问题
Suppose we a data set where each data point represents a single student’s scores on a math test, a physics test, a reading comprehension test, and a vocabulary test.
We find the first two principal components, which capture 90% of the variability in the data, and interpret their loadings. We conclude that the first principal component represents overall academic ability, and the second represents a contrast between quantitative ability and verbal ability.
What loadings would be consistent with that interpretation? Choose all that apply.
a. (0.5, 0.5, 0.5, 0.5) and (0.71, 0.71, 0, 0)
b. (0.5, 0.5, 0.5, 0.5) and (0, 0, -0.71, -0.71)
c. (0.5, 0.5, 0.5, 0.5) and (0.5, 0.5, -0.5, -0.5)
d. (0.5, 0.5, 0.5, 0.5) and (-0.5, -0.5, 0.5, 0.5)
f. (0.71, 0.71, 0, 0) and (0, 0, 0.71, 0.71)
g. (0.71, 0, -0.71, 0) and (0, 0.71, 0, -0.71)
答案
@bob The answers are (c) and (d).