A drop of 3% in R-square should not be a concern as long as the diagnostics checks are there.

Hi Jawad, the R-squared became 3%, from a 40%.  Sorry for the language.

In that case there is a problem for sure. Why don't you formulate a panel based on the zones and then check year fixed effect. I am a bit surprised about n=5000.

Jawad, i'm handle plot level data for a particular state over time.  Unfortunately, the data is not of panel type, not the same plot/farmer is surveyed for each year.  And the sample size differ across years over sub-regions, so that i cant use panel model.

What about the diagnostic checks, are they ok?

Hi,

With this model  y= a+ Bzone+CYear+ D(zone*year) + e : you are implicitly assuming that there is a structural break in the coefficient relative to the zone each year. If you don't have a solid reason to believe this, you don't have to include an interaction for every year, but only for the year in which you suspect the break is happened.

Obviously the dummies are not adding to the explanatory strength of the equation. My guess is that not all dummies have a place in the equation, but a few may. I would try a stepwise regression and see which ones are stat significant while adding to the explanatory power. It is a tedious process but at least you'd know ...

What is it about year that is causing the significant relationship? It is something like rainfall and temperature? Possibly confounded by sporadic extreme weather phenomena that happened to affect one plot in one year. So how about discarding year and substituting temperature and rainfall as continuous variables rather than using the dummy variable "year." You could use the national average, thought more detailed weather map would improve the model if that was available. I would be disappointed if "year" was the best that can be done.

Zones seems like it is also a dummy variable used in place of more useful measurements. What is it about zones that would have an effect on yield? However, I also appreciate that sometimes a dummy variable is the best that we can do given the resources at our disposal.

What you could find is that Year can be replaced by temperature and rainfall, but because the effect of "zones" is also mostly due to temperature and rainfall that "zones" will no longer be significant when year is replaced by temperature and rainfall data. However, zone may also encompass cultural differences, soil type differences, and other factors and therefore remain significant.

I think you need to play with your data. You need to look at other models, other correlations in the data, and other approaches to modeling. Does your data/statistical model satisfy all the assumptions? What effect do the violation of those assumptions have on your result. Have you looked at outliers? Were all the farms equally diligent in collecting the data? What is the within farm variance like, and are there some that seem to be highly variable? Make a histogram of each variable, and a qq plot (http://en.wikipedia.org/wiki/Q%E2%80%93Q_plot). Can you find any data entry errors? If the bosses want a fast answer, just run the regression and move on. If you want the best answer possible then I suspect it will take you several weeks to do a good job of analyzing these data. Large data sets are wonderful, but can take an inordinate amount of time to really understand. I hope you get to enjoy this opportunity.

I agree Nick's suggestion. You must use stepwise method. What software do you use?

You must doubt your software acuracy. I do not believe " the coefficients had sign and significance as expected,". Usually, nobody believe this result.

If you tell me the software name and agree to open my results on Research Gate, I can

analyse your Excel file.

First row is variable name.  5000 cases are stored after 2-rows to 5001-rows. Dependent variable and 55 independent variables correspond to 56 columns.

In statistics, the coefficient of determination, denoted R2 or r2 and pronounced R squared, is a number that indicates how well data fit a statistical model – sometimes simply a line or curve.

There are several definitions of R2 that are only sometimes equivalent.

In linear regression, the R2 is defined as

R2=SSR/SST,   SST=Sum of (y-mean of y)^2,   SSR= Sum of (y^-mean of y)^2, Y^ is the prediction from the model you used.

For such a definition, you add more predictors, no matter dummy or continuous, R2 should increase.

Many investigators like to use R2 to select model, if you add a predictor, the R2 may increase a very small value. Hence there is another statistic: adjusted R2, which define as

Adj R2=1-(1-R2) (n-1)/(n-p-1), where p is the number of the parameters in the regression.

Adj R2 give penalty of using too many predictors. Adding new predictor, the Adj R2 may decrease, if it has weak or no relation to the outcome.

There are also generalized R2, say defined by likelihood function.

You need check, which model did you use?  which R2 did you study? In addition , incude 54 dummy predcitors is nod a good approach to use linear regression. If your data includes year, your outcome is probably not independent, you need check auto-correlation. Also you need check the distribution of yield/h, you may check the residul plots...

R2 will always increase if you add more (linearly independent variables). R2-adjusted penalize for having too many variables an may be reduced by adding a new variable.

If you have as many (linearly independent) variables (n) as you have observations, you will get an R2=1.000. It’s just an transformation in n-space, with no prediction power.

Balaji,

Your R^2 at 40% is already low. It means that 60 percent in the variation of your dependent variables are not explain by your choice of independent variables. You should not worry about adding more dummies but try to find other actual variables to bring up the adjusted R^2 in the 90 percent range. Dummies do not allow you to try different specification, for instance the log(0) is not defined. And do not forget about the "Dummy Variable Trap". Since you are explaining yield, what about fertilizer use, or temperature measures. You can even use readily available global warming data as a background variable. If that does not work, then try system of equation models. Build two or three equations. Then more system estimation techniques will be available to you, and you may have a set of instrumental variables as well. You have many choices  

Very interesting discussion. Just a point of thought - at every time, check the error term distribution, as a lot can be said about what is going on with the predictive power of the equation. If everything fails, just "corc" it (Cochrane–Orcutt estimation) and see what happens...