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I am working on a spatial linear regression and I can tell there is collinearity between covariates. Can I use PCA (Principal Component Analysis) images instead of original covariates to estimate the dependent variable? I am assuming PC1=Variable 1, PC2=Variable 2, etc. Or are there any other methods to solve the collinearity problem?

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    $\begingroup$ What is your goal in fitting the regression model? Collinearity is only a problem in some cases. $\endgroup$ – shadowtalker Aug 25 '14 at 16:17
  • $\begingroup$ I am trying to estimate the response variable from covariates using spatial linear regression. $\endgroup$ – Kaleab Aug 25 '14 at 16:24
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    $\begingroup$ To be more specific: are you interested in the magnitudes and directions of the coefficients, or making accurate predictions, or both? $\endgroup$ – shadowtalker Aug 25 '14 at 16:34
  • $\begingroup$ @ssdecontrol .Both the coefficients and sign of the predictors as well as accurate estimation of response variable using these PC's of covariates. $\endgroup$ – Kaleab Aug 25 '14 at 16:45
  • $\begingroup$ Thanks for clarifying, that will help me write a more helpful answer. $\endgroup$ – shadowtalker Aug 25 '14 at 16:54
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There is a method called partial least square that is something very close to what you are trying to do.

https://en.wikipedia.org/wiki/Partial_least_squares_regression

The choice to use the PCA transformation of the data can lead to a better estimation of the output $y$ but to understand the role of the original variables will be more difficult.

I suggest you to start with the lasso estimator https://en.wikipedia.org/wiki/Lasso_%28statistics%29#Lasso_method

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