Question

10.1

You are analyzing a dataset where each observation is an age, height, length, and width of a particular turtle. You want to know if the data can be well described by fewer than four dimensions (maybe for plotting), so you decide to do Principal Component Analysis. Which of the following is most likely to be the loadings of the first Principal Component?

a) (1, 1, 1, 1)

b) (.5, .5, .5, .5)

c) (.71, -.71, 0, 0)

d) (1, -1, -1, -1)

Answer 1

Since we know that the factor loadings, also called component loadings in PCA, are the correlation coefficients between the variables (rows) and factors (columns). Analogous to Pearson's r, the squared factor loading is the percent of variance in that variable explained by the factor .All the factors age ,height ,length , width of a turtal are positively related to each other upto a certain time therefore first principal component should be mostly option "a"