Linear Regression & R-squared: Reconciling Trends?

Question

My data has generally been trending up for 128 days. The R-squared value for 128 days (where my independent variable, X, equals time in days) is .97. Several days ago, when the highest R-squared value was at 125 days, at 123 Degrees of Freedom my data was more than 3 Standard Errors below this 125 day Linear Regression Trendline (at or around its two-tailed 99% prediction interval). As you might suspect, my data violently regressed upward and is now back within 1 Standard Error of this 128 day LRT.

Here's where I'm having trouble. The time period with the LOWEST R-squared (0.00) is 27 days. Thus, there is no linear relationship for this time period. It's my understanding that when you have a very low R-squared value (where X=time), your data can be explained at least as well by a Simple Moving Average and Standard Deviations because the LRT and SMA are essentially horizontal lines. If I do that analysis, my data is currently 2.7 SD above the 27 day SMA (99% prediction level).

QUESTION:

Do you have any experience reconciling trends? Is my data likely topping at 27 days because its at 99% prediction level, or will the longer term, 128 day trend prevail? How would you analyze these competing trendlines and prediction intervals?

Answer 1

I might be confused about terminology. My understanding is that R-squared is a global measure that involves the residuals over all time for which you have data. When you say that you have and R-squared of 0 at 27 days, does that mean that the global R-squared for all data from t=o to t=27 is 0? This can only be true if all dependent values are constant for all t in that range. I don't think that you mean that. I think that you must be mixing up a squared error for a single t value with the global R-squared.

What are your fit coefficients? What program are you using? What are your min and max residuals? I think that I can help once I know what's going on.

It would help to know what your data represents so that my intuition can get to work.

Answer 2

I don’t know the nature of your experiment as you don’t mention it. Here what my experience would say to me if I can tell nose from tail in your talk:
\1\ I would be suspicious too; so check your data collecting equipment;
/2/ check conditions of experiment if they are still the same as expected;
/3/ if the above are OK, then you have to guess one more function for continued data; but first function and the second one will demand their ‘stitching’ by parameters, which is not an easy but still possible job!
Notice: I find 99% also rather suspicious, I never dealt with so high accuracy.