Determine whether the following statements are true or false. If false, explain why the statement is false, and how one could alter the statement to make it true.

a. Positive correlation indicates that, as one variable increases, the other variable increases as well.

b. Changing the scale of measurement for the covariance matrix, for example, from meters to kilometers, will change the value of the covariance.

c. The total variability in the data set equals the number of records.

d. The value of the ith principal component equals the ith eigenvalue divided by the number of variables.

e. The second principal component represents any linear combination of the variables that accounts for the most variability in the data, once the first principal component has been extracted.

f. For a component weight to be considered of practical significance, it should exceed ±0.50 in magnitude. g. The principal components are always mutually exclusive and exhaustive of the variables. h. When validating the principal components, we would expect the component weights from the training and test data sets to have the same signs. i. For factor analysis to function properly, the predictor variables should not be highly correlated.