RenErg_above_50 = ren_share > 50,
  Trade_above_25 = trade_pct > 25,
  IndVA_above_15 = ind_va_pct > 15
)

regime_checks

    FDI_above_3 RenErg_above_50  Trade_above_25  IndVA_above_15 
          FALSE            TRUE           FALSE            TRUE

For Sudan in 2021, renewable energy consumption exceeds the illustrative 50% threshold, while FDI does not exceed either 3% or 5% of GDP. The logical vector summarizes several conditions simultaneously. This demonstrates how numerical observations can be converted into TRUE and FALSE values for filtering or classification.

Numeric Vectors

Vector Generation from the Full Dataset (1995–2025)

The dataset is loaded and extracted the complete 31-year time series observations for Sudan across our study variables.

Code

# Extract Sudan's time-series vectors
years_sdn <- data$Year[data$Country_Code == "SDN"]
fdi_sdn   <- data$FDI_GDP[data$Country_Code == "SDN"]
trade_sdn <- data$Trade_GDP[data$Country_Code == "SDN"]
ren_sdn   <- data$REN_ERG_CONS[data$Country_Code == "SDN"]

# Inspect vector length and first observations
length(fdi_sdn)

[1] 31

Code

head(fdi_sdn)

[1] 0.1 0.0 0.8 3.3 3.5 3.2

Code

head(trade_sdn)

[1] 14.77240 20.02984 17.85861 21.87515 24.71437 29.40423

Code

# 1. Positional indexing
fdi_sdn[1]       # First FDI observation

[1] 0.1

Code

fdi_sdn[length(fdi_sdn)]  # Last FDI observation

[1] NA

Code

# 2. Conditional filtering
high_fdi_vals <- fdi_sdn[fdi_sdn > 3]
high_fdi_years <- years_sdn[fdi_sdn > 3]

high_fdi_vals

 [1] 3.300000 3.500000 3.200000 3.700000 3.932155 6.317823 5.670906 4.438799
 [9] 4.069107 3.344176 3.500045 3.152349 6.142124 3.923121 3.341353 3.512695
[17]       NA       NA

Code

high_fdi_years

 [1] 1998 1999 2000 2001 2002 2003 2004 2005 2006 2009 2010 2011 2012 2013 2015
[16] 2018   NA   NA

Code

# 3. Vector arithmetic
fdi_sdn_prop <- fdi_sdn / 100
ren_sdn_prop <- ren_sdn / 100

head(fdi_sdn_prop)

[1] 0.001 0.000 0.008 0.033 0.035 0.032

Code

head(ren_sdn_prop)

[1] 0.815 0.836 0.805 0.819 0.808 0.804

Code

# 4. Sorting
sort(fdi_sdn, decreasing = TRUE, na.last = NA)

 [1] 6.317823 6.142124 5.670906 4.438799 4.069107 3.932155 3.923121 3.700000
 [9] 3.512695 3.500045 3.500000 3.344176 3.341353 3.300000 3.200000 3.152349
[17] 2.651934 2.580439 2.552270 2.549810 2.530916 2.526985 2.495328 1.527540
[25] 1.373994 1.110004 0.800000 0.100000 0.000000

Code

# 5. Summary statistics for renewable energy
mean(ren_sdn, na.rm = TRUE)

[1] 69.28519

Code

median(ren_sdn, na.rm = TRUE)

[1] 64.3

Code

sd(ren_sdn, na.rm = TRUE)

[1] 8.745491

Code

# 6. Missing-value checks
is.na(ren_sdn)

 [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[25] FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE

Code

sum(is.na(ren_sdn))

[1] 4

Code

# Without na.rm = TRUE, the result is NA
mean(ren_sdn)

[1] NA

Code

# Count missing observations for every variable
colSums(is.na(data))

Country_Code         Year      FDI_GDP      GDP_USD   IND_VA_GDP     NODA_RCV 
           0            0            5            0            0           10 
REN_ERG_CONS    Trade_GDP 
          19           16

Positional indexing can be used to retrieve individual observations, while logical indexing identifies years in which FDI exceeded an illustrative threshold of 3% of GDP. Vector arithmetic can transform all observations simultaneously. Dividing the percentage variables by 100, for example, converts them from percentage units into proportions. Sudan’s renewable-energy consumption has a mean of approximately 69.3% and a median of approximately 64.3% across the available observations. Its standard deviation is approximately 8.75 percentage points, indicating variation over time. The series also contains four missing observations. Consequently, mean(ren_sdn) returns NA, whereas mean(ren_sdn, na.rm = TRUE) calculates the mean using the available observations.

Missing values are not equally distributed across the variables. FDI_GDP contains 5 missing observations, NODA_RCV contains 10, REN_ERG_CONS contains 19, and Trade_GDP contains 16. Missing observations need to be considered when calculating statistics because many R functions return NA unless missing values are removed explicitly.

Vector Transformations: Deriving New Econometric Variables

Vectorized arithmetic allows the same mathematical operation to be applied to every observation in a variable. The following transformations construct three additional variables from the dataset.

Constant Real Industrial Output (real_industry_output): Approximates industrial value added in constant 2015 US$ by multiplying real GDP by industry’s percentage share of GDP
FDI-to-Trade Ratio (fdi_trade_ratio): Demonstrates vector division by comparing FDI net inflows (% of GDP) with trade (% of GDP). It is constructed here primarily as a programming exercise rather than as a standard economic indicator.
Log-Transformed Real GDP (log_gdp_constant): Applies the natural logarithm to real GDP, reducing the numerical scale of the variable.

Code

# Read the dataset
# 1. Approximate real industrial value added in USD
data$IND_VA_USD <- data$GDP_USD *
                   (data$IND_VA_GDP / 100)

# 2. FDI-to-trade ratio
data$FDI_Trade_Ratio <- data$FDI_GDP /
                        data$Trade_GDP

# 3. Natural logarithm of GDP
data$Log_GDP <- log(data$GDP_USD)

# Display selected original and transformed variables
head(
  data[, c(
    "Country_Code",
    "Year",
    "GDP_USD",
    "IND_VA_GDP",
    "IND_VA_USD",
    "FDI_Trade_Ratio",
    "Log_GDP"
  )],
  10
)

   Country_Code Year      GDP_USD IND_VA_GDP  IND_VA_USD FDI_Trade_Ratio
1           EGY 1995 136218680413       30.2 41138041485     0.019902439
2           EGY 1996 143014263359       29.5 42189207691     0.019169916
3           EGY 1997 150869114035       29.0 43752043070     0.025149613
4           EGY 1998 159280817658       28.6 45554313850     0.031005809
5           EGY 1999 168922784450       28.4 47974070784     0.031281356
6           EGY 2000 179683172290       30.8 55342417065     0.030755087
7           EGY 2001 186035425185       30.9 57484946382     0.012559524
8           EGY 2002 190482051409       32.6 62097148759     0.019518352
9           EGY 2003 196565009504       33.4 65652713174     0.006496369
10          EGY 2004 204608590453       34.7 70999180887     0.027672131
    Log_GDP
1  25.63753
2  25.68621
3  25.73968
4  25.79393
5  25.85271
6  25.91446
7  25.94920
8  25.97282
9  26.00426
10 26.04436

These calculations demonstrate vectorized operations because R performs each transformation across all rows of the dataset. IND_VA_USD converts the industrial value-added share of GDP in constant 2015 US$. FDI_Trade_Ratio compares two GDP-relative indicators, while Log_GDP reduces the numerical scale of the Real GDP.

Matrices

Creating Matrices from Macroeconomic Data

A cross-sectional matrix is constructed for 2011. The rows represent the five countries in the sample (EGY, ETH, KEN, SDN, and UGA), while the columns contain FDI, industrial value added, and renewable energy consumption.

Code

# Filter cross-sectional observations for 2011
data_2011 <- data[data$Year == 2011, ]

# Extract three numeric variables
X_macro <- as.matrix(
  data_2011[, c(
    "FDI_GDP",
    "IND_VA_GDP",
    "REN_ERG_CONS"
  )]
)

# Assign row and column names
rownames(X_macro) <- data_2011$Country_Code
colnames(X_macro) <- c(
  "FDI",
  "Ind_VA",
  "Ren_ERG"
)

X_macro

          FDI  Ind_VA Ren_ERG
EGY -0.200000 36.0000     5.4
ETH  2.000000  9.7000    93.6
KEN  3.100000 19.7000    74.7
SDN  3.152349 20.4000    63.7
UGA  3.208606 27.5583    93.3

Code

# Matrix dimensions
dim(X_macro)

[1] 5 3

Code

# Access matrix elements
X_macro["SDN", "Ren_ERG"]

[1] 63.7

Code

X_macro[1, 2]

[1] 36

Code

X_macro["EGY", ]

    FDI  Ind_VA Ren_ERG 
   -0.2    36.0     5.4

Code

X_macro[, "FDI"]

      EGY       ETH       KEN       SDN       UGA 
-0.200000  2.000000  3.100000  3.152349  3.208606

Code

X_macro[1:2, 2:3]

    Ind_VA Ren_ERG
EGY   36.0     5.4
ETH    9.7    93.6

The resulting matrix has five rows and three columns. Matrix indexing can retrieve a single observation, an entire country’s row, a complete variable column, or a smaller sub-matrix.

Create two illustrative 2 x 2 matrices

Two 2 × 2 matrices are extracted from the 2011 cross-sectional data. Matrix A contains FDI and industrial value added for Egypt and Sudan, while matrix B contains the same indicators for Kenya and Uganda. The matrices contain actual observations from the dataset.

Code

# Create two illustrative 2 x 2 matrices from the 2011 data

# Matrix A: Egypt and Sudan
A <- X_macro[
  c("EGY", "SDN"),
  c("FDI", "Ind_VA")
]

# Matrix B: Kenya and Uganda
B <- X_macro[
  c("KEN", "UGA"),
  c("FDI", "Ind_VA")
]

A

          FDI Ind_VA
EGY -0.200000   36.0
SDN  3.152349   20.4

Code

         FDI  Ind_VA
KEN 3.100000 19.7000
UGA 3.208606 27.5583

Code

# Matrix addition
A + B

         FDI  Ind_VA
EGY 2.900000 55.7000
SDN 6.360955 47.9583

Code

# Element-wise multiplication
A * B

         FDI   Ind_VA
EGY -0.62000 709.2000
SDN 10.11464 562.1892

Code

# Matrix multiplication
A %*% B

          FDI   Ind_VA
EGY 114.88982 988.1586
SDN  75.22784 624.2905

Code

# Transpose of A
t(A)

        EGY       SDN
FDI    -0.2  3.152349
Ind_VA 36.0 20.400000

Code

# Determinant of A
det(A)

[1] -117.5645

Code

# Inverse of A
solve(A)

               EGY         SDN
FDI    -0.17352170 0.306214764
Ind_VA  0.02681377 0.001701193

Since matrices A and B have identical 2 × 2 dimensions, they can be added and multiplied element by element. The operator %% instead performs conventional matrix multiplication. These results should be interpreted as demonstrations of matrix algebra rather than economically meaningful composite indicators. Transposing A interchanges its rows and columns. The determinant provides information about whether the matrix is singular. Since the determinant of A is non-zero, the matrix is invertible and solve(A) returns its inverse. Matrix addition and element-wise multiplication operate on corresponding entries of matrices with equal dimensions. In contrast, %% performs matrix multiplication. The transpose interchanges rows and columns, while det() calculates the determinant. Because matrix A has a non-zero determinant, its inverse exists and can be calculated using solve().

Combine two matrix columns side-by-side

Code

col_combined <- cbind(FDI = X_macro[, "FDI"],
  Ren_ERG = X_macro[, "Ren_ERG"])
  


col_combined

          FDI Ren_ERG
EGY -0.200000     5.4
ETH  2.000000    93.6
KEN  3.100000    74.7
SDN  3.152349    63.7
UGA  3.208606    93.3

Code

# Calculate the mean of each matrix column
apply(X_macro, 2, mean)

      FDI    Ind_VA   Ren_ERG 
 2.252191 22.671659 66.140000

Code

# Calculate the sum of each country's three indicators
apply(X_macro, 1, sum)

      EGY       ETH       KEN       SDN       UGA 
 41.20000 105.30000  97.50000  87.25235 124.06690

cbind() combines vectors as columns of a new matrix. In apply(), MARGIN = 2 applies a function to columns, so the first apply() calculation produces the mean of each indicator across the five countries. MARGIN = 1 applies the function across rows.

Eigenvalues and Eigenvectors

In the following example, a covariance matrix is constructed using three indicators for Egypt: foreign direct investment net inflows (FDI_GDP), industrial value added (IND_VA_GDP), and trade openness (Trade_GDP). Eigenvalue decomposition is then used to examine how the total variation in these three indicators is distributed across the resulting components.

Code

# Extract three indicators for Egypt
egy_indicators <- data[
  data$Country_Code == "EGY",
  c("FDI_GDP", "IND_VA_GDP", "Trade_GDP")
]

# Check whether these variables contain missing values
colSums(is.na(egy_indicators))

   FDI_GDP IND_VA_GDP  Trade_GDP 
         0          0          0

Code

# Construct the covariance matrix
Sigma_egy <- cov(egy_indicators)

round(Sigma_egy, 3)

           FDI_GDP IND_VA_GDP Trade_GDP
FDI_GDP      8.026      1.549    14.404
IND_VA_GDP   1.549      9.754     6.451
Trade_GDP   14.404      6.451   105.946

Code

# Compute eigenvalues and eigenvectors
eig_macro <- eigen(
  Sigma_egy,
  symmetric = TRUE
)

eigenvalues <- eig_macro$values
eigenvectors <- eig_macro$vectors

colnames(eigenvectors) <- c(
  "Component_1",
  "Component_2",
  "Component_3"
)
rownames(eigenvectors) <- c(
  "FDI_GDP",
  "IND_VA_GDP",
  "Trade_GDP"
)

eigenvalues

[1] 108.462607   9.419989   5.842989

Code

round(eigenvectors, 4)

           Component_1 Component_2 Component_3
FDI_GDP        -0.1427     -0.1627      0.9763
IND_VA_GDP     -0.0668     -0.9826     -0.1735
Trade_GDP      -0.9875      0.0899     -0.1293

Code

# Verify that the sum of eigenvalues equals the trace
total_variance <- sum(diag(Sigma_egy))
sum_eigenvalues <- sum(eigenvalues)

c(
  total_variance = total_variance,
  sum_eigenvalues = sum_eigenvalues
)

 total_variance sum_eigenvalues 
       123.7256        123.7256

Code

# Percentage of total variance associated with each eigenvalue
var_explained <- (
  eigenvalues / total_variance
) * 100

names(var_explained) <- c(
  "Component_1",
  "Component_2",
  "Component_3"
)

round(var_explained, 2)

Component_1 Component_2 Component_3 
      87.66        7.61        4.72

The covariance matrix describes how FDI, industrial value added, and trade vary individually and together for Egypt over the sample period. The eigenvalues are approximately 108.46, 9.42, and 5.84. Relative to their sum, the component associated with the largest eigenvalue accounts for approximately 87.7% of the total variance, while the second and third components account for approximately 7.6% and 4.7%, respectively. The sum of the eigenvalues is equal to the trace of the covariance matrix, providing a numerical check of the decomposition. However, this result should be interpreted cautiously. The analysis uses a covariance matrix, meaning variables with greater numerical variance can have greater influence on the eigenvalues and eigenvectors. Trade_GDP has considerably greater variance than the other two indicators. Therefore, the first component is strongly influenced by variation in trade openness.