For a sample 38 of carnivorous animal species, we take a look at the traits: Gro
ID: 3243685 • Letter: F
Question
For a sample 38 of carnivorous animal species, we take a look at the traits: Group Size, Body Weight kg, Brain Weight gl, and Litter Size. A Principal Components Analysis was performed on the pairwise correlation matrix of the four variables: Eigenvalues C1 PC2 PC3 PC4 2.41 1.31 0.23 0.05 Eigenvectors Variable PC1 PC2 PC3 PC4 Group Size 0.025 0.844 0.531 0.068 Body Weight 0.613 0.183 0.350 -0.685 Brain Weight 0.610 0.222 0.232 0.724 Litter Size 0.501 0.452 0.736 0.0482 (a) How much variability in the sample (in percent) can be explained by the first two principal components? 1 marks (b) Can you find any evidence for following statements? (Explain your reasoning.) 3 marks i. Body Weight and Brain Weight are correlated ii. Small carnivores have a large number of offspring, iii. Small carnivores are more social than large carnivorous animals.Explanation / Answer
a)
If you take all eigenvalues and add them up , the total variance of 4.
Variation by first eignenvalue is : 2.41/4 = 0.6025=60%
Variation by first eignenvalue is : 1.31/4 = 0.3275=32%
Therefore, about 92% of the variation is explained by the first two eigenvalues together.
b) i)
Yes.
Analysis of PC is based on finding which variables are strongly correlated i.e away from zero in +ve or -ve side. We are assuming a correlation above 0.5 as important. PC1 most strongly corrlates with Body Weight and brain weight.PC1 increases with increasing Body Weight and increasing brain weight
PC2 most stronly corrlates with Body Weight and brain weight.PC2 increases with decreasing Body Weight and increasing brain weight
b) ii)
No. This trait(number of offspring) is not considered in the analysis
b) iii)
No. This trait(Social) is not considered in the analysis
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