This is a plot of my data
These are the values:
xvalues yvalues
1 1.091186
2 2.653722
3 3.309146
4 5.206479
5 5.115582
6 8.537005
7 10.013147
8 9.802291
9 10.667769
10 5.809750
11 9.624475
12 11.806013
13 13.587066
14 14.146781
15 13.707472
16 12.891355
17 19.435301
18 16.122108
19 17.768536
20 23.813027
21 21.819081
22 23.556074
23 21.170983
24 27.621148
25 22.932580
26 20.704689
27 25.530339
28 26.227371
29 26.051016
30 31.047145
I now do a PCA and a biplot of it:
According to Jeromy Anglim in: Interpretation of biplots in principal components analysis
The left and bottom axes are showing the loadings; the top and right axes are showing principal component scores.
The left and bottom axes are showing [normalized] principal component scores; the top and right axes are showing the loadings.
I want to be sure I really get this.
Let's start with the loadings: these can be visualized in R by writing:
results <- prcomp(your_data)
results$rotation
PC1 PC2
xvalues 0.7235616 -0.6902599
yvalues 0.6902599 0.7235616
summary(results)
Importance of components:
PC1 PC2
Standard deviation 12.0747 1.56606
Proportion of Variance 0.9835 0.01654
Cumulative Proportion 0.9835 1.00000
Now lets look at the red arrow of xvalues. Its tip is around 0.25 in the x-axis of the loadings. But according to the loadings I have just writen, it should be around 0.72. What am I missing?
Finally, lets look at the point 1. According to the axes, that is telling me the principal component score. Is it that the coordinate in the new frame of reference? It doesn't make sense to me because I think that the new origin of the axes is around the point (15,15) in the Plot 3. If I look at that (and I guess that I am completely wrong here), the point one should have a coordinate around -20 or so, and not 40. Where is my mistake?
Update
I tried plotting this:
plot(pca_results$x)
Here it can be seen that the first point has the coordinate that I thought it had to have. But, still, what are the units in the biplot then??
