PCA Dimensionality Reduction of correlated synthetic macroeconomic indicators

Project info

• Field of studyEconometrics
• LevelUndergraduate thesis (S1)
• Method typeMachine Learning
• Estimated build time± 3 working days
• Toolspca, zscore, biplot (Statistics and Machine Learning Toolbox)
• PriceUS$22 - US$131

Research goal

Reduce the dimensionality of correlated synthetic macroeconomic indicators with PCA and assess the variance explained by each principal component.

Variables

Example result

• 64.593PC1 variance (%)
• 29.342PC2 variance (%)
• 93.935PC1+PC2 (%)
• 2Components for 90%
• 3.23Eigenvalue PC1
• 1.467Eigenvalue PC2

Two principal components explain 93.9% of the variance (PC1 64.6%, PC2 29.3%) across five variables including Composite economic condition index, GDP growth and Inflation; 2 components are needed to reach 90%.

Computed from illustrative synthetic data, not from a real study.

About PCA (pca)

pca reduces dimensionality by transforming correlated variables into uncorrelated principal components ordered by variance. It is used to summarise many variables, reduce multicollinearity, and visualise multivariate data.

Steps

1. 1Standardise the data with zscore
2. 2Run pca and obtain coefficients, scores, and variances
3. 3Inspect percent variance explained and the scree plot
4. 4Choose the number of components (for example 90 percent cumulative)
5. 5Interpret loadings to name the components
6. 6Plot the scores or a biplot

Assumptions to check

• Variables are on comparable scales after standardisation
• Relations among variables are roughly linear
• Large variance is assumed to carry information

Reading and reporting the results

Report the variance explained by each component, the number retained, and the main loadings. Name components by their dominant variables, taking care not to over-interpret.

Example MATLAB code

A short starting script with this project's variable names. The delivered version is adapted to your data and fully commented.

rng(9);
n = 300;
f1 = randn(n, 1);  f2 = randn(n, 1);
gdp_growth = f1 + 0.3*randn(n, 1);
inflation = f1 + 0.3*randn(n, 1);
x3 = f2 + 0.3*randn(n, 1);
x4 = f2 + 0.3*randn(n, 1);
x5 = randn(n, 1);
composite_economic_condition = [gdp_growth inflation x3 x4 x5];

Z = zscore(composite_economic_condition);
[coeff, score, latent, ~, explained] = pca(Z);
cum = cumsum(explained);
fprintf('Explained (%%): %s\n', mat2str(explained', 3));
fprintf('Cumulative (%%): %s\n', mat2str(cum', 3));
k = find(cum >= 90, 1);
fprintf('Components for 90%%: %d\n', k);
disp(array2table(coeff(:, 1:2), 'VariableNames', {'PC1', 'PC2'}, ...
    'RowNames', {'x1', 'x2', 'x3', 'x4', 'x5'}));

figure;
subplot(1,2,1); plot(explained, '-o'); xlabel('Component'); ylabel('Variance explained (%)');
subplot(1,2,2); biplot(coeff(:, 1:2), 'Scores', score(:, 1:2), 'VarLabels', {'x1', 'x2', 'x3', 'x4', 'x5'});

Packages and prices

Choose how much help you need. Each higher package includes everything in the lower ones. Prices exclude 11% VAT.

• Payment: 50% down payment before work starts, balance after the deliverables are handed over
• Tax: Prices exclude 11% VAT
• Data and academic integrity: Results are computed from your own research data; you write and stand behind your manuscript, we help with the analysis and your understanding of it
• Revisions: Up to 2 revisions are included in the price (Package 3: 3 rounds)

Frequently asked questions