Linear regression and Logistic regression

Hi,

I'm new in statistics and I'm trying to understand and digest concepts
and how to apply correctly statistics. I'm trying to understand a
procedure for a statistic task.

My questions in linear regression, about how can I compare two
distincts regressors to say one is "statistically" better than the
other? please correct me if I confuse. I'm using spss but my questions
are conceptual.

For example, I've a data set, with: X1, ..., Xn, Y variables
X1, ..., Xn predictors and I want to predict Y (n may be large or
not).

I can see if correlation coefficient R of Y and X1,...,Xn is and near
1 or -1 (how much?) to say Y and (X1,..., Xn) are linearly correlated,
and the sum of square errors.

But the regressor works better if I consider Xi_1,..., Xi_k not
linearly correlated. Then, previosly to regression, I may do a feature
selection. I could get principal components and use some of the
principals, or factor analysis (and get only one variable of each
group of correlated variables).

I construct then one regressor with all variables, other using some
principal components (for example first two or three or four) , others
selecting differents variables of each group of factor analysis.

I see to that spss has an option for select/discard variables in the
execution of the algorithm (forward, backward and stepwise selection),
are all greedy approachs (?), isn't necesarilly to exhaustive test all
variable combinations? (I know there is 2^n combinations, but for
example for n=5, 6, 7 may be useful) or isn't necesary test all to get
the optimal?

Which of all regressors is better statistically? I can compare only
with the multiple correlation coefficient R?

Reading the output of spss, what about the confidence intervals, I see
that there is a t-hypothesis test but I don't understand why at thos
significance levels (0.455, 0.131, ...) what is the meaning (or Sig is
the p value?) what test is doing?? I want to understand for trying to
see if I can compare that properties between two regressors to decide
which is better.


I want to know the same for compare logistic regressors, I've see that
do a Chi-square test, which hypothesis tests???


If you can answer guide me refeering a website, document I'll be
gratefully.

Thanks in advance!
A

.

Relevant Pages

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