You have a raster cell (i,j) is part of a N x M grid say.

Let raster cell (i,j) have the value Y_ijt at time t, for t =1,2,...,30

Suppose as suggested by your questions that the years / times of observation are evenly spaced.

Your question asks for Y_ijt = a_ij + b_ij (t) where a_ij and b_ij are the regression parameters for that ij cell.

I assume others will tell you how to do this, but I am here to question the basic approach. Have you heard of spatial or temporal auto-correlation? Let's look at temporal auto-correlation -- cell ij has values that vary over time -- perhaps there is trend, seasonality, or even periods of "up" or "down" trend. None of these will be handled properly with the regression you are asking about.You can model the time series at cell ij in better ways.  Then there is the spatial auto-correlation -- the value at cell (i,j) may depend or relate to adjacent values at (i+1, j+1),  etc.. It is best to model or account for this similarity than comes from adjacent areas. For example I very much doubt that all the spatial cells (the rasters) have independent values.

Just trying to raise more questions than you have asked so far.

https://geonet.esri.com/thread/15864

http://gis.stackexchange.com/questions/65787/arcgis-make-linear-regression-across-multiple-raster-layers

http://gis.stackexchange.com/questions/65787/arcgis-make-linear-regression-across-multiple-raster-layers/65841#65841

As per my opinion....use Erdas imagine modelmaker

add all raster

then give condition 

define the out put and run it...

You have a raster cell (i,j) is part of a N x M grid say.

Let raster cell (i,j) have the value Y_ijt at time t, for t =1,2,...,30

Suppose as suggested by your questions that the years / times of observation are evenly spaced.

Your question asks for Y_ijt = a_ij + b_ij (t) where a_ij and b_ij are the regression parameters for that ij cell.

I assume others will tell you how to do this, but I am here to question the basic approach. Have you heard of spatial or temporal auto-correlation? Let's look at temporal auto-correlation -- cell ij has values that vary over time -- perhaps there is trend, seasonality, or even periods of "up" or "down" trend. None of these will be handled properly with the regression you are asking about.You can model the time series at cell ij in better ways.  Then there is the spatial auto-correlation -- the value at cell (i,j) may depend or relate to adjacent values at (i+1, j+1),  etc.. It is best to model or account for this similarity than comes from adjacent areas. For example I very much doubt that all the spatial cells (the rasters) have independent values.

Just trying to raise more questions than you have asked so far.

@Franz - Could you please specify the software you use? Otherwise only some general comments can be made.  

@ Morton I would like to ask also if all rasters are from one and same month which is difficult for optical imagery due to clouds? 

If you have a cloud layer from the same time period(s), one effect might be that this cloud acts as a mask on the cell ... in a sense you have missing values for Y_ijt for some (hopefully not all!) t. You might be able to model the missing value with a good model.

Alternatively, you could try to patch the area "under" the cloud by smoothly replacing Y_ijt by values from nearby unclouded patch (depends on how big the raster cells are compared to the cloud cover)

Sorry if this is not a sensible answer to the questions you have

You can use the geopgraphically weighted regression tool in ArcGIS 10

If you are wanting slope at the pixel-level, this is fairly straightforward to do in R, using the raster package.

Specify intercept based on sequence of rasters in stack

X

Giancarlo Ciotoli Can you explain more?

Dear you can convert your data to vector data then do linear regression

Use Erdas modelmaker then do regression, You can use the regression tools in ArcGIS