SPSS LOGISTIC does not handle sampling weights correctly for computing standard errors.
If you have weights $w_i$ for each observation, SPSS will work out the loglikelihood contribution $\ell_i(\beta)$ for each observation, and maximise the weighted sum $\hat\ell(\beta) = \sum_i w_i\ell_i(\beta)$. So will R. The point estimates will agree exactly.
This site works best with one question at a time. You have
asked several. I will try to answer the ones that
might illustrate general principles.
(1) If your goal is to estimate the population mean $\mu$
from which a random sample of size $n = 60$ is available,
then the best estimate comes from analyzing the undivided
Suppose you split the sample ...
The formula works fine for any number of groups. The standard error represents the uncertainty in the observed proportion of one group versus "the rest", and this uncertainty doesn't change whether "the rest" consists of one, two, or fifty groups.
So, the proportion of "x" in your sample is 0.3 +/- 0.014, and this estimate and standard error stay the same ...
Applied to linear regression case.
Multicollinearity happens when your predictors are linearly dependent (or close to be). This means, some of your N predictors can be obtained (or nearly) by linear combinations of the others. If predictor A is linearly dependent, you can remove it, and the ability to fit of your system remains the same. If it ...
A comment relating to your concerns, to quote:
Moderate multicollinearity may not be problematic. However, severe multicollinearity is a problem because it can increase the variance of the coefficient estimates and make the estimates very sensitive to minor changes in the model. The result is that the coefficient estimates are unstable and difficult to ...