Gradient of a line

WillyNelson · 20 Jun 2014 at 14:40

R^2 = 0.0146

rubberduck · 20 Jun 2014 at 14:46

WillyNelson said:
R^2 = 0.0146

This basically means you have very little confidence that the trendline can be used in a predictive fashion.

Tuppy_Glossop · 20 Jun 2014 at 14:52

Extrapolation is a mug's game. Visual analysis suggests a sinusoid with a six month period around a constant.

glenimp617 · 20 Jun 2014 at 14:54

% = (y2-y1) - y2 / 100 x pi

WillyNelson · 20 Jun 2014 at 14:57

rubberduck said:
This basically means you have very little confidence that the trendline can be used in a predictive fashion.

Isn't r-squared more about correlation though...? It wouldn't account for seasonality, which the data has.

Tuppy_Glossop said:
Extrapolation is a mug's game. Visual analysis suggests a sinusoid with a six month period around a constant.

Which would be about right. Underlying (mostly) constant level of activity with seasonality.

Maybe I'm using the wrong measure & something like a 6 month rolling average would be better suited.

Sunbed · 20 Jun 2014 at 14:58

cheesyboy said:
100 is really the starting point, rather than 90

10/90)*100*number of periods (4) = 40%

OK cheers, think I get it now.

rubberduck · 20 Jun 2014 at 15:04

Tuppy_Glossop said:
Extrapolation is a mug's game. Visual analysis suggests a sinusoid with a six month period around a constant.

Agree, although I wouldn't have been able to state it so eloquently!

WillyNelson said:
Maybe I'm using the wrong measure & something like a 6 month rolling average would be better suited.

In which case you will need more than 3 cycles worth of data to be able to prove there is any trend (at least with any degree of confidence).

Baron C · 20 Jun 2014 at 15:06

Op lost me at Linear... :-)

Tuppy_Glossop · 20 Jun 2014 at 15:11

Please don't use a 6 month rolling average. You either need to fit a polynomial to the sinusoid or parameterise it and do an LMS fit in the parameter space. I suggest the second method.

D.P. · 20 Jun 2014 at 15:11

WillyNelson said:
Isn't r-squared more about correlation though...? It wouldn't account for seasonality, which the data has.

Which would be about right. Underlying (mostly) constant level of activity with seasonality.

Maybe I'm using the wrong measure & something like a 6 month rolling average would be better suited.

You can't extrapolate a linear trend from that data, the r-value showing that a linear trend is meaningless. The visual analysis confirms this.

If you want to extrapolate future trends then you will need a much more complex model. I would start with a Fourier analysis of the data to find the periodicity.

I you are certain that the sinusoidal changes relate to seasonal changes then you could create a simpler more linear data set by collapsing all months into a single year (total or average of 12 months) and then you can compare year on year changes. The model would then be limited in only comparing 12-month periods to other 12 month periods and predicting outcomes in periods of 12 months. You will also need much more data in order to create a robust analysis.

For that reason I suggest you work on the former solution and find a better model. there are lots of ways to do it. A polynomial fit wont work well for this kind of function. If you are right about the seasonal changes then you could fit a some function of sine using a least squares fit.

What you are doing at the moment it bogus statistics and will only lead to meaningless outcomes.

Tuppy_Glossop · 20 Jun 2014 at 15:16

Either way you'll be needing QR decomposition :cool:

WillyNelson · 20 Jun 2014 at 16:14

D.P. said:
You can't extrapolate a linear trend from that data, the r-value showing that a linear trend is meaningless. The visual analysis confirms this.

If you want to extrapolate future trends then you will need a much more complex model. I would start with a Fourier analysis of the data to find the periodicity.

I you are certain that the sinusoidal changes relate to seasonal changes then you could create a simpler more linear data set by collapsing all months into a single year (total or average of 12 months) and then you can compare year on year changes. The model would then be limited in only comparing 12-month periods to other 12 month periods and predicting outcomes in periods of 12 months. You will also need much more data in order to create a robust analysis.

For that reason I suggest you work on the former solution and find a better model. there are lots of ways to do it. A polynomial fit wont work well for this kind of function. If you are right about the seasonal changes then you could fit a some function of sine using a least squares fit.

What you are doing at the moment it bogus statistics and will only lead to meaningless outcomes.

I'm not looking to extrapolate data though, I just want a general trend over the periods I have to see the degree of growth/decline. I have a second set which includes additional activity over the same period & I want to compare the rate of growth between the two.

Predicting the future activity would need to account for a whole host of variables, and that's not something I either want or need to get into.

Thanks for all your help though folks, I've got what I was looking for.

D.P. · 20 Jun 2014 at 16:35

Even if you don't want to extrapolate and merely want to understand temporal changes in the data you can't use a linear model on data that is clearly non-linear.
Whatever conclusions you draw from trying to fit a straight line are almost certainly wrong so not worth doing.