Understanding the relationship between variables (revisited)
Rather than using a scatter plot or correlation matrix, a two-dimensional correlation monoplot of the coefficients of the first two principal components can visualize the relationships between the variables.
The correlation monoplot shows vectors pointing away from the origin to represent the original variables.
The angle between the vectors is an approximation of the correlation between the variables. A small angle indicates the variables are positively correlated, an angle of 90 degrees indicates the variables are not correlated, and an angle close to 180 degrees indicates the variables are negatively correlated.
The length of the line and its closeness to the circle indicate how well the variable is represented in the plot. It is therefore unwise to make inferences about relationships involving variables that are poorly represented.
Although the first two principal components only account for 70% of the variance in the original dataset, they still provide a useful approximation of the relationships between the variables.
The relationships between the variables described earlier using the scatter plots are easier to visualize in the monoplot. The negative correlation between affordability and transit is represented by the lines being almost 180 degrees to each other.
Green space is not very well represented as indicated by the short length of its vector. This variable was mostly associated with the third principal component, which is not represented in the two-dimensional plot.