## Sunday, April 17, 2016

### And you thought the similarity showed insignificance

The series starts here

Annual RGDP looks like this:

 Graph #1: Annual RGDP, 1947-2015

Percent change from year ago for annual RGDP looks like this:

 Graph #2: Percent Change in Annual RGDP

Switching to Excel and adding a linear trendline and dots at the data points:

 Graph #3: Percent Change in Annual RGDP, with Linear Trendline Trendline Values Run about 4.5 to 2.0

Sorting the data by 'percent change' value:

 Graph #4: Same Data, Sorted by Growth Rate Trendline Values Run about 7.0 to -1.0
Oddly symmetrical.

I sorted the values from high to low to get a downsloping trend like the one we've been looking at all week. Funny thing: After I sorted the values, the graph didn't change. I had to go in and take the dates off the horizontal axis; when I did that, it took the shape you see here. (Excel added the "1900" numbers.)

Each point on the blue line represents one year's growth number.

The most common growth rates are between 2% and 4% or, say, between 1% and 5%. Growth rates of less than one or two percent are less common, as are rates of more than four or five percent. Where the numbers are more common, they take up more space in the "x" (horizontal) direction. That makes the blue line more flat than the trendline where the numbers are more common.

Growth rates above 4.7% or so are less common; at rates above that number the blue line moves back toward the black, and then above it. Similar story for values of less than one or two percent.

A histogram would show it.

Yesterday I said

In a scatterplot focused on some detail (like the P2P debt ratio) there is no reason to assume you'll get the same range of trend values you get when you look at the data chronologically.

Graph #4, above, is such a graph. It is focused on growth rate values without regard for chronology. There is no reason to assume that we'll get the same range of trend values we got on Graph #3. And we don't get the same range of trend values.

The point I was making yesterday was about the scatterplot of P2P versus RGDP growth. The trendline on that graph runs from about 4.5 to about 1.8. With yesterday's graph we do get almost the same range of trend values.

There is no reason to assume that you'll get the same range of trend values on two related graphs. The fact that we do get similar ranges suggests to me that yesterday's graph is significant in regard to economic growth. As I said yesterday, those are the numbers.

// The Excel file.