Combining 2 sets of coefficients, weighting one of the sets I have two sets of coefficients from similar data taken at different times.  What I want to do is combine the two sets of coefficients giving greater weight to the more most recent set.
The goal is building a predictive model.  So say I have dataset A from 2009, and dataset B from 2010.
My coefficients for A are:
param1: 0.33
param2: 1.224
param3: -0.119

My coefficients for B are:
param1: 0.42
param2: 1.309
param3: -0.011

If I wanted B to be considered twice as important, would it be sound to use a formula like this:
(2*B + A) / 3 = New Coeeficient

And do that for each parameter?  Or am I suggesting something that is fundamentally flawed?
In general could one combine coefficients effectively using the basic forumula:
(Weight * DatasetACoeffcient + DatasetBCoeffient) / (Weight + 1)

Edit
This is a multivariate linear regression problem where the datasets may not be available when someone decides something like this needs to be done.
 A: You are retaining $p$ (=3 in this case) values for each regression: the estimated coefficients.  If you are willing to retain $p(p+1)$ (=12) values per regression, you can weight your results in a way that is equivalent to having all the data and performing a weighted least squares regression with them en masse.
The analysis is simple: let $X_1$ be the design matrix (i.e., an $n_1$ by $p$ matrix of independent variable values) for the first year and $y_1$ be the $n_1$-vector of dependent values for that year.  The estimated coefficients are
$$\hat{\beta}_1 = \left( X_1' X_1 \right)^{-1} X_1' y_1.$$
Let the subscript $2$ designate the same quantities for the second year.  Suppose you would like to uniformly weight all observations with (positive) values $w_1^2$ and $w_2^2$ in those two years.  The design matrix $X$ is the vertical concatenation of $X_1$ and $X_2$, an $n_1+n_2$ by $p$ matrix, and similarly the vector of dependent values $y$ is the vertical concatenation of $y_1$ and $y_2$.  Let $W$ be the diagonal matrix with values $w_1$ along the first $n_1$ places and $w_2$ along the last $n_2$ places.  The weighted least squares solution is
$$\hat{\beta} = \left( (W X)' (W X) \right)^{-1} (W X)' W y.$$
However, $(W X)' (W X)$ = $X' W'W X$ is the vertical concatenation of $X_1 W_1 W_1' X_1$ and $X_2 W_2 W_2' X_1$.  Because both $W_1 W_1'$ and $W_2 W_2'$ are multiples of identity matrices, they factor through, giving
$$\hat{\beta} = \left( w_1^2 X_1' X_1 + w_2^2 X_2' X_2 \right)^{-1} \left(w_1 X_1 y_1 + w_2 X_2 y_2\right).$$
Notice that $X_1' X_1$ and $X_2' X_2$ are just $p$ by $p$ matrices and that $X_1 y_1$ and $X_2 y_2$ are just $p$-vectors.  Therefore you can obtain $\hat{\beta}$ just from the two $p$ by $p$ matrices, the two $p$-vectors, and the two numbers $w_1$ and $w_2$.
This approach generalizes in an obvious way when more than two regressions are involved.  It shows, incidentally, that the weighted combination $w_1^2 \hat{\beta_1} + w_2^2 \hat{\beta_2}$ as suggested in the question will not in general equal the weighted least-squares solution.  Therefore, if you are using least squares for any of its optimality properties, you should not want to use this seductively simple solution, because it will be suboptimal.
In conclusion, if you would store the 12 numbers $X_i' X_i$ and $X_i' y_i$ each year, then retrospectively (without needing the original data) you can fit any regression on all the data for any set of positive weights without any loss of information.
I would recommend saving some additional values such as the estimated error variances: these will help you detect changes in variability over time (heteroscedasticity).
A: This is "taylor made" almost for a Bayesian regression.  First of all, there is nothing "fundamentally wrong" with what you suggest.  You result may not be optimal by some mathematical standard, but it will almost certainly be optimal time wise.  Most other methods will involve much more time than a straight multiplication and division.
I would use a normal likelihood $(y_i|\beta,\sigma,x_i,I)\sim N(x_i^T\beta,\sigma^2)$ and the "jeffreys prior" $p(\beta,\sigma|x_i,I) \propto \frac{1}{\sigma}$.  This gives a posterior for $\beta$ as a multivariate t-distribution, with scale matrix $s^2(X^TX)^{-1}$ and mean vector $\beta_{ols}$ with the standard $n-p$ degrees of freedom.  Now you simply use this posterior based on the "A" data set as the prior for the "B" data set.  Now because you have a "t" prior and a "normal" likelihood, the posterior for beta will favour the normal likelihood, because the t has fatter tails - hence less "pulling power".  This regression will balance the A and B regression between how accurately A was estimated, and how well the B estimate fits the data.
An "add-hoc" way that you could add more weight to "B" is by setting the degrees of freedom to 1 in the "A" posterior.  But then you may as well save some time and do the multiply the B estimate by two.
I don't think there is a simple analytic expression for this posterior, so will likely need to simulate.  But you only require the estimate from the "A" data set, and the covariance matrix from the "A" data set, and the number of observations in the "A" data set.  Once you have these quantities, you don't require the original data set.
A: There is no reason accounting for the use of convex linear combinations of coefficients in order to "average" two models.
At best, you could consider the three coefficients for each dataset are realizations of the same three random variables, and you would be interested in the distribution of each random variable.
What I would do would be to fit the model again with a new dataset (of size $n$) consisting of a random sample of size $\lambda\times n$ taken from the B dataset, and $\left(1-\lambda\right)\times n$ of the A dataset. You could use $\lambda=\frac{2}{3}$ for instance.
A: Maybe you should look into "stacking". Or even "feature-weighed stacking".
The former is using a cross validation method to determine the weights you should use to linearly stack them. The latter is using "meta-parameters" to give even more insight on how to weight the parameters depending on what is being predicted. This is a method that the #2 Netflix competition team developed. http://arxiv.org/abs/0911.0460
