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June 09, 2009

Network Solutions

   At the end of May, I went to Network Solutions to put some money in the domain meter.  I've never really been fond of Network Solutions, but it's getting really ridiculous.  The cost for having a domain name seems a little high to begin with.  How exactly making sure a list of names has a list of DNS servers costs as much as it does--not sure, but whatever.  Then charging money to get your private contact information not publicly listed.  If my bank told me they were going to charge me extra to keep my account balance and address private, I'd stop banking.  But this isn't even the worst of it.  Now when you go to renew (i.e. give them more money for an overpriced service), you have to turn down several "services" they want you to buy.  Not like one or two--like six or seven.  And you have to do this before you can finish the renewal process.  It's totally ridiculous.  But I guess when you don't really have a product , don't really offer any worthwhile services and people need to use your company, you have to come up with something. 

1 comment has been made.

From StaAck


June 15, 2009 at 3:38 PM

I always hate giving them money but after dealing with a cheap Registrar that went belly-up I will stick with Netsol....They were the first and I feel fairly certain they aren't going anywhere.
   An outing at Magnolia Bluff State Park today, organized by Altered Reality and the math club at U-Rock.  Good turn out, a lot of food and a lot of fun.   Pictured are Tazz, Sarah and Allison.

June 01, 2009

Least-square Regression

I was taking a look at hard drive prices over the 2 years for which I have data. The plots all include linear-regression for helping to predict the trend of where future prices should be. However, the longer the time scale, the less useful the linear regression line is. Regression doesn't have to be linear. In fact, I already wrote about 2nd degree (quadratic) regression back in September. I had to learn a little matrix math to do this, and having a slightly better understanding now, I can expand the regression to the nth degree. In doing so, there's a chance of finding a higher-degree regression that is a better curve fit or longer time frames of hard drive prices.

Let's first revisit the equation of quadratic curve fitting.

Here, x and y are the arrays of data. The value n is the number of values in the array and a, b, c are the coefficients.

We can expand this to an arbitrary degree like so:

Here, j is the polynomial degree desired and c0 through cj are the coefficients. We can use Cramer's rule to solve this matrix equation. In order to do this, we need a general determinate function. This function must take a matrix of arbitrary size and compute the determinate. This can be done with a recursive function, continually dividing the matrix into 2x2 pieces. For example, a 3x3 and 4x4 matrix can be solved like this:

The above matrices are solved by a row and column subdivide. For example, in both, the first term has a multiplied by the sub-matrix excluding the row and column that a is in. The signs alternate between columns. This can be expressed more generally as:

Where Mij is the subdivided matrix. This turns out to be fairly easy to code. I found this example written in C.

Now that we can solve a square matrix of arbitrary size, we have all the components needed to do the regression. I created this graph using a 6th degree regression:

Here in red we see the price per gigabyte of 1 terabyte hard drives from Jun of 2008 to June of 2009. In blue is the 6th degree regression curve. It looks to be a pretty good fit. Unfortunately, this fit is a lucky coincidence for this one case. In general I found the trend data never a all-around good polynomial regression curve that fit nicely for all time spans. And as for prediction, even with this curve, which looks like it fits well, the future prediction isn't good—the curve turns upward in about the middle of June. So something else will be needed if I am to make predictions about future prices.

Despite the fact my least-square regression curve fitting algorithm failed to produce a good future prediction, it is a good algorithm to have around. I went ahead and created a PHP class for calculating this regression to an arbitrary degree, and started a project page for it.

Above we see a plot with regression plotted at 7 different degrees. The horizontal blue line is the average, or the 0th degree polynomial, or the mean average. The diagonal line is 1st degree, or linear regression. The remaining curves are increasing degrees until the orange line, which is the 6th degree.

The higher the degree, the larger the numbers become in the summations. In a 6th degree polynomial, there is a sum of the values to the 12th power. Because of this, I had to implement the functions using arbitrary precision arithmetic. This slows an already slow process. The above plot takes about 20 seconds to calculate. Higher orders take much longer, each higher degree about twice as long as the previous. There are probably improvements that can be made to my algorithm, but for now, I have something that functions at a general level. I'll have to wait until I take linear algebra before I can dive into this problem more.

1 comment has been made.

From Pluvius

Madison, WI

June 03, 2009 at 8:41 AM

Very nice, I think I learned something! Maybe re-learned, in any case - looks good! By the way, happy birthday!
Fat Albert going up!

Fat Albert going up!

   In what was one of the most impressive display in the entire show, "Fat Albert"--the Blue Angle's C-130 support plane, took off and did a climb at about 45 degrees.  It looked impossible for an aircraft that size to have such a steep climb angle, and it was slowing down as it rose.  Just when we thought it was going to stall out and come back down, it leveled off and fly away.  The landing was almost as impressive.  As it came in, the announcer said it was going to be landing.  However, it had far too much altitude to make the runway.  Just then, the nose pitched down like Albert was going to dive-bomb the runway.  He lost the altitude and put it down for a perfect landing.  Doing stunts in little planes with plenty of afterburner power is one thing.  Doing it was a big fat transport is an other.  Well done.