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Math Forum » Discussions » sci.math.* » sci.stat.math.independent

Topic: Interpretation of coefficients in multiple regressions which model
linear dependence on an IV
Replies: 146   Last Post: Dec 15, 2012 6:44 PM

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Ray Koopman

Posts: 3,347
Registered: 12/7/04
Re: Results (!!) on average slopes and means for a1_N_1_C (complement
instead of core subset)
Posted: Nov 28, 2012 6:27 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Nov 28, 9:37 am, djh <halitsk...@att.net> wrote:
> Results (!!) on average slopes and means for a1_N_1_C (complement
> instead of core subset)
>
> Len
> Int Avg Slope Mean u'
>
> 1 -2.225882168 0.482402362
> 2 -2.315512399 0.469544417
> 3 -0.769858117 0.485742217
> 4 -1.697049757 0.451420560
> 5 -2.069842267 0.459536902
> 6 -4.427566827 0.457327711
> 7 -0.941379623 0.458781950
> 8 -2.069096413 0.445826306
> 9 -1.620229799 0.442040277
> 10 -3.764328472 0.449422937
> 11 -7.882327621 0.458400090
> 12 -11.82556530 0.458971482
>
> I don?t know if the above results, when compared to the results in the
> previous post for a1_N_1_S, do or don?t indicate that your definition
> of average slope is OK.
>
> As in the a1_N_1_S case, Mean(u?) inversely correlates with LenInt.
>
> But unlike the a1_N_1_S case, average slope ALSO inversely correlates
> with LenInt.
>
> I can readily make a scientific interpretation of these two sets of
> results, but don?t want to do so if you think that these two sets of
> results indicate a problem with the definition of average slope.

The plots look nice, but each point needs standard error bars.
The average slope is a1 + 2*a2*mean_x, so its standard error is
sqrt[ var(a1) + 4*var(a2)*(mean_x)^2 + 4*cov(a1,a2)*mean_x ],
with df = n-3.
Date Subject Author
11/21/12
Read Interpretation of coefficients in multiple regressions which model
linear dependence on an IV
Halitsky
11/21/12
Read The problematic regression is actually ln(c) on ( ln(u), ln(u^2) ),
not c on (u, u^2)
Halitsky
11/22/12
Read Re: The problematic regression is actually ln(c) on ( ln(u), ln(u^2)
), not c on (u, u^2)
Ray Koopman
11/22/12
Read Off-line Zip File with one Summ File and 12 Detl files for lnc on (lnu,(lnu)^2)
Halitsky
11/23/12
Read Re: Off-line Zip File with one Summ File and 12 Detl files for lnc on (lnu,(lnu)^2)
Ray Koopman
11/23/12
Read Re: Off-line Zip File with one Summ File and 12 Detl files for lnc on (lnu,(lnu)^2)
Halitsky
11/23/12
Read Complete "a1_N_1_S" zipfile with results from all 3 new regressions
Halitsky
11/24/12
Read Re: Complete "a1_N_1_S" zipfile with results from all 3 new regressions
Ray Koopman
11/24/12
Read Re: Complete "a1_N_1_S" zipfile with results from all 3 new regressions
Halitsky
11/24/12
Read You now have N_1_S, N_2_S, and N_3_S files for all folds
Halitsky
11/25/12
Read As per your suggestion in the other thread, scaled e on scaled u, c, L
Halitsky
11/26/12
Read Re: As per your suggestion in the other thread, scaled e on scaled u,
c, L
Ray Koopman
11/26/12
Read Re: Interpretation of coefficients in multiple regressions which
model linear dependence on an IV
Ray Koopman
11/26/12
Read Them there is some neat algebraic mechanics !
Halitsky
11/27/12
Read Re: Them there is some neat algebraic mechanics !
Ray Koopman
11/27/12
Read OK – I think I’m set, at least till we get to c
on (e, u, u*e).
Halitsky
11/27/12
Read Re: OK – I think I’m set, at least till we get t
o c on (e, u, u*e).
Ray Koopman
11/28/12
Read Re: OK – I think I’m set, at least till we get t
o c on (e, u, u*e).
Ray Koopman
11/28/12
Read Thanks for your review of Tables I/II from previous analysis
Halitsky
11/27/12
Read Holy Cow! Look at your "average a1" slope regressed on Len Int
Halitsky
11/27/12
Read Re: Holy Cow! Look at your "average a1" slope regressed on Len Int
Ray Koopman
11/27/12
Read Re: Holy Cow! Look at your "average a1" slope regressed on Len Int
Halitsky
11/27/12
Read Re: Holy Cow! Look at your "average a1" slope regressed on Len Int
Ray Koopman
11/27/12
Read Here's how I did logs ...
Halitsky
11/27/12
Read Please note that $u = u in last post (the $ prefix is from PERL - sorry).
Halitsky
11/27/12
Read Re: Here's how I did logs ...
Ray Koopman
11/28/12
Read Average slopes and means of u' for c on (u',u'^2) WITHOUT logs
Halitsky
11/28/12
Read Results (!!) on average slopes and means for a1_N_1_C (complement
instead of core subset)
Halitsky
11/28/12
Read Re: Results (!!) on average slopes and means for a1_N_1_C (complement
instead of core subset)
Ray Koopman
11/28/12
Read Finally! Pay-off for all that work I did with the "A" matrix returned
by Ivor Welch's module!
Halitsky
11/29/12
Read Average Slope SEs for a1_N_1_S and a1_N_1_C (and some questions
regarding them ...)
Halitsky
11/30/12
Read Re: Average Slope SEs for a1_N_1_S and a1_N_1_C (and some questions
regarding them ...)
Ray Koopman
12/2/12
Read Re: Average Slope SEs for a1_N_1_S and a1_N_1_C (and some questions
regarding them ...)
Ray Koopman
12/2/12
Read Re: Average Slope SEs for a1_N_1_S and a1_N_1_C (and some questions
regarding them ...)
Ray Koopman
12/2/12
Read Glad you brought up “singleton” length intervals
... been thinkin’ on ‘em also ...
Halitsky
12/2/12
Read Re: Glad you brought up “singleton” length inter
vals ... been thinkin’ on ‘em also ...
Ray Koopman
12/2/12
Read It's still 24...124 - don't know why I bothered to say "roughly
25...125" instead of "exactly "24...124"
Halitsky
12/2/12
Read You should probably clear your data deck and start fresh with the two
csv's I just mentioned in the last email
Halitsky
12/2/12
Read Re: Glad you brought up “singleton” length inter
vals ... been thinkin’ on ‘em also ...
Halitsky
12/2/12
Read One last thought: definitions for the third regression (will save a
complete re-run if I incorporate them now) ...
Halitsky
12/3/12
Read Number of Bonferroni entries for each singleton length is still 72 (duh!)
Halitsky
11/30/12
Read En passant question: What if a plot of slope CI’s
is lousy, but splits the “m’s” perfectly?
Halitsky
11/30/12
Read Re: En passant question: What if a plot of slope CI
’s is lousy, but splits the “m’s” perfectly?
Ray Koopman
12/1/12
Read I’m glad the perfect m split legitimately suggests
a subset effect; here’s why.
Halitsky
12/1/12
Read Re: I’m glad the perfect m split legitimately sugg
ests a subset effect; here’s why.
Ray Koopman
12/1/12
Read Re: I’m glad the perfect m split legitimately sugg
ests a subset effect; here’s why.
Halitsky
12/1/12
Read Slope and intercept for R'uq in the above example ...
Halitsky
12/1/12
Read Bonferroni tables for p’s from new 2-ways for Auq
per fold and length interval
Halitsky
12/1/12
Read Nope! 24-entry Bonferroni tables for (a1,a3) and (b1,b47) do NOT
improve results for a3 nor b47
Halitsky
12/5/12
Read I'm VERY glad you'll know how to answer this "perms and combs"
question !
Halitsky
12/5/12
Read “L-H Het” Table for Average Slopes Auq, Aubu, Au
bqu
Halitsky
12/5/12
Read In "L-H Het table", L-H Het for N1 Aubu should be 4, NOT 2
Halitsky
12/5/12
Read Holy Moly, were you right about covariances for Rub and Rubq !!!!
Halitsky
12/5/12
Read Re: Holy Moly, were you right about covariances for Rub and Rubq !!!!
Ray Koopman
12/6/12
Read So do we need to "Bonferroni-correct" in this case
Halitsky
12/7/12
Read Re: So do we need to "Bonferroni-correct" in this case
Ray Koopman
12/7/12
Read Response to your last of 12/7 at 12:17am
Halitsky
12/7/12
Read Re: Response to your last of 12/7 at 12:17am
Ray Koopman
12/7/12
Read Thanks for the guidance on how to evaluate the contribution of u^2 in
the second model.
Halitsky
12/7/12
Read Please ignore my first question about "estimated standard errpr" in
my last post !!!! Sorry !
Halitsky
12/7/12
Read The u^2 coefficient in c on (e,u,u*e,u^2) does NOT distinguish among
the four subset x MoSS roll-ups
Halitsky
12/7/12
Read Sorry! Those were the SE's in my last post, not the t's !
Halitsky
12/7/12
Read SE's and p's for four subset x MoSS roll-ups of u*e coefficient in c
= (u,e,u*e)
Halitsky
12/7/12
Read Re: SE's and p's for four subset x MoSS roll-ups of u*e coefficient
in c = (u,e,u*e)
Ray Koopman
12/7/12
Read I'm sorry Ray - excitement (probably unwarranted) has disconnected my
brain from my fingers ...
Halitsky
12/7/12
Read Must we say S,N instead of N,S if we've said "Subset x MoSS" (not
MoSS x Subset) ???
Halitsky
12/7/12
Read Re: Must we say S,N instead of N,S if we've said "Subset x MoSS" (not
MoSS x Subset) ???
Ray Koopman
12/7/12
Read Response to your last
Halitsky
12/8/12
Read Re: Response to your last
Ray Koopman
12/8/12
Read Re: Response to your last
Ray Koopman
12/8/12
Read I think I understand; if so, then here’s what I ex
pect you’ll agree I should do next
Halitsky
12/9/12
Read Thanks so much for the sample picture you sent off-line
Halitsky
12/8/12
Read One other thing - because we're using "c-average", not "c-simple",
"c" is no longer a pure count
Halitsky
12/8/12
Read One other possibly worthwhile observation regarding the term u*e in
the regression c on (e,u,u^e,u^2)
Halitsky
12/8/12
Read Typo's of u^e for u*e in previous post.
Halitsky
12/9/12
Read Could I impose on you for four more ordered p “ref
erence plots”?
Halitsky
12/9/12
Read Have sent off-line a PDF of the four plots themselves graphed all together.
gimpeltf@hotmail.com
12/9/12
Read I'm getting the hang of the plotting now - see PDF SNa1_1_for_Rubq
sent offline
Halitsky
12/9/12
Read Am resending the last PDF sent off-line, since I've now learned how
to highlight the line of interest against the random backdrop.
Halitsky
12/10/12
Read Re: Am resending the last PDF sent off-line, since I've now learned
how to highlight the line of interest against the random backdrop.
Ray Koopman
12/10/12
Read 1) Just u*e and u^2(!!); 2) IOTs vs “proper” tes
ts
Halitsky
12/10/12
Read Re: 1) Just u*e and u^2(!!); 2) IOTs vs “proper”
tests
Ray Koopman
12/10/12
Read Response to your last re Q and p
Halitsky
12/10/12
Read Sorry! I meant set=2, not set =1 in last post ...
Halitsky
12/11/12
Read Re: Response to your last re Q and p
Ray Koopman
12/11/12
Read 1) yes - I am using abs(t); 2) subtraction from 1
Halitsky
12/10/12
Read Results of p's obtained by referring Q’s to the ch
i-square distribution.
Halitsky
12/11/12
Read Correction to harmless "thought-typo" in last post
Halitsky
12/11/12
Read Another way to bring the other folds in might be via investigation of
your average slopes and covar vis a vis "hetness"
Halitsky
12/11/12
Read Re: Results of p's obtained by referring Q’s to th
e chi-square distribution.
Ray Koopman
12/11/12
Read OK then, how ‘bout “hetness”? Are you amenabl
e to its further investigation?
Halitsky
12/12/12
Read Re: OK then, how ‘bout “hetness”? Are you amen
able to its further investigation?
Ray Koopman
12/12/12
Read I need to correct an apparent miscommunication regar
ding derivation of het H’s and L’s
Halitsky
12/13/12
Read Re: I need to correct an apparent miscommunication r
egarding derivation of het H’s and L’s
Ray Koopman
12/13/12
Read The SE's are in the zipped files but here they are for your
convenience ....
Halitsky
12/13/12
Read Re: The SE's are in the zipped files but here they are for your
convenience ....
Ray Koopman
12/13/12
Read Re your question about "linearity of SE’s in lengt
h"
Halitsky
12/14/12
Read Re: Re your question about "linearity of SE’s in l
ength"
Ray Koopman
12/14/12
Read Your question re features of (L,Aubqe) plots
Halitsky
12/13/12
Read I think I may have found something relevant to Aubqe
“het-ness” and heteroscedasticity
Halitsky
12/13/12
Read Re: I think I may have found something relevant to A
ubqe “het-ness” and heteroscedasticity
Ray Koopman
12/14/12
Read Re your questions about the plots sent off-line (and the underlying
data posted here 12/13 at 10:33am)
Halitsky
12/14/12
Read Re: Re your questions about the plots sent off-line (and the
underlying data posted here 12/13 at 10:33am)
Ray Koopman
12/14/12
Read Thanks for the terminological/methodological corrections, and also
for the ref to gnuplot.
Halitsky
12/14/12
Read Re: Thanks for the terminological/methodological corrections, and
also for the ref to gnuplot.
Ray Koopman
12/14/12
Read Response to your last of 12/14 at 227pm re terminology and methodology.
Halitsky
12/14/12
Read Re linearity of the Axxxx SE plots – hold on to yo
ur hat
Halitsky
12/14/12
Read Re: Re linearity of the Axxxx SE plots – hold on t
o your hat
Ray Koopman
12/14/12
Read Thanks for doing those two plots - yes - we agree on what we're seeing
Halitsky
12/14/12
Read Re: Thanks for doing those two plots - yes - we agree on what we're seeing
Ray Koopman
12/15/12
Read Re: Thanks for doing those two plots - yes - we agree on what we're seeing
Ray Koopman
12/15/12
Read Re plot of SEP against L
Halitsky
12/15/12
Read Effect of multiplying SE by sqrt(N), as per your post of 12/14 at 10:34pm
Halitsky
12/15/12
Read Re: Effect of multiplying SE by sqrt(N), as per your post of 12/14 at 10:34pm
Ray Koopman
12/14/12
Read One other general question regarding scaling to [0,1].
Halitsky
12/14/12
Read Re: One other general question regarding scaling to [0,1].
Ray Koopman
12/14/12
Read Sorry - I will be typographically more careful re Aubqe in the future.
Halitsky
12/1/12
Read Re: Interpretation of coefficients in multiple regressions which
model linear dependence on an IV
Ray Koopman
12/1/12
Read Thanks for elucidation of 2nd new regression.
Halitsky
12/1/12
Read Re: Interpretation of coefficients in multiple regressions which
model linear dependence on an IV
Ray Koopman
12/1/12
Read Roger corrected defs; also, will add new cov, just in case it's
needed later
Halitsky
12/2/12
Read Re: Interpretation of coefficients in multiple regressions which
model linear dependence on an IV
Ray Koopman
12/2/12
Read 1) thanks for the 3rd regression defs; 2) Yes - I see why the terms
aren't "symmetrical" in this case.
Halitsky
12/3/12
Read New copies of a1_N_1_C and a1_N_1_S with data for all three
regressions at each singleton length.
Halitsky
12/3/12
Read Since 3rd regression computation needs df = 5, am requiring 15
observations for any given length singleton in any cell
Halitsky
12/3/12
Read Have sent off-line all N_1 regression coefficient files and master N
per length index file for N1
Halitsky
12/3/12
Read Same as above post for f_N_2_ss
Halitsky
12/3/12
Read Same as above post for f_N_3_ss
Halitsky
12/3/12
Read Same as above post for f_R_1_ss
Halitsky
12/3/12
Read Same as above post for f_R_2_ss
Halitsky
12/3/12
Read Same as above post for f_R_3_ss
Halitsky
12/3/12
Read Re: Since 3rd regression computation needs df = 5, am requiring 15
observations for any given length singleton in any cell
Ray Koopman
12/4/12
Read Sparseness of b1 data ...
Halitsky
12/4/12
Read I realized I should clarify my 4-way b1 match table: it's AFTER
subtracting df of 3
Halitsky
12/4/12
Read Re: I realized I should clarify my 4-way b1 match table: it's AFTER
subtracting df of 3
Ray Koopman
12/4/12
Read No - the counts in the files themselves are all OK.
Halitsky
12/4/12
Read Re: Sparseness of b1 data ...
Ray Koopman
12/5/12
Read We cross posted, so I just saw your revised "counts" table after I
made my last two posts ...
Halitsky
12/4/12
Read Let me know if you're ready for some interesting data, or if you're
too busy analyzing
Halitsky
12/4/12
Read Re: Let me know if you're ready for some interesting data, or if
you're too busy analyzing
Ray Koopman
12/4/12
Read Please evaluate this "yield" table of method/subset avg slope 2-ways
per fold and len with p < .05
Halitsky
12/5/12
Read One other question about using Auq avg slope as a constant when
computing the other two regressions
Halitsky
12/5/12
Read Re: One other question about using Auq avg slope as a constant when
computing the other two regressions
Ray Koopman
12/5/12
Read Re: One other question about using Auq avg slope as a constant when
computing the other two regressions
Halitsky
12/4/12
Read Some of your counts apparently ARE off.
Halitsky
12/4/12
Read Sorry! those counts in my last post were for len 63 in b1 (forgot to
tell you the length!!!!)
Halitsky
12/4/12
Read Re: Since 3rd regression computation needs df = 5, am requiring 15
observations for any given length singleton in any cell
Ray Koopman

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