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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: 3,383
Registered: 12/7/04
Re: Re your questions about the plots sent off-line (and the
underlying data posted here 12/13 at 10:33am)

Posted: Dec 14, 2012 3:48 AM
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On Dec 13, 9:45 pm, djh <halitsk...@att.net> wrote:
> You wrote:
>
> ?What are the 1..36? All the other values are monotone increasing.
> Did they come that way, or did you sort them?
>
> The best way to see the difference between the plots is to take cols
> 2 & 3 as x & y coordinates, then plot the points along with a line
> from (0,0) to (1,1). The S-plot is mostly below the line. the C-plot
> is mostly above. I'm not as struck by that difference as you seem to
> be. Where did the numbers come from??
>
> Answers
>
> 1. The 1...36 are irrelevant if the data are plotted the way you
> suggest ? they were just a way of giving Excel an x-axis to plot
> against. And thanks very much for the suggestion as how to plot in
> cases like this ? of course it never would have occurred to me to do
> it that way, and I was delighted to see that Excel lets you do it
> pretty easily (for a Microsoft-owned product, that is.)


You should seriously consider a real plotting program such as
http://www.gnuplot.info/

>
> 2. Yes ? columns 2 and 3 were sorted.
>
> 3. Here?s where the numbers came from.
>
> Recall that:
>
> a) the fold x subset ?het? data which I presented for Aubuqe on L at
> MoSS N, set 1:
>
> Slopes of Regressions of
> Aubqe on Length (L) for each
> Fold x Subset |
> Set 1, Method N
> Fold x Slope
> Subset | # of
> Set 1 of Aubqe
> Meth N L?s on L
> a3_S_1_N 70 -0.000188
> c1_C_1_N 101 -0.000026
> a3_C_1_N 48 0.000052
> c1_S_1_N 101 0.000266
> c2_S_1_N 96 0.000421
> c2_C_1_N 95 0.000550
> b47_C_1_N 99 0.000618
> a1_S_1_N 101 0.001069
> b47_S_1_N 99 0.001079
> b1_S_1_N 31 0.001119
> b1_C_1_N 28 0.002015
> a1_C_1_N 101 0.002210
>
> were selected (because of their low associated ?het? p) from the fold
> x subset data for the regression Aubque on L computed for ALL six
> combinations of Set x MoSS.
>
> b) to get all the fold x subset Aubque on L data for all combinations
> of Set x MoSS, we obviously had to first regress c on (e,u,u*e,u^2) at
> each Len x Set x MoSS x Fold x Subset.


You seem to switch willy-nilly between Aubuqe, Aubqe, and Aubque.
How do they differ?

>
> Call this entire set of underlying data for c on (e,u,u*e,u^2) the
> ?Rubq-base?, and instead of the computing the regression Aubque on L
> over the entire Rubq-base, compute the regression ueSlope on (ubar,
> ebar) over the entire Rubq-base , where:
>
> i) ueSlope is the slope of the u*e term in c on (e,u,u*e,u^2);


Do you mean the coefficient of u*e?

>
> ii) ubar is the mean of ?u? (=u/(1+u) at each L and ebar is the mean
> of ?e? at each L.
>
> From each computation of ueSlope on (ubar, ebar) we have a pair of
> slopes with a pair of associated probabilities, and therefore across
> all combinations of Set x MoSS x Fold x Subset, we have 72 such pairs
> of probabilities, or 144 probabilities in all.


What is the "computation of ueSlope on (ubar, ebar)"?
How do you get a pair of p's from it?

>
> DISREGARDING Fold and Set, divide these 144 probabilities into four
> groups:
>
> 36 at subset S, Method N
> 36 at subset C, Method N
> 36 at subset S, Method R
> 36 at subset C, Method R
>
> Sort each of these groups independently (lowest to highest p), and
> then pair off elements of these four groups as follows:
>
> pair off the 36 from S,N with the 36 from C,N by corresponding rank
> (from the sort of each group)
>
> pair off the 36 from S,R with the 36 from C,R by corresponding rank
> (from the sort of each group)


Regardless of the answers to my previous questions, you can't split
naturally paired p's, sort them, re-pair them, and then compare the
re-paired p's -- which you shouldn't compare in the first place,
even without the shuffling, because p-values are NOT effect sizes.

>
> (Note (!!!!) that these pairings are DIFFFERENT (!!!) from the
> pairings of (S,N) with (S,R) and (C,N) with (C,R) which I presented in
> my post of 12/13@12:33.)
>
> You will then have these two tables of paired p?s (and the associated
> plot ?done your way?, which I?ve sent offline):
>
> SN,CN
>
> 0.004293565,0.000147868
> 0.009398,0.000235407
> 0.019790086,0.002576217
> 0.021645402,0.020854486
> 0.041148681,0.023919
> 0.056848093,0.041120964
> 0.169920851,0.042472596
> 0.236373,0.059794
> 0.248019846,0.079939524
> 0.277783068,0.087268176
> 0.281488299,0.13125994
> 0.287886,0.17489924
> 0.299769,0.180724763
> 0.299875026,0.185042614
> 0.360314613,0.207785097
> 0.370746358,0.21197145
> 0.406029587,0.228176227
> 0.43289,0.252242125
> 0.465398176,0.275296878
> 0.482382234,0.305134999
> 0.530897822,0.309388442
> 0.559333624,0.332112292
> 0.626424347,0.361024514
> 0.702399,0.41780334
> 0.741387901,0.423432022
> 0.768317356,0.476818276
> 0.820922877,0.542145
> 0.831159936,0.559098289
> 0.832584062,0.581960315
> 0.88900441,0.619627105
> 0.893789589,0.646265173
> 0.894253162,0.74717756
> 0.935126553,0.757530416
> 0.977748076,0.884119
> 0.980182674,0.900867429
> 0.984220184,0.938430375
>
> SR,CR
> 0.000503944,0.00011982
> 0.00118415,0.012214573
> 0.041027523,0.029133944
> 0.052112332,0.048936138
> 0.054021335,0.05764761
> 0.057693811,0.05865896
> 0.068659527,0.064182305
> 0.083710757,0.088376406
> 0.094021303,0.107473805
> 0.130456898,0.147682873
> 0.21540961,0.162392478
> 0.236780945,0.181759433
> 0.236936513,0.201847347
> 0.269875322,0.210439736
> 0.294476424,0.226305355
> 0.315561395,0.227038784
> 0.319462902,0.255699197
> 0.327971706,0.288864935
> 0.463861812,0.302035139
> 0.479255866,0.312164668
> 0.564392402,0.388447922
> 0.577382726,0.397416524
> 0.579430243,0.434182601
> 0.588970805,0.438280224
> 0.61542756,0.516128733
> 0.629984706,0.614130775
> 0.698570658,0.675962212
> 0.719544247,0.689950901
> 0.732798731,0.735779895
> 0.813873971,0.778392333
> 0.883957837,0.800207872
> 0.888276157,0.870729822
> 0.888377668,0.911149831
> 0.917545651,0.93512393
> 0.977990461,0.941162349
> 0.980356048,0.986071449
>
> So, depending on one?s ?IOT reaction? to the plot I?ve sent offline
> for the two tables above, one might be willing to say that in general,
> CN p?s plot significantly lower than CR p?s for equivalent SN?s and
> SR?s.
>
> And this result, assuming you?re willing to accept it, is extremely
> important for the following reason.
>
> It says that regardless of dicodon set 1,2,3, the (S,N) subsets
> ?evolved/were designed? (depending on your point of view ? heh heh
> heh) so that mutation away from these sets to (C,N) sets does NOT
> change the predictive capacities of ubar and ebar in ueSlope on (ubar,
> ebar) as much as the predictive capacities of ubar and ebar in ueSlope
> on (ubar, ebar)are changed by the mutation of (S,R) sets to (C,R)
> sets.
>
> Or, to boil that statement down even further, the result says that we
> have found a (relative) INVARIANT UNDER MUTATION for (S,N) sets that
> does NOT exist for (S,R) sets. And the existence of this invariant
> strongly suggests that the (S,N) subsets of dicodon sets 1,2,3 all
> evolved to keep certain thermodynamic properties of protein messasges
> relatively constant despite the mutation which these messages must
> perforce undergo over time.
>
> Finally, apart from this empirical interpretation of the plot I?ve
> sent off line, I have a ?feeling? that the facts above regarding
> ueSlope on (ubar,ebar) must be related somehow to the facts we?ve been
> discussing regarding Aubqe on L. But if you agree, then the ball is
> now in your court for the obvious reason that I have neither the
> knowledge nor experience nor statistical brain-power to determine if
> ueSlope on (ubar,ebar) and Aubqe on L are related, and if so how ...




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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