For the most part we agree. We disagree on the particulars of how to select and use best fit functions to data and the practical applications in the real world.

’nuff said.

Lots and lots of real world data about things which have a random component (like poll results) don’t ever really follow any curve. ([Unless there is a real underlying mathematical component, like data about, oh, I dunno, the height of a kicked football over time.)

Such data is only ever fitted to a curve for the sake of, let's say, a prediction. It's a human action to perform this fitting, and it's important not to lose sight of this. The data is real, the curve is our fantasy. Fantasies vary.

The question remains of why anyone would fit public opinion polling to a parabola, given that a parabola posits an increasing rate of growth or decay. Nothing about the nature of polling suggests that a parabola is an appropriate model. Especially given that EVERY parabolic model will predict that sooner or later the trend will exceed 100% or go below 0%.

Fitting data to a straight line is a basic first stab which tells you where things are headed. It has a very basic utility. When it comes to polls, it's a better choice than a parabola because all it does is average out the changes to give you a rough pointer of the trend. If the fitted line is a horizontal line, tit can be a pretty strong cue of some kind of stability. If it's rising or falling, it also show you what your average basic trend is during the period in question.

Is it perfect? Of course not.

Fitting data to one model instead of another simply on the basis that it currently "matches" one type of mathematical model better than another is not something anyone should ever do lightly. I would venture to say in this case that if this data is currently a decent fit for some sort of parabola, it should be regarded as nothing more than a curiosity unless the model somehow endures. [Which it won't, right? We know that.]

Anyway, “better fit” does NOT necessarily mean better prediction.That this polling data “better fits” a certain parabola is like noticing that a fluffy cloud looks like your Aunt Tilly. It won’t for more than a minute or two.

Suppose we were to look at this parabola. Is it so flat that it looks almost like a straight line? All along, my point has been that this data suggests that support is roughyl static, not growing. I hope no one has missed this.

If I expand the graph it appears to have dipped down to a local minima in April, which is a 10% swing down from January, then a 10% swing up from April till now. The data has a margin of error of +/- 3%. The trend is outside this MOE, so I don’t believe it can be dismissed with a straight line. Do I believe it’s noteworthy? I believe it’s more noteworthy than a horizontal line.

Well. noteworthy is in the eye of the beholder. Which I guess is why folks choose different models. What’s still noteworthy to me is that the approval data starts just below 70, goes up and down in small increments within a band between 60 and 70 no less than 40 times ata glance, and end up about where it starts. If that’s not flat, it is, as I implied at very first, extremely flattish. As I suspect your mythic parabola is.

“If you were to fit a straight line to these data points using uncontroversial statistical practices….That’s what I said Mike. It was correct then and its correct now.
No offense, but I am not sure you have a strong math or statistical background. Incorrect curve fitting, then drawing conclusions using it is controversial because it’s wrong.

“As to why anyone would think that this polling data should be fit to a parabolic trend line, I remain somewhat mystified.”
Data is fit to provide a mathematical representation to a population of data. This allows interpolation and extrapolation for analysis purposes. You use a straight line for simple, linear data, and other methods for non-linear data.

“When you fit data to a straight line, you are just trying to ask the question of overall, where does the data seem to be headed. ”
Correct for linear trends, incorrect for non-linear trends. If the data is curved and symmetrical about an axis, such as a parabola (such as the initial plot which is curved about the y axis), then a straight line will always be flat and not reflect varations within. Drawing conclusions from a linear fit with non-linear data is not correct.

If Obama’s approvals had gone to zero in the middle of this chart, then recovered, what would your horizontal line say?

“Which brings me back to my original point, the one you did not address even though you decided to pick a bone with my comment.”
No bone was picked. I was commenting on the use of your math. Read it again…that’s all it was. What bone there was started with your follow-on comment about “team dummy” To call someone a dummy when they point out an error seems so third-grade.

“So do you think this data shows a noteworthy upward trend or not?”
If I expand the graph it appears to have dipped down to a local minima in April, which is a 10% swing down from January, then a 10% swing up from April till now. The data has a margin of error of +/- 3%. The trend is outside this MOE, so I don’t believe it can be dismissed with a straight line. Do I believe it’s noteworthy? I believe it’s more noteworthy than a horizontal line.

I have read many of your posts, most very articulate, insightful and though-provoking. They tend to be some of the best here, and in most cases resonate with my own attitudes. Although I had no beef with your original post outside the math, your follow-on reactions seemed out of character. Bad day?

If you were to fit a straight line to these data points using uncontroversial statistical practices, the resulting line would be about as close to horizontal as you can get.

That’s what I said Mike. It was correct then and its correct now.

Now, as to the point you seem to be insisting on…I agree with you that if you fit a curved line such as a parabola to the data, it will not be flat, nor will it be straight. Well done. Unfortunately, data never really “follows” any line, it is only ever fit to some sort of line for reasons on analysis.

As to why anyone would think that this polling data should be fit to a parabolic trend line, I remain somewhat mystified. if you fit data to a parabola, then you are making a presumption that the data is following some model where it was going one way, flattened put, and then changed direction.

When you fit data to a straight line, you are just trying to ask the question of overall, where does the data seem to be headed. Which brings me back to my original point, the one you did not address even though you decided to pick a bone with my comment.

So do you think this data shows a noteworthy upward trend or not?

Wow. Thanks for the “team dummy” comment. Expected better.

I did not suggest any conclusions on the graph, if you would have noticed.
The fact is..it is NOT a flat horizontal line. It is a parabola. That’s it.

Bone up on your math, or join team dummy.

If you want to think that graph suggests a demonstrable and noteworthy upward trend at this point, you be my guest. Join team dummy. Or were you already on board?

“Umm, that’s graph’s basically a flat line suggesting that his support is stable. If you were to fit a straight line to these data points using uncontroversial statistical practices, the resulting line would be about as close to horizontal as you can get.”

If you take this chart and expand the y-axis scale (say from 60 to 70%), you would see that it the data follows a gradual parabola, , not a straight line. If, as you recommend, you apply a straight line curve fit to a normal (i.e. y=ax^2) parabola, you will always obtain a flat line.

And you can bet that if you look at the party affiliation breakout, Independents’ support of Obama is right there at 68%.

Despite the complete lack of cross-tabbing for serious analysis in the gallup releases, there are numerous other polls available that DO include the cross-tab info, and that provide a better view in the aggregate than such non-detailed outliers. So I’ll take that bet! Three beers, dude. You know where/when you can pay me. ;-)

Your ongoing ignorance of such basic statistical understanding grows more tedious with each graph, Justin. If the numbers go gradually up over the course of a month or so, then MAYBE you got something.

• Suppose you took a bag and filled it with 1000 marbles, and 650 of them said “I approve of Obama” and 350 said ” I do not approve of Obama.

•Then suppose that every day you randomly took 100 marbles out of the bag.

•Do you understand that you would not get 65 Obama marbles every time?

• Sometimes you would get 63, sometimes 67, sometimes 69, sometimes 62, and so on.

You really, really, really, really, REALLY need to try to get this, and what it means for small changes in polling data.

I hope for the sake of all of us that Obama is NOTHING like the “D” version of Reagan.