Linear Regression

The term is rapidly winding down, but linear algebra is becoming more interesting. Recently we began making linear regressions by treating sets of points (x,y) as sets of equations.

If we have a couple of points, such as:
(-2,3), (-1,2), (0,-1), (1,0), (2,0)

These can all be represented as the hopefully familiar slope-intercept equation y=mx+b, so:

3=-2x+b
2=-x+b
-1=b
0=a+b
0=2a+b

That is an inconsistent system of equations that can be turned into a coefficient matrix, where the coefficient for b is 1 in all cases:

A=\left[\begin{array}{cc}-2a & 1 \\-a & 1 \\0 & 1 \\a & 1 \\2a & 1\end {array} \right]

The right-hand side turns into the column vector b=(3,2,-1,0,0).

Without getting into too much detail, the "least squares" solution can be had in Matlab with the command A\b, which returns (-0.8,0.8). That is, a= -0.8 and b= 0.8. Therefor, our line is y= -0.8x+0.8.

Tezla - "8 Bit Power"

The other day while listening to a streaming trance station, which I find conducive to linear algebra, I heard this song. I can visualize every bleep and other sound from Super Mario Brothers, which plenty of friends and relatives played. Anyway, it is a choice ditty.

Maverick 10.9 Trouble

Don't upgrade to Mac OS X 10.9, as it is absolute crap!

I have repaired permissions, run Disk Warrior, and my Mac crashes multiple times a day. Often it will be three crashes in a row. DefaultFolder is often mentioned in error messages that pop up, as is a GUI failure, a graphics card, and Carbon and/or Cocoa support.

Waking from sleep often results in a system crash. Opening an app (but no apparent consistency in apps) often results in a crash.

Awful, just awful.

However, turning off DefaultFolder has reduced the crashing somewhat; altering its preference file might help. Yet there are still regular kernel panics.

I have since gone to the local Apple Store, where my Mac passed all their diagnostics. As a result, I get to look forward to backing up, erasing, and reinstalling the hard drive.

Which I have now done, but the crashing remains, albeit less frequently. Apparently I have a software conflict, so I will probably spend the start of Christmas break erasing the hard drive, installing 10.9, and adding things slowly. Of course, this could be a good opportunity to get rid of junk I do not use; however, I could just as well reinstall 10.8 and quit having trouble.