Happenings – 2010 Nov 27

Let me start by saying that I have decided to take a holiday this weekend… for me and my American readers, this is Thanksgiving weekend. I have decided that

there will be no technical post on this coming Monday, November 29.

While I expect to be doing mathematics this weekend… it is, after all, my idea of fun… I will treat myself to not having to turn some mathematics into a post this weekend.

I’ve spent some time since last Saturday’s post looking through other data sets available on the Internet. So far, I have found nothing as good as Ramanathan’s data, at least for illustrating stepwise regression and backward selection. While I hesitate to use a third data set from his website, I really haven’t found anything else as good, for what I want to demonstrate.

As for other mathematics… I’ve been nibbling at the edges of aircraft control, abstract algebra, the Kalman filter, and computer performance modeling. Nibbling, I say… getting somewhere, I’m sure… but I haven’t passed any milestones.

So let me tell a story… about final exams, and the stellar interior equations.
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Regression 1: Example 3, Women’s Participation in the Labor Force

Let us work another example from Ramanathan. Perhaps I should emphasize that although I am using his dataset, this is not his analysis. Let me assure you that his analysis is worth reading.

The data

I described how to get the data from his website in the previous regression post. This is dataset DATA4 – 5. XLS, and it appears to be the same for both the 4th and 5th editions of the text. The data for the 3rd edition, however, is different from this, and the regressions are slightly different.

Here is his description of the data from the 4th edition file, which included descriptive information; the 5th edition data contains the variable names but nothing else (that I saw). I am, in fact, using the 5th edition data, despite the 4th edition description.
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Happenings – 2010 Nov 20

Let’s see.

The big news is that I overcame my difficulties with the “magic omega formula” – whatever that is!

As I said last week, I almost had a derivation of the result for which the magic omega formula is used… but I was off by a negative sign. Well, that is accounted for by my using attitude matrices instead of transition matrices.

I also said last week that I knew perfectly well how the derivation of the magic omega formula itself had to be accomplished… but it didn’t work out. Well, all I had to do was be careful. When I tried to work through it slowly and carefully, to find my mistake, it worked out perfectly well.
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Regression 1: Example 2, Demand for Bus Travel

(Dec 6: a couple of edits, which you can find by searching on “edit”.)

Let’s work another example of forward selection, stepwise regression, backward selection and then let’s run all possible subsets just to see how well they did. (I didn’t call it example 1, but that was the Hald Data.)

the Data

The following data can be found on Ramanathan’s website. Here is the page for the fifth edition of his book, “Introductory Econometrics with Applications” (see the bibliography page).

I have attempted to download the text file version of the data, but I get “page not found”. I sent an e-mail at the end of August 2010, but the problem has not been fixed as of 11/14/2010.

You can download a collection of Excel files, instead, from his site.

The particular example I am about to work is from the file DATA4-4.XLS

This data appears to be the same as in the 3rd and 4th editions of the book.
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Happenings – 2010 Nov 13

Good morning.

It’s been an interesting week… although nothing unusual has happened.

Regression. I’m working on all of the examples I expect to put out in the next few posts. If anything, my version of stepwise regression works even better than I thought. But we’ll see what happens after I’ve checked all my work… again. (It’s not that I haven’t run a lot of stepwise regressions, I have… what I have not run much of is all possible subsets.)

Incidentally, I went looking for the latest editions of the econometrics books by Johnston and Ramanathan… I can’t seem to find them new, and there seems to be some variety among used copies of the latest editions… international editions versus US editions. And I’m not sure I trust the bookstores to have associated the correct ISBN with the book they are selling. Let me think about this.

The magic omega formula (infinitesimal rotations). Read the rest of this entry »

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Regression 1: The Hald Data: Forward, Backward, and Stepwise


We pick up where we left off: we have run all possible regressions using the four variables of the Hald data.

Forward Selection

Let me cut to the chase. I have written a Mathematica® function called stepwise; it takes two inputs — the data and the list of variable names. Applied to the Hald data (data d1 and names n1), we get

It has given us 4 regressions. What are they?
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Happenings – 2010 Nov 6

It’s been a relatively uneventful week.

Clearly, I got out a post last Monday. It was even a regression post, and it was even the one I had planned on. Now, of course, I need to work on a post for this coming Monday. I expect that it will be another regression post… but until it’s actually done, I won’t bet on it.

I did something a little different this past week… I spent my spare time following threads through a wide variety of books.

Let’s see. Seismology, in particular waves traveling through the earth, led me to elasticity, for which – of course – I have a few books, none of which I understand and all of which I would like to master.
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Regression 1 – All possible regressions of the Hald data


Well, I’ve been battering you with mostly theory. I’ve shown you all of the properties that Mathematica® can provide for a regression… and I’ve shown you how almost all of them are computed.

Not content with that large collection of properties, I then took Mathematica’s four selection criteria and added 11 more criteria.

And through it all, I’ve only shown you two regressions.

Let me go to the other extreme: our example data set, the Hald data, only has four variables… so there are only 16 possible distinct regression equations (all of which contain a constant term — more about that later, probably in another post).

Let’s run them all, all sixteen.

Hang on one moment. This post has 7 sections:

  1. Introduction
  2. run all sixteen possible regressions, and see what are “best” according to each criterion.
  3. see what are the top six regressions according to each criterion.
  4. study the rankings for each fixed number of variables.
  5. see which regressions have significant t statistics.
  6. provide the supporting material in an appendix.
  7. summary

Note that the summary is at the end of the post, after the appendix.

OK, let’s go. We start with the Hald data.
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Oops again

If you just got an RSS feed for a new post, I apologize. I meant to click “Preview”, not “Publish”, and I have taken it back.

It should be ready this evening. Still, if you want to read what you’ve got, feel free.