FRM Part I · FRM Exam Part I · Machine Learning and Prediction
Two variables are standardized and have a correlation of 0.60. What are the eigenvalues of their correlation matrix, and what proportion of total variance does the first principal component explain?
The eigenvalues are 1.6 and 0.4, and the first component explains 80% of total variance. For a two-variable correlation matrix the eigenvalues equal 1 plus and minus the correlation, and 1.6 divided by their sum of 2 is 0.80.
- A1.6 and 0.4; 80%Correct
- B1.6 and 0.4; 60%
- C1.0 and 1.0; 50%
- D1.36 and 0.64; 68%
Explanation
For a 2x2 correlation matrix with off-diagonal r, eigenvalues are 1+r and 1-r, giving 1.6 and 0.4. They sum to 2, the number of variables. The first component explains 1.6/2 = 80%. Using 60% confuses the correlation with variance explained.
Did you get it right without looking?
One question tells you little. A timed set on Machine Learning and Prediction shows your real accuracy, how long you take and where you lose marks.
More Machine Learning and Prediction questions
- A bank tests a default-prediction classifier on 200 loans. The model flags 40 loans as defaults, of which 30 actually defaulted. In total 50…
- A risk analyst fits a single, very deep classification tree to predict loan default. It classifies the training data almost perfectly but pe…
- A lender lowers the probability threshold used to classify a borrower as a predicted defaulter, from 0.50 to 0.30, using the same fitted mod…
- A bank's credit-default classifier is tested on 200 loans. It flags 50 loans as defaults, of which 40 actually defaulted. In total 60 loans …
- A neural network with many parameters achieves very low error on the training set but substantially higher error on a validation set. Which …
- A model predicts whether a trade is fraudulent. Of 1,000 trades, 20 are actually fraudulent. The model flags 25 trades, of which 15 are actu…