Your correlation is 0.8, thus it is real strong and higher than 0.7. The first solution would be: Decide for one or the other variable and run your modell with just one of both. Don't do mean centering..

Greetings from Berlin

Hi Wiebke Rosler

Thank you very much for the respond, however turn out i did some mistake on finding the VIF score. My predictors are confirmed to have multicollinearity issues. Now, i already edited the question. 

As you can see, if you can still help me, i would be so glad... 

Thank you

Ridge regression is one of several regression methods with regularization. Another popular and similar method is lasso regression. You can find implementations of both methods in the R language. Lasso regression is implemented in the glmnet package, and ridge regression is implemented in the ridge package.

Hi Shane, thanks for your comment.

i have a confession, i dont understand R programs at all... Like at all. i tried to looked it up today, i understand how to input the data, also succeeded in doing multiple regression. However, ridge regression is a whole other thing. The process was way to difficult for me to comprehend.

i manage to download CAR and MASS package and i dont know what to do after that. Google hasnt helped me up to this point. I couldnt find any step by step in doing ridge regression in R, because turn out i need to first do a VIF and Tolerance analysis. 

Do you have link or article that can help me with this?

thank you very much Shane, have a nice day

The best reference for MASS is the text book that it is meant to accompany, Modern Applied Statistics with S. I've never read the book so I can't comment too much on it. But, many R packages have a vignette, which is basically a getting started guide with worked examples. See for example the glmnet vignette. 

You may also be interested in the book, "An Introduction to Statistical Learning: with Applications in R." This book I can highly recommend. The book is made available by the authors for free online.: http://www-bcf.usc.edu/~gareth/ISL/ISLR%20First%20Printing.pdf

Chapter 6 discusses Ridge Regression, Lasso Regression and regularization methods in general. It also contains examples worked out in R.

There are several ways to handle multi-collinearity in the regression.  Principal component analysis and ridge regression are popular used. Those approached are included in most popular Statistical software.

There are usually two aims by using linear regression: identification of the predictor effect and prediction. For prediction purpose, multicoloinerity has no “bad” effect on it. You don’t need use PCA or ridge to make corrections. But for identification, the multicollinearity must be considered, hence you can use PCA or ridge or other approach (say Lasso, as someone suggested).

Ridge regression estimates tend to be stable in the sense that they are usually little affected by small changes in the data on which the fitted regression is based. In contrast, ordinary least squares estimates may be highly unstable under these conditions when the independent variables are highly collinearity.

A major limitation of ridge regression is that ordinary inference procedures are not applicable and exact distributional properties are not known. Another limitation is that the choice of the biasing constant k is a judgmental one. While formal methods have been developed foo making this choice, these methods have their own limitations.

The common used method for selection of the constant of k: assume you have p independent variables (predictors)

1.       Select k from 0 to certain giving value, say as follows

         Ridge (k) = (0.00 0.001 to .009 by .002 0.010 to 0.03 by 0.002 0.03 to 0.09 by 0.01 0.1 to 1.0 by 0.1 1 to 10 by 0.5)

List all estimation of the predictors in a table

Or draw a graph contain p curves: regression coefficients VS k,

For those predictors with collinerity , you can see the big changes of regression coefficients  across k

Select the k such that all of regression coefficient get stable

2.       Using iteration

Initial k=0  

K1=p*regression variance (k=0)/sum of  the regression coefficients (k=0)^2  for all p predictors)

K_(n+1)= p*regression variance (k=n)/sum of  the regression coefficients (k=n)^2  for all p predictors)

3.       When k_n, K_(n+1)  similar , stop.

Dear Shane, thanks for your second reply. I finally manage to do lm.ridge procedure and also linear.ridge procedure from the ridge pacakage. It allows also to find the significant predictor. again thank you for your reply... have a nice day

Dear Yuanzhang Li, thank you very much for your comment. Although i finally did it with a program, your information is useful also. Again thank you very much and have a nice day... :)

Wilibrordus Wisnu T.W. Endro

Dear Wilibrordus;

3 years later, i have almost the same problem. Could you please inform me about conducting ridge regression with SPSS? Do you remember the steps?

Thank you in advance.