Not sure if I understood your problem...

Is it that the change of the response is not constant over time, that is, if you plot the values against time, the points will not scatter around straight line but rather describe some curved shape?

If so, you shouldn't use linear regression at all. Fit a model that is flexible enough to follow the curved structure.

In an ideal situation,

Rn - G (the input energy into the system) = H+LE + storage changes (output energy from the system).

Rn is net incoming solar radiation that is retained in the system for energy use; in H and LE.

G is the ground heat flux;

H is the sensible heat flux;

LE the latent heat flux;

and storage changes can be due to energy used to heat the crops and air and energy used in photosynthesis.

In real field measurements, the measured inputs and outputs does not balance due to many well-known and less-known reasons.

Now, to quantify this imbalance, the input is regressed (linear regression) with the output and the slope of the linear regression is used as a index of imblance or non-closure. This is an accepted procedure.

However,

Ths is normally done using all the time series data put together.

In my study, I suspected there is a change in this index (slope in the equation) with time as noticed in the dispersion of plotted points in either side of the 1:1 curve in an excel plot.

To investigate further, I made sub-samples of this time series and again constructed linear regression equations - to compare the slopes (These slopes can be used as a measure of change in input-output imbalance with time.)

In excel, when we take sub-samples and fit the regression, both slope and intercept changes. so the comparison of slopes becomes a problem - as intercept also changes.

To get around this problem, in all regressions of sub-samples, I used the same intercept (or constant intercept) that was obtained in the whole dataset. In this way, all the regression equations will have to same intercept but with different slopes.

I would assusme this is right thing to do, scientifically.

Let me know if you still can't follow.

thanks,

sasi

Could you provide a scatterplot of the data (index vs. time)?

I do not know, if I can attach a grah with this? I will try.

Is that your data?

Is your question then if - in one diagram - the slope at low x-values is different than at high x-values? or is your question if the slopes between the different plots are different?

slopes between different plots.

It appears your question concerns the comparison of slopes among the different plots. It appears that you wanted to compare slopes, so you forced a constant intercept. What were the slopes when you allowed the intercepts to float? If the data are sequential a to b to c, why did you use the intercept of a instead of the composite of d? You need to justify the constant intercept, show that changing intercept is not important, and indicate the uncertainty of the differences in slopes.

These type measurements may include important measurement error. These errors may be seasonal because of seasonal changes in, say, wind speed and soil moisture depth.

What you should do thenn is sometimes called analysis of co-variance (ANCOVA):

http://www.biostathandbook.com/ancova.html

http://r-eco-evo.blogspot.de/2011/08/comparing-two-regression-slopes-by.html

see also:

http://www.theanalysisfactor.com/assumptions-of-ancova/

Josepth Alvarez,

thanks for your views!

It was the slope (intercept floating) of the whole data that I looked at first. When I wanted to look at the slopes of the sub-samples, I used the intercept the whole data produced as the subsamples are part of it.

I did not look at the slope comparisons with floating intercepts, as I thought it can be a meaningless comparison.