From what I understand of Smith (1962), I gather you are trying to derive the genetic trend from field data. Do you have EBV of all the sires in your study? That makes life a lot easier: you calculate the mean breeding value over all sires from a given birth year, with some restrictions on minimum reliability of EBV, number of daughters and number of herds. The mean BV of successive birth year gives you your trend (on the sire side, it may be wise to do the same on the dam side).

You can you use as alternative the method used by Burnside and Legates, they also discussed the method of Smith, which is easier, I suggest you to read:

E. B. BURNSIDE and JE Legates (1962 ) Estimation of Genetic Trends in Dairy Cattle Populations . Journal of Dairy Sci 50 : 1448-1457 .

Using Smith method, requires to use two models. Model I, in which you include year + sire + other fixed efects and Model II similar, but you exclude sire, then you you will be using the principle of Smith, who is beautiful and simple to understand, I have used Smith method, in some researchs.

I think that you are misinterpreting Smith procedure. The reazon is for the explanation you posted below the question. The linear regression analysis is done on yearly means and must weighted because the linear regression is based on averages with different number observations and probably different variances, for this reazon the weighting factor may be the the reciprocal of the variances or the reciprocal of the number of observations used for each mean.

As Dr Herwing Eding suggested. If you're working under an animal model, the situation is simpler, because the program will give you the BV and the genetic trend can be found simply by doing the regression of BV on year ( you could get te average BV for each year). The phenotypic trend can be obtained by the linear regression of annual averages on year, (of course, here you must know that in an animal model the fixed effects are adjusted by the random and the random effects are adjusted by the fixed effects). Environmental trend may be estimated by difference, between the phenotipic trend and the genetic trend.

To be more clear in helping you!

Let us the following models:

Model I, Yijk = mu + year + month + sire + other fixed effects .

Model II,Yijk = mu + year + month + other fixed effects.

The Smith principle rests on the assumption that the fitting constant for the effect of year of model II estimates the phenotypic change(this is the is the genetic trend + environmental trend). However, the fitting constants from model I estimates half of the genetic trend + environmental trend. Let A and E be the Genetic and environmental change, then:

You must estimate the regression slopes for year with effect of both models. then, take twice the diference Between the slopes for years from model II and model I.

2 ( b (model II ) -b (model I) ) = 2 ( (A + E) - ( 1/2A + E) )

                                               = 2 (A + E -E - 1/2A )

                                               = 2 ( 1/2 A)

 2 ( b (model II ) -b (model I) ) = A

Now , in practice you must not work with the means of the year effects . However These means May have different variances , so analysis of linear regression Both Should be weighted by the reciprocal of the variances of each year.

Note, next to the means of YEAR you would have an estimate of the standard error for each year, so, you can get the variance of each year by squaring the standard deviation of each year (Figure out the formula for the standar error ( you need only the number of observation)). Th weighted regression analysis, which can be simply carried out by PROC GLM.