Combine 2 groups based on the regression coefficient I have two groups of people, N=211 in group 1, N= 310 in group 2.
I would like to combine these groups because they share a certain characteristic that I am interested in. The groups are used in a multiple regression, so I only have the regression coefficients and CI's. They are:
group 1: -.05 (-.21 to .11)
group 2: -.14 (-.27 to .00)
Is it possible to combine the groups? I did a similar calculation fot two other groups with the Cochrane combine groups formula. However, those groups had a mean, N and SE. Does anyone know if I can combine these 'regression' groups as well?
Edited in response to answer
Thank you for the response, In following your advice I came to the following outcome:

SE= (upper limit-lower limit)/3,93 (Cochrane handbook)
y= width CI/2*1,96
S2= SE*SE

This resulted in:

 SE y   S2 group 1 0,08163  0,3136  0,006663457
group 2 0,06888 0,2646  0,004744454

Applying the inverse method resulted in: S2 combinede = 102,833/360,845= 0,285. Is that correct or am I missing something? And I only have the weighted shared variance now, right? How do I calculate the average weighted regression coeffiecient?
Thanks to mdewey for the correct solution:
w1  1 / v1  150,0722545     b1  -0,05
w2  1 / v2  210,7723914     b2  -0,14
Overall estimate of coefficient y   and variance w              
sum (wiyi)/sum(wi)
wiyi    -37,01174753        y   -0,102569757
som(wi) 360,844646          w    0,002771276    
 A: You have the estimated coefficient and from its confidence interval you can work out its standard error. Assuming they used a normal approximation you divide the width of the confidence interval by 2 * 1.96. If they used $t$ then replace 1.96 by the corresponding value of $t$ for your degrees of freedom. Square the standard error to get the sampling variance. You now have enough to combine the estimates using the inverse variance weighting method.
Edited in response to additional calculations posted by OP
Your calculation of the sampling variances is correct but you do not need to estimate a shared variance, you need to weight each coefficient by the inverse of its sampling variance then average them. It would be much easier at this point to use your favourite software to do this. There are several packages in R for meta-analysis and you can also use Stata.
So you have two estimates $y_i$ where $i=1,2$ and their sampling variances $v_i$. You then form the weights $w+i = \frac{1}{v_i}$ then your overall estimate $y$ and its sampling variance $w$ are
$$
y = \sum \frac{(w_i y_i)}{\sum w_i}
$$
$$
w = \frac{1}{\sum w_i}
$$
