Interpretation of principal component regression results

Posted by RuudM123 on Jun 22, 2012; 7:47am
URL: http://spssx-discussion.165.s1.nabble.com/Interpretation-of-principal-component-regression-results-tp5713752.html

Hello,

I have a question about the interpretation of individual variables using a PCA regression method. And because PCR requires a different interpretation procedure I would like to ask how the following information should be interpreted?

First it should be noted that I use a metric DV, revenue. In addition, I have 6 IV, all metric.
A correlation matrix of these 6 IV indicate very high pearson correlation coefficients, even above .90.
In order to remedy the problem of multicollinearity I have used a principal component analysis to transform the correlated variables into uncorrelated principal components (factor scores) using the VARIMAX rotation method. In sum the 6 IV can be explained by 3 components.

Next I run a OLS multiple regression, with revenue as dependent variable and the three factor scores as independent. Results indicate significant R2 changes when a new factor score is added to the first that was included. Overall, the model with 3 factor scores shows an adjusted R2 of .875.
Is there a reason why this R2 is so high based on the use of PCA?

In addition, all factor scores have large t-values ranging from 2,875 to 14,505 that are significant at p < 0,01.

Now I come to the point of interpretation, and I understand that interpreting beta coefficients will only tell me that a one-unit increase in factor 1 will increase revenue by .892. Although I would like to go further and interpret the effect of the individual IV included in the factors. I thought that I need the factor loadings in order to do so, the results are provided below:

The beta coefficients for the factors are as follows:
Factor score 1 = .892 (sign at p < .001)
Factor score 2 = -.246 (sign at p < .01)
Factor score 3 = .177 (sign at p < .001)

The factor loadings for factor one are as follows:
IV1 = .971
IV2 = .985
IV3 = -.952

Example interpretation: Factor score 1 is positively related to revenue, and therefore an increase in factor score 1 will increase revenue by .892. In addition, the positive loadings for IV1 and IV2 indicate that an increase in IV1 and IV2 will cause an increase in revenue. Although the negative loading of IV3 indicate that a decrease of IV3 will cause an increase in revenue. Is this interpretation correct?

In addition, I would like to conclude that a one-unit increase of IV1 (IV2 and IV3) will cause an increase (decrease) in revenue of .???? Is it possible to make such an interpretation, and if so how can I do this in SPSS??

Thanks in advance for your help!!