A sensor records two readings, and , on every sample. Four samples came back:
| Sample | ||
|---|---|---|
| 1 | ||
| 2 | ||
| 3 | ||
| 4 |
Run PCA on this data: centre it, build the covariance matrix, and find the first principal component.
What angle does the PC1 direction make with the positive -axis?
Report the acute angle in degrees — a number strictly between and — rounded to two decimal places.
Once you get it right, the reasoning behind the answer shows up here.
Rotate the axis until it lines up with the data. Find the angle where the spread is easiest to see.
The information never changed. Only the viewpoint changed. PCA searches for the best viewpoint automatically.