Test 1

Question 1

If x is an eigenvector of A, does Ax point in the same direction as x?

Answer 1

True – Ax = λx means x is only scaled, not rotated.

Question 2

If C is a covariance matrix, then C’ = C.

Answer 2

True – Covariance matrices are always symmetric.

Question 3

If R is a correlation matrix, then R is always invertible.

Answer 3

False – If two variables are perfectly correlated, the determinant is 0, making R singular (non-invertible).

Question 4

If I is the n × n identity matrix, its trace is n.

Answer 4

True – The trace is the sum of diagonal elements, all of which are 1.

Question 5

A covariance matrix could possibly be diagonal.

Answer 5

True – If all variables are uncorrelated, the off-diagonal elements are 0, making it diagonal.

Question 6

For any square matrices A and B, does AB = BA?

Answer 6

False – Matrix multiplication is generally not commutative.

Question 7

If a T 2-test is significant for multivariate data, at least one of the univariate t-tests on the same
data will be signficant at the same level.

Answer 7

False - it may be that none of the individual tests are significant, but the accumulated difference
across variables is.

Question 8

If all univariate t-tests are significant, must the multivariate T²-test be significant?

Answer 8

False – If variables are highly correlated, T² may not be extreme.

Question 9

Performing multiple univariate t-tests increases the likelihood of a Type I error compared to a single t-test.

Answer 9

True – The probability of at least one false positive increases as more tests are performed.

Question 10

Distance between two points is always non-negative.

Answer 10

True – By definition, a distance cannot be negative.

Question 11

Euclidean distance does not account for relationships between variables.

Answer 11

True – It treats all dimensions independently, unlike Mahalanobis distance, which considers covariance.

Question 12

what do you interpret distances with the project distance formula?

Answer 12

0 < x < 1. 1 being the most dissimilar and 0 being the most similar

Question 13

what are the steps for performing a standard t-test?

Answer 13

1. find means
2. find variances
3. find the pooled variance
4. calc t
5. run hypothesis test

Question 14

what are the steps for performing anova?

Answer 14

1. find means
2. calc dof 1 and 2
   3.find ssb
3. find ssw
4. find F stat
5. hypothesis test

Question 15

what are the steps for running the hotelling T^2 test?

Answer 15

1. find means
2. create cov matrix for each group
3. find the pooled covariance matrix
4. find T^2
5. find F
6. run hypothesis test