The Index of Economic Freedom, published by the Heritage Foundation, ranks countries according to their performance in terms of twelve economic freedoms. These twelve economic freedoms are in turn divided into four categories; rule of law, government size, regulatory efficiency and open markets. The Index is computed by taking an average of all the twelve economic freedoms, which assumes that each individual basic freedom contributes equally to the Economic Freedom Index. Principal Component Analysis (PCA) was used and employed on a matrix composed of the twelve economic freedoms in order to perform dimensionality reduction. The result indicated that the first two principal components could capture 62.9%, or ~ 2/3 rd of the variance in the data for 184 countries. Examination of the eigenvector values of the PCA indicated that the tax burden and business freedom were approximately orthogonal attributes and plotting one against the other captured a variance comparable to that obtained from the first two principal components. This result was verified by using a process of orthogonality detection using the correlation data between the principal components and the twelve economic freedoms obtained from an online PCA calculator. It may thus be possible to obtain an accurate relative ranking of the economic freedom of individual countries by using only two of the twelve economic freedoms. This greatly simplifies, reduces the expenditure and effort, and increases the speed, of data collection, analysis and presentation. This may, in turn allow for a significant adoption expansion of the Index as the barometer of Economic Freedom. It may also allow other suitable multifactorial indices to be depicted relatively accurately using reduced dimensions.