Dear Roy: it is recommended that regression should be significant then you proceed the analysis.

Then, if there is a significant correlation that will act positively together with the regression to make highly significant relationship. Wish you luck.

Hi Neelabha Roy

what is your research question? Are all 45 variables expected to correlate on the item-level? Why did you choose PCA over EFA? Please provide more information! There is no rule that independent variables in a regression analysis must be correlated. On the contrary, very high correlations may indicate redundancies (e. g. measuring one's height in m and cm and using both measures as IV for predicting the chance of scoring more points in a basketball game - stupid example, but it illustrates my point).

Best

Marcel

Before any suggestion you need to elaborate your question.

Tariq A Raja Marcel Grieger Medhat Elsahookie

Ok. Thank you everyone for your response. I am now explaining my problem in details.

I am doing a Negative Binomial Regression, i.e. Count Data Regression. In my data set there are 44 independent variables. Before running regression when I conduct pearson correlation, I found 35 variables are eliminated due to higher correlation value. The threshold value is taken as.7. For that I want to do PCA for that 35 variables.

My first question is that, may I use the combination of 9 variables (which are not correlated in correlation test) along with some principal components (principal component found from PCA among 35 variables)?

My 2nd question is whether I need to run the correlation test among those 9 variables and the resulted Pricipal components? Suppose, I get 3 principal components after running PCA among 35 variables. Then should I again run correlation test among 9 variables and 3 principal components, i.e. among total 12 variables?

Tariq A Raja Marcel Grieger Medhat Elsahookie

Any sugession Sir?

As for my opinion is concerned, better to use PCA for all the variables together.

Hi Neelabha Roy

I am still struggling to understand your problems and questions. Why do you even check for correlation among your variables in the first place? The PCA does that for you with regard to what items belong to what components. Afterwards, you may still check inter-component-correlations (i. e. correlation of all items from one component). Furthermore, there is no threshold that defines r > .7 as "too high" (i. e. multicollinearity). Also, you have not explained why you chose PCA over EFA.

In short: Unless you can find a more comprehensible way to phrase your queries, I doubt I can be of any help.

Best of luck

Marcel

yes!

before you are doing the principal analysis, first you have to check the correlation between the dependent variables.

Teshita Uke Chikako

Thank you, Sir.

You can’t do any correlation in PCA. PCA is unsupervised learning which is trying to find a pattern in data. You are simply running PCA to bring out the multicollinearity so that you can reduce the variables. Scaling is Ofcourse required if the variables’ units are of diff scales. Don’t forget to use rotation.

Once you find the PCA scores, you can use them for new data. Correlation is not required as the rotation has already made them independent.

Anuraj Nayarisseri but multicollinearity means high correlation? right?

No... A high correlation of X with Y is good.

But the high correlation of One X with another X is multicollinearity :)

I think there is a correlation test before PCA, use [P R] = corrcoef(data) in MATLAB.

P is the p-value for hypothesis testing while R is correlation coefficient.