# PCR interaction of PCs

#### szm

##### Member
Hi,

I am using PCA to avoid multicollinearity problems and then I want to use the first 2 PCs in linear regression.

The 1st PC contains 60% of variability and the 2nd 32%.
Is it valid if I use a data step in SAS, create a new variable which is the interaction of these 2 PCs and say that this new variable accounts 92% of variability?

Thanks

#### Dason

What do you mean by "create a new variable which is the interaction of these 2 PCs"? Do you mean create a single variable from the two PCs? Because that won't work. If you could magically create a single variable from the combination of two PCs that accounted for more variable than either of them individually ... then that variable itself would have been chosen as a PC.

#### TheEcologist

##### Global Moderator
What do you mean by "create a new variable which is the interaction of these 2 PCs"? Do you mean create a single variable from the two PCs? Because that won't work. If you could magically create a single variable from the combination of two PCs that accounted for more variable than either of them individually ... then that variable itself would have been chosen as a PC.
The OP mentions the interaction of the two PC axes, so I would imagine he/she means a 2D plain?

#### szm

##### Member
Thank you Dason and TheEcologist for replying!

Sorry if I don't explain things clearly..!

This is the SAS code:

Proc princomp data=x out=prins;
var x1 x2 x3 x4 x5;
run;

/* the output shows:
PC variability
Prin1 0.60
Prin2 0.32
*/
Data new; set prins;
new_var = prin1*prin2;
run;

Then I am using the new_var for subsequent analysis. I was hoping that this is valid and that the new_var accounts for the variability of both, prin1 and prin2.

I am not sure if that is valid and if the new_var accounts 92% of variability (60% from prin1 and 32% from prin2)

I hope this clarifies things a bit.