Regression 1 – Multicollinearity in Review

As I draft this, I plan to do four things in this post.

1. Summarize the methods I’ve used to analyze multicollinearity.
2. Suggest that multicollinearity is a continuum with no clear-cut boundaries.
3. Summarize the conventional wisdom on its diagnosis and treatment.
4. Flag significant points made in my posts.

Let me say up front that there is one more thing I know of that I want to learn about multicollinearity – but it won’t happen this time around. I would like to know what economists did to get around the multicollinearity involved in estimating production functions, such as the Cobb-Douglas.

Happenings – 2012 Apr 28

It’s been another slow week.

As I said, my alter ego the kid had picked up a recent textbook on seismology… and now I’m looking at continuum mechanics again. Although the impetus is the modeling of solids, I refuse to specialize yet, so I’m still looking at continua in general.

And I am beginning to understand the distinction between the Eulerian and Lagrangian points of view. I need to play with this some more. 13 months ago, I posted some links to videos about the 2 points of view.

Speaking of seismology, there were 3 earthquakes within 100 miles of me during the past week – all were between 2.6 and 2.7 in magnitude. So earthquakes that small are nowhere near as frequent as I expected, at least not in my “immediate” vicinity.

An Overview of Truss Designs

Introduction

I want to close the recent examples of trusses by providing a sampler of truss designs. This is far from encyclopedic. In fact, this post is limited to planar trusses.

First, however, let me give you a link to an online calculator. I checked it out on the Howe truss with a snow load.

As you can see, I scaled the loads by a factor of 10. I had to, for the program – not a big deal.

There are plenty of websites with information. You can search for yourself… you could start with the usual wiki article – the merit of which is that it has a lot of external links.

Personally, I have kept a link to bridge trusses in western PA and a link to roof trusses by an Australian contractor.

Okay, what do we have?

Happenings – 2012 Apr 21

There isn’t a whole lot new going on.

I did ask the USGS to notify me of magnitude 2.5 earthquakes “in the Bay Area” – and in a week I haven’t seen a single one. So much for daily occurrences! Now, I got to define what area I wanted, and perhaps I made it too small.

While I was out there I saw something I had missed – and I’m very glad I had, because if I had seen this earlier I would never have taken the time to forecast earthquakes.

That’s what I had said: 8s are annual, 7s are monthly, 6s are more than weekly, and 5s are more than daily.

Incidentally, my alter ego the kid picked up a book on modern global seismology – and I have had to add the continuum mechanics of solids to his nanny’s list of things to clean up after him. Well, it’s another one of those things I look at every once in a while.

Trusses – Snow Load on Howe, Fink, and Pratt trusses

Intoduction

I want to work another snow load problem… using three different trusses. I found a pair of these, for a Fink truss and a Howe truss, on a professor’s university website – his name is Zig Herzog and his main statics page is this. Individual links for the two problems will follow.

Each of these trusses is 12 meters across the bottom, and 4 meters high. Each has a total snow load of 2400 Newtons. As ever, I have used Mathematica® for the computations and graphics.

One of the things I liked was that Herzog asked us to find the maximum values of stress (both compression and tension), and the total length of the beams used in each truss. In addition to using Fink and Howe trusses, I will do the Pratt truss again, with the parameters of this problem.

The purpose of this post was to see how different the trusses are, under the same load. In one respect they are the same: the maximum values of both compression and tension are the same for all three trusses. And that’s the summary!

Here are screenshots of the author’s assigned problem… for which he does provide solutions, so I’m not giving away any secrets.

For comparison, here’s the Pratt truss I used in the previous post.

Happenings – 2012 Apr 14

Some few of you may know right away what the following picture portends.

Back in September I predicted that there would be at least one magnitude 8 earthquake before the end of 2012. As it happens, there were 2 of them on Wednesday of this week, essentially in the same place… offshore near western Indonesia.

Trusses – Example 4, Pratt roof truss with snow

This problem, like the Howe truss, comes from J.L. Meriam, “Statics”, John Wiley & Sons, 1966.

This diagram actually shows concentrated forces at the joints – which is where they must be for what we’re doing. Nevertheless, the problem as posed says that we have a total weight of 4000 pounds distributed uniformly across the top of the truss. We take the 1000 pounds on each of these four beams, and assign 500 pounds to each of its endpoints. Points A and E have 500 pounds, but the other three joints connect two loaded beams and get 1000 pounds.

Happenings – 2012 Apr 7

I’ve been all over the place, mathematically speaking, this past week. Not that that’s unusual.

The new book – bought used thru ABEbooks, but new to me – about computer vision came in last Saturday afternoon. I looked through the entire thing as soon as it arrived. It’s “introductory techniques for 3-D computer vision” by Trucco and Verri, Prentice-Hall, 1998. It is far less specialized than the previous 2 I talked about, and provides a nice overview – with supporting detail! – of the things we need to do or can do in the field.

I suspect that if I want to do computer vision, this is where I will look 1st. If I want, instead, to do projective geometry, then I will look at the projective geometry book… it’s significant that I think of it as that, rather than as computer vision (Hartley and Zisserman’s “Multiple View Geometry in computer vision, Cambridge, 2003).

Trusses – Example 3, a Howe truss

Introduction

This is a sample problem from “Statics”, by J.L. Meriam, John Wiley & Sons, 1966; #105, p. 88.

It is called a Howe truss – or, sometimes, a double Howe truss. Here’s a link that will give you the names of some trusses so you can look for more information. There’s a lot to be had, but it doesn’t seem all that standardized.

And here’s a link to some class notes, in case you want more explanation than I have been providing. And, since this is the third post about trusses, you could go look at my first truss post and my second truss post.

Anyway, we see that it is fixed at points A and G… and it has three external loads, each of 2 kips (a kip is a kilogram-force), at points B, C, I.