Statistics and Probability Commons^™

Multicollinearity And The Estimation Of Regression Coefficients, John Charles Teed

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The precision of the estimates of the regression coefficients in a regression analysis is affected by multicollinearity. The effect of certain factors on multicollinearity and the estimates was studied. The response variables were the standard error of the regression coefficients and a standarized statistic that measures the deviation of the regression coefficient from the population parameter.

The estimates are not influenced by any one factor in particular, but rather some combination of factors. The larger the sample size, the better the precision of the estimates no matter how "bad" the other factors may be.

The standard error of the regression …

Interpretation Of Principal Components, Marwan A. Dabdoub

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The principal component analysis can be carried out two ways. First the R-mode:

R = K'K

and the second is the Q-mode:

Q = K K'

where K is a data matrix centered by column or by row. The most commonly used method is the R-mode.

It has been suggested that principal components computed from either the R-mode or the Q-mode may have the same interpretation. If this is true, then interpretation of the principal components could be put on a much more intuitive level in many applications. This will occur whenever one type of principal component …