How much of the variance is explained by the first principal component?
The 1st principal component accounts for or “explains” 1.651/3.448 = 47.9% of the overall variability; the 2nd one explains 1.220/3.448 = 35.4% of it; the 3rd one explains . 577/3.448 = 16.7% of it.
What does the first principal component measure?
The first principal component is the linear combination of x-variables that has maximum variance (among all linear combinations). It accounts for as much variation in the data as possible.
How is the first principal component related to the original variables?
The first principal component is strongly correlated with five of the original variables. The first principal component increases with increasing Arts, Health, Transportation, Housing and Recreation scores. This suggests that these five criteria vary together.
How to calculate percentage of variance accounted for by each component?
After having the principal components, to compute the percentage of variance (information) accounted for by each component, we divide the eigenvalue of each component by the sum of eigenvalues. If we apply this on the example above, we find that PC1 and PC2 carry respectively 96% and 4% of the variance of the data.
Which is the principal component of the covariance matrix?
The first principal component can equivalently be defined as a direction that maximizes the variance of the projected data. The principal components that maximizes the variance of the projected data. From either objective, it can be shown that the principal components are eigenvectors of the data’s covariance matrix.
What is the standard deviation of the principal components?
Because of standardization, all principal components will have mean 0. The standard deviation is also given for each of the components and these are the square root of the eigenvalue. The correlations between the principal components and the original variables are copied into the following table for the Places Rated Example.