Comment #1

maximumfun — Mon, 21 May 2012 21:07:08 GMT

man alive! i wish you had been one of my teachers. you make this fascinating. (im still very confused but im working through/on that)

Original Blog Entry: Counter to Popular Regression

JADELottery — Sat, 19 May 2012 23:15:55 GMT

To understand why the Linear Regression is suggesting the solar activity is going down, we need to talk about a few other things first.

1 - The Sun is in a relatively constant state of equilibrium.

This means the overall activity tends to even out over time.

Sometimes low, sometimes high, but on an average of zero.

That's what equilibrium dose, it's a zero sum outcome over a period of time within the equilibrium state.

If it's been high for a while, we can expect some low periods to balance things out.

Yes, there will come a time when the activity will go much higher, but that's in the far future near the end of the Sun's existence.

2 - The Linear Regression can only be calculated based on the available data at the time of the calculation.

If we go back to a time before now and calculate the Linear Regression then, based on the available data we have at that time, we will have a different line than we do now.

The line can be expressed as an equation of y = m x + b, where m is the slope and b is the y - intercept.

The m value determines the slope of the line or how much it tilts.

If it goes up from left to right, the slope is positive.

If it goes down from left to right, the slope is negative.

And if it stays flat from left to right, the slope is zero.

You can see this in the following graph.

Going back the the equilibrium and combining it with the Linear Regression, we should expect the slope of the Linear Regression to strive to a Zero value over successive recalculations of the line.

This means if we take the data at a point in time from then to the beginning and calculate, we'll have the slope of the line for that particular point in time.

Then we move forward and add more data and recalculate, we should have another slope for that point in time, and so on.

Eventually, we can plot the Linear Regression's slope over time and see how the line performs as more data is added.

Below is a graph of the recalculations at each day of the newly added data as it is observed on that day.

The reason the plot starts just after 1860 is because the calculation of the Linear Regression's slope at that point produces very large number with such few data points.

As you can see, the slope actually was in the negative for a time in the late 1800's to early 1900's.

It wasn't until about the 1950's did the slope become positive.

You can also see the plot of the slope is tending back towards zero, which is to be expected for a star in a steady state of equilibrium.

But with that in mind, the only way the slope can go to zero, or even negative is if there is less solar activity on the Sun.

That would drive the slope down and is evident in the plot we see here.

... [ More ]